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By H. C. Chang, N. J. Grant

REEP studies and measurements in most in-V> stances are based on a relatively gross gage length. Even in some recent theoretical studies on the mechanism of creep, changes were followed by means of X-rays and metallography without regard for the behavior of the individual grains and grain boundaries.'" Analytical studies of creep have frequently indicated that more than one competing process is operative and that the ultimate creep performance depends on the effects of temperature, time, and strain rate as well as grain size.'-" he grains and grain boundaries are known to respond differently to these variables but the extent of the response is still little known, especially in poly-crystalline materials where the relative orientations of grains and grain boundaries are important. This paper reports some experimental observations of the behavior of the grain boundaries and their effect on the deformation in the grains. High purity aluminum was used to avoid complications of aging reactions, second phase, inclusions, etc. Experimental Procedure A small vertical nichrome wound furnace was built to permit direct loading on the test specimen. This furnace is capable of operating up to about 1300°F with reasonable temperature distribution. A ground rectangular quartz window, 1.25x0.5 in., is imbedded in the external stainless steel tube to permit observations of the creep process with a microscope. An argon atmosphere ,was provided to prevent oxidation. The quartz window caused a temperature gradient between the back and front surfaces of the specimen of 15" at 700°F. The temperature gradient could be cut down to 3°F along the length of the specimen by adjusting shunts across the furnace windings. An ordinary metallurgical microscope with a working distance of 14 mm was rebuilt so that it could be moved in three mutual perpendicular directions. Visual examination could be made with either a 30X eyepiece or a 15X filar eyepiece. Using an objective of focal length 24.3 mm and a numerical aperture 0.20 a total magnification of 120X or 240X could be obtained. High purity aluminum rated at 99.995 pct was supplied by the Aluminum Co. of America as % in. then the gage portion was further machined to 3/16 in. diam. The ends were Y4 in. diam and threaded to fit available specimen holders. Two opposite flat surfaces of the gage portion were obtained by milling, giving final dimensions of the gage portion of 3/4x3/16x3/32 in. Machined specimens were first electropolished in Jacquet's solution.' Reference marks were produced by pressing a thin sewing needle into the surface of the specimen. The specimen was then annealed at 900°F for 24 hr and at 1150°F for 12 hr. Typical macrostructures of specimens treated in this manner are shown in Fig. 1. The range of the grain size was 1 to 5.5 mm (see Fig. l), but most of the grains were of 2.5 mm and went through the whole thickness of the specimen. The specimen was re-electropolished and etched electrolytically to reveal the grain boundaries. In order to reveal the orientation difference of the grains, etch pits were produced on the surface of the grains by etching in a mixture of hydrochloric and nitric acids (HC1, 45 pct; HNO,, 10 pct; H,O, 45 , by volume). The specimens were very carefully put into the holders and furnace; yet even with this care, fine slip lines were developed on the specimen surface.

Jan 1, 1953

By D. W. Akins

The case history of a combination gas and water flood instituted early in the life of a field is described. It was recognized from the beginning that recovery would be low, under normal production methods, from the several separate, thin beds of porous limestone which had such poor native permeability that the wells would not produce without acidizing. It is thought that the combination flood gives excellent recovery efficiencies for this type of reservoir. The chief function of the gas flood now is to maintain bottom hole pressure in that part of the reservoir which will not be affected by the water injection program until later. Present estimates are that ultimate recovery will be approximately double the recovery expected under the original solution gas drive mechanism. Wide (80-acre) spacing has enhanced the economics of the over-all field program by the elimination of more than $5,000,000 worth of unnecessary wells. INTRODUCTION The Haynesville Pettit Field was discovered in November, 1941, with the completion of T. L. James Co.'s Callie Akin No. 1, located in the W 1/2 of the NE 1/4 Section 27-23N-8W, Claiborne Parish, La., at an approximate depth of 5,300 ft. The center of the field is about two miles north and a mile west of the town of Haynesville, La. A total of 189 producing wells have been drilled on 14,500 acres. An additional nine dry holes were drilled. The Louisiana-Arkansas state line divides the field so that 34 wells are in Arkansas and 155 are in Louisiana. Governmental sections are divided equally to contain eight production units making 80-acre spacing where the sections are regular. Along the state line in Louisiana there is an irregular tier of sections, each of which contains approximately 456 acres. When divided equally into eight production units the spacing is 57 acres per well for these three and a fraction productive sections. All Haynesville Pettit wells are identified by their section number followed by their position in the section as determined by numbering the production units counterclockwise beginning in the upper right corner of the section. All of the producing wells in the field except two are unit-ized and operated by the Haynesville Operators Committee. These two wells are located in the extreme northern part of the field in Arkansas. Efforts to bring them into the Unit are being continued. The Pettit operators organized the Haynesville Operators Committee and the field became a unit operation May 1: 1944. GEOLOGY The Pettit is Lower Cretaceous in age and is defined as the uppermost porosity in the Sligo formation. The unitized area known as the Haynesville Pettit Field is composed of two separate zones of porosity approximately 40 ft apart and without connection between the two, except in wells. These zones are known as the Upper Pettit and the Lower Pettit. The Upper Pettit is separated into two sections throughout most of its area by a relatively thin but quite impervious shale streak. These are called the "A" and "B" sections of the Upper Pettit. All of these lenticular zones are composed of coquina limestone and a small percentage of normal oolites. The large

Jan 1, 1951

By D. W. Akins

The case history of a combination gas and water flood instituted early in the life of a field is described. It was recognized from the beginning that recovery would be low, under normal production methods, from the several separate, thin beds of porous limestone which had such poor native permeability that the wells would not produce without acidizing. It is thought that the combination flood gives excellent recovery efficiencies for this type of reservoir. The chief function of the gas flood now is to maintain bottom hole pressure in that part of the reservoir which will not be affected by the water injection program until later. Present estimates are that ultimate recovery will be approximately double the recovery expected under the original solution gas drive mechanism. Wide (80-acre) spacing has enhanced the economics of the over-all field program by the elimination of more than $5,000,000 worth of unnecessary wells. INTRODUCTION The Haynesville Pettit Field was discovered in November, 1941, with the completion of T. L. James Co.'s Callie Akin No. 1, located in the W 1/2 of the NE 1/4 Section 27-23N-8W, Claiborne Parish, La., at an approximate depth of 5,300 ft. The center of the field is about two miles north and a mile west of the town of Haynesville, La. A total of 189 producing wells have been drilled on 14,500 acres. An additional nine dry holes were drilled. The Louisiana-Arkansas state line divides the field so that 34 wells are in Arkansas and 155 are in Louisiana. Governmental sections are divided equally to contain eight production units making 80-acre spacing where the sections are regular. Along the state line in Louisiana there is an irregular tier of sections, each of which contains approximately 456 acres. When divided equally into eight production units the spacing is 57 acres per well for these three and a fraction productive sections. All Haynesville Pettit wells are identified by their section number followed by their position in the section as determined by numbering the production units counterclockwise beginning in the upper right corner of the section. All of the producing wells in the field except two are unit-ized and operated by the Haynesville Operators Committee. These two wells are located in the extreme northern part of the field in Arkansas. Efforts to bring them into the Unit are being continued. The Pettit operators organized the Haynesville Operators Committee and the field became a unit operation May 1: 1944. GEOLOGY The Pettit is Lower Cretaceous in age and is defined as the uppermost porosity in the Sligo formation. The unitized area known as the Haynesville Pettit Field is composed of two separate zones of porosity approximately 40 ft apart and without connection between the two, except in wells. These zones are known as the Upper Pettit and the Lower Pettit. The Upper Pettit is separated into two sections throughout most of its area by a relatively thin but quite impervious shale streak. These are called the "A" and "B" sections of the Upper Pettit. All of these lenticular zones are composed of coquina limestone and a small percentage of normal oolites. The large

