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By S. Shapiro, G. Krauss

RECENT investigations1 3 of the products of marten-sitic transformation in Fe-Ni and Fe-Ni-C alloys have made use of light microscopy to describe mar-tensitic fine structure. The application of conventional metallographic techniques to this problem was possible because of the similarity of distributions of parallel striations developed by etching polished surfaces to distributions of transformation twins which are positively identified in thin films by transmission electron microscopy. The surface striations frequently are not well-defined, and could also be due to, for example, rows of etch pits which are not resolved by the light microscope. This note describes the etching effects revealed by examination of surface replicas of mar-tensite in the electron microscope. The application of a replica technique both extends the observations of fine structure made with the light microscope and allows the results of conventional metallography to be used with more confidence. Samples of an Fe-33 wt pct Ni alloy were used for this study because of the detailed knowledge of the fine structure of martensite which has been developed'-4 for alloys of about this composition. Samples transformed to martensite at -120°C, and transformed samples heated to 340°C to effect a small amount of reversal of martensite to austenite, were examined. Surfaces were first prepared for replication by elec-tropolishing in a chromium oxide-acetic acid electrolyte at a current density of 0.1 amp per sq cm and a temperature of 15°C or a perchloric acid-acetic acid electrolyte at a current density of approximately 2 amps per sq cm and a temperature of 15°C. The polished surfaces were then etched for 4 to 7 sec by immersion in a solution of equal parts HC1, HNO,, and H20. Application of the etchant for this period of time produced discrete attack of certain features without loss of resolution due to overlapping of areas most susceptible to etching. The etched surfaces were replicated by 1) preshadowing with Pt-Pd alloy at an angle of 20 to 30 deg, 2) depositing a thin carbon film, and 3) stripping the film and shadowing material by immersion in a 5 pct nital solution. Two types of etching effects were observed by examination of the surface replicas in the electron microscope: l) continuous striations centered at the bottom of long grooves or the tops of pyramidal elevations on the sample surface, and 2) high densities of fine etch pits. Examples of both types of features are shown in Figs. 1 to 4. The striations are in each case continuous and have the same characteristic configurations as do transformation twins in martensite. Fig. 1 shows that the density of grooves decreases toward the edge of a martensite plate and Fig. 2 shows a region where the striations are of varying length. Similar examples of transformation twin arrangements determined by transmission electron microscopy of thinned foils of martensite have been shown in the literature,'~ and, based on these similarities, the striations and their associated grooves or mounds are considered to be evidence for the presence of transformation twins. The transf~rmation twins in martensite are on the order of l00 A thick, much too fine for resolution by the light microscope. It appears that orientation-dependent etching of the matrix martensite about the twins results in grooves or surface elevations which

Jan 1, 1967

By D. J. Pye

Certain high molecular weight synthetic polymers in very dilute solutions decrease water mobility in porous media 5 to 20 times more than would be expected from the solution viscosity. This indicates that increasing water viscosity to reduce adverse mobility ratios in water floods is economically feasible in many situations. Laboratory results are consistent with accepted theory with respect to improved areal sweep, permeability distribution and displacement efficiencies as would be predicted from the solution mobility measured in the core. The laboratory results have been confirmed by field pilot floods which recovered 80 per cent and 100 per cent more oil than comparative water-flood pilots in fields containing 16 cp and 130 cp oil respectively. Economic analyses based on pilot data indicate the method to be profitable. INTRODUCTION The desirability of improving the water-oil mobility ratio in waterflood-ing operations has long been appreciated, especially for high viscosity crudes. Methods of reducing the oil viscosity by application of heat, gas resaturation and miscible drives have met with some success. Conversely, it has been generally conceded that increasing the water viscosity would also be effective, but the amount of thickening agent required to effect an appreciable increase in viscosity is discouragingly high. The use of such materials as glycerin, sugar, or glycols is completely out of the question economically, so that considerable attention has been given to the use of the much more efficient synthetic water-soluble polymers as viscosity improvers; but even these materials are not economically attractive. If increased water viscosity could be economically realized, marked improvements in areal sweep efficiency, as discussed by Caudle and Wittel and others, would be realized in field operations. Similarly, the improved mobility ratio would bring about increased recoveries by correcting permeability distribution problems as discussed by Stiles2 and Dykstra and Parsons,' and improvements in displacement efficiency would be obtained as recognized by Buckley and Leverett4 and Welge.5 LABORATORY STUDIES THE RESISTANCE EFFECT In the course of research to develop a more efficient water-soluble polymer viscosity builder, we discovered that a very few types of water-soluble polymers exhibited a most unusual and very interesting property not previously observed. Among the earliest materials showing such activity were polymers containing acry-lamide. Fig. 1 shows a typical plot of the solution viscosity vs concentration for one of these polymer solutions as determined in an Ostwald viscometer. As usual, such a plot is an approximate straight line on semi-logarithmic paper. Now, an inspection of Darcy's law, shows that a viscosity value can also be determined in a formation sample if the pressure, flow rate and permeability are known. If the core permeability is previously determined with wa- ter or brine, then the viscosity of another aqueous fluid may be determined from the equation. The viscosities so determined for glycerin (glycol or polyvinyl alcohol solutions, for example) agree with the viscometer determinations. However, in the case of the water-soluble polymer solutions in which we are interested, the viscosities measured in the formation sample depart very markedly from the viscometer values. A typical relationship for a polymer solution is also shown in Fig. 1. This unusual departure from the expected response is referred to as a resistance property of the polymer and is quantified as "resistance factor". Since the resistance factor R can best be determined in a core under study, the term has been defined on the basis of the ratio of the brine mobility to the polymer solution mobility at residual oil saturation so that:

Jan 1, 1965

By P. Dayal, L. S. Darken

THE migration of carbon in austenite under the influence of an electric current has been observed qualitatively several times.14 Lebedev and Guterman5 recently have reported quantitative measurements; their method consisted of welding a low-carbon to a high-carbon wire, passing current, and later estimating the carbon distribution metal-lographically. We believe the method reported in this paper is superior in principle since electrolytic migration and ordinary diffusion are not necessarily coupled as in the weld method; also for the first time the extent of migration is determined by combustion analysis for carbon. A uniform tubular specimen (S.A.E. 1045 or 1095) was mounted as illustrated in the figures. the whole assembly being in an atmosphere of purified nitrogen. Direct current (129 to 226 amp at 0.65 to 1.0 v) served as source both of heat and of potential gradient for carbon migration. The duration of experiment was 7.5 to 12 hr, during which time the temperature was controlled (±10°C) manually. The experimental conditions are indicated in the first five columns of table I. With this experimental arrangement, the temperature initially has a maximum value at the central plane. Also, in this vicinity (by virtue of the symmetry), the carbon entering any volume element is equal in quantity to that leaving; the loss or accumulation of carbon occurs near the electrodes since the carbon moves uniformly near the center and is "frozen" at the cold ends. Hence, providing the time of experiment is not sufficiently long to seriously influence the conditions at the central plane, carbon crosses this plane only under the influence of the electrical potential gradient and not under the influence of temperature or concentration gradient. The amount of carbon which has crossed this plane was determined by combustion analysis of the two halves of the specimen. The results of these analyses are shown in the sixth and seventh columns of table I. It will be noted that substantial amounts of carbon migrated from the anode portion to the cathode portion (except at 920°C, which temperature was too low to exhibit the effect in the allotted time). In spite of precau-tions taken, considerable decarburization occurred as may be seen by comparing cols. 8 and 5. In three cases (indicated by asterisks in table I) the specimen was ground on one side, polished, and examined metallographically before analysis. One specimen was normalized and re-examined. Micrographs of selected areas in specimens 4 and 6 are shown in figs. 1 and 2, respectively. Evidence of carbon migration from the anode toward the cathode is quite apparent. Fig. 2 shows abundant graphite as well as cementite in a region near the cathode. The temperature of this zone is estimated at about 800°C. In fig. 1, particularly in the micrograph on the extreme right (the right side of which is of unaltered carbon content), there is evidence of slight depletion of carbon in the immediate vicinity of the cathode as contrasted to the general increase in carbon of the cathode half of the specimen. Although this may be attributed in part to decarbur-ization, it is believed that it is occasioned also by thermal diffusion—migration (of carbon) from a cool to a hot zone4—a phenomenon superimposed upon the electrical migration. Evidence of carbon migration was visible particu-larly during the course of the high-temperature,

Jan 1, 1951

By David J. Mack, T. V. Philip

The effects on the Cu-A1 eutectoid transformation of the addition of a third element from the second long period and from Group IIB of the periodic table, were studied by isothermal transfomation techniques. The valency of the third element shows the most pronounced effect on the eutectoid decomposition. With some exceptions, the atomic size factor of the third element shows some consistent effects on pearlite nucleation and growth. The atomic concentration or the electronegative valency of the third element shows wo consistent effect on the eutectoid decomposition. Addition of the third element helps spheroidization of pearlite. SINCE the pioneering work of Davenport and Bainl on the eutectoid decomposition in steel by the isothermal transformation technique, an enormous amount of data has been accumulated on the eutectoid transformation characteristics of commercial steels. While the eutectoid reaction in steel is of tremendous industrial importance, it appears to be quite unique among the eutectoid reactions. Though the metal-lographic structures developed in the Fe-C and Cu-A1 eutectoids are similar, it is now evident that the two eutectoid reactions are quite dissimilar. The eutectoid decomposition in the Cu-A1 system is more complicated partly due to the appearance of transitional phases in addition to the equilibrium phases. * The first isothermal studies of aluminum bronzes were made by Smith and Lindlief2 and later by Mack,3 Klier, and Grymko,4 and recently Hayne 5,6 A few other systems, structurally analogous to the above, have been studied by the same technique.7-10 Kasberg and Mack1' studied the effects of iron on the transformation of commercial aluminum bronze. The effects of manganese and nickel on this aluminum bronze and those of iron, manganese, and nickel on the binary Cu-A1 eutectoid have been recently studied.12 The object of the present investigation was to study, by isothermal transformation techniques, the effects (with respect to the fundamental factors of alloy formation) of the addition of a third element on the transformation of a Cu-Al eutectoid alloy, 11.8 pct Al. The third elements chosen for the purpose were silver, cadmium, indium, tin, and antimony from the second long period, and beryllium, zinc, and cadmium from group 11B of the periodic table. They were added in nominal amounts of 0.5, 1.0, and 2.5 pct by weight to a eutectoid Cu-A1 alloy. These third elements were expected to show the effects of electron valency, atomic size factor, and electronegative valency effects on the binary eutectoid transformation. PFLEPARATION OF ALLOYS AND PROCEDURE All alloys were made as 400-g heats by induction melting in a graphite crucible with a graphite lid. The molten alloy with a layer of graphite powder on top was stirred at regular intervals by a graphite rod. When the melt was judged to have acquired sufficient superheat, a pinch of common salt was sprinkled on top and any crust scraped off to one side. It was then chill cast into a 5/8 in. rod. The alloys with silver were prepared by remelt-ing the high-purity Cu-A1 eutectoid alloy used by Mack3 with high-purity silver (99.99 pct pure from Hardy and Harmon, Inc.). In the preparation of all the other alloys, polished electrolytic copper shot (from Belmont Smelting and Refining Co.) and high-purity aluminum (99.99 pct pure from Aluminum Co. of America) were used.

Jan 1, 1962

By R. Floyd Farris

A method is presented for determining minimum waiting-on-cement time, which takes into account the differences that exist between types and brands of cements and such individual well conditions as depth, temperature, and pressure. The basis for the method was determined by laboratory tests. Being a laboratory development, several steps were required to prove its merit. The first step consisted of laboratory tests designed to determine the minimum cement strength required in wells. Basis was found for setting a minimum value of 8 Ib. per sq. in. tensile strength. Next, it was shown by laboratory tests that the time to 8 Ib. per sq. in. tensile strength may be expressed as a function of consistometer stirring time to loo "poises," the approximate relation being "the time to 8 Ib. per sq. in. tensile strength equals the time to I00 'poises' times three." Next, it was shown that the time of maximum temperature development in cement slurries, due to heat of hydration, is also related to consistometer stirring time to loo poises, but only by a factor of approximately two. It was shown also that the shut-in casing pressure will build up after cement is placed and register a maximum pressure at approximately the same time the slurry down the hole attains maximum temperature. From this and the relationships listed above, the general rule was established that minimum waiting-on-cement time (time to 8 Ib. per sq. in.) after casing cement jobs in any well is equal to the time when the shut-in casing pressure reaches a maximum, as measured from the initial mixing of cement, times a factor of 1.5. Cement plugs drilled in the field at the time prescribed by this formula were found to drill "firm to hard," thus confirming the laboratory tests. These tests prove that many of the present regulations for waiting on cement require a longer time than is absolutely necessary. Use of the method herein proposed offers the possibility of a saving of $1200 per well. Introduction The length of time allowed for cement to set after casing is determined either by state-wide rules, field rules, or self-imposed rules written into drilling contracts. In general, the time is dictated by experience and common practice. However, owing to differences in opinion and in experience of the various groups involved, waiting-on-cement time often varies from one area to the next. For example, an operator in an area where no rules exist may drill out of surface pipe at 24 to 36 hr., while another operator in another area may wait 48 hr. or more to comply with state or field rules, although the depth of the well, hole size, type of cement, and other data are identical. An even greater difference in practices will be found by making similar comparisons with respect to oil-string cement jobs. Differences in waiting-on-cement times of 36 to 48 hr. are common. Further complicating the picture is the rather common practice of allowing more waiting time for cement to set at the greater depths than is allowed at the shallow depths. This practice has existed for years in spite of the common knowl-edge1,2,3 that the temperature of the earth at the usual setting depths of surface

