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By R. J. Schilthuis, T. V. Moore

In a previous paper,' the results of some experimental work on the measurement of slippage in the flow of oil and gas mixtures through vertical pipes were presented. The data obtained were correlated and equations were deduced from which the performance of the experimental gas-lift could be predicted with reasonable accuracy. However, attempts to apply the equations to the calculation of pressure drops in actual flowing wells yielded erroneous results. At the time the results of the experimental work were published, no satisfactory explanation could be offered for the failure of the empirical equations to express properly the performance of wells. However, recent work has led to the development of a new hypothesis which presupposes certain conditions affecting the flow of oil and gas in wells. When the proposed equations are corrected to allow for these conditions, an agreement between the observed and calculated performance of the actual wells is obtained which in most cases is quite satisfactory, although it is subject to certain limitations. In this paper, the method of calculating the pressure drop in actual wells is considered, and the application of the method to the design of tubing is discussed. (For nomenclature used in this discussion, see Table 1.) Factors Affecting Slippage and Efficiency At the outset, a few of the principle factors affecting slippage and efficiency in the gas-lift discussed in the previous paper will be reviewed. In the flow of the mixture of oil and gas in a vertical pipe, slippage is the phenomenon of gas moving upward with a. linear velocity greater than that of the oil. Under steady conditions, if given quantities of oil and gas enter the tubing per unit of time, the same quantities of oil and gas per unit time must, on the average, pass every section of the tubing; otherwise, there would be accumulation or depletion of the oil or gas at some sections, and the flow would be unsteady. Therefore, if the gas is to flow at a greater linear velocity than that of the liquid,

Jan 1, 1933

By Garth M. Crosby, F. McIntosh Galbraith, Bronson Stringham

THE Hercules mine is located in the northeastern section of the Coeur d'Alene district, approximately 1 1/2 miles north of the town of Burke, Idaho. Surface indications of the ore deposit were first discovered in 1886, but regular mine production was not started until 1902 and was continuous until April 1925, when the known ore had been extracted. Incomplete records show that from 1912 until operations were suspended the mine produced 2 1/2 million tons of ore containing 9.4 pct lead and 7.7 oz of silver per ton, together with an estimated 2 pct zinc, 0.3 pct copper, and 20 pct iron. This operation was the first in. a series of mining enterprises culminating in October 1947 with the consolidation of Day Mines, Inc. In the same year it was decided to unwater the levels below the collar of the Hercules shaft in the hope of finding some indication of a recurrence of ore. The unwatering operation has been described in a. previous paper.' The initial exploration, following recapture of the workings, showed sufficient promise to warrant a detailed study of the mineralogy with modern techniques. The general geo1ogy of the Coeur d'Alene district, including a detailed description of the rock types encountered, has been comprehensively treated by Ransome and Calkins' in their classic paper, and only local background description, therefore, is felt to be appropriate here. The Hercules deposit transects a portion of the trough of a broad south-trending synclinorium which has been greatly complicated by faulting. More locally, it lies within a block of ground bounded on the east; by the O'Neil Gulch fault, a steep north-south overthrust of considerable magnitude, and on the west by a monzonite stock, the outcrop of which is 1/2 mile or more wide and 5 miles long. The country rock is composed of thin to medium-bedded argillites and argillaceous quartz-ites of the Prichard and Burke formations, the oldest members of the Pre-cambrian Belt Series of sediments in the area, believed to be of Algonkian age. The contact between them is a conformable gradation. The argillite is colored gray to tannish-gray and is fine-grained, compact, and generally massive in structure. Under the microscope the unaltered argillite is seen to be composed principally of anhedral quartz and a few feldspar grains which were at one time presumably partly rounded sand grains, but as a result of recrystallization and cementation by silica, the interstices are now almost obliterated and quartz grains show crenulate boundaries. The sizes of these crystals vary from 0.5 mm down to 0.1 mm in greatest dimension. In all specimens sericite comprises 10 to 20 pct of the rock and is present abundantly between most of the grains as flakes or shreds which vary considerably in size. Sometimes they form a fine felt-like mat or aggregate, and sometimes flakes are seen which appear to be good muscovite. In some specimens, separated rhombic-shaped carbonate grains are abundant, and in some instances these have been changed to sericite. Mining operations to date have explored the Hercules vein to a maximum vertical depth of 3600 ft below its outcrop, and along a maximum strike-length of 3600 ft on certain of the lower mine levels. The main orebody is irregular in outline, extending over a variable strike-length of 400 to 1500 ft; and it is intersected by a strong transverse fault that has been traced from the surface to the bottom level. This has been named the Hercules fault, and apart from the vein itself, it is the most prominent structural feature in the mine. There is good evidence that it existed prior to the introduction of ore solutions and may have influenced ore deposition, but it was also the locus of important post-ore displacement and shows a progressive right-handed horizontal component reaching 200 ft on the deeper levels. Its vertical component is not definitely known but may be considerably greater. The fault strikes 20° N to 50° E and dips westerly at angles of 70" to 45", flattening in dip where it crosses the original orebody from east to west between 1000 and 1600 ft below the surface. At about 3000 ft in depth the Hercules fault is joined by a vertical fault of similar strike, and the major post-ore dis-placement below their junction is taken up along this vertical branch of the structure, now called the Mercury fault. Recent work has been concentrated in this vicinity. Another structural feature of special geologic interest, though of little economic importance, is the occurrence of a porphyritic dike in this area. This lies a short distance above the Hercules fault, essentially parallel to it, and is 5 to 15 ft in thickness. It appears at first glance to cut the mineralization, suggesting push-apart relationship, but small stringers of the vein minerals have been observed to penetrate the dike for a matter of inches at several points. The dike is thought to be related to the monzonite intrusion. A vertical longitudinal projection of the mine is shown in Fig. 1, which illustrates most of the features discussed above. The Hercules vein was deposited along the course of a strong, persistent shear zone that now appears as a braided network of gouge seams running through more or less crushed and shattered country rock. It strikes 70° N to 80° W and dips southerly at an average of 75". Barren parts of the structure vary in width from less than 1 ft to more than 15 ft. The width of mineralized segments may be double that. Although the evidence is not conclusive, pre-mineral, normal movement along the zone may be 1000 or 1500 ft. The horizontal component is unknown. Post-ore movement appears to have been