Jan 1, 1951

By K. J. Brondyke, P. D. Hess

Two processes have been developed for improving the quality of molten-aluminum alloys before casting. The Filtration Process. which involves passing molten metal through a packed bed of granular filter material, is a rapid means of removing finely divided particles. It has the most potential in those instances where removal of inclusions is of primary importance. The Combination Fillration-Inert Gas Fluxing Process inuolzles introduction of an inert gas so that it will diffuse countercurrent to metal flow through the filter bed of granular material. Dissolved hydrogen is removed from the metal in addition to removal of finely divided particles. The Combination Process is most useful where both inclusion removal and attainment of conistently low-hydrogen-content metal are important. Metal treated by the Combination Process is of higher and more uniform quality than heretofore attainable with prolonged chlorine fluxing. Costs of the Combination Process can, for the most part, be offset by savings derived from high recoveries and increased production of superior-quality products. IMPROVEMENT in the quality of molten-aluminum alloys is secured generally through the use of some fluxing practice in a crucible, holding furnace, or ladle involving either gaseous or solid fluxing media. Typical fluxing agents may include the gases nitrogen, argon, or chlorine used either singly or as mixtures and the solids aluminum chloride or hexachloroethane. Regardless of the fluxing means used, the primary objectives are the adequate removal of both metallic and nonmetallic inclusions and reduction of hydrogen content to an acceptably low level. The ultimate goal is to produce ingots and cast products of high quality free from inclusions and porosity. The development of ultrasonics for measurement of internal quality, tightening of quality controls, and the application of the aluminum alloys to new or different commercial fields have been responsible for an ever increasing demand for improvement of quality of both cast and fabricated products. This demand for high quality has not been restricted to any single type of product. On the contrary, the demand encompasses about the entire variety of products including those for fabrication, those to be machined, buffed, or finished for decorative purposes, and those for critical applications where both surface and internal quality is of utmost importance. In many instances products acceptable in the 40's would now be scrapped as unacceptable by these higher present-day standards. With this ever increasing demand for higher quality, it became apparent at Alcoa that conventional means of melt treatment were inadequate in many instances and new approaches were necessary. Consequently the research program was intensified with attention focused on metal treatment during transfer in order to reduce the furnace processing time to a minimum in an effort to attain the desired results at a minimum of additional expense. As a result of this intensive research program which covered numerous variations and adaptations of conventional methods in addition to new methods of melt treatment, several new processes were developed, two of which will be described here. The first of these, a method of melt filtration, was patented in February, 1959.l The second process involving combination filtration—inert gas fluxing was patented in June, 1962. 2 Other melt-treatment processes developed during this period of investigation were patented as listed.3 FILTRATION PROCESS General Description. The Filtration Process, which involves passing molten metal through a packed bed of granular filter material, is a rapid method of effectively removing finely divided particles. It is an impingement-type filter; hence the size of the particles removed from the metal are considerably smaller than the interstices of the

Jan 1, 1964

By E. L. Dougherty, J. W. Sheldon

Using the numerical techniques shown in this paper it is possible to compute the simultaneous dynamical behavior of multiple fluid-fluid interfaces in two dimensions. Hence, fluid-fluid inter face models of several oil recovery processes can be constructed which allow prediction of the effect of fluid flow in two dimensions on the behavior of these processes while taking into account various physical effects, such as saturation gradients, phase changes and thermal stimulation. Techniques for constructing fluid-fluid interface approximations for several oil recovery processes are reuiewed. The validity of these techniques is established by comparison to experimental results. The availability of a computer program for computing the behavior of multiple fluid-fluid interface problems makes the use of potentiometric models uneconomic. The results indicate the areal sweep efficiencies obtained from potentiometric model studies at high mobility ratios may be somewhat optimistic. The results also indicate that the areal sweep efficiency curves obtained at high viscosity ratios 2—4 using miscible fluids in porous media are misleading and that considerable care must be taken in defining the mobility ratio for a displacement process, especially for miscible fluids. INTRODUCTION Many of the methods used to estimate areal sweep efficiency assume that the oil recovery process can be represented by one or more fluid-fluid interfaces. When the mobilities of the displaced and displacing phases are assumed equal, this quantity can be computed using analytical mathematical methods.l.2 For non-unit mobility ratio, experimental methods based upon the fluid-fluid interface concept include potentiometric and electrolytic blotter models. Scaled models of porous media have also been used to study this problem. Fay and Prats3 and Aronofsky4 used numerical techniques to compute breakthrough sweep efficiency, but neither of these studies were extended beyond breakthrough. Numerical techniques which have been developed for solving a general fluid-fluid interface problem are presented in a companion paper.5 These techniques have been incorporated into a program for a large-scale digital computer which can treat simultaneously the dynamical behavior of as many as six fluid-fluid interfaces. Thus it is possible to simulate the behavior of several oil recovery processes taking into account such effects as saturation gradients. Techniques for representing several oil recovery processes by fluid-fluid interfaces are presented. Processes considered are conventional water flooding with and without a mobile gas phase, hot water flooding, miscible flooding and enriched gas drive. Other processes, whose effects could be studied by this technique, but are not considered in detail here, are underground combustion and steam injection processes and various slug processes such as gas-water injection and alcohol-solvent processes. Theoretical results obtained with single interfaces for mobility ratios of 0.25, 1, 2, 4, 8, 16, 32 and 64 in a repeated five-spot are compared to experimental results for this geometrical configuration obtained using miscible fluids and conductive analogs. Predicted recovery curves for water flooding in a repeated five-spot are compared to experimental results reported in the literature. Example calculations are shown for a conventional water flood in the presence of a free gas phase and for a hot-water flood. MATHEMATICAL PRELIMINARIES We assume that the rock matrix is homogeneous with constant thickness, absolute permeability and porosity. The fluids are incompressible. We also neglect the effects of gravity.

