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By Robert L. Dean, Michael Hoch, Samuel M. Wolosin, Chung K. Hwu

The general shape of the 1450°C isotherm of the Ti-TiO-ZrO2-Zr region was evaluated from the surrounding binary phase diagrams and from thermo-dynamic data on the metal-oxygen binaries. The phase boundaries were accurately determined using X-ray and metallographic techniques. At 1450°C the system shows a large bcc ß field, which extends from the two metal-oxygen binary systems as a Gaussian error function, and is stable up to 30 at. pct 0 when Ti and Zr are present in equal amounts. At higher O Concentrations, the ß field is in equilibrium with t-ZrO . The following four regions, with three solid phases, are present: two a ß t-ZrO,, a TW t-ZrO,, and TiO t-ZrO2 c-ZrO2. On cooling the ß phase transforms into the a phase, going through the w transition phase. The isotherm at 1500°C for the region TiO-TiO,-ZrO, was obtained by using X-ray diffraction. At 1500°C a large c-ZrOz region is present as well as a large two-phase field, Ti0 c-ZrO,. The following regions, with three solid phases in equilibrium, were found These regions are relatively small. The solidus and liquidus relationships were determined by observing samples suspended in a tungsten crucible by means of a fine tungsten wire and heated in vacuum. Eleven univariant points were found. C-ZrO, decomposes through a peritectic reaction into liquid t-ZrO2. The activities of Ti and TiO in the TiO t-ZrOz and in the two a ß t-ZrO regions were measured using the Knudsen effusion method. In the a TiO t-ZrO, region the activities of Ti and Ti are the same, as in the a — Ti TiO binary. In the two a t-ZrO, regions, the Ti activity is high and the Ti0 activity very low, although all phases present contain at least 30 at. pct 0. This indicates a short-range order in the solid phases, Zr atoms being preferentially surrounded by 0. 1 HE system Ti-Zr-0 is of interest because of the wide ranges of solid solubility exhibited by the boundary systems; as titanium and zirconium both belong to the same group of the periodic table, large single-phase regions should occur within the system, with a great variation of properties (as the composition changes within the single-phase region). Furthermore, the possibility of modifying ZrO, to make it a more usable refractory by the addition of other metals makes this system also of interest. Because of the high affinity of titanium and zirconium for oxygen, the oxygen partial pressure is very low at all compositions; thus, there exists a ternary metal-metal-oxygen system in which the oxygen pressure is not an important variable, so long as it is low enough. When a sample is heated in vacuum to a temperature high enough for vaporization to occur, the vapor phase will consist of metal and metal-oxide gas, the oxygen concentration being very low. The phase relationships in the surrounding binary systems have already been reported in the literature; therefore, the study of the ternary diagram

Jan 1, 1962

By A. H. Underwood, M. –Ls. Trépanier

INTRODUCTION The King and Beaver mines of Asbestos Corporation Limited (ACL) were joined in 1957 to form the King-Beaver mine. In 1964, ACL purchased the Johnson's Asbestos Company. The combined underground workings are a part of the King- Beaver mine. Asbestos ore is mined at the rate of 4080 metric tons per day (mtpd) to provide 15% of the company's daily requirement in the Thetford Mines area. Figure 1 shows the location of Thetford Mines. Two shafts service the underground. No. 3 shaft, 457 m deep, is used for personnel and material transportation, downcast ventilation, and ore hoisting. No. 4 shaft, 820 m to the south, is 389 m deep. It is used for material transportation and upcast ventilation. Figure 2 shows the relative locations of the shafts and the underground workings. The ore is mined by block caving. HISTORY The orebody outcropped at surface and was first mined as an open pit. Underground mining commenced when open pit mining became impractical. Shrinkage stoping, used initially, was unsatisfactory in the highly fractured ore. Sublevel stoping improved ore recovery and safety, but did not overcome the adverse effects of the un- stable rock. Observations of the rock failures indicated that block caving would be satisfactory. This was confirmed by careful investigation and testing. A method of block caving similar to that used at the Miami Copper Company was adopted. The first block commenced production in June 1933. BLOCK CAVING General A large block of ore is undercut above pre- pared drawpoints. The ore above the undercut caves by its own weight. Caving progresses up- ward as the caved ore is drawn. A large proportion of the rock breaks up in the caving action so that it will pass through the drawpoints. Oversize blocks are broken by drilling and blasting or mudcapping. Figure 3 shows the progressive stages of block caving. In the central part of the ore zone, the vertical dimension of a block is determined by the 132 metres between production levels. When isolated ore pockets are developed, the vertical dimensions of a block depend on the extension of the ore zone above the undercut. The minimum horizontal dimension of an under- cut determines the cavability of the overlying block. When necessary, caving is assisted by drilling long horizontal holes into the block above the undercut and blasting them. This procedure speeds up or restarts caving. It will not ensure complete caving of blocks having undercuts less than 30 m wide. Orebodies suitable for block caving are highly fractured and wide enough to cave freely without excessive dilution. Undercutting must

Jan 1, 1981

By Lyman Johnson

Single crystals qf copper in "single slip" orientatiorzs have been deformed in compression. During defortnation all of the independent deformation parameters have been measured. These parameters consist of thefive strain components and three components descrihing the lattice rotation. By a finite strain analysis these pararmeters , forrming a deformation gradient martrix, are related to the amounts of slip on each of the twelve slip systems. The results show that the amount of secondary slip is about equal to the amount of primary slip. This is an order of magnitude larger than has been believed previoutsly. ACCORDING to early theory and experiments, when a single crystal of a fcc metal is deformed in tension or compression it should deform by slip on only one slip system until the stress axis reaches a symmetrical orientation.' However. the observation of a large increase in the secondary dislocation density during ..single slip" makes it clear that some slip does occur on secondary systems. Knowledge of the amount and distribution of this secondary slip is essential to a complete understanding of the mechanisms of single-crystal deformation. Ahlers and Haasen 2 and Mitchell and Thornton1 have tried to detect the amount of secondary slip in single crystals of silver and copper, respectively. Each simultaneously measured the angle A, between the tensile axis and the primary slip direction and the length 1 of a gage section of the specimen after incremental amounts of deformation in tension. The measured A, was then compared with the theoretical single slip angle hp. given by sin Ap = j sin . hO where ?o was the initial angle between the tensile axis and the primary slip direction and lo was the initial gage length. In both sets of experiments a small but systematic difference between ?e and ?p was found. This difference must be due to the occurrence of secondary slip. However, as Mitchell and Thornton1 pointed out. nothing quantitative can be said about the amount and distribution of this secondary slip from the measurements that they made. The reason that no quantitative conclusions could be made is because no unique solution for the distribution of slip on the twelve fcc slip systems can be determined from only two measured deformation parameters such as A and 1. There are, in fact, eight independent macroscopic deformation parameters that can be measured when a single crystal undergoes a homogeneous deformation. Physically these can be thought of as the five finite strain components and the three angles describing the crystal lattice rotation. All eight of these parameters were measured by Taylor4,5 for aluminum deformed in tension and compression. At that time the concern was to show that slip occurs on {111 (110) systems in fcc metals, and the mathematics were not available to determine what slip distributions were compatible with the measurements. In this paper the mathematics6,7 are developed that allow the slip distribution to be determined from these measurable macroscopic deformation parameters. The analysis is applied to the measurements of the strain and lattice rotation of copper single crystals deformed in compression. The results show that the amount of secondary slip is an order of magnitude larger than had previously been thought. CRYSTALLOGRAPHIC DESCRIPTION OF A HOMOGENEOUS DEFORMATION The deformation of a solid body can be represented by a transformation matrix F that transforms the un-deformed state into the deformed state. Consider a vector X connecting two material points in the unde-formed material and the vector x connecting the same two material points after deformation, where both vectors are referred to the same set of Cartesian axes. The final vector x is related to the initial vector X by the equation: X = FS. [2] Eq. [2] can be considered as the equation defining F, which is called the deformation gradient matrix. Its components are: If the deformation is homogeneous, the transformation is linear and the components of F are constants. Using subscript notation, if P is the unit vector in the initial direction of a material line, the components of the unit vector p in the direction of the same material line after deformation are given by:

Jan 1, 1970

By Oren C. Baptist, Carlon S. Land

Laboratory research has been conducted to evaluute the effect of clay hydration on the permeability to gas of water-sensitive reservoir sands. Samples of a .sandstone containing trace amounts of montmorillonite and a sample of montmorillonite were .studied in the laboratory to detertnine whether swelling or dispersion was the cause of permeability reduction in these samples. Heliuin, containing various amounts of water vapor, was used to hydrate the clay minerals and to determine the gas permeability at various stages of clay hydration. The amount of water adsorbed by the samples using this method is small. The nonwetting-phase permeability at higher water saturations war investigated by saturating the with water and measuring the permeability to humid helium while decreasing the water saturation, Relative-permeability curves obtained from results of these procedures were used to estimate the effect of the swelling of trace amounts of mont/tlorillonite on the permeability of the .samples. Most of the damage to the permeability when reservoir sands containing trace amounts of montmorillonite are exposed to fresh water is due to dispersion and movement of clays. Blockage of pores by the increased volume of expanded montmorillonite is believed to result in permeability damage that is small in comparison to the observed damage to the samples tested. INTRODUCTION Studies have shown that permeability is severely damaged when sands containing only small amounts of montmorillonite are contacted by fresh water.15 When samples of sands containing large amounts of montmorillonite are placed in fresh water in the laboratory, these samples may completely disintegrate, forming an unconsolidated mass of larger volume than that occupied by the dry sample." In this case, it is apparent that the swelling of montmoril-lonite has destroyed the pore structure of the sand. If only a trace of montmorillonite is present in a sand. samples may remain intact when saturated with water, although the permeability to water is a small fraction of the gas permeability of the dry sample. Many workers in the field of water sensitivity have attributed this reduction in permeability to the blocking of pores and reduction of pore size by the increased volume occupied by expanded mont- niorillonite. if the sand contains a detectable amount of montmorill'onite or mixed-layer clay containing rnontmorillonite. Logically3 the smaller amount of montmorillonite present in a sand, the smaller should he the effect of montnlorillonite swelling on permeability; however, the quantity of montmorillonite sufficient to cause severe damage by swelling is not known. Although hundreds of samples have been tested in our laboratory, no correlation has been established between the amount of montmorillonite in samples and the permeability reduction caused by fresh water. To many petroleum engineers, the phrase "clay swelling" is synonymous with "water sensitivity", or "permeability reduction" implying that any formation damage due to the hydration of clays is caused by swelling. Although all clays adsorb water on their surfaces, montmorillonite is the only clay mineral commonly found in reservoir rocks which adsorbs water between intercrystalline layers, resulting in expansion of the clay particle. As montmoril-lonite swells, the first few layers of water adsorbed between platelets are strongly held and well oriented, and the montmorillonite retains its crystalline structure, although expanded. As swelling of sodium montmorillonite continues, the platelets become farther apart and the forces orienting the platelets in the crystalline structure become weaker, resulting in a less orderly orientation of platelets. In an abundance of water, small groups of platelets may become detached from the original monl-rnorillonite particle and may be dispersed throughout the water phase. Because of its swelling properties, sodium montmorillonite is very easily dispersed in water. Particles of other clay minerals. such as illite and kaolinite may also be dispersed in water. causing water sensitivity of sands not containing montmorillonite. The presence of an immobile layer of water adsorbed on the surface of clays has been considered a possible cause of the low permeability to water of dirty sands. Grim states that the thickness of the layer of immobile water held by sodium montrnorillonite is three nlolecular layers or 7.5 A (angstroms), with some orientation of water extending to 100 A. Assuming a very thick, immobile water layer adsorbed on the surface of a pore represented by a capillary tube, the maximum effect of the water layer on permeability can be calculated. Using a pore radius of 10 ' cm and an immobile water layer of 50 A. the calculation shows the permeability to be reduced only 2 per cent. Similar calculations can be used to show that the effect of electro-osmotic counterflow is of the same order of magnitude as that of bound water. The reduction of the permeability to water by either an immobile water layer

Jan 1, 1966

By Arnulf Muan, Klaus Schwerdtfeger, L. S. Darken

The equilibrium ratios CO/CO, of. a gas pharse coexislitrg with selected oxide phase assemblages of the system "FeO"-MnO-SiO2 and metallic iron have been determined at 1150°C. The data obtained are combined wilh the thermodynamic data on fayalite (Fe2SiOi) and "FeO"-MnO solid solutions to derive the actiuity-coiHpQsiUon relations for the various oxide components of the olivine (Fe2SiO4-,lIn2Si04) and pyroxenoid (standard free energies of formation of ferrosilile (FeSiO,), tephroite , and rhodonite from their oxides have been evaluated. In the Appendicc~s by Darken and Schivcerdtjeger the ideal solution law for solid deri oed. THE quaternary system Fe-Mn-Si-0 is of interest in many important phases of iron- and steelmaking. For instance, reduction in the blast furnace of ores containing Fe-Mn silicates, deoxidation of liquid steel with Mn-Si alloys, formation and subsequent alterations of oxide inclusions in steels, and the oxidation of manganese- and silicon-containing steels during processing are all governed largely by the thermodynamic relations existing in the system Fe-Mn-Si-O. Although the equilibria between liquid iron and Fe-Mn silicates have been studied in detail previously,' experimental data are lacking for equilibria among the solid phases. The present paper provides such data for a selected temperature, 1150°C. I) PREVIOUS WORK The general feature of subsolidus phase relations in the system iron oxide-manganese oxide-silica under strongly reducing conditions is known.' Fig. 1 represents an isothermal section at 1150°C. The phases present, in addition to silica, are three solid-solution series, viz.. the oxide solid-solution series "Fe0"-MnO (manganowiistite), the orthosilicate solid-solution series Fe2SiO4-Mn2SiO4 (olivine), and the metasilicate solid-solution series FeSi03-MnSi03 (pyroxenoid). The "FeO"-MnO solid solution is continuous between the two end members wustite and manganositeV3 as is the orthosilicate series between the two end members Fe2SiO4 and Mn2 SiO4. 4 The metasilicate solid solution, on the other hand, extends only part way from the MnSi0.l end member toward FeSiO because the latter end member is unstable relative to the phase assemblage fayalite + silica. The letters a through m in Fig. 1 identify end members of the individual solid phases dealt with [for instance, c designates fayalite (FeZSiO4) in equilibrium with wustite, e designates fayalite in equilibrium with silica, and so forth]. In addition to the phase relations there are some thermodynamic data available for the end members of the silicate solid solutions and for the "FeO" -MnO solid solution. The free energy of formation of fayalite (Fe2Si04) from its oxide components has been studied by several investigators. Unfortunately, the data obtained show considerable discrepancies. According to recent tabulations by Kelley, the change in standard free energy Affn for the reaction