Jan 1, 1954

By Chas. Y. Clayton, Francis B. Foley, W. E. Remmers

DuRing the summer of 1919, the late Dr. Henry M. Howe, then Chairman of the Division of Engineering of the National Research Council, organized a committee to obtain a better insight into the behavior of carbon steels under the influence of various treatments by a proper control of the time and temperature factors. During part of 1919 and 1920, work in connection with this investigation was carried on at Dr. Howe's laboratory at Bedford Hills, N. Y. During 1921 there was an enforced hiatus in the work, occasioned by the illness which resulted in Dr. Howe's death in 1922. At that time one of the present authors compiled the results of the work which had been done and this was published in 1923.' Following the publication of this work, it seemed desirable to carry on in the same manner an investigation of steel of C 0.75 per cent., which steel had not been as fully treated as had the other steels of C 0.34 and 0.52 per cent., used in the published work. Furthermore, certain unusual results have been obtained in the treatment of C 0.52 per cent. steel by quenching and drawing, and repetition of this part of the work seemed advisable. This has been done during the past year at the School of Mines and Metallurgy of the University of Missouri at Rolla, Mo., by a cooperative undertaking of the School and the Bureau of Mines, working in conjunction with the Committee on Heat Treatment of Carbon Steels of the National Research Council. The present paper is a report of the results obtained in this work.

Jan 1, 1926

By Robert W. Hunt

Delays in the completion of the alterations to the plant at the works of Messrs. Oliver Bros. and Phillips, in Pittsburgh, coupled with the increased demand for metal made from regular Bessemer pig, placing the firm many hundreds of tons behind in their deliveries, prevented Mr. Henry W. Oliver, Jr., from redeeming his promise to place his works at my disposal for further tests of high-phosphorus irons, until May 5th. Upon that date, I assumed charge of the operations in his steel-plant. Mr. Oliver had purchased Neshannock pig as a basis for a supply of phosphorus. My information is to the effect that this iron is made from low-grade Lake Superior ores and mill-cinder, the latter "ore" being utilized to about 40 per cent. of the total mixture. At all events the pig had quite as much phosphorus, and in as varying quantities, as the most exacting could desire. My experiments of last fall had well satisfied me as to the effect of from 0.35 to 0.55 per cent. of phosphorus in the Clapp Griffiths metal. Hence at this time my first trials were directed to

Jan 1, 1886

By M. J. Marcinkowski, K. S. Raghavan, A. S. Sastri

A detailed transmission electron microscopy investigation was carried out in connection with a manganese Hadfield Steel. At small plastic strains, numerous individual intrinsic stacking faults are observed. With increased plastic deformation, the stacking faults thicken into twin lamellae which in turn subdivide the original austenite matrix into smaller domains. The twin boundaries act as strong barriers to subsequent dislocation motion and is in a sense equivalent to grain refinement. It is this "grain refinement" which is believed to be the cause of the very high work hardening rates in the Hadfield Steels. In many cases, especially where an hcp phase is the stable one at low temperatures, the stacking fault energy in fcc metals and alloys decreases with decreasing temperature.' Since stacking faults of the intrinsic type are precursors of both twins as well as the hexagonal close packed structure, both of these entities should become more frequent as the temperature of a fcc crystal is lowered. In the case of the twin, there is no chemical driving force for its formation and it is generally necessary to provide the required driving force by an applied stress, i.e., strain energy. In the case of the hcp structure the transformation from the fcc modification can occur spontaneously (marten-sitically) since a decrease in chemical energy does in fact occur; however, an applied stress will provide an even greater driving force toward complete transformation. Since the transformation products mentioned above occur in an inhomogeneous manner throughout the crystal and since these can act as potential barriers to further plastic deformation2 marked strengthening effects can be anticipated. Also because metal and alloy strenghening is in general proportional to the shear modulus, these effects should be greatest in steels of the austenitic type (y), i.e., the fcc types. Perhaps the two most important steels in this category are the austenitic stainless steels and the Hadfield manganese steels. Both may be quenched from elevated temperatures so as to retain the austenitic states characteristic of those temperatures. The effect of subsequent deformation at lower tem- peratures has a profound effect on the stress-strain curves of these alloys. In particular Fig. 1 shows the compressive stress-strain curves obtained with an 18-8 stainless steel which was quenched from 1850°C after annealing for 1 hr so as to produce all y. As the temperature is lowered, the work hardening rate increases markedly. Although some hcp or c mar-tensite can be generated by plastic deformation as the temperature is lowered,~ it is believed to be a transition phase4 and most of the martensite produced is of the bcc or a variety.3 It is this stress induced martensite which gives rise to the very low initial work hardening at 77°K as can be seen in the stress-strain curve in Fig. 1. Similar low initial work hardening rates have been observed in the stress induced Ni-Ti martensites.5 Fig. 2 shows that an even more rapid rate of work hardening occurs in the Hadfield steels treated in the same way as that described for the 18-8 stainless steels a; the temperature is lowered. It is this ability to work harden to such high stress levels that makes the Hadfield steels particularly suitable for armor plate and heavy construction equipment. However, unlike the case of Fig. 1, no initial low rate of work hardening is observed in any of the curves in Fig. 2. Thus the stress induced formation of any low energy martensite phase in any significant quantity must be ruled out. This observation is in accord with the X-ray findings of Otte.~ On the other hand, small quantities of the E phase have been observed by other investigators using transmission electron microscopy (TEM) above Even more significant was the fact that large numbers of deformation twins were observed in the deformed Hadfield steels,678 which were postulated to be one of the reasons for the high work hardening ability of this class of steels.8 It is the purpose in what follows to discuss a series of experimental observations pertaining to the stress induced transformation in a Hadfield steel and to formulate a dislocation mechanism which adequately accounts for the observed results. EXPERIMENTAL PROCEDURE The stainless steel used to obtain the curves shown in Fig. 1 was of the AISI Type 303 containing approximately 18.0 pct Cr and 8 pct Ni. On the other hand, the Hadfield manganese steel used to obtain the curves shown in Fig. 2 contained between 1.00 to 1.25 pct and 11.5 to 13.5 pct Mn. In all cases the samples were in the form of compression cylinders 0.220 in. in diam and 0.370 in. long. Prior to testing the samples were annealed for a hr at 1050°C and rapidly quenched into a brine solution. This treatment was sufficient to preserve the y phase for subsequent testing at lower temperatures. All samples were compressed in an Instron testing machine using a cross head speed of 0.02 in.