Jan 1, 1965

By P. Shahinian, R. L. Stegman, M. R. Achter

Creep strength has been determined as a function of oxygen pressure for nickel at 510" and 600°C. Creep-rupture life drops from its highest value at the ultimate vacuum of 10-7 torr to a high pressure plateau of nearly constant life which, at 600°C, commences at torr. This behavior is described in terms of a model that relates surface gas adsorption and the generation of fresh crack surfaces. In a calculation based a this model the predicted pressure beyond which the creep strength should not decrease further has been found to agree well with the observed value. The introduction of oxygen during creep in vacuum was found to cause a prompt rise of the creep rate. The magnitude of the environmental effect was much less than generally observed in fatigue and this is attributed to the diffarent crack morphologies in creep and fatigue. GASEOUS environments are known to affect creep resistance adversely1-5 but the effects have received less attention than the much larger ones in fatigue. At low temperatures it has been shown for nickel that the creep rates are faster and the rupture lives are shorter in air than in vacuum and that these environmental effects can be correlated with faster crack growth rates in the reactive environment.' In support of a mechanism of gas adsorption at the crack tip to explain the above effects, a calculation based on kinetic gas theory showed that surface coverage by gas was not as rapid as the exposure of fresh metal at the crack tip in the ultimate vacuum but was in air.7 In fatigue a number of investigations have demonstrated that the reduction of life with gas pressure usually follows a step curve with most of the reduction occurring in a transition range at intermediate pressures and little or no change at high and low pressure.8 There have been no studies, however, in which creep strength has been determined as a function of reactive gas pressure to see whether similar effects would be found. This investigation was undertaken to study the kinetics of the environmental effect in the creep of nickel. EXPERIMENTAL PROCEDURES The environmental creep apparatus was constructed to minimize many of the experimental conditions which can cause scatter in data. Dead weight loading is employed and weights are contained within the environmental chamber to eliminate bellows and the necessity for compensation for gas pressure changes. Elongation over the specimen gage length is recorded from a Riehle Model DV Controlled Environment Extensometer which provides readout to 2.5 x 10- in. Temperature is monitored and controlled from a thermocouple at- tached to the specimen gage length to +0.5oC or better. The freon trapped oil diffusion pump vacuum system included an auxiliary liquid nitrogen trap and, with a wide range variable conductance leak valve, pressures from the ultimate vacuum of 10"7 to l03 torr of any desired gas are obtainable. Pressure is measured by means of a hot filament ionization gage below 10"3 torr and a NRC Model 530 Alphatron Vacuum Gauge above 10-3 torr. The oxygen, which was leaked into the environmental chamber, was an Aviator's Grade of 99.5 pct purity with a dew point of -80°F. Analysis of the nominal 99.8 pct Ni showed the following percentages of major impurities: 0.02 C, 4.01 Mn, 0.005 Si, 0.01 Cu, 0.02 Fe, and 0.034 Mg. Cylindrical specimens were machined with a 0.180

Jan 1, 1970

By M. R. Annis

Drilling mud rheological and gel property changes due to elevated temperatures frequently cause problems in drilling deep wells. A laboratory investigation of the effects of time, temperatures up to 3001; and mud composition on these properties was made with concentric-cylinder, rotational viscometers of the Farm type. The viscometers were sealed from the atmosphere to prevent dehydration of the sample. Gel strengths were found to be more sensitive than viscosities to changes in temperature and mud cornposition. The high-temperature gel strengths of bentonitic clay drilling fluids were not predictable from low-temper.atl4t-e measurements. At high temperatures, [lie clay flocculates. The floccu-lation temperature depends on the concentration and type of solids in the mud and the degree of chemical defloccula-tion. As the bentonite content of a mud increases, floccrrla-tion temperature decreases. Lignosulfonnte treatment raises the flocculation temperature. To minimize adverse high-temperatrrre effects on mud properties, the mud should be maintainted at minimum solids content, properly treated with. a defloccullant which is stable at the maximum ten?perature encountered and maintained at a pH high enough to insure activation of the deflocculant for the duration required. The Methylene Blue Test for cation exchange cnpacity of a clay was found to be a useful guide in deter.niinirig when a mud contains a dangerously high clay conWnt. INTRODUCTION In drilling a well it is desirable, for several reasons, to know the effects of time and temperature on the rheological and gel properties of the drilling fluid in the hole. Problems associated with drilling fluids normally occur down-hole: so it is reasonable to be interested in the properties of drilling fluids at the conditions which exist down-hole. It has long been observed that high pump pressures are often needed to start circulation after a trip and that the "bottom-up" mud that is circulated back to the surface is usually more viscous than it was before "cooking" at the bottom of the hole for several hours. Burk-hardt' showed that a knowledge of rheological proper-ties of muds under down-hole conditions is necessary to predict pressure surges. He showed that the viscosity of a mud greatly influences the magnitude of pressure surges and the likelihood of lost returns. McLean et aL~ showed that the rheological properties of a mud under down-hole conditions are very important to cementing operations. This paper presents data showing the effects of time and temperature on rheological and gel properties of water-base drilling fluids. Measurements of gel strengths and rheological properties were made with two different concentric-cylinder rotational viscometers of the Fann type. One was the conventional six-speed viscometer modified to operate at temperatures up to 350F and at the vapor pressure of the liquid at test temperature. The other viscometer was newly designed to operate at temperatures up to 500F and pressures up to 1,000 psi. Tests with both instruments were made under essentially the same operating conditions. The new viscometer is shown in Fig. I. In this investigation, great emphasis has been placed on the rheological properties of clay suspensions, since clays are largely responsible for a mud's thixotropic and gel-

By W. A. Tiller, D. H. Lane

A simple zone melting technique for investigating the effect of ultrasonic irradiation upon ingot solidification is described. The effect of i) ultrasonic power level, ii) freezing velocity, iii) constant or variable frequency, iv) direction of irradiation, and v) transducer-cozlpling bar joint upon the grain size of type 316 stainless steel have been investigated. The results of this study support the postulate that the ultrasonic vibrations increase the nucleation probability in the layer of liquid adjacent to the freezing interface. In the first paper of this series,l the possible mechanisms whereby ingot structure may be altered by irradiating a solidifying melt with ultrasonic vibrations have been discussed. A new technique for efficiently introducing the ultrasonic energy into the solid-liquid interface region was presented and applied to ingot preparation by the consumable-electrode arc-melting technique. The experimental results support the postulate that the ultrasonic vibrations may refine the ingot structure by increasing the nucleation probability in the zone of liquid adjacent to the solid-liquid interface. The present paper describes the application of the same technique to a relatively simple laboratory-scale zone-melting apparatus. This apparatus is found to be well suited to the detailed study of ultrasonic technology in this area and allows one to determine, in particular, the minimum ultrasonic power level needed to produce a certain grain size in a particular material. The results of this study support the nucleation mechanism for grain refinement, but do not provide any deeper insight into the specific nucleation mechanism responsible for the effect. EXPERIMENT The apparatus used in these experiments is shown in Fig. 1 and illustrated schematically in Fig. 2. The material to be studied, type 316 stainless steel, was in the form of a 3/4-in. sq bar 30 in. long. This bar was placed in a square open-topped mold with open ends made from high-purity graphite coated with a flame-sprayed Al2O3, skin. Surrounding the crucible was a molybdenum susceptor with 3/8-in. diam holes spaced at 1-in. intervals along its length to serve as sight ports. A tapered transducer horn was brazed to one end of the specimen. The entire assemblage was enclosed in a quartz tube, the transducer itself projecting out one end and resting in a cooling tank. A vacuum seal between the coupling bar and the end plate enclosed one end. A similar plate and seal enclosed the other end. The system is gas tight and can be operated under vacuum or an inert atmosphere. For these experiments, flowing argon at 15 in. of Hg pressure was used. The heat source for melting the stainless steel specimen was a 2-in. long 3-kc induction coil placed around the quartz tube; this source heated the susceptor, inductively melting about a 3-in. zone of the sample by radiation. To move the molten zone at a specified rate, the induction coil was moved down the tube at this rate with the aid of a simple pulling device. Thus, the sample could be irradiated at varying ultrasonic frequencies and power levels and could be solidified at varying rates. The power input to the transducer was measured using a "John Fluke Model 120 VAW-Meter." 1 The power delivered to the interface region is probably only about 50 pct of that measured on the VAW-meter. In a typical run, when the ultrasonic power was turned on, the interface of the molten zone closest

