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By G. E. Perry, J. F. Bruskotter, D. G. Russell, J. H. Goodrich

The depletion performance of gas wells has been investigated by mathematical simulation techniques. The gas well model which was studied consisted of a single well located in the center of a bounded, cylindrical, homogeneous reservoir. Dependency of gas compressibility and viscosity on pressure was considered in studies of well performance at both constant mass flow rate and constant flowing pressure conditions. To carry out the investigation, the nonlinear, second-order, partial differential equation which describes Darcy flow of a nonideal gas through porous media was solved numerically. Some of the previous investigations of gas well performance have been of limited general use, because assumptions were introduced to simplify either the gas properties or the basic differential equation. Other studies have been rigorous in these respects but have presented a very limited set of calculated results. The present study was attempted to present a rigorous theoretical model and sufficient numerical results to permit meaningful conclusions to be drawn. It was found that all terms must be retained in the partial differential equation to make accurate predictions. The neglect of higher-order terms, e.g., terms of the order of the "gradient squared", leads to serious material balance errors at large times and to conservative estimates of gas well performance. The higher the gas flow rate and/or the lower the permeability-thickness product of the formation, the more pronounced are these deviations. For example, in a well draining 640 acres in a 25-md-ft formation (8,120 MMcf gas in place) at a constant rate of 993 Mcf/D, the rigorous solution predicts a bottom-hole pressure decline from 4,000 to 1,000 psia in 8.7 years. If higher-order terms are neglected in the differential equation, this decline in pressure is predicted to occur in 5.3 years. With the results of the numerical solution of the differential equation as a basis, simple, easy-to-use approximations for predicting gas well performance for Darcy flow conditions have been developed. These simple approximations are based on the familiar equations for flow of a single, slightly compressible fluid. The approximate methods possess a high degree of accuracy and enable the prediction of long-term gas well performance to be made quickly and accurately without the use of a digital computer. Both transient and stable flow period approximations were developed. INTRODUCTION In recent years income from the sale of natural gas and associated products has represented an ever-incre as ing fraction of the industry's total revenue from operations. To meet the surge in demand for natural gas, the industry has depended heavily upon established reserves and has actively pursued development of new reserves. The search has progressively led to reservoirs which yesterday were too tight and/or deep to yield the desired return on invested capital. More than ever before, evaluation accuracy is now required to forecast the criteria upon which engineering recommendations and management decisions are based. Considerable effort has been expended by both research and operations personnel on the development and application of methods for analyzing and predicting the performance of gas wells. Fundamentally, the problem is the familiar one of extracting data during the drilling, testing and early production life of a well and applying these data within an accurate simulation model to predict long-term behavior. During the past 30 or more years a voluminous literature dealing specifically with gas field problems has been generated. A recent book' lists a comprehensive bibliography of published material through 1959. Over 1,200 references are cited. Since then 39 additional articles on natural gas technology have been published in Transactions volumes of the Society of Petroleum Engineers of AIME. Most existing theory for predicting gas well performance requires that one or more idealizations (e.g., steady-state flow, ideal gas of constant viscosity, small and constant compressibility and constant-viscosity fluid) be applied. Although existing theory may apply directly or be adapted by various artifices to describe specific gas well and reservoir behavior, no widely applicable method is available, and existing methods appear to be subject to appreciable error unless better limits of applicability are defined. The objectives of this paper are (1) to present numerical solutions to the partial differential equation describing gas flow under conditions of general interest in gas well performance prediction work, (2) to present solutions which possess a high order of accuracy for both transient and stabilized flow periods of a well producing at constant rate or constant pressure, and (3) to develop and present simplified relationships which can be used as high-order approximations to the exact numerical results for fast and accurate predictions of gas well performance at the operating level. Combined, these objectives are designed gen-

Jan 1, 1967

By E. C. Wright

The following article is based on observation of college graduates entering the steel industry in technical work made during the Past 25 Years, the first five of which were spent as a college instructor in two engineering schools, and the last 20 in the employ of a large steel company that has hired hundreds of engineering graduates for steel-mill operations. The college graduates encountered during this period have come from many colleges representing schools in Eastern States, Midwestern Universities, many Southern colleges, and many smaller colleges and normal training schools mostly in western Pennsylvania and Ohio. The college training of these students for engineering work naturally has varied widely and the educational qualifications of the entrants have been in many ways different. It was found at an early date that graduates of standard engineering colleges were much more adaptable than graduates in science from nontechnical schools. The engineering students seemed to be more suited to actual work in steel plants and in general were better able to grasp a knowledge of the operations they observed. However, although the graduates of engineering schools have had somewhat better training in physics, mathematics, and engineering, it has been a general and continual observation that most of the students employed have had inadequate training in the fundamental sciences. Since this discussion relates entirely to metallurgical engineers it should be emphasized that students taking metallurgical engineering courses in college seem to be poorly trained in organic chemistry-physics, physical chemistry, thermodynamics, and any higher form of mathematics than simple calculus. It has been noted frequently that young engineers faced with problems in a mill that involve some mathematics generally flounder badly, and that they have little conception of physical chemistry. Another common deficiency lies in the young graduate's lack of knowledge of where to look for the more detailed literature on any subject. He reverts instinctively to some college textbook whose coverage is usually very elementary. It is recommended that such textbooks contain a bibliography of the source literature. and that students be taught to use the original data. Many of the students had had previous courses in college dealing with metallurgical work such as steel melting, metallograhy, etc.r but it was found that their grasp of these subjects was extremely sketchy. It was soon realized that an ordinary engineering graduate could be taught more about steel melting and manufacturing processes in a few weeks in a plant than he could learn in a college course on such subjects. A similar statement may be made regarding the ability of students to conduct laboratory work. Their lack of technique and skill in handling equipment and setting up experiments was soon apparent. It became neces-