Jan 1, 1946

By W. R. Purcell, C. S. Brooks

The internal surfaces of rocks which are in contact with interstitial fluids are known to influence in some degree the recovery of hydrocarbons from pay zones. Despite the admitted importance of the influence of solid surfaces on hydrocarbon recovery, little information is available concerning the extent of surface of reservoir rocks. In this paper a description is given of the apparatus and procedure employed in the determination of the surface areas of sedimentary rocks, and values are reported for a variety of sandstone and limestone cores. In addition, consideration is given to the Kozeny equation, which relates surface area to porosity and permeability. A colliparison is made between the surface areas as calculated from this equation and the geometrical areas of a series of packs of spherical glass beads. Also, for a group of sandstone cores. Kozeny areas are compared with surface areas as determined by the gas adsorption method employed in this investigation. INTRODUCTION It has long been recognized that many processes which are of importance to hydrocarbon production are controlled in some degree by the extent of the surface of the reservoir rock through which the hydrocarbons move. For example, the recovery efficiency that is obtained in a given reservoir is certainly determined in part by the action of interfacial forces between the reservoir fluids and rock, and this action is influenced in turn by the extent of solid surface. Despite the admitted importance of surface effects to problems of petroleum recovery, little information is available concerning the extent of surface of reservoir rocks." It is the purpose of this paper to describe an apparatus which has been employed for the measurement of the surface areas of rock samples and to present the values which have been obtained for a variety of sandstone and limestone cores. In addition, the relationship of surface area to permeability and porosity, as given by the Kozeny equation, will be discussed. METHOD OF MEASURING SURFACE AREA The method of determining surface areas as employed in this work has previously found wide use in studies of porous solids such as catalysts. The method involves the measurement of the amount of physical adsorption of an inert gas, such as nitrogen or argon, on the bare surface of the solid at reduced pressure and constant temperature near the normal liquefaction temperature of the gas. With the aid of the theory of isothermal adsorption as developed by Brunauer, Emmett, and Teller,' it is possible to ascertain the amount of gas (and hence the number of molecules) which is required to cover the solid surface with a single layer of molecules. From a knowledge of the covering area per molecule the total surface ares of the solid can be computed. Since the Brunauer. Emmett, Teller (BET) theory has been adequately discussed elsewhere: it will suffice here merely to present their final equation as ordinarily employed for surface-area calculations. This equation relates the volume of gas, V, which is adsorbed at pressure, P, to the liquefaction pressure, Po, of the gas, and to the volume of gas, V.,, that is required to form a monomolecular layer: In this equation C is a quantity which is related to the heats of adsorption and liquefaction of the gas; for a particular solid-gas system at Constant temperature, C is considered to have a constant value. The basic adsorption data can be presented in the form of Equation (1) by plotting the quantity P/V(Po- P) as a func-

Jan 1, 1952

By F. W. Jessen, R. W. Durie

The dissolution of salt in the development of salt cavities is controlled by free-convection boundary layer flow along the salt surfaces. It is the purpose of this paper to expand upon results published previously, and primarily to illustrate the influence of surface features on the boundary layer and hence the dissolution process in the development of underground salt cavities. General dissolution equations are presented that apply to a surface inclined to the vertical. A salt surface inclined so as to be overlain by water is dissolved by boundary layer flow, while an inverted surface is dissolved by a combination of boundary layer and cellular flow. Detailed investigation of the boundary layer was limited to laminar free-convection flow. Truly laminar free-convection boundary layer flow may be encountered only in laboratory solution cavities, but the boundary layer will control dissolution even where cavity dimensions are such that free-convection turbulence will occur. The factors found to significantly affect the laminar boundary layer will affect dissolution with a turbulent boundary layer. INTRODUCTION Underground salt cavities have been used extensively for the storage of LPG products, and the use of these cavities is expanding each year. The increasing requirements for such cavities suggest the need for a better understanding of the mechanisms involved, for the purpose of the control of cavity geometry and the most effective use of the injected water. A previous paper outlined a quantitative approach to the determination of salt dissolution rates in the laminar free-convection dissolution of salt. It is the purpose of this paper to expand upon the results previously published and to point out significant factors in the application of these results to the dissolution of field cavities. The dissolution of salt in laboratory scale cavities is controlled by the free-convection boundary layer, which is the region of flow along the salt surface caused by the difference in buoyancy forces resulting from the salt dissolution. The transfer of salt into solution at the salt face causes an increase in salinity, and hence a greater density, in the water at the salt surface. The region of higher density tends to fall through the lighter, less saline water and a flowing boundary layer is the result. The water remains stationary at the contact with the salt surface,l so the resulting velocity profile is such that the influence of gravity is opposed by a viscous shear force at the salt surface. For salt to be transferred into solution from a solid surface to a boundary layer of fluid, it must diffuse through a stationary film of water at the salt contact. According to Fick's first law, the rate of mass transfer by diffusion is the product of the diffusion coefficient and the concentration gradient, with diffusion transfer in the direction of decreasing salinity. Once the salt has passed into the boundary layer, it will be transferred by a combination of molecular diffusion and convection. The convection transfer will in turn affect the rate of dissolution by influencing the gradient of the salt concentration at the surface. In the previous investigation by the authors to determine the basic mechanism of the salt dissolution process, an equation was developed that agreed very well with the experimental rates of free-convection salt dissolution from a smooth vertical surface. The technique was taken from the work of Eckert2 in the analogous heat transfer system and will be referred to as the integral method. The rate of salt transfer from a vertical section of height H was found to be:

Jan 1, 1965

By J. D. Rice, P. L. Wearden, W. L. Hensou

Solutions to the unsteady-state partial water-drive reservoir performance problem can be obtained through the use of analogue computers or high-speed electronic digital computers. The solutions that have previously been resolved for use on digital computers, however, demand a knowledge of the aquifer parameters. Generally, the analogue computers now in use do not require this knowledge. A solution is presented herein where the aquifer performance, expressed in terms of difference equations, is related to the reservoir performance as expressed by the modified Scbiltbuis material-balance equation. A numerical procedure for a medium-sized digital computer also is presented in which a solution to the set of equations defining the aquifer and reservoir performance is obtained and the aquifer parameters (permeability and sand thickness) are automatically optimized while simultaneously matching the known pressure behavior. Predicted pressure behavior can be calculated using rates from any assumed future production practice. The procedure provides an output format which presents the cumulative, incremental and average rate of natural water influx, the per cent gas-cap expansion, the calculated reservoir pressure, the measured reservoir pressure, and the difference between the measured and calculated pressures. Results of a test problem are presented in comparison with results obtained by the Bruce Analyzer, Ohio Oil Co. 's Pace General Purpose Analogue Computer, and Sun Oil Co.'s Single-Pool Electronic Reservoir Analyzer. These results indicate that unsteady-state reservoir perlormance for a single-pool system can be adequately simulated by a numerical method employing a digital computer and that the special-purpose analogue computer can be supplanted by this method. INTRODUCTION The numerical approach to the unsteady-state partial water-drive reservoir performance problem heretofore has been limited in that solutions have been resolved only for certain fixed parameters. Also, prior to the advent of high-speed electronic digital computers in the last few years, calculations were so tedious and time-consuming that they ordinarily were neglected, or some other means of obtaining the solutions were used. The analogue approach had been used for obtaining solutions to the transmission-of-heat problem and, consequently, means were developed for applying the electrical analogue to the unsteady-state reservoir performance problem. Bruce submitted a paper for AIME publication in Sept. 1942, in which he described an electronic device (now called the Bruce Analyzer) for analyzing the water-drive performance of any reservoir, based on either steady or unsteady-state flow characteristics. 1 Sun Oil Co. adopted the analogue approach in 1949 and now has two special-purpose high-speed electronic reservoir analyzers in use.2,3 Two main features of Sun's analyzers are (1) the high repetitive rate of reproducing the entire history of reservoir performance cyclically a number of times per second, and (2) the elimination of the necessity of knowing the properties of the associated aquifer. Since the advent of larger and faster digital computers, the possibility of incorporating this second feature into a numerical approach appeared feasible. Previous work has been done and material published covering the application of numerical methods to the behavior of the pressure with respect to time at any point in an associated aquifer? However, the aquifer parameters must be known from some source. The material presented in Ref. 4 has been used to a great degree in developing the numerical method described herein. DIFFERENTIAL EQUATION AND BOUNDARY CONDITIONS The problem of simulating the performance of a reservoir and the associated aquifer is to determine the characteristics of the aquifer such that the

By N. S. Stoloff, R. G. Davies

The annealing behavior of a heavily cold-worked FeCo-V alloy has been studied at temperatures both above and below Tc, the critical temperature for ordering. It was found that re crystallization and grain growth can take place below Tc in the ordered state and that, in agreement with results for fcc alloys, order retards grain growth. The activation energy for pain growth is -55 kcal per mole in the disordered condition; it was not possible to assign a value to the activation energy for grain growth below Tc because the degree of order is changing rapidly over the temperature interval investigated. Precipitation of an fcc y phase was observed upon annealing the cold-worked alloy at temperatures of 675°C and below. SINCE it is known that diffusion constants are greatly affected by long-range order,' it is not unreasonable to anticipate that order will influence the diffusion-controlled phenomena of recrystallization and grain growth. In the course of a study of strain aging of ordering alloys around the composition Ni3Fe Vidoz, Lazarevic, and cahn2 noted that a disordered cold-worked alloy annealed at a temperature T1 just below Tc will order but not recrystallize; Tc is the critical temperature for order. The same alloy annealed at a temperature T2 just above Tc, or an alloy of different (nonordering) composition annealed at either T1 or T2, will recrystallize after equivalent amounts of cold work. Initially Selisskii and coworkers,3,4 who examined a series of cold-worked and annealed bcc Fe- Co alloys, reported that alloys forming the B2 FeCo super lattice could not be recrystallized below Tc. However in a later paper5 it was shown that FeCo ordered alloys could be recrystallized below Tc. Thus the first question to be answered by the present investigation was whether or not a heavily cold-worked Fe-Co-V alloy could be recrystallized below Tc. When it was found that the alloy would indeed re-crystallize below Tc, the influence of long-range order upon subsequent grain growth was studied. EXPERIMENTAL PROCEDURE The grain-growth measurements were made upon FeCo-2 pct V wire of 0.031 in. diam; the alloy was the same as that used in an earlier study of the mechanical properties of FeCO-v.6 The wire was produced by cold swageing and drawing a rod 0.125 in. diam that had been quenched into iced brine from 850°C to disorder the alloy; the initial grain size was 0.05 mm. Rates of grain browth were measured after isother-mally annealing the wire in the temperature range 675° to 825°C; T, is -720°C. Grain diameters were measured on the transverse cross section of the wires. The line-intercept method of determining the grain diameter was used; conventional light photomicrographs were taken when the grain size was greater than 10 . Carbon replicas were produced and examined in the electron microscope if the grain size was less than Dislocation configurations after recrystallization anneals were studied by electron transmission microscopy of foils produced by cold rolling a 0.125-in.-thick strip of the quenched material to 0.012 in. The foils, after heat treatments similar to the wire samples, were thinned by electropolishing in a chromic-