Jan 1, 1961

By F. R. Brotzen, A. R. Troiano, E. L. Harmon

Precipitation processes leading to drastic property changes are a frequent occurrence in titanium alloys containing large amounts of the retained high temperature P phase. In order to establish the kinetics and nature of these precipitation processes, a series of Ti-V alloys was studied. Time-temperature-transformation diqgrams were obtained for 12.5 and 15 pct V-Ti alloys. These diagrams consisted of two intersecting C-shaped curves: one in the high temperature region for the euilibrium transformation P +u+P, and another at lower temperatures depicting the formation of the meta-stable transition phase, o. Presence of the transition phase retarded the precipitation of the equilibrium a phase. Deformation of retained P resulted in the formation of the o phase. Reversion and retrogression phenomena of the transition phase were observed. A negative temperature coefficient of resistance was found in quenched alloys containing from 15 to 20 pct V. CERTAIN titanium-base alloys can be heat treated to produce appreciable changes in properties. For example, remarkably high hardness values may be obtained by aging or isothermal quenching treatments. Most of the information available to date on the hardening of titanium-base alloys has been systematized recently in an article by L. D. Jaffe.' It was pointed out by that author that the hardening was the result of the decomposition of the retained j3 phase to the equilibrium constituents, a and p, and that this decomposition had many of the characteristics of an age-hardening reaction. Recent work by Frost et al.' 3 has contributed much to the fundamental understanding of the hardening mechanism in titanium-base systems. These authors established the presence of a transition phase in the transformation from j3 to a + j3, which they designated o. The transition phase, in their opinion, was at least partially responsible for the hardening and embrittling effects which accompanied low temperature aging. The present investigation of the mechanism and kinetics of the hardening reaction was carried out for the Ti-V system. Ti-V alloys were ideally suited for a study of the decomposition of j3, since age hardening was known to occur readily in this system." Moreover, no intermetallic compounds occur in this system, Fig. 1, thus simplifying the interpretation of the results. Material and Procedure Alloys containing 12.5 and 15 pct V were prepared by Battelle Memorial Institute from iodide titanium furnished by Watertown Arsenal and vanadium of 99.8 pct purity. Ingots of 8 Ib each were prepared by arc melting in an inert atmosphere with a tungsten electrode and water-cooled copper crucible. Each of the ingots was melted once, forged at 1600°, and rolled at 1400°F. Following this, the ingots were remelted, forged, and then rolled to % in. sq bars, which were subsequently grit blasted, pickled, and wire brushed. Another set of alloys containing nominally 17.5 and 20 pct V was produced by the Research Div., New York University. These alloys were arc melted in an inert atmosphere in lots of 20 g each. Heat-Treating Procedure: Whenever feasible, specimens were heat treated in high vacuum resistance furnaces at pressures below 5x10." mm of Hg. Aging and isothermal quenching treatments were generally carried out in salt baths. Specimens were not attacked by the salt, provided the tempera-

Jan 1, 1956

By N. A. D. Parlee, I. D. Shah

The solubilities of oxygen in liquid Ag-Au, Ag-Pt, and Ag-Pd alloys have been determined in the range of 940° to 1200°C at 1 atm pressure of oxygen using an improved Sieverts technique. The additions of gold (0 to 57 pct), platinum (0 to 27 pct), and palladium (0 to 22 pct) to liquid silver continuously decrease the solubility of oxygen in liquid silver. Activity coefficients and interaction coefficients of oxygen in these alloys and have been calculated. The interaction coefficientscan be described by the following equations: Approximate second-order interaction coefficients (pM have been calculated. The contribution of the product, pMxNM, to In yo only becomes significant at high alloy concentrations. RECENTLY several investigators1"3 have redeter-mined the solubility of oxygen in liquid silver. In general the recent findings1" for Po, = 1 atm are in good agreement with the equation:4 log %O = 695.4/T + 1.086 [1] It is established1, 2 that the solubility of oxygen follows Sieverts' law reasonably well, at least up to 1 atm partial pressure of oxygen. It should be noted that a very slight deviation from Sieverts' law has been reported by Lupis and Elliott.3 Only recently has the solubility of oxygen in Ag-X binary liquid systems received much attention, and only the Ag-Cu, Ag-Au, Ag-Pt, and Ag-Pd systems have been studied. Par lee, Sacris, and zoellners reported that the solubility of oxygen in liquid silver increases progressively with the small additions of copper (0 to 0.5 pct) up to the point where the copper oxide phase appears. Lupis and ~lliott~ have reported that the solubilities of oxygen in liquid silver decrease progressively with the additions of gold, platinum, and palladium. However, their investigation was limited to 0 to 5 pct of these alloying elements, a range too limited to satisfy the requirements of the research program of this laboratory, where the solubilities of oxygen in the range of 0 to 30 pct were required for the calculation of chemical diffusion coefficients of oxygen in these alloys. The present paper deals only with the solubilities of oxygen in these alloys while another paper will deal with the diffusion of oxygen in these alloys. EXPERIMENTAL METHOD A Sieverts technique was employed which involved an improved design of the reaction tube, Fig. 1, as described briefly in a previous communication.4 Liquid melts (70 to 100 g) were held in Norton Alun-dum crucibles. The induction furnace used had a maximum output of 2.5 kw with very fine control. This induction system had excellent stability and the final equilibrium temperatures measured by calibrated Pt-Pt, 10 pct Rh thermocouples are believed to be within ±2C. These thermocouples were checked against the melting point of pure gold wire, and the results agreed with standard tables (±l°C). Each run involved a careful sequence of operations. The sample was heated to and held at about 900°C in vacuum for 3 to 4 hr with the thermocouple in a retracted position. After melting, the melts were usually exposed to a small amount of oxygen (0.5 to 2.0 cu cm) and then degassed slowly for 1 to 2 min to remove any oxidizable volatile impurities such as carbon and sulfur as CO, CO2, SO2, and SO forth. Argon gas was then allowed to enter the system. The protection tube containing the thermocouple was then