Jan 1, 1948

By E. C. Wright

The following article is based on observation of college graduates entering the steel industry in technical work made during the Past 25 Years, the first five of which were spent as a college instructor in two engineering schools, and the last 20 in the employ of a large steel company that has hired hundreds of engineering graduates for steel-mill operations. The college graduates encountered during this period have come from many colleges representing schools in Eastern States, Midwestern Universities, many Southern colleges, and many smaller colleges and normal training schools mostly in western Pennsylvania and Ohio. The college training of these students for engineering work naturally has varied widely and the educational qualifications of the entrants have been in many ways different. It was found at an early date that graduates of standard engineering colleges were much more adaptable than graduates in science from nontechnical schools. The engineering students seemed to be more suited to actual work in steel plants and in general were better able to grasp a knowledge of the operations they observed. However, although the graduates of engineering schools have had somewhat better training in physics, mathematics, and engineering, it has been a general and continual observation that most of the students employed have had inadequate training in the fundamental sciences. Since this discussion relates entirely to metallurgical engineers it should be emphasized that students taking metallurgical engineering courses in college seem to be poorly trained in organic chemistry-physics, physical chemistry, thermodynamics, and any higher form of mathematics than simple calculus. It has been noted frequently that young engineers faced with problems in a mill that involve some mathematics generally flounder badly, and that they have little conception of physical chemistry. Another common deficiency lies in the young graduate's lack of knowledge of where to look for the more detailed literature on any subject. He reverts instinctively to some college textbook whose coverage is usually very elementary. It is recommended that such textbooks contain a bibliography of the source literature. and that students be taught to use the original data. Many of the students had had previous courses in college dealing with metallurgical work such as steel melting, metallograhy, etc.r but it was found that their grasp of these subjects was extremely sketchy. It was soon realized that an ordinary engineering graduate could be taught more about steel melting and manufacturing processes in a few weeks in a plant than he could learn in a college course on such subjects. A similar statement may be made regarding the ability of students to conduct laboratory work. Their lack of technique and skill in handling equipment and setting up experiments was soon apparent. It became neces-

Jan 1, 1948

By J. L. Wyatt

The electrical resistance of titanium as a function of purity and temperature was measured from —325" to 2800°F. Two points of inflection in the data plots were found, and an increase in resistance with increase in temperature above the transformation was observed. IN 1948 Greiner and Ellis' reported on the thermal and electrical properties of titanium, including a study of the effect of temperature on the electrical resistance. The materials used in the research were obtained from the United States Bureau of Mines, where powder metallurgy techniques were being employed for consolidation purposes. These authors found a decreasing resistance with increasing temperature above 1625°F, and concluded that the latter temperature represented the point of transformation from hexagonal close-packed to body-centered cubic structure on heating. They reported a specific resistivity value of 55x10-6 ohm-cm, and showed that dp/dt was positive, decreasing with increasing temperature above ambient. In one of his early texts Hume-Rothery2 mentioned that certain metals, including titanium, exhibited minima in plots of resistance vs temperature. He indicated that this occurred at 212°F. Reporting many years ago on the effect of temperature on the electrical resistance of zirconium, de Boer and Fast³ showed that phase transformation in this sister metal occurred over a range of temperatures, the extent varying with its purity. Graphs of resistance vs temperature, showing transformation effects over a range of several hundred degrees, were presented for relatively impure metal. In the latter case the resistance decreased with increasing temperature throughout the region of partial phase transformation, thereafter increasing as predicted for normal metals by modern theories of the solid state. Since the quality of metal used in previous studies was substandard compared with iodide-type titanium, and in view of the fact that there seemed to be some rather unusual observations in the reported literature, it was decided to undertake a more extensive study of the thermal effects using high purity titanium, and to include temperature ranges beyond those which had been studied in order to ascertain whether or not the characteristics of zirconium would be duplicated. Experimental Materials Materials used in this investigation included commercial quality titanium (Ti-75A produced by the Titanium Metals Corp. of America) in the form of ¼ in. diam rods, and high purity iodide titanium (produced by the Foote Mineral Co.) in the form of crystal bar of irregular size. The latter was cold-swaged into rod form and machined to the desired size. Lead wires to all specimens consisted of 18 gage Ti-75A. Chemical analyses of the stock materials are given in Table I. Experimental Procedures Specimens 2½ to 3 in. in length were prepared with diameters nominally 0.15 to 0.20 in. Two holes,