Jan 1, 1967

By A. L. Jr. Pozzi, A. O. Garder, D. W. Peaceman

A new numerical method is proposed for the solution of multidimensional miscible displacement problems. Besides the usual stationary grid associated with numerical procedures, the method uses moving points for which positions and concentrations are computed each time step. Based on the method of characteristics for treating combined transport and dispersion, the method applies equally well to any number of dimensions and, in contrast with other numerical procedures, properly takes into account the physical dispersion, no matter how small. Extensive tests show that accurate solutions of one-dimensional problems can be obtained over a wide range of values of the dispersion coefficient, including zero. They also show that the moving points do not need to be uniformly spaced, and that increasing the number of moving points beyond 2/grid interval does not significantly improve the accuracy of the solution. Two-dimmsional calculations using the new method were carried out to simulate laboratory model displacements in which gravity caused overriding of solvent. Good agreement between observed and computed profiles and measured and computed concentrations of produced fluid was obtained for a viscosity ratio of 1.89; at higher viscosity ratios, fair agreement was obtained Computed results were found to be significantly affected by vertical dispersion, and negligibly affected by dispersion in the direction of flow, in agreement with conclusions based on experimental observations. INTRODUCTION Although miscible displacement processes are potentially of great economic significance, limited progress has been made in developing mathematical methods for predicting the outcome of a solvent flood. Because of the complexity of the partial differential equations which describe multidimensional miscible displacement, numerical methods are a natural approach to their solution. The task of finding suitable numerical approximations to one of the partial differential equations, which involves both dispersion and convective transport, has been particularly difficult. Dispersion in the absence of transport is described by the heat flow equation, a second-order equation of parabolic type. This equation has been very successfully treated by numerical methods. Transport in the absence of dispersion is described by a first-order equation of hyperbolic type. This equation has been treated numerically with some success in one dimension, both by Lagrangian and Eulerian techniques, 1.2 but extension to two or more dimensions has not been satisfactorily accomplished. Usually one of two things happens: either the numerical solution develops oscillations or it becomes smeared by artificial dispersion resulting from the numerical process. When transport and dispersion are considered simultaneously, this numerical dispersion may dominate the low physical dispersivicy that generally characterizes miscible displacement. Stone and Brian2 have developed a new difference equation for treating combined transport and dispersion in one dimension. By suitable choice of certain parameters, they succeeded in markedly reducing both oscillation and numerical dispersion. However, a satisfactory extension to higher dimensions has not yet been found. Peaceman and Rachford3 presented a centered-in-time and centered-in-distance difference equation combined with a 1,transfer of overshoot" procedure which was demonstrated to work well in one dimension. The technique was applied to the two-dimensional miscible displacement problem, but subsequent calculations with zero dispersivity showed little change in results compared with the calculations they presented. This indicates that their method involved a numerical dispersion of the same order as the physical dispersion. The present paper describes an alternate method for solving the combined transport-dispersion

Jan 1, 1965

By Robert A. Colten, Frederick C. Hull, Robert F. Mehl

It is known that pearlite forms from austenite by a process of nucleation and growth, and that the rate of formation of pearlite may be described by a rate of nucleation and a rate of growth.l,2 The manner in which these two quantities operate to produce the observed isothermal reaction curve has been analyzed in a paper published in I939.3 Two types of process were described: (I) that in which nucleation occurs at the grain boundaries of the parent phase, with the nodules growing toward the centers of the grains, initially as hemispheres and then after impingement as roughly radial-columnar structures; and (2) that in which nucleation occurs generally, with the nodules growing to full spheres until impingement with other growing nodules restricts growth. Both cases are met in the formation of pearlite from austenite (Fig. I);2,4 the former, occurring near the knee of the S-curve, has been named "grain-boundary transformation," and the latter, occurring at temperatures near Ael, has been named "group-nodule transformation." In developing our knowledge of the factors that determine the rate of formation of pearlite from austenite, it is important1,2 to obtain data on the rate of nucleation and the rate of growth of pearlite. Such data, when obtained near the knee of the S-curve, will furnish information of use in understanding the factors that affect hardenabil-ity; when obtained at higher temperatures, such data will be useful in understanding the behavior of steels that during heat-treatment react to pearlite.2 It is the purpose of this paper to present data on the rate of nucleation and the rate of growth of pearlite in dependence upon composition, grain size, temperature, and the degree of homogeneity of the parent austenite. The studies are restricted chiefly to plain carbon commercial steels." Previous Data on Rate of nucleation and rate of Growth Data on the rate of nucleation and the rate of growth of pearlite have been published by Scheil and Lange-Weise,5 by Mirkin and Blanter,6,7 by Meh1,l and by Dorn, De Garmo and Flanigan.2, It is difficult to interpret the data, for in most cases too little information is given on austenitizing temperatures and times, the state of homogeneity of the austenite (presence or absence of carbide, etc.), austenite grain size, and mode of formation of pearlite at the temperatures given. Except for the approximations of Mehl and the work of Dorn, austenite grain size was disregarded, though it is well known

Jan 1, 1942

Safety Factor Characteristic Curves. Their Application to Mine Hoisting Ropes. (Paper by W. A. Boyer, Transactions AIME, 199, 989; Mining Engineering, October 1954. Discussion by B. E. Grant.) ............................................................................................................................. 1101 The Use of Wooden Rock Bolts in the Day Mines. (Paper by Rollin Farmin and Carville E. Sparks, Transactions AIME, 196, 922; Mining Engineering, September 1953. Discussion by Edward Thomas.) ................................................................................................................................. 1101 An Analysis of Mine Opening Failure by Means of Models. (Paper by Bernard York and John J. Reed, Transactions AIME, 196, 705; Mining Engineering, July 1953. Discussion by J. P. Zannaras.) ... 1102 B — Minerals Beneficiation Flotation and the Gibbs Adsorption Equation. (Paper by P. L. de Bruyn, J. Th. Overbeek, and R. Schuhmann, Jr., Transactions AIME, 199, 519; Mining Engineering, May 1954. Discussions by W. E. Ewers and Masayoshi Wada.)........................................................................................... 1103 Manganese Upgrading at Three Kids Mine, Nevada. (Paper by S. J. McCarroll, Transactions AIME, 199, 289; Mining Engineering, March 1954. Discussion by J. Bruce Clemmer, J. B. Rosenbaum, and C. H. Schack.)............................................................................................................. 1105 A Physical Explanation of the Empirical Laws of Comminution. (Paper by D. R. Walker and M. C. Shaw, Transactions AIME, 199, 313; Mining Engineering, March 1954. Discussions by Dimitri Kececioglu, George B. Clark, and Fred C. Bond.) ......................................................... 1106 F — Coal Underground Electrocarbonization of Coal and Related Hydrocarbons. (Paper by T. C. Cheasley, J. D. Forrester, and Erich Sarapuu, Transactions AIME, 199, 908; Mining Engineering, September 1954. Discussions by John G. Tripp and James L. Elder.)....................................................... 1108 Longwall Mining and Mechanization, with Special Reference to Nova Scotia. (Paper by Frank Doxey, Transactions AIME, 199, 701; Mining Engineering, July 1954. Discussion by Louis A. Turnbull.) ........................................................................................................................................ 1109 Cleaning Various Coals in a Drum-Type Dense-Medium Pilot Plant. (Paper by M. R. Geer, W. A. Olds, and H. F. Yancey, Transactions AIME, 196, 696; Mining Engineering, July 1953. Discussion by John Griff en.)................................................................................................................................. 1110 Frontiers in Heat Extraction from the Combustion Gases of Coal. (Paper by Elmer R. Kaiser, Transactions AIME, 199, 304; Mining Engineering, March 1954. Discussion by G. A. Vissac.) ............ 1112 Exploration of the Oaxaca Coal Fields in Southern Mexico. (Paper by Luis Toron and Salvador Cortes-Obregon, Transactions AIME, 199, 505; Mining Engineering, May 1954. Discussion by John D. Price.).................................................................................................................. 1113 H — Industrial Minerals Alkali Reactivity of Natural Aggregates in Western United States. (Paper by William Y. Holland and Roger H. Cook, Transactions AIME, 196, 991; Mining Engineering, October 1953. Discussions by Dexter H. Reynolds and W. L. Merritt.) ......................................................... 1114 Characteristics of Titaniferous Concentrates. (Paper by L. E. Lynd, H. Sigurdson, C. H. North, and W. W. Anderson, Transactions AIME, 199, 818; Mining Engineering, August 1954. Discussion by D. R. Grantham.)........................................................................................................................ 1116