Jan 1, 1969

By D. W. Fuerstenau

Recently R. J. Charles1 showed that comminution of brittle or semi-brittle materials in batch operations is described more appropriately by a variable energy relationship than by the specific relationships proposed by Rittinger,2 Kick,3 and Bond.' That is, the value of n in the empirical differential operation which applies to crushing and grinding (Eq. 1) is variable. Independently, Holmes' developed an identical generalized equaton for size reduction. The experimental data of Charles and Holmes show that the value of n is determined by the material and the comminuting machine and is constant for a given combination of these two conditions. The general objective of the present article is to extend the Charles-Holmes concepts to continuous ball milling. The specific objective is to analyze the operation of a vibratory ball mill dry-grinding chromite in a continuous open circuit and to develop an equation for the comminution of chromite in this mill. Basic Principles: In a batch mill the length of time during which the material is ground is a direct measure of the energy expended on the material, except possibly for exceedingly fine grinding. However, in a continuous operation, the fraction of the total expended energy which is useful for grinding will vary according to feed rate and amount of material in the mill. If the amount of material within a continuously operating vibratory mill is low enough so that only part of the expended energy is used for grinding, the extent of size reduction at constant power input must depend upon the length of time the material is retained within the mill, namely, upon retention time. The following analysis pertains to a continuous mill operating under these conditions. The empirical differential equation that applies to the comminution of brittle materials is:" dE = -Cdx/x" [1] where dE is an infinitesimal energy expenditure, C a constant, dx an infinitesimal size change, x the particle size, and n a constant. For continuous grinding in an open circuit at constant power input, P, Eq. 1 must be written as (dtr)P = -C dx/x" [la] where dt, is an infinitesimal time during which a particle of size x is in the mill, and C' is a constant. A ground product never consists of particles of single size but always comprises a distribution of sizes. In comminution, the expenditure of energy causes a lateral shift in the size distribution.', ' " The general objective of any engineering study of comminution is to correlate the magnitude of this size distribution shift with the energy expended, the ultimate aim being to cause the greatest shift with the least amount of expended energy. Although a number of criteria can be used to measure this shift, Schuhmann's size modulus has been found convenient.' Mathematically, the Schuhmann size distribution can be expressed as follows:" y = l00(x/k) [2] or in differential form: dy = [F- xa-' dx ] K, where y is percentage of material finer than size x, a is a constant that determines weight distribution among particles of various sizes, and k the size modulus that denotes the theoretically maximum-sized particle in any size distribution. By considering the energy required to reduce an element of weight of material, dy, from size x, to size x, the element of time during which the material must remain in the mill at at power will be (dt..).= J'-Cax!(dy) [3] Summing up all the elements of weight from zero to 100 for a product that conforms to the Schuhmann size distribution yields C C f Cdx,\( 100«x°-'dx\

Jan 1, 1960

By H. W. Hockin, D. r. Brandt, R. H. Walsh, P. L. Dietz, P. R. Girardot

New Jersey, Florida, and Canadian ilmenites were reduced with hydrogen or coke under various experimental conditions and the phase changes occurring in the ilmenite upon reduction have been studied by microscopic examination of polished sections and by X-ray diffraction. The products formed were dependent upon the type of ilmenite, temperature, time and reducing agent. Of the reducing agents, hydrogen was the more effective at lower temperatures. 1 HE possible utilization of ilmenite as a source of both iron and titanium has resulted in the development of a number of methods for the separation of the iron and titanium content. Slagging processes as currently used in Canada are typical of such methods. Somewhat less attention has been given industrially to the reduction of the iron content at less than the slagging temperature. Although references maybe found to such work, in general only one type of ilmenite, either natural or synthetic, has been studied by each author. We have attempted to draw some relationship between the results of experimental reduction and the type of deposit from which the ilmenite was derived, as evidenced by phases occurring in the ores and in the reduction products. Ilmenite ores having from 27 to 61 pct titanium dioxide were included in this study and in each case reduction was carried out at such temperatures that only limited coalescence of the particulate iron product occurred within the ilmenite grains. The history of the individual ilmenite samples and the temperature of reduction were found to determine the occurrence of various phases and the mode of distribution of the iron. REVIEW OF EARLIER WORK ON REDUCTION One of the earliest references to the reduction of ilmenite at less than the slagging temperature was made in 1917.' The metallic iron produced was_____ leached out by the action of dilute sulfuric or hydrochloric acid, to leave a product high in titanium dioxide. Subsequent to this, numerous patents2-'? and other references13"21 have appeared concerning reduction of ilmenite by carbon, hydrogen, carbon monoxide, methane, coal gas, water gas, or the like in the absence of fluxing agents. Mineragraphic examinations were not reported, and in the main, the only examinations made were chemical analyses. However, in two cases3,13, titanium suboxides were reported in the products and in one case2' rutile was reported, in addition to metallic iron. Both were identified by X-ray diffraction. While reductions in the absence of fluxing agents were generally followed by either a wet or dry chemical process for removal of the metallic iron, a Canadian source17 reported removal of the metallic iron by magnetic separation. By the addition of fluxing agents during reduction, the metallic iron has been coalesced into "pearls." Each reference to such a process23-28 has shown that the coalesced iron could be removed by magnetic or gravity means after the product was crushed. In the absence of fluxes, the coalescence did not generally occur. The major part of the present study has been limited to reductions without fluxing agents in order to determine the primary reactions of naturally occurring ilmenites. Titaniferous iron ores have also been studied,29-33 17, l9 their reduction having been used as the basis of a commercial process for beneficiation of such ores in Norway29 and more recently considered in the United States34,35. The ease of reduction of titaniferous iron ores relative to that of hematite or magnetite has been referred to,33 with the conclusion that the more

Jan 1, 1961

By F. G. Miller, R. C. McFarlane, T. D. Mueller

During the process of gas storage in pressure-depleted oil reservoirs, it has been observed that in some instances additional liquid oil is recovered and that the composition of the storage gas is materially altered. A mathematical study was made of the dynamic behavior of such a depleted oil reservoir undergoing gas injection. The important variable considered in this study, not included in previously published work, was that of compositional effects on the phase behavior of two-phase flow. Pressure, saturation and component composition profiles were developed for a linear, horizontal and homogeneous porous medium containing oil and gas but undergoing dry gas injection. Special new techniques were developed to overcome the problems of numerical smoothing which arise in the solution of the equations representing such systems. The method of solution includes the development of partial differential equations describing the behavior of the system, representing these equations by finite difference approximations, making certain simplifying assumptions and, finally, applying methods of numerical analysis with the aid of a high-speed digital computer. In an example calculation, results using the mathematical model are compared with field observations made on a gas storage project in Clay County, Tex. This field project involved a depleted oil reservoir used 'for gas storage and gas cycling purposes. As a result of these processes, the reservoir yielded substantial amounts of secondary oil, both in the form of stock tank oil and as vaporized products in the produced gas. The methods derived in this study may be applied to a variety of oil reservoir problems which are dependent on compositional effects. In recent years the number of oil reservoirs being used for gas storage purposes has increased greatly, and there has been at least one published account of additional oil recovery resulting from gas cycling a depleted oil reservoir after repressur-ing with dry gas for storage purposes. Additional oil recovery from oil reservoirs resulting from gas storage operations could become an important secondary recovery process. This is especially true since the use of natural gas in large metropolitan areas continues to increase and more gas storage volume near these areas is needed. These facts provided the motivation for the work reported here. This paper reports on a study of the inter-relations of composition, saturation and pressure changes which occur when hydrocarbon gas is injected into an oil reservoir system. From an understanding of the process, prediction methods may be developed for use in forecasting the secondary recovery products from gas storage operations in oil reservoirs and, consequently, .the economics of such projects can be developed. The process of storing hydrocarbon gas in an oil reservoir and the cycling process both involve the transient multi-phase flow of oil reservoir fluids with changing fluid compositions. There is a scarcity of work published on the subject. One of the first laboratory models developed to study a problem similar to the one posed here was published in 1948 by Standing, Lindblad and Parsons. l They developed a model to study gas condensate recovery by gas cycling, including the effect of heterogeneous reservoir permeability. Their results showed the compositional effects of injecting a gas of known composition into a two-phase condensate reservoir of known composition. A major finding of their study indicated that maximum oil recoveries from gas cycling projects result when low cycling pressures are used. Previous to their work it was generally considered