Jan 1, 1970

By R. H. Jacoby, V. J. Berry

When dry gas is injected into a reservoir containing a volatile crude oil, a significant amount of the reservoir liquid phase may become vaporized. The resultant rich gas phase, when subsequently produced, con-tributes to tank oil production. This contribution assumes greater importance, the more volatile the oil in-olved. Oil recovery may be sub-stantially greater than that predicted by conventional frontal-drive methods, which do not consider the vaporization equilibrium between the reservoir oil phase and the injected gas. A calculation method has been (developed to account for vaporiza-. tion of the reservoir liquid phase during gas-injectiorz operations, and for the tank oil production which results from this factor. Recovery performance calculations are presented for a reservoir containing a highly volatile oil. Tank oil recovery is calculated to be about twice that predicted by the use of the conven-rional frontal-drive equations. In contrastto usual pressure maintenance performance results, in which the gas-oil ratio rises at an increasing rate after gas breakthrough, the pre-dicated gas-oil ratio rises rapidly to about 12,000 scf/bhl and then rises much less rapidly. During gas inje-tion, most of the reservoir liquid phase contacted is evaporated by the dry injection gar. The gas-oil ratio during this period is dependent upon reservoir pressure. The higher the operating pressure, the lower the gas-oil ratio. The predicted behavior i., in accordance with laboratory PVT tests made to .simulate the vaporization behavior. In addition to recovery performance predictions, results of the calculation procedure include complete wellstrearn composition data of value in the design of gasoline plant facilities often used in con-rrction with gas-injection operations. INTRODUCTION In the cycling of gas-condensate reservoirs, dry gas is injected to maintain reservoir pressure during wet gas production and to thereby eliminate or reduce ultimate loss of liquids due to retrograde condensation within the reservoir. Gas injected into crude oil reservoirs has a dual function. It displaces oil to the producing wells and at the same time serves to partially or fully maintain reservoir pressure. Oil shrinkage which would occur upon pressure reduction is thereby minimized or eliminated. Accepted calculation methods are available'= for predicting recovery performance of either gas-condensate reservoirs or crude oil reservoirs which are being subjected to gas injection. In gas-condensate reservoirs, any retrograde liquid formed does not flow, and it is necessary to account only for the vaporization equilibrium between this liquid and the injected gas. Conversely, in normal crude oil reservoirs, both the oil and gas phases flow, but it has not been considered necessary to account for any vaporization of the reservoir liquid which might occur upon contact with the dry injection gas. Recently, high shrinkage reservoir fluids known as "volatile oils" have been found in increasing amounts. These oils are characterized by tank oil gravities above 4.5" API, solution gas-oil ratios above 1,000 scf/bbl, and reservoir volume factors above two. Special techniques have been devised for predicting depletion performance of reservoirs containing such oils.74.5.1; One of the characteristics of reservoirs producing volatile oils is that the reservoir gas phase carries a significant amount of oil which is recoverable as stock-tank liquid. This unusual vaporization be-havior implies that an appreciable amount of reservoir liquid would be vaporized upon contact of the oil with dry injection gas. In a gas-injection operation, tank oil recovery would he obtained not only through frontal displacement of the reservoir liquid by the injected gas, but also through production of the rich gas phase. This means that not only are improved methods needed to predict recovery of such oils from reservoirs undergoing gas injection, but it would also be expected that high oil recoveries might be obtained by such operations. When relatively dry gas is injected in to a volatile oil reservoir, phase equilibrium between the injected gas and the reservoir oil will tend to bc established. Initially the most volatile components, such as propane, the butanes and the pentanes, will account for most of the material transferred from the oil phase to the gas phase. As the partially stripped oil phase is contacted with additional dry injection gas, the heavier intermediate components, such as the hexanes, the heptanes and the octanes, will gradually transfer to the gas phase in increasing amounts. This is because the supply of lighter components in the oil phase dwindles due to the stripping action of the injected gas. This stripping action will usually continue to be effective down

By A. A. Bauer, M. S. Farkas, F. A. Rough

An investigation of the d-phase relationships between the uranium-zirconium and uranium-molybdenum systems was conducted. A ternary cut joining U-31.5 at. pct Mo to U-74 at. pct Zr is presented on the basis of differential thermal analysis, metallographic and X-ray diffraction data. HyDothetical isothermal ternary sections, inferred from the determined d-phase relationships, are presented for the uraniztm-zirconium-molybdenum system. A ternary eutectoid, at 454ºC, was found in zirconium-rich alloys. Its composition, based on metallography and electron-beam micro-analysis, is estimated as U-61.7 at. pct Zr-7.1 at. pct Mo. URANIUM binary systems have been studied extensively in the past to supply basic information needed in reactor-fuel development. Alloys of uranium with zirconium, molybdenum, and titanium are of particular interest because, in these binaries, extensive or complete solid solubility between the body-centered-cubic forms of these elements and y uranium exists. In addition, an intermediate phase of limited solid solubility forms in each of these systems by transformation of the high-temperature ?-uranium phase. Previous investigation of the phase relationships existing between the intermediate 6 phases in the uranium-zirconium-titanium and the uranium-molyb- denum-titanium ternaries have already been reported.1,2 The results of an investigation of the phase relationships existing between the 6 phases in the uranium-zirconium-molybdenum system is reported here. The phase equilibria that occur in the solid-state portions of the pertinent binary systems are shown in Fig. 1. Phase nomenclature appearing throughout the report is as shown in these diagrams. The crystal structure of the phases in this system are given in Table I. EXPERIMENTAL PROCEDURES Alloys were cast and fabricated to 1/4-in.-diam rod. Specimens were heat treated and examined by metallographic and X-ray techniques. Thermal-analysis data were obtained.

Jan 1, 1960

By Reaves. M. J.