Jan 1, 1955

By J. R. Long, E. T. Hayes, D. C. Root, R. S. Dean

THE U. S. Bureau of Mines has recently reported on the development of a process for preparing pure ductile titanium in substantial quantities' and on the physical properties that may be attained in the metal, when consolidated by powder metallurgy methods and fabricated by certain hot and cold-working procedures.2 The high physical properties (Table I), combined with excellent corrosion resistance and light weight, will lead no doubt to appropriate applications of the metal. In any application, methods of joining will be of considerable importance. The relatively high activity of the metal toward the common gases raises the question of weldability and conditions that might be required for successful welding. Since hydrogen, oxygen, and nitrogen embrittle the metal, it should be protected from these gases at elevated temperatures. This was demonstrated by a few preliminary trials of arc, gas, and resistance welding. In these trials only the resistance method proved to be immediately applicable. While atomic hydrogen welding of titanium may be successful in some instances, a considerable amount of development work will be required to prove its worth. In addition, it would be suited only to small assemblies that could be heated subsequently in a high vacuum to remove embrittling hydrogen. Heli-arc methods likewise would be limited to small assemblies, which could be completely protected by a helium atmosphere. It was quite apparent that titanium required more protection than was afforded by the normal flow of helium gas used for welding magnesium and aluminum. The hot metal is attacked by oxygen and nitrogen, and the rapid diffusion of the oxide into the metal prevents the formation of a protective coating and requires the helium atmosphere to be maintained until the weld has cooled nearly to room temperature. The preliminary work indicated that titanium could be successfully spot-welded without deterioration of the metal and that the microstructures of the welds were normal, exhibiting good bonding, and no oxidation. The high resistivity of titanium (53 microhms per cu. cm.) suggested that it would behave somewhat like stainless steel and allow considerable latitude in the several welding variables. The results reported here are intended to give a general picture of the effects of varying welding current, welding time, and tip pressure on single spot welds made on several different thicknesses of titanium sheet. The work was undertaken to demonstrate the feasibility of welding titanium rather than as an exhaustive study of spot welding. There are, therefore, a number of factors that will require further investigation to establish the specific controls required for actual applications.

Jan 1, 1946

By Robert A. Colten, Frederick C. Hull, Robert F. Mehl

It is known that pearlite forms from austenite by a process of nucleation and growth, and that the rate of formation of pearlite may be described by a rate of nucleation and a rate of growth.l,2 The manner in which these two quantities operate to produce the observed isothermal reaction curve has been analyzed in a paper published in I939.3 Two types of process were described: (I) that in which nucleation occurs at the grain boundaries of the parent phase, with the nodules growing toward the centers of the grains, initially as hemispheres and then after impingement as roughly radial-columnar structures; and (2) that in which nucleation occurs generally, with the nodules growing to full spheres until impingement with other growing nodules restricts growth. Both cases are met in the formation of pearlite from austenite (Fig. I);2,4 the former, occurring near the knee of the S-curve, has been named "grain-boundary transformation," and the latter, occurring at temperatures near Ael, has been named "group-nodule transformation." In developing our knowledge of the factors that determine the rate of formation of pearlite from austenite, it is important1,2 to obtain data on the rate of nucleation and the rate of growth of pearlite. Such data, when obtained near the knee of the S-curve, will furnish information of use in understanding the factors that affect hardenabil-ity; when obtained at higher temperatures, such data will be useful in understanding the behavior of steels that during heat-treatment react to pearlite.2 It is the purpose of this paper to present data on the rate of nucleation and the rate of growth of pearlite in dependence upon composition, grain size, temperature, and the degree of homogeneity of the parent austenite. The studies are restricted chiefly to plain carbon commercial steels." Previous Data on Rate of nucleation and rate of Growth Data on the rate of nucleation and the rate of growth of pearlite have been published by Scheil and Lange-Weise,5 by Mirkin and Blanter,6,7 by Meh1,l and by Dorn, De Garmo and Flanigan.2, It is difficult to interpret the data, for in most cases too little information is given on austenitizing temperatures and times, the state of homogeneity of the austenite (presence or absence of carbide, etc.), austenite grain size, and mode of formation of pearlite at the temperatures given. Except for the approximations of Mehl and the work of Dorn, austenite grain size was disregarded, though it is well known

Jan 1, 1942

By R. W. Shoenberger, J. D. Clendenin, W. L. McMorris, N. Schapiro, B. R. Kuchta, A. A. Terchick, R. J. Gray, J. G. Price