Jan 1, 1967

By Marius S. Darrow, William B. White, Rustum Roy

The PbS-PbTe systen has been studied by quench-ing and D.T.A. techniques f?om 400' to 1150°C. Runs were made in evacuated silica tubes so that all equilibria are at the vapor pressure of the system. Lattice parameters of the quenched salnples , measured by X-ray diffraction, show a complete crystalline-solution series existing over a narrow temperature range between approximately 805" and 871°C. An exsolution dome extends from a maximum of about 805"C (approximately 30 mole pct PbTe) to 1 and 96.5 pet PbTe at 400°C. A narrow melting region, deternined by D.T.A., extends form 918c (mp PbTe), The shapes of the liquides and solidus curves imply the existence of a minimum at 871°C at approximately 65 pct PbTe. THe exact composition of the minimum could not be established due to the very narrow two-phase region. At compositions containing less than 50 pet PbTe, liquidus temperatures begin to increase, while the solidus remains almost flat to about 15 mole pet PbTe before beginning to vise toward the mp of PbS (1075 C). LEAD sulfide and lead telluride are isostructural (NaC1 type) semiconductors whose electrical and optical properties have been extensively studied and used in recent years. If appreciable crystalline solution exists between these compounds, the variation of physical properties with composition could be of interest. The purpose of this investigation was to determine the extent, if any. of crystalline solution, and to obtain the phase diagram for the system. To the knowledge of the authors, only three studies of the system PbS-PbTe have been reported, and, in chronological order, each investigation found an increasing amount of crystalline solution. In 1956, Yamamoto reported finding no evidence of crystalline solution between the compounds. Sindeyeva and Godov-ikov,' in 1959, found very limited crystalline solution. but only under conditions of excess tellurium concentration. Finally Melevski s3 investigation in 1963 indicated that one solid phase exists in the region from PbS to 7 pct PbTe and from 82 pct PbTe to PbTe at 886'C, with an eutectic at 55 pct PbTe at that temperature. Detailed data on the solvus boundary were not given. EXPERIMENTAL EQUIPMENT AND MATERIALS Commercially produced PbTe and PbS powders were used as starting materials. Batches of specific mole percent composition were accurately weighed and mixed in a plastic bottle, in a shaker mill. An analy- sis of impurity content is given in Table I for pure PbS and PbTe and for two randomly selected batches after the powders were mixed. Individual samples, ranging in weight from 0.2 to 0.5 g, were sealed in evacuated silica tubes which had been thoroughly washed and rinsed with acetone and distilled water. Thus all data taken were at the pressure of the system. Subsolidus relations were studied down to 400°C by heating the samples in a vertical tube furnace for 24 hr. The sealed tubes were quenched in water with quench time from the hot zone not exceeding 1 sec. Temperatures were measured by a chromel-alumel thermocouple and controlled to 53°C for most runs. The number and composition of phases present were determined from powder X-ray diffraction patterns taken at room temperature on a Norelco diffractome-ter, using silicon as an external standard. Above 850°C quenching techniques were, in general, found to be unsatisfactory, and differential thermal analysis (D.T.A.) was used to determine melting relations. The evacuated tubes were recessed about 1 cm at one end to accommodate the differential thermocouple. Al203 was used as the reference material in a similar tube containing the other side of the differential couple. For temperature measurements, a separate thermocouple was placed in the recess of the tube containing the sample to be measured, thus providing an opportunity to obtain thermal, as well as differential, analysis. All thermocouples for these measurements were Pt-Pt 10 pct Rh. Temperature and differential curves were recorded separately on synchronized strip-chart recorders. Thermocouples and recording equipment were calibrated using NaCl and gold standards, using the melting points 801" and 1063 C, respectively, which span most of the temperature range of interest. Heating and cooling rates generally were from 4 to 7°C per min. It was found, in fact. that rates ranging from 1.5 to 25°C per min did not significantly change the data obtained.

Jan 1, 1967

By W. A. Jr. Slippy, E. P. Dahlberg, R. B. Reed-Hill

A large room-temperature mechanical-hysteresis effect under cyclic tensile loading was observed in zivconium specimens prestrained at 77°K so as to form large numbers of (1121) twins. The observed hysteresis loss was a maximum when the prestrain was just under 1 pct It also depended strongly on the maximum applied cyclic stress, but only moderately on loading rate and temperature (-72°to 100°C). The phenotnena have also been studied in terms of the elastic aftereffect where the data has been found to cotlforln closely to the functional relationship between strain and time, c = -RT/a In tank ft. t to)/Zr, for strains cts large as about 10-4 This eyication can be derived directly from the strain-rate equation There may be important commercial implications to the present discovery since it appears that within rather wide limits it may be possible to obtain any desired magnitude of damping capacity in zirconium melal. The damping propevties may also be given directional characteristics. It is shown that the observed anelaslic phenomena can he explained on the assumiplion that they are the resuilt of stress-induced twin-boundary movements in which the average twin increases its thickness by only a few percent. In polycrystalline zirconium, a grain is least favorably oriented for slip when its basal plane, containing the (1130) slip directions, lies nearly perpendicular to the principle normal stress. Mechanical twinning is favored by this orientation and under simple tensile deformation at room temperature the primary twinning mode is {1012).' The (1012) twinning shear is small (0.17) so that, during deformation, twin growth does not greatly enhance ductility. At 77°K, on the other hand, the predominant twinning mode shifts to {1121), and many thin (1121) twins can form at small strains.' Twins thus nucleated can grow readily during subsequent room-temperature deformation and permit easy deformation in unfavorably oriented grains. In addition, the (1131) twinning shear is large: 0.63. These facts have lead to a process' for greatly improving the room-temperature ductility of zirconium when it contains a sizable fraction of grains with basal planes nearly normal to the stress axis. Optimum results are obtained by slightly less than 1 pct prestrain. The effect is large so that a 50 pct elongation increase is readily attained. A large room-temperature mechanical-hysteresis effect has also been observed in zirconium specimens prestrained at 77°K. The present paper is concerned with some aspects of this effect which the experimental observations strongly indicate is primarily the result of strain-induced {1121) twin-boundary movements. This clearly suggests that mechanical twins formed by plastic deformation can cause anelastic effects similar to those previously observed2 for annealing twins and twins associated with phase transformations. EXPERIMENTAL PROCEDURES All specimens were prepared from arc-melted sponge zirconium plate stock as previously described,3 which has a preferred orientation with basal planes aligned parallel to and uniformly distributed around the rolling direction. Both lonti-tudinal and transverse tensile specimens, with axes parallel and transverse, respectively, to the plate rolling direction, were cut from this plate. In a longitudinal specimen most grains are favorably oriented for slip, while in a transverse specimen a large fraction are unfavorably oriented. Prestraining at 77°K was performed in two ways. In one, annealed zirconium plate stock was cooled in liquid nitrogen and then rolled in the transverse plate direction to strains varying from 0.5 to 12 pct. Cylindrical 1/8-in.-diameter by 1-1/4-in.-gage-length tensile specimens were machined from this material. In the other, previously machined tensile specimens were prestrained in tension at 77°K between 0.2 and 3.8 pct. Type FA 25-12 SR4 strain gages were cemented to all specimen gage sections. All tests were performed on an Instron testing machine of 10,000-lb capacity. EXPERIMENTAL RESULTS Fig. 1 shows a typical two-cycle room-temperature stress-strain diagram for a specimen prestrained 0.65 pct by rolling at 77°K. The maximum stress in both cycles was 14,500 psi. Note that in the first cycle the loading and unloading curves are unsymmetrical so that a residual strain, er, remains after unloading. In the second cycle the stress-strain curves form a nearly symmetrical hystere-

Jan 1, 1965

By Robert Mehl

THE Widmanstätten figures found in the steels have been long recog-nized and in some aspects carefully studied,1 especially as they occur in cast hypoeutectoid alloys. Aside.from the practical importance of the structures obtained in the steels by various heat treatments, a study of the characteristics of these figures is interesting because of the rich opportunity the system affords, to, obtain new data on the mechanism of segregation from solid solutions. This opportunity is twofold: first, by changing composition within the austenite range the proeutectoid precipitate may be changed from that of ferrite to that of cementite, thus offering the same opportunity for changing the type of precipitate while maintaining the same basic lattice as that afforded by the Cu-Zn alloys;2 and second, the eutectoid inversion leads upon drastic quenching to the formation of martensite, a Widman-stätten figure of unique interest from ;the crystallographic viewpoint, particularly in comparison with those formed on-slow cooling.3 We have, therefore, two types of structure to study: that formed on slow cooling of hypoeutectoid and hypereutectoid alloys, and that formed on quenching hypoeutectoid, eutectoid, and hypereutectoid alloys. For each of these types of structure we require the crystallographic plane in the mother austenite along which the precipitate forms (we shall see that the precipitates in these alloys are invariably platelike in form), and also the orientation of the precipitate upon this plane. Some of these