Jan 1, 1954

By R. W. Gurry

WHEN a steel in the austenitic state, with all its carbon in solution, is maintained, at constant temperature, in contact with a gas that removes the carbon from the surface, vet without otherwise altering the composition of the steel, the change in weight of the specimen, after any period of exposure, is a direct measure of the amount of carbon it has then lost. The purpose of the present paper is to show how, by application of established mathematical reasoning based on the fundamental diffusion law and on certain postulates, this loss of weight yields a complete picture of the distribution of carbon throughout a specimen of regular shape after any period of exposure, with all the accuracy required in any practical occurrence of decarburization. Precisely the same is true for the gain in weight during the reverse process of carburization, or for the gradual gain or loss of any element, so long as the steel comprises only a single phase at temperature, provided always that the experimental conditions conform to the postulates. The change in carbon content from surface to center of the specimen is always continuous, when everything is in solution, even though under the microscope the decarburized zone (or carburized rim) may appear to be sharply defined. The experimental procedure is described and some typical results are presented, which are then interpreted by application of the diffusion law. EXPERIMENTAL PROCEDURE Initially an endeavor was made to follow the gain of weight during the process of carburization in a hydrogen-toluene atmosphere, but it was soon found that the specimen became coated with graphite, which could not be removed without some loss of metal; therefore it was decided to continue carburization until the steel was saturated throughout, to remove all graphite from the surface of the specimen, and then to follow the loss of weight during decarburization in a moist hydrogen atmosphere at the same temperature as that used for carburizing. The carburizing procedure has been described in an earlier paper;1 it suffices to state here that the carburization lasted about 140 hr. at 760°C. (1760°F.) and 44 hr. at 1110°C. (2030°F.), these periods being long enough-on the basis of the calculations presented later-to ensure that the specimen was about 9.99 per cent saturated at each temperature. The speci¬men was a cylinder about 3.8 cm. long and 0.475 cm. in diameter; the materials were carbonyl iron, a commercial low-metalloid iron, and a steel with 3.6 per cent nickel and the usual proportion of other elements. The fully [carburized] specimen, after cooling at the top of the furnace tube, was placed in a lathe and sandpapered to remove all graphite; then the diameter was measured with a micrometer caliper, and the initial weighing (corresponding to complete saturation) was made. By means of a

Jan 1, 1942

By C. H. Cheng, C. E. Birchenall

The fundamental problem in the thermodynamics of solid solutions is the determinatiorl or calculation of the activities of the components as a function of temperature and composition. Since the theory of metals is not suficiently developed to allow a priori calculation of these quantities, they must be obtained from experiment. C. Wagner1 has reviewed the literature of this subject for the period before 1940. Although several important and extensive studies have been made in the meantime, the number of systems to which any sort of quantitative information can be assigned is vanish-ingly small. These data have become of great potential importance in studies of the structure of solid solutions2 and intermetallic compounds, the nature of the diffusion process,3,4 and perhaps even the mechanism of mechanical deformation.5 For these reasons, it. seems very worthwhile to extend the experimental data in this field. Although there is little use in duplicating Wagner's review, attention should be directed to the most recently reported investigations. A brief enumeration of the methods of measurement previously employed also should be valuable. The most direct method is the determination of the partial pressure of the components in the vapor phase in equilibrium with the solution. Both equilibrium and kinetic methods have been tried in metal systems, but almost exclusively on liquid phases. Only in the ease of carbon in iron alloys and in the copper-zinc system have extensive measure- ments been made which include solid phases. When one of the components is an element, such as nitrogen or carbon, which forms compounds which are very volatile and stable at normal temperatures and pressures (CH4, Co2, CO NH3), it is frequently possible to equilibrate mixtures containing these (such as CH4-H2, CO2-CO, NH3-H2) independently with the elernents (C, X) and with the metal (Fe, Ni, etc.). Such measurernents have been made for carbon in iron, iron-silicon, and iron-manganese alloys by Smith6 and in iron and iron-nickel alloys by Toensing.7 Differences between carbon activity values at the same temperature and carbon content when carboil is introduced from CH4-H2 rnixtures or CO-CO. mixtures indicate that the effects of hydrogen and oxygen in the system are not negligible, and one can only hope that the true value lies somewhere between these sets of results, probably nearer the CH4-H2 data since hydrogen is less soluble in iron than oxygen. This is essentially an equilibrium method, although flowing gas is employed. A kirletic method has been employed which consists of sweeping an inert gas (generally hydrogen) over the alloy at a series of rates, condensing the metal vapor out,, and analyzing it. The metal content can be extrapolated to zero flow rate (equilibrium). Wejnarth's8 work on Cd-Mg and Zn-Mg is a good example of this frequently used method. A variant of this consists of equilibrating a known volume of inert gas with the alloy, sweeping it out quickly, and analyzing for metal. In common with the above method, it has the disadvantage that the "inert" gas is generally somewhat soluble in the alloy. Moreover, the former continuously displaces the system from equilihrium and may give low values if solid diffusion is involved. The dew point method applied by Hargreaves9 to the alpha and beta brasses and by Schneider and Stolll0 to A1-Zn avoids the introduction of another component to the system, but is useful only in systems in which one component is much more volatile than the other. The alloy sealed in one end of an evacuated silica tube is heated to the desired temperature. The temperature of the other end is lowered until droplets of the volatile component condense. When the temperature is raised slightly, the droplets will evaporate. By careful adjustment of temperature, the range between evaporation and condensation can be narrowed appreciably. An independent determination of the vapor pressure of the . pure volatile component is necessary to give the partial pressure over the alloy. This is the method employed here to determine the vapor pressures of zinc and cadmium over their silver alloys up to 34 pct in cadmium and 76 pct in zinc. The former involves only the a solid solution, but the latter covers the a, ß, y, and e fields. In recent determinations, Herbenar, Siebert, and Duffenbarkl1 used the