INTRODUCTION * The United States is fortunate in having enormous reserves of metallurgical-grade coals. Although these coals are better in quality and more accessible than most coals found throughout the rest of the world, the best grades of these coals are being depleted. Consequently, more efficient exploration tools and techniques, such as advanced methods of core drilling and logging, correlation by palynology,** stratigraphy, paleontology and petrography are being used to help assess the extent and quality of the remaining coal reserves. Exploration and assessment of new and existing coal properties become of utmost importance in determining (1) the economic justification for mining the coal, (2) the optimum design of the preparation plant and (3) the most effective use of the coal. Fortunately, the cost of mining coal has remained stable because of better mine planning, more efficient operations and increased mechanization of mining operations. However, increased mechanization raises the amount of impurities in the coal mined, and this requires more and better coal beneficiation to meet the more stringent quality requirements set by the market. Besides, mechanical miners also produce relatively fine coal and, to ensure maximum liberation of impurities, much of the coal presently being used must be crushed to a finer size prior to preparation. The bulk of all coals presently used in this country is mechanically cleaned, much of it at a lower specific gravity than in the past. This necessitates the use of new and improved processes and equipment for coal washing and recovery, such as heavy-medium cyclones and vessels, and froth flotation cells. However, because wet-cleaning processes are pre- dominant in the United States and fine coal retains large amounts of moisture, the increased production of cleaned fine coal accentuates the need for new or improved methods and equipment for dewatering and drying this coal. The larger amounts of coal being beneficiated and the use of new and improved beneficiation processes will aid in controlling and ultimately eliminating sources of pollution. Modem coal markets demand coals that meet rigid specifications. Most coals are purchased under contracts that specify moisture, ash, and sulfur contents, or heating value, depending upon the end use. There has also been a growing trend toward specifying other properties, including particle size and coking capability. These specifications may include not only the * Editor's note: Because of the numerous and varied contributions of the associate authors of this chapter, the text does not differentiate between sections prepared by each individual as has been done in other chapters. ** Palynology is the study of plant microfossils, especially spores, pollen, and other types of fossils not usually studied by paleontologists.

Jan 1, 1968

By D. E. Peacock, B. Harris

The mechanical behavior of a niobium (columbium)TUNG alloy containing 20 wt pet Ta. 15 wt pet W, and 5 wt pct Mo has been studied in the temperature range 77° to 423°K. All specitrzens tested, apart from those into which oxygen was introduced deliberately, were fully recrystallized at 1500°C, had an average grain diameter of approximately 0.03 mm, and a combined carbon, ox-vgen. nitrogen, and hydrogen content of not not more than 250 ppm The meckatnical behavior of this alloy was found to be similar in seine respects to that of unalloyed bcc transilion metals. Both yield and flow stresses were sensililae to changes in deformation rate and both increased rapidly as the temperature was lowered below 150°C. A detailed examination revealed, however, that most of the temperature dependencc of the yield stress could be accounted for by the temperature dependence of the elaslic, modulus, whish is not true of the unualloyed metals. In lension at moderate strain rates, the trunsition fvom ducfile to hvittle behavior occurred just belour room teunperature bur incveasing the oxygen content from 190 to 200 pptn raised the transition temperature to about 4000K. TUNGSTEN and molybdenum have been found to be very effective high-temperature solid-solution strengtheners of niobium, but the amounts of these elements that can be added are limited if the alloy is to retain useful room-temperature ductility. It has been shown, however, that partial replacement of niobium with tantalum lowers the ductile-to-brittle transition temperature of such alloys and allows larger additions of molybdenum and tungsten to be made. Some of the high-temperature properties of niobium alloys containing these elements have been reported by Bartlett et al.,' and the work presented here describes the low-temperature behavior of one of these, a solid-solution alloy containing, by weight, 20 pct Ta, 15 pct W, and 5 pct Mo. The elastic modulus, the temperature and strain-rate dependence of the yield and ultimate tensile stresses, and strain-hardening effects are discussed and compared with those of unalloyed niobium. EXPERIMENTAL MATERIAL AND PROCEDURE The material used in this investigation was produced from a 6-in.-diameter, double arc-melted ingot. This was can-extruded at about 1150°C to a 3-in.-diameter billet, and after annealing for 1 hr at 1345°C the billet was heated to 1315OC and part rolled and part forged to 0.5-in.-thick plate. The resulting material exhibited a cold-worked structure

Jan 1, 1965

By T. V. Philip, R. E. Lenhart

When commercial silicon iron sheets of varying magnetic quality are isothermally annealed at high temperatures, extremely large grains develop in the material having good magnetic properties. These grains are of the (110) [001] orientation and are formed by secondary recrystallization. The primary driving force for this secondary recrystallization is grain boundary free energy. For the secondary grains, activation energies of 103 kcal per mole for nucleation, and of 75.5 kcal per mole for growth, were obtained. The activation energy for nucleation of the secondary grains is consistent with a model involving redistribution of a precipitate acting as the primary grain growth inhibitor. SINGLY oriented silicon iron sheet was first produced in 1935.1 The material as commercially produced today has a very highly developed preferred orientation or texture; up to 95 pct of the grains are crystallographically oriented with their (110) planes in the plane of the sheet and their [loo] directions parallel to the rolling direction. This texture, usually written as (110) [00l], is referred to as the "GOSS" or the "cube-on-edge" texture. Because the magnetic properties of this material are superior to those of the nonoriented sheets in the direction of rolling, the oriented silicon iron has acquired tremendous industrial importance especially in the manufacture of transformer cores and other electrical equipment. The commercially produced material is essentially an iron-silicon alloy containing about 3 1/4 pct Si with minor impurities totaling less than 0.15 pct. The silicon steel heat is melted in the open hearth or electric furnace. The ingots are hot rolled, with or without being slabbed, to strips of 0.100 to 0.080 in. thickness. They are then cold reduced to an intermediate thickness, recrystallized, cold reduced to final thickness, decarburized, and finally annealed at a high temperature. During this high-temperature anneal, extremely large grains with the cube-on-edge texture are produced in the sheet. Several papers have appeared in the literature2-10 relating to the production of the Goss-textured material. Most of these describe the textures produced on cold rolling and on subsequent annealing of single crystal or polycrystalline silicon iron. May and Turnbull11,12 have recently shown the necessity of a second-phase dispersed impurity in the material for the production of the Goss texture. However, none of these papers describes in detail the nucleation and growth kinetics of the (110) [001] grains during the final high-temperature anneal.* The present work, therefore, is an attempt to understand the nucleation and growth kinetics of the cube-on-edge grains in the silicon iron sheet during the final high-temperature anneal.