Jan 1, 1933

By A. L. Barnes, A. M. Rowe

A heat transfer study was made of hot gas injection into oil shale through wells interconnected by vertical fractures. This analysis involved the simultaneous numerical solution of a nonlinear, second-order partial differential equation that describes two-dimensional conduction heat transfer in oil shale and a nonlinear first-order partial differential equation that describes convection heat transfer in the fractures. Three nonlinear, temperature-dependent coefficients were used in this work; they are thermal conductivity, thermal capacity and retorting endothermic heat losses of oil shale. Vertical fractures were considered to be of finite height. Although vertical conduction heat transfer was not considered, an estimate of the error resulting from this limitation was made. The effects of injected gas temperature, injection rate, system geometry, cyclic injection and time upon retorting efficiency were investigated. Results from this study show that the rate of retorting oil shale is a direct function of both injection temperature and rate, and the theoretical producing air-oil ratio:(AOR) is an inverse function of temperature. Retorting rates are constant until "breakthrough" of the 700 F isotherm at the producing well, assuming constant injection parameters. Retorting rates for bounded systems are higher than the analogous unbounded systems and likewise AOR's are less. The use of an alternating injection-soak routine with high injection rates is less efficient than continuous injection at lower rates. These results indicate that injection temperatures on the order of 2000F or greater may give theoretical AOR's in the economic range. INTRODUCTION Over half of the known oil shale reserves are located in the U.S., and most of them lie in the Piceance Creek basin of Western Colorado. The Colorado oil shale outcrops on the edges of the Piceance Creek Basin. At the outcrops the shale beds are relatively thin, from 25 to 50 ft thick. In the center of the basin the oil shale is as great as 2,000 ft thick and is covered with 1,000 ft of overburden. It has been estimated that there are over 1,000 billion bbl of oil in shales having an oil content over 15 gal/ton in this basin. Oil shale does not contain free oil but an organic matter called kerogen. Kerogen yields petroleum hydrocarbons by destructive distillation. It must be heated to approximately 700F, at which temperature it decomposes into shale oil, gases and coke. The U.S. Bureau of Mines and, more recently, oil companies have conducted considerable research on surface retorting methods to economically recover oil from this shale. Another approach to exploit the oil shale deposits, in particular that portion having 1,000 ft of overburden, is to retort the oil shale in place and produce the liquid and gaseous hydrocarbons through wells drilled into the shale. Some research has been done on this approach.l,2 There are several variations to the in situ retorting approach. These variations fall into one of two groups, depending upon the geometry of the system: (1) retorting in a highly fractured or broken up matrix; (2) retorting from single fractures between production and injection wells. The latter is the group studied. Several investigators,3-6 using various assumptions, have studied flow of heat through horizontal systems. The objective of this work was to make a heat transfer study of in situ retorting oil shale by hot gas injection through wells interconnected by single vertical fractures of finite height. The oil shale thermal conductivity, thermal capacity and retorting endothermic heat losses were considered to be functions of temperature. A knowledge of the

Jan 1, 1969

By A. K. Mukherjee, J. E. Dorn, J. D. Mole

Investigations were carried out on the effect of polyslip on the strain hardening of aluminum single crystals. The orientations investigated were those lor which the tensile axis was in the [001], [111], [112], and [012] directions plus another for which the Schmid angles for {111}(110) slip were 1 deg. The experimental data were analyzed on a model based on the intersection of dislocations with particular emphasis on the effect of polyslip on the activation volume for inter-section. It is shown that the rate of strain hardening inreases for those orientations wherein attractive dislocation intersections occur and that those orientations which produce the greater number of such intersections exhibit the greater strain hardening. Good correlation of the data is obtained with the concept that attractive junctions, as proposed by Saada, Play an important role in accounting for the rate of strain hardening. EXISTING concepts on the nature and cause of strain hardening in fcc metals have been deduced principally from experiments on the deformation of single crystals under single slip. The effect of crystal orientation on the shapes of the stress-strain curves for single slip have been summarized by seegerl and more recently by Clarebrough and Hargreaves.2 Tensile specimens whose axes fall near the center of the [001]-[011] line of the standard triangle of the stereographic projection exhibit the longest range of easy glide (Stage I) and the lowest rates of linear hardening (Stage 11) whereas specimens whose axes lie near fie [001]-[111] line of the standard triangle have limited or no easy-glide range and exhibit somewhat higher linear strain-hardening rates. Specimens whose axes lie near the [001] or the [ill] poles do not exhibit easy glide and have the highest rates of linear hardening. Kocks3 has shown that the highest rates of linear hardening Occur under Polyslip when the tensile axis coincides with the [111] or the [ 001] pole. Since the rate of strain hardening is sensitive to specimen orientation and the incidence of polyslip, these relationships might help to discriminate between various dislocation models for strain hardening in fcc metals. Previous attempts to analyze the effect of orientation on strain hardening,1"3 however, did not provide a unique answer to this problem. Consequently the present investigation was undertaken wherein additional data, particularly that for the effect of polyslip on the activation volume for intersection, was also determined in order to provide more complete information on the details of strain hardening. Whereas analyses of these data reveal that several recommended models for strain hardening are at variance with the facts, good correlation of the data is obtained with the concept that attractive junctions4 play an important role in accounting for the rate of strain hardening. I) EXPERIMENTAL APPROACH seegerl demonstrated that slip in fcc crystals at low temperatures is dependent on thermally activated intersection of glide dislocations with forest dislocations. This has been confirmed by tests on single crystals of aluminum by Mitra, Osborne and Dorn5 and on polycrystalline aluminum by Mitra and Darn.' Thus in accord with Seeger's theory, the shear strain rate, ?, below a critical temperature, T, is where .V is the number of points of contact per unit volume between forest dislocations and glide dislocations, A is the area swept out per successful intersection, b is the Burgers vector, v is the frequency of vibration of the segment of the glide dislocation undertaking intersection, U is the activation energy for intersection, k is Boltzmann's constant, and T is the absolute temperature. For aluminum, which has an extremely high staeking-fault energy, the constriction energy is negligibly small and therefore the activation energy decreases practically linearly with the stress according to as will be recomfirmed later, where Uo is jog energy at the absolute zero, G and Go are the shear moduli at the test temperature T and O°K, respectively, L is the spacing of the forest dislocations, t is the applied shear stress for slip, and tGo is the stress field that must be surmounted athermally.