Jan 1, 1950

By F. Keller, J. D. Edwards

THE anodic treatment of aluminum presents problems of scientific as well as of commercial interest.1-3 Of particular interest is the fact that, during the anodic oxidation process, the oxide continues to form at the metal-oxide interface under any oxide previously formed. This has led to speculation as to the mechanism involved in the formation of the relatively thick oxide coatings that are used commercially for decorative or protective purposes. Furthermore, the ability of certain types of oxide coatings to adsorb dyes and other substances has stimulated research to determine the actual structure of these adsorptive coatings. It has been found that anodic oxide coatings on aluminum are composed essentially of aluminum oxide. They are formed by the action of oxygen ions penetrating to the metal surface during the electrolytic oxidation treatment. These coatings can be formed in a number of different electrolytes, as for example, those which contain sulphuric acid, chromic acid, oxalic acid, or boric acid. These are the commonest and most useful electrolytes employed commercially. Except for certain specific conditions of formation, the coatings in general have been found to be amorphous alumina, as far as can be determined by X-ray or electron-diffraction methods. Anodic oxidation processes can be arranged in three rather general classes if they are grouped in relation to the solvent action of the electrolyte on the coating.4 In the first class, the electrolyte has little or no solvent action on the coating that is formed. In general, coatings produced under such circumstances are nonporous and non- adsorptive. In the second class, the electrolyte exerts an appreciable solvent action on the coating. These coatings are porous and adsorptive. Finally, for the third class, the electrolyte tends to dissolve the coating about as rapidly as it is formed. This action produces electrolytic brightening or anodic polishing of the aluminum surface and at most leaves only a very thin film of oxide. The nonporous and nonadsorptive type of oxide film is represented by the coatings that are formed when solutions of boric acid are employed as the electrolyte. It is especially significant that these impervious films are formed in electrolytes that exert little or no solvent action on the coating. Where a boric acid electrolyte is used, the coating tends to form rapidly, with the result that the flow of current is soon reduced to substantially zero. This indicates that the growth of the coating has stopped. As a rule, the thickness of the coating is roughly proportional to the voltage employed for formation and the coatings of this type are exceedingly thin. In an electrolyte of this type, the coating has a high resistance when the aluminum is made anode; consequently, any current that may flow (leakage current) is very

Jan 1, 1944

By George J. Clark

One of the major problems of operation in the anthracite industry is the disposal and handling of refuse—not because of its complexity but because of the quantity and type of material involved. It is the purpose of this paper to describe the kinds of refuse, methods of disposal, quantities of material to be handled and equipment used, together with present day application at specific operations in the Northern, Eastern Middle, Western Middle and Southern anthracite fields. For the purpose of this paper, refuse is considered to be any material that has no present or foreseeable future value and that must be handled and disposed of in the process of mining and preparing anthracite for market. Included in this classification are tunnel rock, mine rock, cleaner plant refuse, breaker refuse, old timber, ashes and silt. Disposal Methods Old timber is disposed of either by burning or by depositing on the refuse bank. Burning is preferred because timber on the refuse bank is a potential fire hazard. Ashes are deposited on a separate bank, mixed with other refuse, or flushed into old mine workings. In many places, the latter practice has caused considerable difficulty in preparation of coal mined from these areas. In depositing ashes on the surface, it is wise to refrain from mixing them with material containing coal as such contamination may prevent reclamation of the coal in future years. Tunnel work, mine rock, cleaner plant and breaker refuse compose the bulk of the material to be disposed of and handled, and are referred to collectively as "refuse" in this paper. Waste material in or adjacent to the coal beds may be removed at the working face wherever possible. This can be done in flat or lightly pitching beds, and in the Northern field represents a sizable percentage of this type of refuse handled. In the other three coal fields, this method of disposal cannot often be used. Refuse not removed at the working face is taken to the surface and generally is deposited on banks; occasionally it is crushed and flushed into old mine workings. Breaker refuse often is used for constructing berms for silt-retention basins. Disposal Problems The problem of handling refuse is different for each operation, owing to topographical conditions, quantity of material to be handled, anticipated requirements and types of equipment in use elsewhere at the operation. Preparation plants with limited refuse-disposal areas, excessive grades to reach the required elevation and long hauls to disposal areas not readily accessible require the selection of equipment to best meet the conditions. The quantity of refuse to be handled from a given amount of raw material varies considerably throughout the four fields. In mine coal, this varies from a low