Jan 1, 1962

By R. M. Brick, Arthur Phillips

The Institute of Metals Division Lecture in 1936, given by R. F. Mehl, on diffusion in solid metals1, was introduced with the statement that "the phenomena of diffusion are intimately related to many basic problems of the metallic state, but in addition to this the process of diffusion is of first importance practically." In view of the scope of that lecture, it does not seem necessary to review the importance, history or present status of diffusion problems. One aspect of the subject of diffusion that has received little attention became of some immediate importance in the course of a study on segregation. When a solid solution alloy freezes, the familiar mechanism of solidification requires that the first nuclei formed be low in solute concentration, with a resultant normal segregation or coring effect during freezing. Theoretically, musion of solute atoms during solidification should result in a homogeneous solid solution. Actually, of course, it is impossible in most binary alloys to obtain a cooling rate that will permit diffusion to eliminate coring in the freezing dendrites. For a given alloy, the extent of diffusion attained up to the point of final solidification will determine the degree of enrichment in solute atoms of the final liquid phase. The flow of this liquid into dendritic contraction channels and the solute concentration of the liquid seem to be the determining factors as to whether the final gross segregation is normal, inverse or absent. The purpose of the present study of diffusion was to determine to some extent the separate diffusion rates of copper and magnesium into pure aluminum with a view to clarifying previous results on segregation in these alloys; i.e., the fact that under similar freezing conditions aluminum-copper alloys segregate inversely and aluminum-magnesium alloys segregate normally. Of concomitant interest were the questions of the homogenization times required for segregated ingots or partially melted, i.e., "burnt," structures, and the solution heat-treatment times required for cast, hardenable aluminum-copper and aluminum-magnesium alloys, for worked and annealed structures, and so forth.

Jan 1, 1937

By Ramesh Malhotra, Hubert E. (Deceased) Risser

THE WORLD Coal, as a source of energy and as a source of coke for the smelting of iron ore, has contributed significantly to the development of every major industrial nation of the world A number of other materials-oil, natural gas, wood, waste materials, water, and, in some applications, nuclear materials -can be used satisfactorily for the generation of heat and energy, but no generally acceptable and economic substitute has been found to supplant coke in iron ore smelting in conventional blast furnaces. In the development of many nations, coal provided the initial source of energy for industrialization Although coal provided more than 60% of the world's energy each year between 1902 and 1929, oil and natural gas have surpassed it as a source of energy in more recent years (Ref. 38, pp. 439, 441). Despite the rapid rise in importance of other fuels, a considerable amount of the total energy consumed is still supplied by coal. In 1972, coal supplied 32.1 % of the total world energy (Ref. 49, pp. 2-3). To produce this energy, 2.4 billion metric tons of coal were consumed-a 16.0% increase over the amount consumed in 1962. A further worldwide increase in the amount of coal used to supply energy is projected. According to Dr. Karlheinz Bund (Ref. 37, p 145), by the year 2000 world coal consumption could amount to 5 billion mt. Coal Resources and Production The world's coal resources are estimated to be about 10,872 billion mt. Of this amount, 1,297 billion mt are classified as measured reserves (Ref. 50, p. 57). In Table 13.A.1 the estimates of measured reserves and total resources, recent production, and the ratio of measured reserves to production of major coal-producing countries are shown. About 90% of the world's total coal resources are estimated to be in the USSR, the United States, and China. The United States ranks second in the world in coal resources, but in measured reserves, it ranks first. Because of the difference in rate at which available coal resources are being exploited, the ratio of measured reserves to actual production varies widely among areas and countries. France and East Germany have the lowest reserve to production ratios, 49.5 and 60.1, respectively. In Mexico, where currently less than 5 million mtpy of coal are produced, the ratio is 1257 For all countries producing more than 200 million mtpy of coal (except East Germany), the ratio ranges from 350 to 670. For the United States, the ratio is 669.7. In Table 13.A.2, distribution of the world's coal resources by area is shown. More than 97% of the total resources lie in the northern hemisphere, with Asia, including European USSR, having 63.4%. Only 1.9% of the total coal resources are estimat-

Jan 1, 1976

By H. I. Aaronson

Isothermally formed plates of proeutectoid a, lengthen at approximately the rates predicted by the Zener-Hillert equation, indicating that their lengthening kinetics are controlled by the volume diffusion of chromium in the ß matrix. Solution annealing treatments in the vicinity of the transus introduce a second mode of transformation, in which the lengthening rate is at least 1.8 x 104 faster than predicted by this equation. Little or no volume diffusion appears to accompany the latter transformation. The Presence of oxygen is evidently a Prerequisite for the occurrence of this reaction. X HE effects of thermal history prior to the initiation of transformations which proceed by nucleation and diffusional growth are currently evoking considerable interest. The rate of nucleation (but not the rates of growth) of pearlitel and of bainite,2 and the over-all rates of aging reactions in Al-cu3 and Al-si4 alloys have been shown to be appreciably dependent upon thermal history in the solid-solution region"' or in the two-phase region prior to the onset of pre~ipitation.3,4 In none of these reactions, however, was the transformation mechanism changed by variations in the temperature-time path used to reach the reaction temperature. Preliminary experiments reported by M. K. McQuillan5,8 and a systematic investigation by Farrar and Margolin7 have disclosed that the transformation behavior of hypoeutectoid Ti-Cr alloys is considerably more sensitive to thermal history. Qualitative evidence strongly suggests that not only the rate of nucleation but also the rate of growth and even the mechanism of the ß — a reaction can undergo remarkable changes when a solution annealing treatment in the vicinity of the ß/a +ß, or transus temperature, is interposed between a high-temperature solution anneal (conventionallq at 1000°C) and the isothermal reaction treatment. The present investigation was undertaken in an attempt to ascertain the nature and origin of these effects. Study of the changes in the kinetics and morphology of the ß - a, reaction produced by varialtions in thermal history was the primary means employed for this purpose. EXPERIMENTAL PROCEDURE The compositions of the alloys used in this in~esti~ation are given in Table I. These alloys were homogenized for 5 days at 1050° C in evacuated (2 x 10 -5 mm of Hg), zirconium-gettered fused quartz capsules. The capsules themselves were enclosed in a porcelain chamber evacuated with a mechanical pump during the homogenization anneals. Upon completion of homogenization, the alloys were cooled to room temperature and then reheated to 550°C for 3 1/2 days in order to transform the alloys to a finely divided mixture of a and TiCr2, and thus provide an approximately constant initial mi-crostructure. Individual specimens were sealed in evacuated and internally gettered Vycor capsules and heat treated as previously described.8,9 EXPERIMENTAL RESULTS Ti-10.64 Pet Cr. This investigation was largely performed on the 0.64 pet Cr alloy. The "base"

Jan 1, 1962