The title of my talk, "What Happened to the Uranium Boom?" is old news. Certainly it is for this group. All of us that make our living in uranium know that the boom of the last half of the 1970's is over. U.S. production has been exceeding consumption by more than two to one. Mines and mills are closing and yellowcake prices have been dropping for over 20 months. The gloomy outlook for the industry in the near term has been well documented by soothsayers of various descriptions, your daily newspapers, and in the Nuexco Monthly Reports. I'd like to attempt to describe the next upturn in the market (speculate, really) based upon the clues we're seeing now. In order to do that, I'd first like to go over briefly, some of the market factors that contributed to the recent price drop and resultant production cutbacks, and then hypothesize on the way these factors are changing and will change. Market prices are greatly affected (maybe even entirely determined) by buyer perceptions. This is particularly true with uranium, because of the long lead times associated with nuclear plant construction and also with conventional mine/mill development. Before the price rise (say, 1975) utility uranium buyers believed that: 1) U.S. producers would have difficulty expanding to meet U.S. demand. 2) Australian and Canadian production was essential to avoid shortages in the early 1980's. 3) Uranlum prices would continue to rise as demand exceeded supply. 4) Enrichment capacity would become inadequate. It was thought necessary, therefore, to build enriched inventory in the early 1980's for use in the late 1980's. Artificially accelerated expansion of the uranium producer industry was necessary to accommodate anticipated enrichment demand. Current perceptions are largely the opposite. These are the beliefs that were held most of this year and late last year as prices dropped. 1) U.S. production is far in excess of domestic need. Contraction of the U.S. production lndustry is necessary. 2) Canadian and Australian supply is optional and not essential. Producers in those countries are expanding mainly by displacing higher cost production and not because they fill a void, 3) Prices may be essentially stable for some time. 4) Enriched uranium is in excess supply. That is 1981. 1982 is shaping up to look like this: 1) Prices will have bottomed out. (That is not Nuexco's opinion necessarily, by the way, but it is my opinion.) 2) There will still be substantial utility inventories, but fewer spot sales. 3) Canadian and perhaps Australian sellers will have made substantial sales in the U.S. and will be aggressively seeking more. 4) U.S. production will have been dramatically curtailed. U.S. utilities that wish to con- tract long term will have difficulty in finding domestic sellers. Concern will develop about the availability of U.S. production capability. Virtually all long term con- tracts signed will be with non-U.S. sellers. 5) An awareness will begin to develop among U.S. buyers that we are approaching a period of dependence upon foreign uranium (which will be true). The history of the uranium market has been one of dramatic changes and overreaction to those changes. The rapid price rise of a few years ago generated excess U.S. production capacity and the rapid price drop of the last two years will almost certainly result in too little capacity. It will soon be difficult for U.S. buyers to buy domestic material except on the spot market. The question is, "will they care?" The lack of demand, of course, is the underlying reason for the current poor health of the uranium industry. In 1972, 1973 and 1974 collectively, there were 105 nuclear reactors ordered in the U.S. That ordering rate was expected to continue and accelerate throughout this century. In 1975, 1976, 1977, 1978, 1979, and 1980 altogether, there were 56 more reactors cancelled than ordered. The net growth of our only customer since 1974 has been a negative 56. TO put this in perspective, if these 56 reactors were operating now it would more than double present U.S. uranium consumption. Underlying lack of demand is something that is simply not going to change in this decade. Time is going to be required. The NRC indicates that the maximum feasible number of new reactors that can be licensed each year is six. That would increase uranium consumption by only 10% per year. New reactors, if ordered tomorrow, would not generate new uranium demand until after 1990. Even so, United States' consumption of uranium will rise from the 1980 level of 18 million pounds per year, to

Jan 1, 1982

By Thomas C. Wilder

The activities of both components and the partial and integral molar thermodynamic properties of mixing for the liquid Al-Ge system at 1200°K and for the gertnanium-rich Al-Ge liquidus have been determined from data for eighteen alloys of compositions in the range 0.0593 < 0.880 using the reuersible gal-vanic. cell in the temperature interval 9320 to 1258°K. The liqui-dus compositions above 93 2 °K loere also ve determined by observing the discontinuities in the C us T plots for the high-melting alloys. This system shows moderate negative deviation from ideality throughout, the values for y° being 0.212 and 0.189 for aluminum and germanium, respectively, at 1200°K. Pavtial molar Properties of aluminum on the germanium-rich solidus and at infinite dilution in Ge(s) oboue 932°K were estimated from the foregozng measurements and the equlibrium data of previous investzgators. RECENT compilations of data1" have shown an increasing demand for knowledge of the thermodynamic properties of mixing of metallic alloy systems. In the case of binary-liquid systems where one of the components is a semiconductor this information is useful because, primarily, properties of the second (dopant) component on the liquidus, solidus, and at infinite dilution may be determined more accurately than from calculations based on the phase diagram. In this investigation a reversible galvanic cell was used to determine the chemical potential of aluminum in the two-phase region, liquid + [Ge], on the germanium-rich side of the A1-Ge system in the temperature range 932" to 1193°K. In addition, similar measurements for homogeneous liquid A1-Ge alloys for the entire composition range were obtained for the temperature interval 932" to 1258°K. The cell used was: The experimental technique and the treatment of the data were essentially the same as described earlier394 and are elaborated upon only briefly here. Each cell consisted of a liquid aluminum anode and three A1-Ge alloy cathodes of different composition which were held in Morganite alumina crucibles. The alloys were made up from aluminum and germanium weighed to the nearest 0.1 mg to a total weight of 5 to 10 g. Aluminum was a gift of Aluminum Co. of America and had a purity of 99.995+ pct. Germanium of transistor grade was a gift of Bell Telephone Laboratories. The four electrodes were contained in a larger alumina crucible which also held the prepurified fused chloride electrolyte. Contact to the electrodes was made by tantalum wire leads sheathed in alumina. The tantalum leads were centered in the electrodes by suitable positioning of an alumina radiation shield which fitted on the top of the - alulnina crucible. Two chrome l-alumel thermocouples, sheathed in quartz wells, completed the internal cell arrangement. The entire assembly was enclosed in an alumina tube, fitted with a water-cooled copper head so the system could be evacuated and then flushed with purified argon. *