Jan 1, 1949

By Leonard Austin

WHAT Colonel Dwight says regarding the treat-ment of oxidized ores1 holds true also of the silver-lead smelting operations in Utah. The ore sought for was such as would, with appropriate fluxes, yield slag, and "lead bullion," as the lead reduced from the ore and carrying its gold and silver, was called. No matte, and probably little or no speiss, was yielded, and hence there was nothing to roast, either of ore or matte. But, by 1880, when I first took hold in smelting, there was quite a production of matte at the works of the Ger-mania Smelting and Refining Co., Utah, because, by that time, ores containing some pyrite and galena were being smelted. This was due, as at the Grant Works, Denver, to the more attractive price paid for the treatment of such ores. The matte, containing about 5 per cent. copper, was accordingly heap-roasted and returned to the blast furnace for the recovery of its contained metals. By this time there had been built a long-bedded, hand-rabbled reverber-atory roaster with a hearth of about 40 by 10 ft. in size, and in this matte and ore, crushed at the sampling mill, was treated. When, in 1892, I took control of this works, called& now the Germania Lead Works, three other roasters had been added, but the prac-tice of heap-roasting continued. This had the merit of needing no equipment, and of doing good work, because the pieces that were imperfectly roasted went back upon the next roast heap. At this time, when some suitable lump ore was obtainable, I roasted in heaps, in a satisfactory way. By 1892, the Bruckner cylinder roaster had been installed, which, compared with the reverberatory roaster, reduced labor. As such a cylinder revolves, a talus of ore is formed within it and at the same time fresh surfaces are exposed to the air, but the trouble was that the air did not reach to the bottom of the cylinder. This we corrected by placing a steam jet at the fire-box end, to project the air down-ward upon this stagnant ore, thus increasing the speed and completeness of roasting without at the same time increasing dust formation. The firing, if skilfully done, gave a somewhat sintered product, but with certain ores a slight access of heat over the normal would cause accretions to form within the cylinder near the fire end. These could be cut off by running back the fire box and barring off the crusts. It was in 1895 that the Bruckner cylinders at the Arkansas Valley plant, Leadville, were giving unsatis-factory service and I was called in to investigate. The steam jet was put in use as at the Germania Lead Works, but we found that, due to the altitude (10,500 ft.), combustion was feebler than at sea level or even at 4000 to 5000 ft. Later it appears, as Colonel Dwight states, that R. D. Rhodes and Mots sought to increase the air supply by admission through perforated tiles, but the trouble was due to the air itself.