Jan 1, 1965

By R. Grierson, L. J. Bonis

The high-temperature Strength oF TD nickel has been observed to be dependent upon the previons thermal and mechanical history of the material. Variations in both the level and the anisotropy of strength have been observed. 01 this paper- these variations are correlated with the storing of annealing resistant elastic strain energy in the matrix of the TD nickel. An x-vay line -broadening tecknique is used to measure the maLrTis elastie strain. THE inclusion of a finely dispersed second phase into a ductile matrix has long been recognized as an extremely effective method of strengthening the matrix both at high and at low homologous temperatures. It has been found, however, that the factors which determine the high-temperature strength are not the same as those which are important at low temperatures. Below 0.5 Tm the size and distribution of the second phase particles are of prime importance in determining the strength,')' while above this temperature the strength is mainly dependent upon the previous thermal and mechanical history of the alloy,3-7 This paper is primarily concerned with explaining the response of the high-temperature mechanical strength of one of these alloys (DuPont's TD nickel) to various thermo-mechanical treatments. It will be shown that this response is not associated with the occurrence of any form of dislocation substructure within the matrix of the alloy. It has been found, however, that a correlation does exist between the elastic strain level in the matrix and the previous thermomechanical history of the alloy and that the observed changes in elastic strain level parallel the measured changes in high-temperature strength. It therefore must be concluded that variations in high-temperature strength are a direct result of the variations in elastic strain level. MATERIAL TD nickel contains approximately 2 vol pct of Tho2 in an unalloyed nickel matrix. It is formed, as a powder, by a chemical technique and this powder is compacted to form ingots which are then extruded to give 21/2-in.-diam rod. Rod of smaller diameter is prepared from the as-extruded rod by swaging. In the studies reported in this paper, 1/2-in.-diam rod was used. This rod received an anneal of 1 hr at 1100°C prior to being used in any of these studies. EXPERIMENTAL TECHNIQUES Two methods were used to examine the structure of the nickel matrix of the TD nickel. These were: 1) transmission electron microscopy; 2) the analysis of the position and profile of X-ray diffraction lines obtained using the nickel matrix as the diffracting media. To prepare thin foils for electron-microscopical examination, slices of TD nickel approximately 0.050 in. thick were cut from the as-received 1/2-in.-diam rod. These were then chemically polished down to 0.045 in., rolled to 0.009 in., given a predetermined heat treatment, and thinned, using a modified Bollman technique, to provide the foils for observation. All observations were carried out at 100 kv, using a Hitachi HU-11 electron microscope. Specimens of the undeformed rod were prepared by grinding down the 0.050-in.-thick slices to approximately 0.015 in. and then thinning chemically and electrolytically to give the thin foils. The X-ray specimens were prepared by rolling 0.375-in.-thick rectangular blocks down to 0.075 in. The surfaces of the rolled material were ground flat, chemically polished to remove the layer disturbed by the grinding, and given a predetermined anneal in an inert atmosphere. They were then ground lightly to check their flatness and given a final chemical polish prior to being examined. The X-ray diffraction line profiles were measured using an automated Picker biplane diffractometer. A special specimen holder was built to allow a more accurate and reproducible positioning of the specimen. The line profiles were determined by carrying out intensity measurements at intervals of either 1/30 deg or 1/60 deg over a range of 3 deg on either side of the nickel peaks of interest. A piece of pure nickel which had been recrystallized to give a large grain size was used as a standard to give the X-ray line profile generated by a strain-free matrix. The analysis of the X-ray diffraction line profiles is a modification of that due initially to Warren and Aver-bach8and has been described elsewhere.3 This analysis gives a measurement of two parameters associated with the structure of the nickel matrix. These parameters are: 1) the size of the coherently diffracting domains within the nickel matrix; 2) the magnitude of the elastic strains in these domains. Both of these parameters are first determined in terms of a Fourier series. These series are obtained from other Fourier series which describe the measured profile of the X-ray diffraction lines. Thus, for both the coherently diffracting domain size and the elastic strain level, it is possible to plot Ft (the Fourier coefficient) against t (the term in the Fourier series), where t can be expressed in terms of a distance L and the Fourier coefficient Ft(S) (associated with elastic strain level) can be expressed in terms of the root mean square strain (e2)1/2. Thus a plot of (F 2)1/2 vs L can be obtained. Plots of this type are shown graphically in Figs. 6 and 8. Interpretation

Jan 1, 1968

By Evans B. Mayo

This study examines the structural framework of the Southwest for evidence of the four principal trends of lineament tectonics. It attempts to classify their intersections and compares the positions of those trends that appear most favorable with the positions of the presently known mining districts. This is a controversial topic. The author, in presenting his analysis, is aware that the study of lineament tectonics and relation of ore districts to regional structure is complicated by insufficient data and, unavoidably, by personal bias. The development of lineament tectonics has been summarized by Umbgrove.' Early attempts to fit ore districts into the Cordilleran framework were made by Billingsley and Locke, who do not refer to lineament tectonics, although their appoach is similar; they observe that heat and fluids, including the ore-depositing fluids, are most likely to rise at or near intersections of major structures where the crust is fractured, or weakened, to great depth. As a result of studies distributed over the earth-including ocean basins as well as continents— some tectonists recognize four dominant structural trends: 1) northwest; 2) northeast; 3) nearly east-west, or equatorial; and 4) nearly north-south, or meridional. Baker' proposed a theory to account for these trends and Sonder" called their world-wide arrangement the regmatic shear pattern. Moody and Hill proposed a much more complicated shear network which, although fascinating and perhaps ultimately useful, will not be followed here. In a recent review of deformation within the Cordillera, Wisser mentioned the four fundamental directions. The fact that many geologists deny the existence of the regmatic shear pattern implies that the fundamental structures are far from obvious. It may mean, also, that some geologists are not accustomed to examine regional and world maps analytically. The maps require much study, and certain features should be isolated on overlays. Even so, with the present limited knowledge, uncertainties remain. The following analysis is a qualitative experiment, subject to change as information accumulates, and should be supplemented by the western sheet of the Tectonic Map of the United States.' Many have probably gained the impression that the Cordillera of the West is oriented northwest-southeast and from this, unless experience rules otherwise, it is natural to assume that the structure likewise trends northwest-southeast. To an important extent this is true, yet anyone tracing off the western sheet of the Tectonic Map all the recorded north west-southeast structures may be surprised to see what a small part of the entire area they occupy. In southwestern U. S. (Fig. 1) the northwest-southeast structures are mostly restricted to the eastern, southern, and western parts. The eastern margin of the Cordillera from northern Colorado to the International Boundary near El Paso, Tex., is obviously determined by some structure other than northwesterly ones. In eastern Nevada and far southward toward the Gulf of California many mountain ranges, valleys, and faults are meridional. In the Rocky Mts. of Colorado, and at many places in southern Arizona, the crystalline Pre-Cambrian is foliated northeast-southwest. The Uinta Mts. of Utah trend approximately east-west, in much the same way as a broad belt of transverse, west-northwest structures—the Texas lineament of Hill",' and Ransome10 in southern Arizona, southwestern New Mexico, and southern California. It seems, then that there are four regmatic shear directions in the Southwest, but at many places they are discontinuous, and their projections must be inferred. To clarify these trends the four sets have been isolated into two systems: 1) northwest-northeast and 2) east-west-north-south (Figs. 2 and 3). Northwest-Northeast System: A number of prominent northwest-trending zones of structure are easily recognized. They are designated by circled Roman numerals, the northeast-trending structures by circled capital letters. Perhaps no two geologists would agree completely on the positions of all these belts. Names given below are for convenience only, and may be discarded where other names have priority. (I) The Sierra Nevada-Lower California belt contains the Jurassic-Cretaceous granitic massifs of the Sierra Nevada and Lower California. These

Jan 1, 1959

By Rollin A. Slater

This paper presents a composite of ideas on materials handling systems by describing the design of an over-all system for a hypothetical steel pellet plant located on the Great Lakes. The bulk materials handling industry has served for years as the skeleton and the central system of nerves and nourishment for the body of basic industries. During the past two decades, this body has undergone substantial growth and mutation to meet the surging demands of our national economy for more and better products. The steel industry has kept pace with spiralling demand by innovation which has resulted in new processes and improved designs which generally yield greater production from fewer units. Materials handling technology has likewise improved its techniques and currently has a new, stronger generation of equipment to perform its necessary supporting function. Drawing upon excerpts from several recent plant designs, this paper describes a basic approach to the selection and application of modern bulk materials handling systems to an entirely new steel plant. Specific details are not available for publication, and therefore the plant described herein is a composite of ideas. This imaginary plant will be located on the United States side of the Great Lakes and its owner will be called the Hypothetical Steel Corp. for purposes of discussion. TYPES OF EQUIPMENT The basic bulk materials handling systems and components required in a plant so situated are: lake boat unloaders; railroad train unloading systems; storage pile stackers and reclaimers; large bins and regulating feeders; and the conveyor systems — with their attendant controls— which connect the foregoing. PROGRAM OF DEVELOPMENT The initial work on the plant must be that of the process engineers who develop and refine the basic data, i.e., the logistics of all raw materials, waste materials and products within the plant. During this phase of study, the materials handling engineer may advance his planning only in basic areas such as movements at the dock and movements at the railroad. This initial planning work is concerned only with defining logical plant locations in the light of channels, currents, existing traffic, governmental regulations, locations of existing railroads and available rights-of-way. These systems alone have their own individual criteria which must be respected and accommodated in the final layout. All other elements, such as the arrangement of the blast furnaces, power house, coke plant, by-product plant, scrap preparation plant, BOF shop, and facilities for continuous casting, degassing, calcining, etc., are dictated by their own specific needs and their relation to each other. In the arrangement of these latter facilities, the materials handling system is secondary and must be designed to accommodate. BASIC LOGISTICS The result of the process engineer's work can be expressed in terms similar to those shown in Table I. Plants are customarily rated in terms of annual tons of ingots. Therefore, the basic size of this plant can be determined by referring to the BOF Shop wherein it is sized at 5 million tpy. From the base, the required hot metal can be traced to the blast furnace, which in turn indicates the amount of required flux, iron bearing materials and coke —which in turn establishes the demand for coal. Likewise, the total demand for flux can be determined by the combined demand of the lime plant and blast furnace. The generation of fines and waste products, which have significant value but are not usable as such, create the need for a sintering plant. From projections such as the foregoing, the complete flow of materials can be established and accommodated. The basic premise upon which this typical materials balance is predicted is that the plant will be a producer of high tonnages of non-SpecialtV- products. All basic raw materials (flux bearing, iron bearing, coal) will be prime quality. For example, the basic iron charge will be pellets, and the iron ore fraction will be sized lump, all of which