By C. P. Besse, N. F. LeBlanc

Described in this paper are oceanographic data which should be considered by an offshore design engineer and methods for developing a design wave height from the oceanographic data. The selection of a design wave is predicated on contemplated waves which might affect the site throughout the life of the structure. Selection of a design wave height may be based on (1) arbitrarily established recurrence Frequencies of hurricanes affecting the structure (predicted wave heights are associated with the expected variations of forces resulting from these waves) and (2) a risk-type evaluation wherein all possible storms affecting the area are considered (anticipated wave heights are associated with both investment plus risk costs and expected variations of forces). It is shown how the following oceanographic predictions are integrated into design considerations: (1) a classification of storm intensity which considers all recorded storms which affected the design area, (2) the recurrence interval of storms of a given- intensity (this interval is dependent on the extent of the geographical area considered in the design problem) and (3) a forecast of all wave heights which might affect the area (geometry of a structure often necessitates consideration of waves from a multiplicity of directions). The authors believe that the described techniques can result in selecting an adequate and reasonable design wave. INTRODUCTION Since the inception of offshore operations in the Gulf of Mexico, engineers engaged in designing suuctural facilities have been plagued with the problem of selecting an adequate and reasonable design wave. In the development of any offshore structure it is mandatory that the engineer evaluate the ability of the structure to withstand the ocean waves to which it will be subjected. Selecting such design waves quite naturally necessitates a coalition of the oceanographer and the design engineer. The oceanographer must provide a detailed knowledge of scientific principles which govern the behavior of waters in the Gulf of Mexico. He should also have an adequate knowledge of the manner in which design waves are utilized by the engineer. Although the design engineer's primary responsibility is applying the oceanographer's specialized knowledge in the creation of real structures, it is important that he possess some knowledge of related oceanographic principles to reasonably evaluate and apply the recommendations of the oceanographer. In the Gulf of Mexico it is the hurricane wind waves which generally govern the design of an offshore facility. The oceanographer must therefore develop techniques for predicting the heights, periods and frequency of all hurricane waves which might affect a particular structure. From this mass of oceanographic data, the design engineer must select the design waves which will apply to his particular design. PAST STUDIES ON FREQUENCY AND AMPLITUDE OF HURRICANE WIND WAVES Past oceanographic studies on the frequency of hurricane wave heights in the Gulf of Mexico have been devoted largely to predicting the recurrence interval of hurricanes which will generate maximum significant waves of given heights. The maximum significant wave height is the average height of the highest one third of the waves in that portion of the storm producing maximum wave heights. Since these waves occur over a relatively small portion of the storm (Fig. 1) and since the paths of hurricanes vary considerably (Fig. 2), the recurrence frequency of such heights is largely a function of the extent of the geographical area considered. In establishing the frequency of maximum significant waves for the entire American Gulf coast, the major fully developed hurricanes which affected the coastline from BrOwnsville, Tex., to Key West, Fla., were considered (Fig. 2). These Storms were selected and described by C. L-

By J. W. Axelson, J. N. S. Kwong, J. T. Adams, E. L. Pire, J. F. Johnson

CRUSHING has always been a major operation in the chemical and metallurgical industries, yet little is known about the theory of crushing, and today, the design of crushers is still based almost entirely on empirical knowledge and accumulated practical experience. In view of the increasing national need for the economic working of poorer grades of ores, the lack of a fundamental understanding of this unit operation hardly presents a satisfactory situation. Basic investigations of crushing have been concerned mainly with three phases of the problem, 1—the mechanism of the fracture process itself, 2— the particle size distribution of the crushed product, and 3—the relationship between the energy input and the amount of new surface produced. Probably adequate information on these phases will be required for a comprehensive understanding of the process of crushing. A bibliography covering these phases will be given as well as a review of the work done in recent years at the University of Minnesota on the relationship between the energy input for crushing and the amount of new surface produced. Fracture of Solids This phase of the crushing problem is the most fundamental because it is concerned with the actual mechanism of fracture. The main problems in a study of the fracture process are concerned with the questions of why and how fracture occurs and why there is such a discrepancy between the actual and theoretical energies needed in a fracture process. In considering the how of fracture, Poncelet40 carried Out experiments On the crushing of glass under compression. Actual photographs were taken of the glass plates in various stages of fracture-From these experiments Poncelet was able to postulate a probable mechanism of fracture. Probably because of the quantitative nature of the problem, considerable effort has been expended to find an explanation for the low tensile strength of materials and the conversely high energy for crushing. Tensile strengths are often only 1/500 of the theoretical while the energy for crushing is usually at least 500 times the theoretical. A review of the work to explain the low strength of glass is given by Weyl,52 in which the work of Griffith," Joffe,32 and Powell and Preston " are discussed. In a recent paper Seitz46 holds that the presence of flaws and fissures, as originally expounded by Griffith, is the most probable reason for the low strength of metals. Since a mass of data has been accumulated on the fracture strength of materials, several investigators have attempted to correlate this data in the form of an equation. Glathart and Preston," Taylor,40 Ponce-let,40 Machlin and Norwich," and Frederickson and Eyring,20 have all considered this problem, and the final relationship has always been that the stress for fracture is proportional to the logarithm of time. Murgatroyd30 arrived at a very similar relationship by a different method. The study of the fracture process has used many methods. Among some of these are the thermody-namic approach used by Furth21 which was based on the work of BornxL and later used by Saibel,43 and the statistical method applied by Fisher and Hollo-mon.10 In recent years metallurgists have concerned themselves with the problem of brittle .fracture as opposed to the usual plastic failure of metals. The great amount of interest shown is reflected by the number of contributors to the recent symposium on the fracture of metals.' Repeated failures of welded ships during World War II have accelerated these Studies.31,50,34 The shifting of thought from an emphasis on the