Jan 8, 1922

By W. C. Ellis, E. S. Greiner, M. E. Fine

Discontinuous changes of Young's modulus, internal friction, coefficient of expansion, electrical resistivity, and thermoelectric power are evidence for a transition in chromium near 37OC. Although the X-ray diffraction pattern gives no clue, a difference between the thermal expansivity and the temperature dependence of the lattice parameter suggests a crystal-lographic change. Young's modulus data disclosed another transition near THE thermal dependence of a number of proper- ties of chromium indicates a transition occurring over a temperature range near room temperature. Bridgman' noted this first from a minimum in the electrical resistivity near 12°C. In a sample of greater purity, Sochtig' observed the minimum at 41 °C. Erfling3 reported an inflection in the thermal expansivity curve at 36°C. These temperature-dependence curves are reversible with no hysteresis being detected. No discontinuity or inflection has been observed in the heat capacity' or the paramagnetic susceptibility.' Likewise, no one has noted a change in crystal symmetry. In the present investigation Young's modulus, internal friction, coefficient of expansion, electrical resistivity, illustrated in Fig. 1, lattice constant, Fig. 2, thermal electromotive force, Fig. 3, and paramagnetic susceptibility, Fig. 4, were measured over an extended temperature range. The samples were prepared in two ways: (1) By cold pressing a sintered electrolytic powder compact,' and (2) by electroforming from an aqueous solution. The electroformed samples were prepared by R. A. Ehrhardt and G. Bittrich by plating on copper or nickel tubes from an aqueous solution according to the method of Brenner, Burkhead, and Jennings.' The pressed powder samples (method 1) were finally annealed at 1400°C in purified helium: the electroformed samples, packed in powdered chromium, were vacuum-annealed at 1000°C. From the composition of the original powder' the purity of the pressed powder samples is estimated to be 99.8 pct Cr. Spectrochemical analysis furnished by E. K. Jaycox, revealed only slight traces of impurities in the electroformed sample (less than 0.001 pct), neither iron nor nickel being detected. Chromium deposited by this method is reported to contain approximately 0.05 pct 0.- Methods and Data Young's Modulus: For measurement of Young's modulus, an annealed, pressed powder sample, 0.114 x0.237x1.845 in., and an electroformed sample, 0.10 in. od, 0.01 in. id, and 1.86 in. long, were prepared. The resonant frequencies of the rod samples in forced longitudinal vibration were measured at a series of temperatures from —192" to 200°C by a method previously de~cribed.6,7 Because the samples were nonferromagnetic, iron- silicon or molybdenum permalloy tips (0.013 in. thick) were soldered to the ends. The softening temperature of the solder limited the temperature of measurement. Young's modulus, E,, of chromium at temperature, T, may be calculated from the resonant frequency of the composite rod, f,; the thickness of the tips, t; the length of the chromium sample at 25°C, l,.; the density of chromium at 25°C, pc (7.20 g per cc);5 and the thermal expansivity, Al/l25. Modulus differences for two temperatures, ET and E, are accurate to +0.002x10" dynes per cm2. ET = 4PAlc+2tyf Young's modulus at 25°C, Fig. la, is 28.2~10" dynes per cm' (40.8xlO" si) in wrought chromium (upper curve). The modulus of the electroformed sample is apparently lower due to cracks. From the modulus measurements two transitions were observed: one with a critical temperature at 37°C, the other at —152°C. Internal Friction: The internal friction, 1/Q, was determined from the width, Af, of the strain amplitude-frequency curve at 0.707 times the strain amplitude at resonance;' the internal friction, 1/Q, then equals Af/f. Fig. lb shows a sharp peak in internal friction at 38°C. The internal friction of the electroformed sample had a similar maximum. Thermal Expansion: The expansivity measurements, shown in Fig. 2, covering the temperature range —195" to +400°C were made by D. MacNair in an interferometric dilatometer8 sing a sample consisting of three pyramids 0.25 in. high prepared from wrought electrolytic chromium. Below —120°C the experimental points deviated up to ±2x10 from the drawn expansivity curve in Fig. 2 because of decreased precision of the quartz wedge thermometer at low temperatures. Near 38°C the thermal expansivity curve, Fig. 2, goes through an inflection corresponding to a minimum in the coefficient of expansion, Fig. ld, and a relative volume decrease on heating. Electrical Resistivity: The variation of electrical resistivity with temperature measured by the po-tentiometric method is also shown in Fig. l. The resistivity of the wrought chromium (upper curve) at 20°C is 13.6 microhm-cm; of electroformed chromium (lower curve) 12.8 microhm-cm. The lower value reflects higher purity and agrees closely with a published value." A minimum at 40°C occurs in the resistivity curves of both samples. No conclusive evidence for a transition near — 150°C was observed, but the points, Fig. 1, appear to deviate from a smooth curve between —120" and —160°C.

Jan 1, 1952

By R. Hoffmann

The Waelz process produces oxides of volatilizable metals from ores, metalliferous products and residues. The process was originally used for recovering zinc and lead, where tailings and residues containing those metals had accumulated at mines or smelters, but it is applicable for obtaining tin, arsenic or other volatilizable metals. It is useful when other methods of obtaining the metals from the ores or residues are too difficult or expensive or show too low a recovery. The Waelz process was developed in 1923 for the treatment of large calamine dumps in Upper Silesia, which showed zinc contents of 8 to 10 per cent. and lead contents up to 3 per cent. The rapid development of the process, from the first trials up to the plants now working or in course of erection, is shown in Fig. 1. The first industrial Waelz plant was started in 1925. Within two years the capacity of the working plants reached 700 tons material per day of 24 hr. During the year 1928 the daily capacity of the plants now at work or in course of erection will rise