Jan 1, 1970

By M. Murakami, Y. Murakami, O. Kawano

The formation and growth of Guinier-Preston zones in Al-Zn alloys containing 4.4, 6.8, 9.7, and 12.4 at. pct zn have been studied by the X-ray small-angle scattering method. Particular attention was paid to the effects of small amounts of third elements silver, silicon, and magnesium on the formation and growth of G.P. zones. It was noticed that an appreciable number of G.P. zones were formed during the course of rapid cooling and that the size, volume fraction, and number of these G.P. zones were influenced by the existence of the third elements. During subsequent aging it was also found that the addition of both silver and silicon lowered the temperature for the growth of G.P. zones, whereas the addition of magnesium raised it. These results were explained in terms of the mutual interactions among zinc atoms, vacancies, and the third elements. A number of studies on the formation and growth of Guinier-Preston zones in Al-Zn alloys have been reported.1-4 Panseri and Federighii have found that the initial stages of zone growth take place at temperatures as low as around -100°C. For investigation of the mechanism of the initial stages of zone growth, growth studies must be carried out at low temperatures. In order to investigate the possibility of the formation of G.P. zones by the nucleation mechanism or the spinodal decomposition during quenching which was reported by Rundman and Hilliard,5 the examination of the as-quenched structure must be performed. In this paper the investigation of the early stages of the formation and growth were determined by means of the X-ray small-angle scattering method. With this technique, change of X-ray scattering intensities was measured while quenched specimens were heated slowly from liquid-nitrogen temperature to room temperature. At as-quenched state and after heated to room temperature, investigation of zone size, volume fraction, and zone number per unit volume was carried out. Measurements on these specimens yielded information on the early stages of zone formation and growth. Measurements were made also on specimens quenched to and aged at room temperature. From these measurements the previously reported model6 for the later stages of growth is confirmed; namely, the larger zones grow at the expense of smaller ones. Three elements, silver, silicon, and magnesium, were chosen as the third elements for the following reasons: Silver. In the binary A1-Ag alloy the spherical disordered 77' zones were observed immediately after quenching.7 Therefore, in the Al-Zn-Ag alloys, it is suggested that silver atoms might induce cluster formation during quenching. Also, since the migration energy of the zinc atoms was found to be raised by the addition of silver atoms,' silver atoms may have a great effect of the zinc diffusion, especially during low-temperature agings. Silicon. The effects of the addition of silicon atoms were found to be marked, especially at low-tempera-ture aging. In the binary Zn-Si system, no mutual solid solubilities between silicon and zinc9 and no in-termetallic compounds10 are reported to exist. Shashkov and Buynov11 investigated the behavior of silicon atoms in Al-Zn alloys and showed that silicon was not in the G.P. zones. The interaction between silicon atoms and vacancies is strong enough to increase the quenched-in vacancy concentration.* Magnesium. Magnesium atoms are reported to trap quenched-in vacancies and after much longer aging times these trapped vacancies will become free and act as diffusion carriers.13 Therefore at intermediate aging times, the diffusion of zinc atoms in Al-Zn-Mg alloys will be slower than in the binary Al-Zn alloys, whereas at longer times zinc diffusion will become faster. EXPERIMENTAL PROCEDURE The alloys used in this investigation had compositions of 4.4, 6.8, 9.7, and 12.4 at. pct Zn with or without 0.1 and 0.5 at. pct Ag, Si, or Mg. The alloys were prepared from high-purity aluminum, zinc, silver, silicon, and magnesium, with each metal having a purity better than 99.99 pct. The analyzed composition of the specimens is given in Table I. The measurements of the X-ray small-angle scattering were carried out with foils of 0.20 mm thick. The change of the scattering intensity was always measured at the fixed scattering angle of 20 = 2/3 deg. This angle exists nearly on the position of the intensity maximum. The value of the interparticle interference function14 which has large effect in this range of angles may not change abruptly in the case of the spherical shape of small zones. Therefore, from the above considerations, it is concluded that an increase of the intensity measured at this constant angle corresponds to an increase of the average radius and volume fraction of G.P. zones. The specimens were homogenized at 500°, 450°, and 300°C for 1 hr in an air furnace. For the study of the formation and growth at low temperatures, the foil

Jan 1, 1970

By H. H. Kellogg

Available high-fernperatzwe equilibrium measurements and other thermochernical data have been critically reciewed for sulfation reactions of the type: Recommended values for log K and ?Fo as junctions of temperature are given for thirty-six suck reactions involving twenty-six different metals. Methods of calculation and choice between conflict-ing data are discussed. SELECTIVE sulfation now enjoys a considerable renaissance as a metallurgical unit process due, in large part, to the available of the fluid-bed re- actor—a device capable of the close control of temperature and gas composition necessary for a successful sulfation process. An additional need, however, if sulfation chemistry is to be approached in a scientific manner, is a reliable body of data on the equilibrium and kinetics of sulfation reactions in simple and complex systems. This paper offers a critical review and compilation of equilibrium data on pure sulfates (simple systems). The last such review, by K. K. Kelley in 1935:30 has proven itself most useful, but the existence of many new data makes necessary a re-evaluation of the available information. METHODS OF CALCULATION For a simple sulfation reaction such as MS04(c) = MO(c) + SO3 [1] there are two approaches one may take toward establishing the value of ?Fo or K as a function of