Jan 1, 1967

By G. R. Heckman, H. J. Murphy, C. T. Sims

An incestigation has been made of the effects of heat treatment and alloy composition on the long-time stress-rupture properties and structural stability of the similar nickel-base alloys Udimet-500, Lrdimet-520, and Udimet-700. Rupture test data are presented at stresses ranging from 4 to 50 ksi at temperatures from 1450° to 1900°F for times up to 14,000 hr. Ductility response is emphasized. Optical and electron tnicroscopy were complemented by X-ray diffraction analyses of extracted phases to relate microstructural stability to the observed rupture properties. Particular attention is paid to Udimet-520 since structural characteristics of this alloy appear to vary somewhat from its sister alloys. Both cast and wrought performance of Lrdimet-500 are discussed. The computerized PHACOMP calculational technique, based on electron-vacuncy theory, is discussed and related to structural stability where appropriate. Electron microscopy and microprobe techniques were used to conduct evaluation of the oxidation characteristics of Udimet-500 exposed in air for 16,100 hr. The steady advance in strength and reliability of nickel-base superalloys continues to be one of the high points of modern metallurgy. The stress capability of these materials has increased steadily, allowing higher and higher operating temperatures in the highly sophisticated aircraft and industrial gas turbines now on the market. The attendant increase in efficiency, of course, means greatly improved power output. Gas turbines for industrial and marine use have long been designed with these objectives paramount the usual design requirements in terms of time of service being 100,000 hr. High-efficiency, long-life aircraft such as the supersonic transport require superalloy engine materials with high-strength and long-time structural stability. Thus, materials studied for and operating experience from industrial gas turbines provide a good reservoir from which technology of high value to the SST program can be drawn. This study is one such case. Three prominent nickel-base super alloys—Udimet 500, Udimet 520, and Udimet 700 were extensively evaluated for industrial gas turbine bucket use. Particular attention was directed toward structural stability as a requisite property. Within the present context, structural stability is defined as freedom from the propensity to form strength-robbing or embrittling phases such as u,p,x,or Laves, and the ability to maintain useful rupture strength and ductility throughout design life. MATERIALS The three alloys, cast Udimet 500 (U-500C), Udimet 520, and Udimet 700, were chosen for detailed evaluation based on preliminary studies which indicated that U-500C and U-520 possessed comparable rupture strength capabilities, and that U -700 had a greater strength capability but somewhat poorer ductility than wrought U-500. The nominal compositions of the three alloys, along with the compositions of the heats investigated, are presented in Table I. PROCEDURE Dimensionally rejected U-520 buckets from Special Metals Corp. heat 63370 were heat-treated using the four cycles delineated in Table 11. Cycle A was investigated to determine the effects of a shortened 1700°F primary age. Cycle B was considered a "standard" treatment. Cycle C investigated a higher solution temperature in combination with a shortened primary age, while cycle D assessed the effect of the higher solution temperature alone. These heat treatments were designed to produce optimum combinations of rupture strength and ductility through maximum y&apos; development, the development of a y&apos; grain boundary cushion, promotion of MC carbide degeneration reactions, and agglomeration of resultant M23CB. Since one of the premises of the evaluation of U-520 was that rupture strength would be equivalent to U-500, forged U-500 buckets from Special Metals Corp. heat 62916 were heat-treated with cycles A, B, and C to provide comparison. The heat-treated structures of U-520 and U-500 are illustrated in the 8700 times electron micrographs of Fig. l. The U-700 tested was all from 3-in.-diam hot-rolled and centerless-ground rod from Special Metals Corp. heat 2-1426. Two heat-treatment cycles were employed, E and F of Table 11. Cycle E is a standard four-step, triple-age treatment intended to provide an optimum match of strength and ductility through well-developed matrix and grain boundary y&apos;, as recommended by U-700 vendors. Treatment F is a shortened , single-age cycle which could provide a significant processing cost reduction should adequate strength and ductility be maintained. Following heat treatment, rupture specimens of U-500 and U-520 were machined from the buckets and tested. Standard rupture bars of U -700 were machined from the heat-treated rod and rupture-tested. Failed and withdrawn rupture bars were prepared and examined by optical and electron microscopy. Select specimens were electrolytically digested, and the residues analyzed for carbide and topologically close-packed phases using CrKa or CoKo radiation. Of the six different U-500C heats evaluated, five were cast by Misco Precision Casting Co. and one was cast by Haynes Stellite Co. Cast-to-size rupture bars

Jan 1, 1968

By P. M. Kelly, E. P. Butler

Four Mn-CLL alloys, containing 60, 70, 80, and 90 pct Mn, respectively, have been examined in the quenched and the quenched and aged conditions using electron microscopy and electron, neutron, and X-ray diffraction. After certain heat treatments the alloys transform from fee to fct and in the tetraom1 condition show a domain structure parallel to {101} planes. Neutron diffraction indicates that the domains are antiferrornagnetically ordered. The domain boundary contrast has been examined using bright- and dark-field microscopy, and the contrast effects observed under favorable conditions have been used to deduce the c axis orientation in each domain. The domains are extremely mobile and can be nucleated at precipitate particles and screw dislocations. The domain mobility is responsible for the high damping capacity. In the aged material a Mn precipitates in the Kurdjumov-Sachs orientation and results of both electron microscopy and neutron diffraction indicate that the matrix separates into two components—one rich in manganese and the other rich in copper. ALLOYS of manganese and copper have the unusual combination of a high damping capacity and good mechanical properties and have been the subject of a number of investigations as part of a general interest in high damping capacity alloys for engineering purposes.&apos;,&apos; SO far, however, there has been no reported electron metallographic study of these alloys. The Mn-Cu system has an extensive range of solid solubility at high temperatures, and the equilibrium phases are expected to be y (fee) and a Mn. The high damping capacity is associated with a metastable tetragonal structure of variable c/a ratio, which forms from the high-temperature y phase. This latter phase becomes more difficult to retain as the manganese content increases, and alloys containing more than 82 wt pct Mn undergo a reversible martensitic fcc — fct transformation on quenching. The X-ray work of Basinski and christian3 showed that the Ms temperature for the transformation was below room temperature for alloys in the range 70 to 82 pct Mn and increased linearly with manganese content. When quenched from the y region, alloys in the range 50 to 82 pct Mn are cubic at room temperature, but become tetragonal if aged at temperatures between 400" and 600°C. The martensite transformation occurs on cooling from the aging temperature. Tetragonal alloys have a banded microstructure and the bands analyze to be traces of (110) planes. Similar microstructures have been observed in In-Tl4 and in other manganese-base systems, such as Mn-Au5 and Mn-Ni.6 The mobility of the bands in Mn-Cu alloys can be demonstrated by optical examination of a polished specimen surface subjected to a cyclic stress.7 The bands appear and disappear as the stress is varied, and X-ray measurements of the (200,020) and (002) peak intensities confirm that a reversible reorientation of the tetragonal structure occurs. Meneghetti and sidhu8 investigated the magnetic structure of Mn-Cu alloys and found antiferromagnetic ordering in furnace-cooled alloys of composition >69 at. pct Mn. Magnetic super lattice reflections occurred at the (110) and (201) positions and the proposed structure was fct with the spins along the c axis. A more complete investigation by Bacon et al.9 confirmed this structure. The magnetic ordering temperature Tn was found to increase linearly with manganese content in the same way as the Ms temperature, and at any composition, Tn > Ms. This relationship suggested that the magnetic ordering was responsible for the cubic — tetragonal transformation in the manganese-rich alloys. The purpose of this investigation was to study the mechanism of high damping and the structural changes that occur on aging. The main technique used was transmission electron microscopy, but X-ray and neutron diffraction experiments were also carried out. EXPERIMENTAL Materials and Heat Treatment. The four alloys, provided by the Admiralty Materials Laboratory. were of nominai composition 60, 70, 80, and 90 Mn and all had low impurity levels, <0.05 pct C, <0.2 pct Fe. This material was cold-rolled to 200-µ strip with intermediate annealing and then given a final heat treatment of 24 hr in the range 800° to 900°C followed by water quenching. An identical heat treatment was given a length of 3/4-in.-diam bar of the 70/30 alloy from which the neutron diffraction specimens were machined. It was suspected that the tetragonal structures would be metastable at room temperature, and so the alloys were not aged until required for experiments. After aging in a salt bath the alloys were water-quenched. Thin Foil Preparation. Initial thinning to 50 to 75 µ was possible in a solution consisting of: 50 ml nitric acid 25 ml acetic acid 25 ml water The surface deposit and grain boundary etching was removed by a final electropolish at around 20 V in an electrolyte consisting of:

Jan 1, 1969

By R. L. Bell, T. G. Langdon

A technique was developed- for determining the grain strain, and hence the grain boundary sliding contribution, occurring during the high- temperature creep of a magnesium alloy, from the distortion of a grid photographically printed on the specimen surface. The results were compared with those obtained from measurements of grain shape, both at the surface and interrwlly, and it was concluded that the grain shape technique may substantially underestimate the grain strain and overestimate the sliding contribution due to the tendency for migration to spheroidize the grains. ALTHOUGH a considerable volume of work has been published on the role of grain boundary sliding in high-temperature creep, many of the estimates of Egb (the contribution of grain boundary sliding to the total strain) have been in error due to the use of incorrect formulas or inadequate averaging procedures.&apos; One of the most easy and convenient measurements from which to compute Egb is that of v, the step normal to the surface where a grain boundary is incident. Unfortunately, this parameter is also the one associated with the treatest number of pitfalls. Values of v have been used to calculate Egb from the equation: egb =knrVr [1] where k is a geometrical averaging factor, n is the number of grains per unit length before deformation, v is the average value of v, and the subscript ,r denotes the procedure of averaging along a number of randomly directed lines. If the dependence of sliding on stress were assumed, it would be possible, in principle, to calculate k from the known distribution of angles between boundaries and the surface. This in itself is difficult because the distribution depends on the history of the surface,&apos; but the problem is even further complicated by the fact that v depends on other factors such as the unbalanced pressure from subsurface grains.3 However, the great simplicity of the measurement procedure for v makes it highly desirable that this problem of k determination should be overcome. In the present experiments, this was achieved by the use of an indirect empirical method in which the grain strain, eg, at the surface was determined by the use of a photographically printed grid. The assumption here is that the total strain, et, is simply the sum of that due to grain boundary sliding, egb, and that due to slip or other processes within the grains, eg. SO that: Et = Eg + Egb [2] Thus k is given by: In practice, it is customary to indicate the importance of sliding by expressing it as a percentage of the total creep strain; this quantity is termed y (= 100Egb/Et). The determination of Eg from a printed grid within the grains avoids the difficulties due to boundary migration which should be considered when the grain strain is calculated from measurements of the average grain shape before and after deformation. As first pointed out by Rachinger,4,5 however, this latter technique has the particular advantage that it can also be applied in the interior of a polycrystal. Recently, several workers have produced evidence on a variety of materials6-&apos;&apos; to support the observation, first made by Rachinger on aluminum,4,5 that 7 can be very high, 70 to 100 pct, in the interior, even when the surface value, determined from boundary offsets, is very much lower.10&apos;11 Although there have been criticisms both of the shortcomings of the grain shape technique&apos;&apos; and of the different procedures used to determine y at the surface,&apos; it seemed important to check whether measurements of sliding by grain shape gave values of y which were truly representative of the material. In the present experiments, grain shape measurements were therefore made both at the surface and in the interior for comparison with one another and with the independent measurements of grain strain using the surface grid technique. EXPERIMENTAL TECHNIQUES The material used in this investigation was Magnox AL80, a Mg-0.78 wt pct A1 alloy supplied by Magnesium Elektron Ltd., Manchester. Tensile specimens, about 7 cm in length, were prepared from a 1.27-cm-diam rod, with two parallel longitudinal flat faces each approximately 3 cm in length. The specimens were annealed for 2 hr in an oxygen-free capsule, at temperatures in the range 430° to 540°C, to give varying grain sizes, and, prior to testing, the grain size of each was carefully determined using the linear intercept method. This revealed that the grains were elongated -0.5 to 5 pct in the longitudinal direction. Testing was carried out in Dennison Model T47E machines under constant load at temperatures in the range 150" to 300°C. At temperatures of 200°C and below, tests were conducted in air with the polished flat faces coated with a thin film of silicone oil to prevent oxidation; at higher temperatures, an argon atmosphere was used. To determine v,, each test was interrupted at regular increments of strain and the specimen removed from the machine. At the lower strains, when v, was less than about 1 pm, measurements were taken on a Zeiss Linnik interference microscope;

Jan 1, 1969

J. B. MCGRAW, New York, N. Y. (written discussion*).-In Mr. Burke Baker&apos;s description of the process of the American Briquet Co., he speaks only of the attractive features, but every process which uses a compound or emulsified binder has certain undesirable features which must be considered. In making an emulsion, the success of which depends upon the introduction of the various ingredients at certain fixed temperatures and the complete intermixing of a soluble solution with an oil which has absolutely no affinity for it, considerable difficulty is found in keeping the various factors in strict accordance with the formula. To serve its purpose properly or, in other words, to be right for easy mixing with the coal, it should be of a certain predetermined density. Among the controlling factors of this ate the proportion of moisture contained and the temperature of the oil when introduced. If the latter is higher than intended, a greater proportion of moisture will be evaporated than is proper, and if the oil is not sufficiently hot the process of emulsification is retarded. These various factors can be controlled with more or less certainty where working in a laboratory or in a small experimental way, but when it is attempted on a large commercial scale, certain obstacles not otherwise apparent are likely to be encountered.