Jan 1, 1928

By Yuri D. Tretyakov, Robert A. Rapp

The stoichiometry ranges ofNiOl+y and LiFe,O,-d were established by high-temperatwe electrochemical meas7rements in a stabilized-zirconia electrolyte cell. The results were consistent with doubly ionized cation vacancies in NiO,+y and interstitial lithium or iron ions in . The defect structure of the ternary ferrite was derived from the consideration of equilibration with respect to oxygen between the solid and the gas phase. The absolute magnitudes of defect concentrations were calculated. Pavtial molar enthalpies of oxygen in the compounds were calculated and interpreted in terms of the enthalpy of defect formation in these crystals. NICKEL oxide (NiO,,?) is a metal-deficient, p-type, extrinsic semiconductor whose properties are consistent with a structural model based on the presence of cation vacancies as the predominant ionic defect at sufficiently high temperatures and oxygen activities. A survey of previously reported conductivity studies and the presentation of some more recent conductivity measurements will be given in a later paper.' The absolute magnitude of the equilibrium vacancy concentration in NiO has been reported from combined conductivity and thermogravimetric data of ' However, disagreement exists concerning the state of ionization of the nickel vacancies in NiO. Some authors3-' have proposed that the predominant defects in NiO are singly ionized nickel vacancies and positive holes (h') formed by the reaction where, accorhng to the notation of Kroger and Vink,6'7 Oq represents an oxygen ion on its normal lattice site. Other authors"27E have proposed that doubly ionized nickel vacancies (V{i ) and positive holes are predominant and are formed by the reaction One purpose of the present investigation was to establish the nature of the predominant defect in NiO,+? as well as its equilibrium concentration and thermo-dynamic properties at elevated temperatures and known oxygen activities. To accomplish this purpose, the coulometric titration of oxygen into and out of NiO was accomplished using a galvanic cell involving the calcia-stabilized zirconia electrolyte. The ternary oxide, lithium ferrite (LiFe50,-6) is ferromagnetic and has the inverse spinel structure LiFe,O,-d Thus, in the ideal stoichiometric XY204 lattice, Fe3 ions occupy one-eighth of the tetrahedral (A) sites, and i' and Fe3' ions share at random one-half of the octahedral (B) sites within the fcc sublattice of oxygen ions.g The structure and thermodynamics of the spinel structures have been comprehensively decribed.'-' A recent compilation of literature for lithium ferrite is also available. 15 Oxygen-excess LiFe50sis not expected to exist because both i' and 17e3& ions are in their highest normal valency states (positive hole formation is not favorable). As will be discussed, equilibration of the ferrite crystal with oxygen of a surrounding gaseous phase will result in the introduction of equilibrium concentrations of ionic and electronic defects. In the Results and Discussion section a defect model for LiFe50,-d is proposed. This defect model is tested by high-temperature coulometric titration experiments. EXPERIMENT The oxygen activities in nonstoichiometric NiOl+, (and also LiFe,O,-d) were measured by means of coulometric titration with the high-temperature galvanic cell The critical characteristic of a suitable experimental cell is the complete isolation of the phase to be investigated in a minimum sized chamber which is free from extraneous sources and sinks for oxygen (leakage). Then oxygen is only admitted to the chamber or removed from it in known amounts by coulometric titration, which involves the passage of oxygen ions through the solid electrolyte with electrochemical oxidation and reduction reactions at the platinum contacts to the electrolyte. The experimental cell is shown in Fig. 1. The cap of the cell was the tip from a closed-end alumina tube, which was found to be leak-free from a helium leak-detector test. This alumina cap was about 1.2 cm OD and about 1.5 cm high. A Zircoa calcia-stabilized zirconia tablet (crucible lid) of 1.5 cm diam and 0.3 cm thickness served as the solid electrolyte. A Pyrex ring of about 0.1 cm thickness was placed between the electrolyte and the cap. The electrolyte tablet was painted with platinum paste on the entire outer face and on that part of the inner face which would be within the enclosure; these electrodes were further prepared by heating in air at 1000°C for 2 hr. Nickel oxide powder, listed as 99.999 pct pure, was purchased from Leico Industries, Inc. Pills of the NiO were cold-pressed and sintered at 1050°C for 3 hr in a platinum crucible. This poorly sintered NiO was crushed, and chunks were wrapped in 52-mesh Pt gauze (to catalyze the solid-gas exchange) for place-

Jan 1, 1970

By K. M. Myles

The vapor pressure of palladium over a series of Rlz-Pd alloys has been measured by the torsion-effusion method. The thermodynamic properties of the alloy system at 1575=K have been calculated from the vapor pressure data. The activities and the free energies of formation exhibit large positive deviations from ideal behavior. The enthalpies of formation are endother-mic. The entropies of formation are positive and larger than the ideal entropy of mixing. All of the thermodynamic properties suggest that a strong tendency toward phase separation exists in the solid solutions. The possible origin of the phase instability and the various factors that influence the thermodynamic properties are discussed. RECENT studies of the thermodynamic properties of alloys of palladium with nontransition elements have indicated that a significant contribution to the enthalpy of formation is related to the redistribution of the conduction electrons upon alloy formation.'-' The present work was undertaken to ascertain the importance of this contribution in Pd/transition-metal alloys. The Rh-Pd system was chosen for this investigation for several reasons: 1) The thermodynamics of the system were unknown. 2) Rhodium and palladium are completely soluble at high temperatures; below 1118OK the solid solution becomes immiscible.', 3) The difference in magnitude between the vapor pressures of rhodium and palladium permitted the use of an existing effusion apparatus. 4) Additional information was known about the alloy system that would facilitate the interpretation of the thermodynamic results. EXPERIMENTAL PROCEDURE The thermodynamic properties of the Rh-Pd alloy system were calculated from the vapor pressure of palladium over solid palladium and over several solid Rh-Pd alloys. The vapor pressure was measured by means of the torsion-effusion apparatus that has been described previously. In this method, an effusion cell is suspended from a tungsten filament inside a high-temperature furnace. Two orifices are located eccentrically such that the effusion of the vapor creates a rotational torque in the filament. The angle of rotation is directly related to the total vapor pressure within the cell. As the vapor pressures of rhodium and palladium are approximately five orders of magnitude apart," the total vapor pressure was considered to be effectively equal to the equilibrium vapor pressure of palladium. The effusion cells were made from high-purity alumina since auxiliary experiments indicated that essentially no reaction occurs between alumina and solid Rh-Pd alloys. Unfortunately, because the orifices were irregular, an accurate calculation of the Free- man-Searcy correction factors" could not be made. The constants were determined in an independent experiment where the vapor pressure of copper, as measured in the alumina cell, was compared with an accurate value of the vapor pressure, which had been determined previously.4 Depletion of palladium from the surfaces of the specimens was minimal as the deflection of the cell remained constant, for at least 15 minutes, at each of the experimental temperatures. Lattice parameter measurements of the postrun alloys also indicated that no changes in the composition of the surfaces had occurred. The alloys were prepared by arc melting the requisite amounts of the 99.99 pct pure elements. The four most palladium-rich alloys were remelted in a levita-tion furnace since complete melting of the components had not occurred in the arc furnace. All of the alloys were subsequently homogenized at elevated temperatures in sealed alumina thimbles. After heat treatment, the alloys were analyzed chemically and were in essential agreement with the nominal compositions. The thermal histories and nominal compositions of the alloys are given in Table I. Lattice parameters of the heat-treated alloys were computed, by means of the method described by Mueller et a1. ,I2 from X-ray diffraction powder patterns obtained with filtered copper radiation in a 114.6-mm-diam Straumanis-type Debye-Scherrer camera. The results, which are tabulated in Table I, exhibit a slightly greater negative deviation from Vegards' law than the values reported by Raub et al.13 The diffraction lines were sharp and well-resolved and thus indicated that the alloys were homogenous. RESULTS The logarithms of the individual values of the vapor pressure of palladium were fit, by the least-squares method, as a linear function of the reciprocal of the absolute temperatures. The constants of the equations are given in Table I along with the temperature range over which the data was accumulated. The latent heat of vaporization at 298.15"K for pure palladium, calculated by the third-law method,14 showed no systematic temperature dependence. The average value of 88,920 * 20 cal per g-atom agrees favorably with the average of the results obtained in the most reliable previous investigations.15"19 The activities of palladium were computed from the vapor pressure data at 1525', 1575", and 1625OK. Consistent with the mass spectrometric study of the atomicity of palladium vapor,lg the vapor was assumed to be monoatomic. The activities of rhodium were determined by integrating the Gibbs-Duhem equation with the aid of the a function.20 In the calculations, the activities of the pure solid metals were assigned the value of unity. From the activities, the partial and integral free energies, entropies, and enthalpies of formation at 1575° K were computed; they are assembled in Table 11.