Jan 1, 1964

By Gerhard Bockstiegel

Kuczynski's formula has been derived for the case of nonspherical particles. TWO formulae of Kuczynski's type have been derived, one describing the increase in tensile strength, the other describing the progress of shrinkage of a powder compact. It has been strength,shown that the exponents of all three formulae each contain two magnitudes of different physical characters, viz, the geometrical factor a and the kinetic factor ß. The interrelationships between the three exponents are stated. SOME years ago Kuczynski1 experimentally showed that the radius, x, of the area of contact between very small spherical metal particles and a metallic block is related to the time of sintering, t, by the following equation x = constant tk [11 where k has the value 1/5 or 1/7. Assuming that the metal particles were perfect spheres and the metallic block was perfectly flat, he derived the foregoing equation from theoretical considerations of the process of material transport in metals, and he showed that exponent k is different for different mechanisms of transport, e.g., k = 1/2 for viscous flow (according to Frenkel2), k = 1/3 for evaporation and condensation, k = 1/5 for volume diffusion, and k = 1/7 for surface diffusion. From this Kuczynski concluded that the mechanism of transport was either volume diffusion or surface diffusion, depending on whether the value of k, as found in his experiments, was 1/5 or 1/7. Subsequently. Cabrera8 corrected Kuczynski's calculations with regard to surface diffusion, showing that the theoretical value of exponent k is 1/5 for both volume and surface diffusion. He supposed that the different experimental values of k were due to slight differences in the shape of the metal particles. An exponential relationship similar to the aforementioned was found by Okamura, Masuda, and Kikuta,4 Masuda and Kikuta, and Takasaki8 when studying the rate of shrinkage on powder compacts during sintering. The authors measured the shrinkage by means of the fraction w = Vp — V./Vp — V,,,, where V,, is the volume of the green compact, V, is the volume of the sintered compact, and V,,, is the volume of the compact in its densest state. This fraction, w, they found, is related to the time of sintering, t, by the equation w == constant tm. [21 Further, Bockstiegel, Masing, and Zapf7 observed that the tensile strength, s, of sintering iron powder compacts can also be related to the time of sintering, t, by an equation of the foregoing type, i.e., s = constant tn. [3] For exponent n the values 0.28 (S=2/7) and 0.35 ( 2/5) were obtained, and the authors pointed out that there might exist a simple interrelation between exponent n as found in their experiments and exponent k in Kuczynski's equation. The authors supposed that 2k = n, since the strength of adhesion between a metal sphere and a block (as in Kuczyn-ski's experiments) must approximately be proportional to their contact area, p. x2. Theoretical Considerations This paper is an attempt to correlate the fundamental experiments of Kuczynski's type with the results obtained with powder compacts as represented by Egs. 2 and 3. In particular, the paper is to show how the rate of sintering is influenced by the geometry of the sintering particles and by the type of material transport. As the geometry of particles conglomerating in a powder compact is very complex, some simplifying assumption has to be made, of course, in order to adapt the problem to mathematical treatment. In the following paragraph a suitable simplification is introduced, and Kuczynski's formula is derived for the case of nonsphcrical particles. Relation Between Area of Contact and Sintering Time—As the face of contact between two particles in a sintering powder compact is not necessarily a circle (as in the case of spheres sintering to a block), Kuczynski's formula is modified as follows: Let the perimeter of the face of contact be described by means of polar coordinates R, 4, as shown in Fig. la, so the area of contact, f, is determined by f= 1/2 . S112p[R(Æ) ]2 dÆ [4] Then, let the two particles be intersected by a plane perpendicular to area f. The intersection is shown in Fig. lb. According to the nomenclature in this figure, the distance, h, between the surfaces of the two particles is a function of T and Æ: h = h(r,Æ). For the particular case of spherical particles, as in Kuczynski's theory, this function becomes: h = constant r2. It shall be assumed here that in the close neighborhood of their

Jan 1, 1957

By B. W. Levinger

THE lattice parameter of the ß form of pure titanium has been measured at elevated temperature.', ' No attempt was made, however, to correct the parameter obtained to room temperature. In the course of phase diagram studies at Armour Research Foundation and elsewhere, the variation of ß-phase lattice parameter with composition has been established in a number of binary and ternary systems involving titanium. It was possible to extrapolate in these instances to 100 pct Ti to find the apparent lattice parameter of ß titanium at room temperature. Table I lists the results thus obtained. The suggested value for the lattice parameter of ß titanium is the average of the extrapolated values 3.276 ±0.003 kX. This suggested value gives an interatomic distance in ± titanium of 2.837 kX and hence a Goldschmidt atomic diameter (coordination number 12) of 2.925 kX. The latter agrees closely with the value of 2.93 given by Hume-Rothery." From the data of Adenstedt and coworkers' it was possible to determine by extrapolation the mean coefficient of linear expansion for /3 titanium in the range from room temperature to 1000°C. This value, 10.1x10-8 per degree C, compares with about 11x10-8 for a titanium in a similar range." It was thus possible to calculate the parameter at 900 °C. The value of 3.305 kX agrees well with 3.3065 given by Eppel-sheimer.' The majority of values reported in the literature7-', ' were given as Angstroms. In at least one case, ref. 8, it was shown that they actually represented kX units. The source of this confusion appears to be that a large number of tables of X-ray emission spectra list wavelengths as Angstroms and give values in kX units. The accepted conversion factor for kX units to Angstroms (10.' cm) is 1.00202. Thus the parameter of ß titanium suggested corresponds to 3.282A. References J. H. de Boer, W. G. Burgers, and J. D. Fast: Proc. Acad. Amsterdam (1936) 39, p. 515. 2D. S. Eppelsheimer and R. R. Penman: Nature (Dec. 2, 1950) 166, p. 960. 3 W. Hume-Rothery: The Structure of Metals and Alloys (1945) London. Inst. Metals. 4 H. K. Adenstedt, J. R. Pequignot, and J. M. Raymer: Trans. ASM (1952) 44, p. 990. 5 Gmelins Handbuch der Anorganischen Chemie. Titan, Verlag Chemie, Weinhein (1951). 8 P. Pietrokowsky and P. Duwez: Trans. AIME (1952) 194, p. 627; Journal of Metals (June 1952). 7 P. Duwez and J. L. Taylor: Trans. ASM (1952) 44. D. 495. 8 M. Hansen, E. L. Kamen, H. D. Kessler, and D. J. McPherson: Trans. AIME (1951) 191, p, 881; Journal of Metals (October 1951). 8 Unpublished Research, Armour Research Foundation.

Jan 1, 1954

By J. W. Graham

For many years the author has been cognizant of the difficulty encountered by some in treating with the water influx formulas for unsteady-state fluid flow as pertain to the material balance equation. This has particularly applied in establishing reservoir performance and identifying reservoir pressure, which to the practicing engineer has entailed a trial-and-error procedure, and for others has necessitated resorting to computing devices and reiteration processes. In retrospect this difficulty stems from the fact that reservoir pressure in the material balance formulas, as well as associated with the water influx equations, is an inexplicit term, and the work reported in the past is irrefutable. However, what will be presented in this paper is another approach to the problem, whereby the entire material balance equation will be treated by the Laplace transformation, and reservoir pressure which hereto has been inexplicit, can now be isolated by mathematical procedure to relate that parameter with all the factors contributing to its change. This is the simplification entailed, that treats first with an undersaturated oil reservoir as an integrated effect from the inception of production. The second phase pertains to saturated oil reservoirs that encompass a survey traverse. Although both methods of approach are necessarily different in aspect, the most interesting fact is that the mathematics so deduced are identical. Both the linear and radial water-drive systems are incorporated. for which an illustrated factual example is offered for the latter, treating with a saturated oil reservoir. INTRODUCTIO N What is performed in this work is the simplification of an involved computation by advanced analysis. Although such may be construed as a contradiction when one treats with higher mathematics; nevertheless, when direction is given to such an undertaking the results car. be most revealing. Likewise, it is to be mentioned that the bases for these mathematics have been developed on the expediency of the occasion. This is not to be inferred as a qualification of this work, but rather the demands frequently placed upon the author in his private prac- tice in meeting a time limit. A situation, instead of being fraught with hazards, often has given emphasis to creative thought. What will be entailed in this work is the simplification of the material balance formulas by the Laplace Transformation., Although this reveals entirely new horizons that will be given expression in a forthcoming tract, it suffices in the present instance to limit our attention to this phase of the development that treats both with an undersaturated and saturated oil reservoir. To orient the reader's thoughts as to what is involved in this simplification is the recognition that reservoir pressure, as such, is an inexplicit term in the material balance equation. This is the independent parameter that defines the total history of performance in the author's' unsteady-state water influx formulas, as well as the basis for the physical dependency of fluid behavior within the formation as prescribed in the Schil-thuis' material balance equation. Therefore, to isolate reservoir pressure, which is the most essential factor in any reservoir study, is rather a cumbersome procedure entailing either a trial-and-error calculation for the engineer; or as some prefer, a reiteration process performed on a computing device. However, once such an equation can be transcribed as a Laplace transformation, this inexplicitness so expressed can be alleviated to identify reservoir pressure as an explicit function of all the factors contributing to its change. This is the simplification encompassed, that will treat first with an undersaturated oil reservoir as an integrated effect from the inception of production, and secondly, with a saturated oil reservoir as a survey traverse. Although the two approaches are necessarily different because of the uhvsics involved. it is an interesting commentary that the mathematics are identical, showing the interdependency of the two methods. In order to acquaint the reader with this development, the simplest case will be treated first; namely, an under-saturated oil reservoir subject to a linear water drive. However, what may be construed for this example as an idealistic case is actually a most practical application in certain parts of the world, where the size of the fields are so large that radial water-drive approaches the configuration of a linear drive. Further, to avoid the repetition of much symbolism, frequent references will be made to the work of the author and an associate on Laplace Transformations3,