Jan 1, 1952

By S. C. Schaeker, A. W. Schlechten, A. H. Larson

PARRAVANO and Malquori' studied the equilibrium of H2S-Hz with molybdenum and its lowest sulfide which they believed to be MoS2. Mc Cabe' has shown that its composition is actually Mo2S3 and determined its dissociation pressure by means of Knud-sen effusion measurements. Stubbles and Richard- son3 have recently studied the equilibrium of gas mixtures of H2S-HZ with the two-phase solid mixtures of Mo-MozS3 and Mo2S3-MoS2. The latter investigators found that M02s3 deviated slightly from the stoichiometric composition, but they did not determine the homogeneous region of the disulfide phase. Morimoto and Kullerud, studied the Mo-S system by quenching, microscope, and X-ray methods and concluded that the disulfide is stoichiometric. The present investigation was concerned with the measurement of the sulfur vapor pressure variation with composition at 1100°C in the homogeneous region of "MoS2". These measurements were made by reacting: 1) molybdenum powder (99.97 pct Moj with sulfur vapor, and 2) MoS1.g9 (formed by reaction of Mo + H2S) with sulfur vapor in a quartz capsule. Conditions were controlled to form an equilibrated phase within the homogeneous region of the disulfide. The quartz capsule was sealed off initially under a vacuum and the residual gases were gettered by titanium powder contained in one end of the capsule. A mixture of Mo + S or MOS,., + S was in the other end. The section containing the titanium powder was heated for 24 hr at 700°C and then removed by flame sealing. The end of the capsule containing the charge was then heated to 1100°C. The other end of the capsule was maintained at a temperature which would produce the desired sulfur pressure in the capsule (liquid sulfur distilled from the charge mixture was retained in this end). After equilibration, the capsule was removed from the heating assembly and rapidly air-cooled. It is assumed that equality existed between the total sulfur pressures (PT) in the two ends of the capsule and not between the partial pressures of the different molecular species (S, SZ, Three separately controlled heating elements were used to maintain the proper temperature gradient over the length (approximately 12 in.) of the capsule. A thermocouple-Wheelco "Capacitrol" system was used for temperature control of the two end heating elements within 2"C. The center heating element was controlled directly by a " Power -stat". Separate controlling and measuring thermocouples were used for both end heating elements. Pt-Pt(l0 pct Rh) thermocouples were used for 1100°C and Chromel-Alumel thermocouples were used for lower-temperature control and measurement of the assembly. Silver foil was wrapped around the end of the capsule containing the liquid sulfur to insure a constant temperature zone. The thermal gradient over the entire length of the capsule was measured to: 1) ascertain that the length of the constant temperature zone of the liquid-sulfur end and the sulfide end was sufficient, and 2) ascertain that the liquid-sulfur zone was the zone of lowest temperature. The data obtained in this investigation are shown in Fig. 1 and Table I. The total sulfur pressure (PT) and p(S2) were calculated from the data of Braune et UZ.~ The compositions of the equilibrated disul-

Jan 1, 1964

By J. B. Clark, A. S. Yue

PfANN1 has shown that when a cylinder of molten binary alloy freezes directionally, the solute distribution can be described analytically by cg=k(l-g)k-1 [1] in which Cg is the solute concentration in the solid at the point where a fraction g of the original liquid has frozen and Co is the initial solute concentration. The term k is the effective distribution coefficient of the solute and is defined as the ratio Cx/CL where Cl is the solute concentration in the main body of the liquid. Both the slope and the intercept at -log (1 - g) = 0 of a logarithmic plot of Eq. [I.] provide a measure of k. Under conditions of freezing where diffusion in the solid is negligible and the solute concentration in the liquid is uniform, the effective distribution coefficient k, derived as above, is equal to the equilibrium distribution coefficient taken from the phase diagram. However, under ordinary freezing conditions, even though solid-state diffusion is negligible, the solute rejected from the freezing solid does not have sufficient time to diffuse uniformly throughout the main body of the liquid. A concentration gradient is formed in a boundary layer in front of the advancing solid-liquid interface as pointed out by Rutter and Chalmers.' Thus, under these conditions, the concentration of the freezing liquid in the boundary layer is higher than that predicted from the equilibrium phase diagram and consequently the effective distribution coefficient k, obtained from directional freezing experiments, is larger than the equilibrium distribution coefficient. The symbol k will designate the effective distribution coefficient in the discussion which follows. In this paper, the determination of the effective distribution coefficient is demonstrated for several dilute binary alloys and a polynary magnesium alloy. The effect of freezing rate on the value of the derived k is presented in detail. An example for the calculation of the solidus in a dilute binary solution using the experimentally determined effective distribution coefficient is given. MATERIALS STUDIED Binary magnesium alloys of copper, nickel, and zinc containing approximately 0.10 wt pct solute and a polynary alloy containing approximately 0.10 wt pct each of several elements were selected for study. The spectrographic analyses of these alloys are given in Table I. The analyses are believed accurate to within +5 pct of the stated value. EXPERIMENTAL PROCEDURE Extruded rods of the alloys, 3/8 in. in diam and 11 in. long were used for directional freezing studies. The alloy rods were melted horizontally in a high-purity graphite boat by a Nichrome-wound tube furnace which moved parallel to the length of the rod. The boat was supported inside a Vycor tube suitably connected to provide a protective atmosphere of dry SO2. For an experimental run, the following procedure was used. The alloy rod was cleaned in dilute HNO, and dried. The graphite boat containing the alloy rod was placed within the Vycor tube and the tube connected to the gas train' The 'ystem was purged for 20 min with dry argon and then a flow of dried SO, was maintained for the duration of the run. The movable furnace was positioned and either all or a desired portion of the alloy rod was melted. After attainment of steady-state temperature gradients the molten bar was solidified from one end to the other at a controlled rate by pulling the furnace along the length of the bar at the desired speed. At the conclusion of the run, the directionally frozen alloy rod was analyzed spectrographically at 1 1/4-in. intervals.

Jan 1, 1961

By S. J. Rothman, L. T. Lloyd

S. J. Rothman and L. T. Lloyd (Argonne National Laboratory)— Hagel's paperz0 discusses the question of the mechanism for self-diffusion in bcc transition metals. Recent work21"23 has led us to agree with him in reabandoning the ring mechanism in favor of a defect mechanism, most likely vacancies. On the other hand, we think that Hagel's attempt to group together all self-diffusion in bcc transition metals is wrong. We prefer the scheme of Peart, Graham, and omlin," who separate them into two groups. One group contains the anomalously behaved metals P titanium,', y uranium, and perhaps zirconim.' The other group contains a iron," this alloy was held at 1800°C for 2 hr before quenching, its structure was all a. B. C. Giessen, I. Rump, and N. J. Grant (Authors' reply)—We very much appreciate the discussion by Deardorff and Kato regarding the a to /3 transformation temperature of hafnium. In the W-Hf program, as well as in a current study of the system Cr-Hf, standard precautions were exercised against contamination, including vacua of less than 10"5 mm Hg and a weight control check of all specimens to insure an impurity rise of less than 100 ppm. Following receipt of the above discussion, a revision was made in the annealing process. Arc-cast specimens were etched with a 10 pct HF-90 pct HNO solution until 1 mm of surface, including a possible oxide film, was removed. Annealing was done in a hafnium container which provided a long diffusion path for gaseous contaminants. Finally, the heat treating time was shortened. Structural changes were noted to occur quite slowly. A 99.5 at. pct Hf alloy showed 70 pct /3 after 30 min at 1700°C and was 100 pct /3 after 10 min at 1715°C. After 24 hr at 1740C, the alloy was found to be 10 pct/3. This change is due to contamination; it was estimated that it corresponds to an increase of 60°C in the transformation temperature over a 24 hr period. The corresponding change in 30 rnin would be slight. Using the same hafnium as in the above publication, and three new alloys at 98, 99, and 99.5 at. pct Hf, the transformation temperature was indicated to be 1715" 15°C. Since this hafnium contained 4.4 at. pct Zr, a correction of 40 5C, based on an assumed approximately linear transformation temperature curve, must be made for pure hafnium. This yields a value of 1755 20°C in good agreement with Deardorff and Kato's value. Because the slope of the boundary is small, this permits a good extrapolation, and we regard the W-Hf alloys as well suited to check the Hf transformation temperature. niobirn,'' and molybdenum,22 whose activation energies correlate with the melting temperature and whose Do values follow Zener's predictions.28 We have no quarrel with Hagel's placing chromium into the second group; we disagree with his interpreting our data to make uranium fit into that group. Hagel considers that the measurements of self-diffusion in uranium below about 950°C represent combined volume and grain boundary diffusion. This contention is based on the curvature of the penetration plot for our 891°C run,4 which also has a nearly straight line plot of log c vs x. Hagel has extrapolated these characteristics to our 803.5C run and fitted his Arrhenius plot for self-diffusion in y uranium to our four highest temperature points only. We think this is wrong for the following reasons.