Jan 5, 1918

By AIME AIME

TUESDAY afternoon the annual meeting was devoted to a general session, in the auditorium, on production control. George Otis Smith presided and in opening the meeting recalled that the session in 1920 on the stabilization of the coal industry was the first time this subject had been discussed by Institute members in a general session and then introduced Carl Snyder, of the Federal Reserve Bank of New York, who spoke on "Long-time Growth and the Factors In Its Variations." He spoke without notes and a full presentation of his views must be deferred until the stenographer&apos;s report is available. He said that of the total production some 80 to 90 per cent represents goods for consumption and the other 20 to 10 per cent for construction. He discussed various indices of production, concluding that bank clearings are the best, and showed by charts that when they are plotted, allowing for various disturbing factors, they are seen to increase quite regularly at the rate of about 4 per cent per year. The production curve rises at only 3y2 per cent per year, because agricultural production does not in- crease as fast as manufacturing postal revenues in- crease at the rate of 5 per cent per year while the use of electricity increases twice as fast.

Jan 1, 1929

The following is am incomplete list of members and guests who called at Institute headquarters during the period May 10, 1918 to June 10, 1918. Arthur K. Adams, Potrerillos, Chile. J. M. Mahoney, Wilkinsburg, Pa. John Carter Anderson, Tucson, Ariz. Benjamin L. Miller, South Bethlehem, Pa. George S. Blair, Camp Cordon, Ga. Wilbur A. Nelson, Nashville, Tenn. W. A. Deane, Summitville, N. Y. Miles G. Nixon, Chicago, Ill. Charles H. Fulton, Cleveland, Ohio. Walter G. Perkins, San Francisco, Cal. Rudolf Gahl, Inspiration, Ariz. G. M. Ponton, Ottawa, Canada. C. C. Griggs, Eureka, Utah. D. A. Powell, Columbus, Ohio. J. F. Hanst, Potrerillos, Chile. H. W. Reed, Salt Lake City, Utah. Stanley C. Herold, Pittsburgh, Pa. J. C. L. J. Seelig, Padong, East. Indies. Floyd D. James, Boston, Mass. Oberlin Smith, Bridgeton, N. J. Charles Janin, San Francisco, Cal. Harrison Souder, Cornwall, Pa. E. Horton Jones, Copper Cliff, Ont. Stanley A. Spellmeyer, Camp Meade, Md. William Kelly, Vulcan, Mich. Roger S. Sperry, Waterbury, Conn. Ichiro Kitsunezaki, Tokyo, Japan. D. R. Thomas, Toronto, Canada. P. K. Lucke, San Antonio, Tex. Thor Warner, Phoenix, Ariz. E. Francis McCrossin, Birmingham, Ala. L. Douglass Anderson, formerly superintendent of the United States Smelting Co., Midvale, Utah, is now manager of smelters, Intermountain District, United States Smelting, Refining & Mining Co., Salt Lake City, Utah.

Jan 7, 1918

By Ward W. Minkler

Since 1978, the titanium metals industry, throughout the non-socialist world, has experienced a period of growth and prosperity unparalleled since the late 1950s. Sponge producers, melters and mill product manufacturers have operated at capacity, record shipments have been attained, new producers have entered the industry and established producers have implemented expansion plans. However, there is now mounting evidence that the underlying elements which generated this vigorous surge have abated, at least temporarily. It now appears that in 1982, the industry will encounter overcapacity, excessive inventory accumulations and the probability of declining prices. Therefore, it does seem appropriate that we now take inventory of the present and future markets for titanium with the hope we can identify both near term opportunities as well as challenges the industry now faces. If we view the development of titanium markets as a function of time, they fit rather neatly into three sectors.

Jan 1, 1982

HUDSON MAXIM, Brooklyn, N. Y.-Immediately after the creation of the Naval Consulting Board, Admiral Strauss, Chief of the Bureau of Ordnance of the Navy, told members of the Board that the most important problem for the scientists to solve was erosion in large guns. The Navy, for years, had been working on the problem with marked suceess, but there was much yet remaining to be accomplished. As Chairman of the Committee on Ordnance and Explosives of the Naval Consulting Board, I communicated with several experts in the manufacture of steel, principal among whom was Prof. Howe. He generously agreed to help in every way possible, and the work that he has done and the time that he has spent upon it can he appreciated only by reading his paper. Prof. Howe asked for some rings. from a, certain 14-in. gun which Admiral Strauss had mentioned in particular, and in which, he had informed us, at each shot the bore of the gun, was enlarged about 0.001 in.,&apos; and that after a relatively small number of rounds it was considerably eroded. It has puzzled scientists for a long time to account for the peculiar erosive effect produced by the powder gases in a gun, arid: what Prof. Howe has done in his paper is worthy of Sherlock Holmes. He is a veritable Sherlock Holmes of science.

Jan 4, 1918

By D. G. Swarthout, J. W. Savage, R. W. Guard

The Nb-N constitution diagvam has been examined from 1100° to 1450°C at 1 atm N2 pressure. On the basis of- our work plus that of Brauer and coworkers the stable nitvide Phases are: a) a solid solutlion, basic niobium (bcc) with nitrogen contained interstitially; NbN,, x = <0.40; b) ß NhNx,x = 0.39 to 0.45; hexagonal (W2C type) (NbzN); a =3.058A,c = 4.961 + 0.001A c) y NbNx x = 0.75 to 0.80; tetragonal (distorted NaCl type) (Nb4N3); a = 4.386A,c = 4.332 + 0.001A; d) 6 NbN,, x = 0.88 to 0.91; cubic (NaCl type); a = 4.3885 + 0.0007A; e) E NbNx x = 0.92 to 1.00; hexagonal (Tip type); a = 2.958A, c = 11.272 * 0.0015A. In addition, a metastuble transition phase 6&apos; has been observed and occurs only during the transition 6 — E. 6&apos; NbN has these distinguishing parameters: NbNx,x = 0.96; hexagonal (anti-NiAs type); a = 2.94A, c = 5 .46A. The high-temperature phase fields in the system are governed by two reactions: a) 6 + Y + E, a entectoid reaction occurring at 1270" ± 20° C; b) o + N2 = E, a 2 012 1 reaction occurring at 1370" ± 20° C. As part of a study of the electronic low-temperature. properties of transition metal nitrides, a number of specimens of niobium nitride were prepared. Preliminary observations on these specimens showed several points of disagreement with data already in the literature. It was, therefore, decided to determine the constitution diagram for the Nb-N system between 1100" and 1450°C. The objective of this research was to define the temperature and composition regions of stability of the various phases and to explain the differences among previously proposed diagrams. Review of Previous Literature. The research on the Nb-N system to 1964 has been summarized by storms.&apos; Although he does not present a phase diagram, his review covers the research on the system thoroughly. One of the earliest works on NbN is that of Ascher-mann and coworkers2 who studied the superconductivity of the cubic 6 NbN. Subsequent work by Horn and ziegler,3 Cook, Zemansky, and Boorse,1 Rögener:5 Schroder6 and sellmaier7 has qualitatively confirmed the first results on superconductivity, although their methods of preparation differed considerably. The constitution diagrams proposed for the system by Brauer and Esselborn8 and Elliott9 are shown in Fig. l(a)and (b). The diagram in l(a) has been modified by more recent results in Brauer&apos;s laboratory (private communication). Although 6&apos; is shown on this diagram, Brauer has indicated that he now believes 6&apos; to be a metastable phase in the temperature range shown. The diagram of Elliott, Fig. l(b), is based primarily on the results of Elliott and Komjathy10 on ni-trided niobium strip or rod specimens examined by X-ray diffraction and metallography. It will be noted that these proposed diagrams are in conflict with respect to the temperature and composition ranges of