By R. A. Wolfe, H. W. Paxton

Self-diffilsion coefficients for cr51 and Fe55 in 12 pct Cr-Fe and 17 pct Cr-Fe for Fe55 in chromium, and for Cr51 in vanadium have been measured. The results are compared with other values for the Fe-Cr system, and with the various theories of diffusion in hcc metals. Some empirical correlations are discussed between Do and Q in hcc systems, or, expressed differently, the constancy of ?G*/T solidus for seveval bcc metals and alloys is noted. It appears very probable that a vacancy mechanism is operative in bcc metals, hut this cannot he stated with certainty. THE great bulk of work on diffusion in metals, both experimental and theoretical, was for many years concentrated on those with close-packed and, in particular, fcc lattices.1,2 There appears to be little doubt that the mechanism of diffusion in these solids is vacancy migration, leading to mass transfer and in substitutional solid solutions to a Kirken-dall effect.3,4 For bcc metals, the picture is much less clear. The Kirkendall effect certainly occurs in several alloys.5-10 However, attempts to understand the factors contributing to the pre-exponential in the usual expression for the diffusion coefficient D =D, exp {-Q/RT) by extension of ideas useful in close-packed lattices have not always been successful. Zener,11 Leclaire,12 and Pound, Paxton, and Bitlerl3 have suggested that various forms of ring diffusion may be important in some bcc metals. For close-packed metals, Do is usually about 1 sq cm per sec and Q - 35Tm kcal per mole (Tm = melting temperature in OK). The theory of Pound et al. suggests for ring diffusion that Do may be about 10-4 and Q, although difficult to calculate with any precision, would be significantly less than 35 T,. The experimental results on self and solute diffusion in ? uranium14,15 and ß zirconium,10 and for solutes in 0 titanium,17 and possibly for self-diffu- sion in chromium below about 0.75 T,," gave some credence to this theory. However, not all bcc materials display low values of DO and Q, and the exceptions were not predicted by any theory. Furthermore, it has recently become apparent that, in bcc materials, log D is not always linear with T-l if a sufficiently wide range of temperature is studied.16,18 This variation may be such that Q may increase18,19 or decrease20 with increasing temperature. The present work was undertaken in an attempt to provide further diffusion data on bcc metals, and to try to understand the factors which contribute to differences in behavior between the various elements. For part of this work, the Fe-Cr system was chosen since it is of considerable technological importance, and data on 12 pct Cr and 17 pct Cr alloys appeared well worthwhile to supplement that existing for the remainder of the stern.18,22 The diffusion of Fe55 in chromium was studied as an example of a more or less "normal" tracer element in a possibly abnormal host lattice. Finally, no data were available for vanadium, the neighbor of chromium in the periodic table, because of lack of a suitable isotope so cr55 was used as a tracer in a few preliminary experiments. For convenience, we shall refer to elements whose Do and Q are low compared to those predicted by Zener's theory as "anomalous". PROCEDURE This investigation determined self-diffusion rates by means of radioactive tracers and the integral-activity method first utilized by Gruzin.23 In this method a thin layer of radioisotope of the diffusing element is plated or coated onto a planar surface of the diffusion sample, which is then given an isothermal-diffusion annealing treatment. The determination of an activity-penetration curve involves measuring the residual activity of the specimen after each successive layer or section has been removed parallel to the original planar surface. The method used here is essentially the same as that used by Gondolf18 and Kunitake.21 Two radioactive tracers, cr51 and Fe55, were used in this investigation. Diffusion coefficients were determined for the diffusion of one or both of these tracers in four different materials, viz., Fe-12 wt pct Cr alloy, Fe-17 wt pct Cr alloy, chromium, and vanadium. The diffusion samples had nominal dimensions of 1.5 cm diameter and 0.5 cm thickness. The grain size was several millimeters for the Fe-Cr alloys and at least 1 mm for the chromium and vanadium samples. Accurately planar surfaces

Jan 1, 1964

By L. D. Jaffe, F. W. Cotter, E. Cordon

The hardenability of titanium-base alloys was studied by metallographic examination and hardness survey of Jominy specimens end-quenched from the B range. Analyses of the data led to the equation log J = -0.57 + 0.25 @ct Fe + pct Mn + pct Mo) + 0.19 @ct Cr) +0.16 @ct V) + 0.03 @ct Zr). Here J is the distance, in sixteenths of an inch, from the quenched end of a Jominy hardenability specimen in the position of peak hardness, for material quenched from the B range. This equation fitted the experimental data with a standard deviation of approximately 0.29. The effects of the elements Al, Sn, W, Cu, Ni, B, C, N, 0, and H, and of pain size, were not statistically significant or not practically significant. A check against hardenability measurements in the literature showed agreement within the stated standard deviation. The equation should be useful in estimating hardenability of new or modified titanium alloys. HARDENABILITY in a titanium-base alloy is the ability of the alloy to retain the B structure on quenching. An alloy with high hardenability will retain the /3 structure even when cooled relatively slowly from a temperature at which B or P plus a is stable. A low hardenability material will retain P only if quenched extremely rapidly from the range of p or 0-plus-a stability, or will not retain it at all, at room temperature. High hardenability is desirable in titanium alloys to be heat-treated to high-strength levels. Its value is by no means limited to large section sizes. With high hardenability, a material can be solution-treated and cooled at a variety of rates, either to give high strength directly or, more generally, to give a soft ductile condition from which high strength can be obtained by subsequent aging. With low hardenability, high strength can be obtained, if at all, only by very rapid quenching, and there will generally be little increase in hardness on subsequent aging; an alloy of this type is limited in its applicability. On the other hand, alloys of very low hardenability have some advantages in weldability; essentially, they are always in the annealed condition, after welding as well as before. For commercial alloys, hardenability data are usually available, in the form either of property data after cooling from the solution temperature at various rates, with or without subsequent aging, or of results of a standard hardenability test, such as that originally developed for steels by Jominy and Boegehold.' When modifications of an available alloy are considered, or preparation of new alloy compositions, it would be Very convenient to be able to estimate the hardenability of the new material without having to make and test it. A method of estimating hardenability of titanium alloys from their composition was suggested by one of the authors some time ago, on a preliminary basis, utilizing scattered data found in the literature.' It seemed worthwhile to carry out a systematic experimental study of the effect of composition upon hardenability. EXPERIMENTAL PROCEDURE Approximately fifty heats of various compositions, weighing 8 to 10 Ib apiece, were melted in a small inert-gas tungsten-arc furnace with water-cooled copper walls. The starting material was 110 Brine11 titanium sponge, with high-purity metals added for alloying. Each heat was bottom-poured under vacuum through a molybdenum burnout strip into a cold graphite mold, to form an ingot approximately 4-1/2 by 3-1/2 by 3 in.* From each ingot were cut *The material was melted and cast by Pitman-Dunn Laboratory, Frankford Arsenal, to whom the authors must express their thanks. two pieces 4-1/2 by 1-1/2 by 1-1/2 in. These were forged, at temperatures adjusted to the composition, into 1-1/4-in. rounds, from which standard 1-in.-diam hardenability specimens3 were machined. A number of small samples were also prepared from forged materials of each heat, annealed, quenched from various temperatures, and examined metallographically. The P-transus temperature was determined by observation of the degree of resolution of primary a in these pieces. samples for chemical analyses were also taken from the forgings. One hardenability specimen of each heat was solution-treated for 1 hr approximately 50°F above the measured transus temperature, and the other for 1 hr approximately 250°F above the transus. (An additional hour was allowed for the specimens to reach furnace temperature.) These are not necessarily the temperatures that would be selected for

Jan 1, 1964