Jan 1, 1963

By W. A. Backofen, B. B. Hundy

THE pole figure interpretation in a recent paper' on the torsion texture of copper was questioned in discussion,2 nd a simpler alternative interpretation was proposed. In the hope of reaching a positive decision in favor of one or the other, further studies were undertaken with 70-30 brass and Armco iron. This additional work has not answered all the questions about torsion textures, but the new pole figures do offer support for the original interpretation and show that the texture is more complicated than the alternative suggests. From the previous paper,' the appropriate method of describing the texture in a twisted bar is known to be a pole figure plotted on a plane tangent to the surface of the bar. The axes of the pole figure are chosen to coincide with directions in the tangent plane which are parallel and at right angles to the bar axis (the longitudinal direction, L.D., and the transverse direction, T.D.), for these directions define symmetry axes of the texture. Therefore any ideal orientation that might be selected to represent the texture gives the crystallographic plane parallel to the tangent plane and the crystallographic direction parallel to the axis of the torsion specimen. A unique texture was assumed in the original interpretation, and the four ideal orientations, (112) [111], (111) [112], (110) [001], and (112) [131], were used in its description. Of the four orientations, the first three provide possible slip directions along the direction labeled T.D. in the pole figure, which is one of maximum shear stress in a specimen being twisted. The alternative, however, simply considered the texture to be made up of two components, one a [Ill] alignment along the specimen axis with a random orientation about the axis as in the wire texture, and the other a superimposed orientation (110) [0011. Experimental evidence for this simpler interpretation was derived from two observations: 1—twisting did not alter the orientation of a single-crystal torsion specimen of a brass in which an octahedral plane was perpendicular (and a [Ill] direction parallel) to the axis, and 2—deformation bands with approximately the (110) [001] orientation were seen to develop in the crystal during the test. The new pole figures were obtained with a brass and an iron torsion specimen of 3/4 and 1 in. gage length diameter, respectively. After annealing, polishing, and twisting, seven rods, about 0.030 in. in diameter and with different orientations, were prepared from material near the surface of each specimen; these were required for the method of constructing pole figures by using a Geiger counter as developed by Norton.5 Since the shear strain gradient in plastic torsion is linear, it was readily computed that the material supplying the brass rods had been subjected to a shear strain of about 3.2, and that supplying the iron rods had received a shear strain of about 2. All details concerning specimen design, testing procedure, rod preparation, and use of the Norton technique can be found in ref. 1. Only this procedure was followed in working out the (111) and (100) pole figures for brass, Figs. 1 and 2. However, X-ray photograms were also involved in the construction of the (110) pole figure for Armco iron, Fig. 3. The photograms were made according to the conventional transmission diffraction technique using a small sheet taken parallel to the specimen surface and etched to a thickness of about 0.0025 in. They were especially important in locating the boundaries

Jan 1, 1954

By J. F. Smith

ELASTIC constants of yttrium and eleven of the rare earth elements have been measured. This has been accomplished by measuring the propagation velocities of ultrasonic pulses. The velocity measurements were made by noting the elapsed time between an applied pulse and the appearance of successive echoes. The pulse-echo technique has become relatively common, and the basis of the measurement is outlined in several standard tests, e.g., Heuter and Bolt.1 Two important assumptions are made when using this method for the determination of elastic moduli. First, the pulse is assumed to propagate as a plane wave. To justify this assumption, the cross section of the test specimen should be large compared to the wave length of the transmitted pulse. For these measurements on the rare earth elements the minimum cross section wave length ratio was about 20. A second assumption which must be made when using polycrystalline specimens is that the grains are sufficiently numerous and randomly oriented so that the specimen may be approximated as elasti-cally isotopic. The grain size in the as-cast specimens which were used is believed to be sufficiently fine for this approximation, and the degree of preferred orientation is believed to be small. Supporting this viewpoint is the fact that elasticity measurements by the pulse-echo technique on as-cast specimens of other metals give results which are in satisfactory agreement with values obtained by other techniques. Hence, it is believed that the measured elasticity values for the rare earth elements are not apt to be seriously in error due to the assumption of elastic isotopy. The apparatus used in this determination was a modified Sperry Reflectoscope with a precisely calibrated time base circuit. Piezoelectric transducers were used both to generate the pulse and to detect the echoes. X-cut quartz crystals were used for the longitudinal modes, and Y-cut quartz crystals were used for the shear modes. Frequencies of 2.25 and 5 megacycles per sec were employed. Most of the specimens were 2.5 to 5.0 cm in length. Results Table I is a tabulation of the measured propagation velocities of longitudinal waves and of shear waves, together with densities obtained by Sped- ding, Daane, and Herrmann2 from lattice parameter measurements. The shear modulus, Poisson's ratio, and Young's modulus were calculated from the data in Table I through use of the following relationships: µ = pv32 [1] s=2-(vb/vs)2/2[1-(vb/vs)2] [2] and Y= 2µ(l+s) [3] where s is the shear modulus, Y is the Young's modulus, s is Poisson's ratio, p is the density, V0 is the longitudinal wave velocity, and v, is the shear wave velocity. The calculated quantities are shown in Table 11. Compressibility values can be computed from the relationship and the computed values may be compared with measured values obtained by Bridgman.8 Table III lists the data for such a comparison. The agreement is satisfactory, being particularly good for neodymi- um and gadolinium, poor for samarium, and intermediate for the other elements. Some variation is expected since Bridgman's measurements are isothermal, whereas the present measurements are adiabatic. In addition there may be some effect due to small variations in purity. Though most of the rare earth metals measured by Bridgman and all of the metals used in the present measurements were prepared at this laboratory, minor purity variations might exist since the samples came from different lots. Also, any imperfections such as dislocations, vacancies, voids, grain boundaries, microcracks, etc., should contribute to the volume change of a com-

Jan 1, 1958