Jan 1, 1968

By Edward F. Winter, C. E. Ruoff

A silicon solid-state array image scanner is described. This paper deals with structural and performance properties of the array which basically consists of PIN photo and gating diodes, and low capacitance isolation diodes. Each chip of the array is composed of an 8 by 9 matrix of photo detector cells; each cell contains one each of the three diode types mentioned. This x-y matrix is read a column at a time with an access delay of approximately 100 nsec per column. It is designed to detect the presence or absence of illumination within 10-mil diam image spots located on a 15- by 15-mil grid. Radiant power level of an illuminated spot is low; of interest is the range around I uw with a of 8400g Structural improvements to the original array which will result THE purpose of this paper is to describe the results of a solid state scanner exploratory development activity. The scanner is intended to sense the presence or absence of low-level illumination falling upon a matrix of 10-mil wide squares arranged on a 15- by 15-mil x-y grid pattern. The light of interest has a wavelength of 8400, characteristic of radiation emitted from a GaAs lasing diode. This wavelength matches well the spectral absorption of silicon,&apos; thus the well-developed silicon processing technology can be applied to fabricating large integrated arrays of PIN photocells to sense the radiation. The illumination state of the cells of the array is read, one column at a time, by addressing a drive line of the particular column in question and examining the state of those sense lines which are orthogonal to the drive Lines of in greater sensitivity at various wavelengths, both above and below 8400Å, and in greater speed are presented. These include variations in diffusion depth, resistivity of N and P regions, isolation techniques, and packaging. Trade-offs between access speed, cycle frequency, and sensitivity are discussed. A packaging approach to achieving an array composed of several chips is described. Requirements on this package are: 1) maintenance of 15- by 15-mil pitch of the light sensitive cell position, therefore positional accuracy of mounted 8 by 9 cell photo detector chips; 2) maintenance of inherent high array speed even though signal levels are low through high density close proximity mounting of monolithic sense amplifier circuitry. the array. One bank of N sense amplifiers is required, where N is the number of photodiode cells in each column of the array. CELL AND CHI" STRUCTURE A photograph of a single monolithic cell is shown in Fig. 1. Each cell is composed of three junctions, an isolation junction, a logic or blocking diode junction, and a photodiode junction; all of these junctions are connected electrically by a common N region. An electrical schematic of four cells of the array is shown in Fig. 2 with the associated driver and sense amplifier circuits in block diagram form. Note the common cathode configuration of the three diodes of each cell. Fig. 3, a diagram of the cell vertical struc ture, illustrates how the electrical configuration of

Jan 1, 1970

By M. Cohen, C. Wagner, J. E. Reynolds

If the total volume of a diffusion couple changes during the diffusion, the measurement of distance becomes ambiguous. Use of distance parameters as suggested by Hartley and Crank is discussed. For small concentration differences, the standard form of Fick&apos;s second law is retained with conventional length units and the in- terdiffusion coefficient D. It is shown how D can be calculated from experiments involving large concentration differences and analyzed in terms of distance parameters. &apos;The merits of incremental diffusion couples involving small concentration differences are emphasized. THE conventional form of Fick&apos;s second law for one-dimensional diffusion of component B in a binary solution of A and B is where c, is the concentration of component B; x, the distance; t, the time; and D, the interdiffusion coefficient which may depend on ca. Hartley and Crank&apos; have pointed out that Eq. 1 applies only if the total volume of the diffusion couple does not change during the diffusion process; otherwise, the definition of x becomes ambiguous. No change in total volume takes place if the specific volume of the solution is a linear function of the weight fraction Wb, or if the molar volume is a linear function of the mol fraction N. In some alloys, however, these relationships do not hold, and then it is necessary to introduce a modified measure of distance, 4 in order to retain the general form of Eq. 1. The application of Hartley and Crank&apos;s suggestions to diffusion in alloys has been discussed by Wagner.&apos; Relation Between Measure of Distance and Units of Concentration The definition of [ depends on the choice of units for the concentration c,, as follows: 1—If the concentration ca is measured as the weight fraction W, (or weight percent), [ = 5, has to be defined so that equal increments of contain equal increments of mass m of the solution, e.g., dm = pSdx = Sdw [2] where p is the local density of the solution, and S is the cross-sectional area in sq cm which is taken to be constant in this problem of one-dimensional diffusion." * da Silva and Mehla have demonstrated the constancy of the cross-sectional area in the usual type of diffusion couple. However, experiments involving diffusion into thin wires4, 5 may exhibit changes in cross-sectional area, and therefore are excluded from the present treatment. Thus and the unit of is gram per sq cm instead of cm. 2—If the concentration c, is the mol fraction N, must be defined so that equal increments of contain equal numbers of mols of solution, e.g., dn= (S/V)dx= Sd [41 where V is the local molar volume of the solution. Thus dt, = dx/V [51 and the unit of is mols per sq cm. 3—If, as may be advisable in the case of interstitial solutions, the concentration C is measured in terms of the molar ratio of components B and A (c,, = Y, = nH/nA, where n and nl are numbers of mols of B and A), = Y has to be defined so that equal increments of contain equal numbers of mols of A, e.g., dnA= (NAS/V)dx = Sdf [6]

Jan 1, 1954