Jan 1, 1969

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 D. H. Davis, I. Fatt

Oil bearing rocks, usually found at depths of 2,000 to 10,000 it, are elastically deformed by overburden pressure. Although the change in porosity with pressure in a number of example rock.: has been shown to be small, it was thought that overburden pressure might have a significant effect on permeability. This note presents results of an investigation to determine the magnitude of the change in permeabilty with pressure. In routine core analysis permeabilities are measured on rock samples which are not under overburden pressure. If permeablity measured in this way differs from permeabilities measured under overburden pressure, a systematic error is introduced into well productivity calculations. The experiments described in this report were made to determine the magnitude of the change and thus to give an estimate of the error introduced into the calculations. The error introduced by the neglect of the change in permeability when overburden pressure is removed may account for part of the difference between well productivity calculated from core analysis and the actual well productivity. The results obtained in this investigation have only quali-tative significance because of the difficulty in reproducing in the laboratory the stress conditions on the rock buried in the earth. The assumption which is usually made is that the rocks in the earth are under a uniform pressure equal to the weight per unit area of the vertical overburden column from the rock in question to the surface of the earth less the pressure of the liquid in the pores of the rock. For an overburden consisting of sandstones and shales (of assumed average specific gravity of 2.3) and for a liquid pressure equal to the pressure in a salt water column (of specific gravity 1.0) reaching from the rock to the surface, the resulting net pressure on the rock is approximately 0.56 psi per ft of depth. EXPERIMENTAL METHOD Clean, dry sandstone core plugs one in. in diameter and about three in. long were mounted in a copper foil jacket as shown in Fig. 3 or molded in a Lucite jacket as shown in Fig. 4. All cores except those labeled "2" in Fig. 1 and "8" in Fig. 2 were measured in the copper foil jacket. Cores "2" and "8" were measured in the Lucite jacket. The jacketed core was placed in a high pressure hydraulic bomb in which the liquid pressure outside the jacket could be raised to 15,000 psi. Flow lines from the core were brought out of the bomb through special fittings in the bomh head and connected to a laboratory type gas permeameter. Measurements were made with nitrogen gas; the maximum mean gas pressure in the core was 16.1 psia. RESULTS The specific permeability of sandstone decreases with in. crease in overburden pressure. Most of the decrease takes place over the range of zero to 3,000 psi overburden pressure. If the net pressure on the rock is assumed to be 0.56 psi per ft of depth as discussed above, 3,000 psi of overburden pressure is equivalent to about 5,000 ft of overburden. At 3,000 psi overburden pressure, the permeability of the eight sandstone core samples tested ranged from 59 to 89 per cent of the permeability without overburden pressure. Figs. 1 and 2 show the permeability reduction as a function of overburden pressure. The permeability of the eight cores without overburden pressure ranged from 4.35 md to 632 md; these permeabilities are listed in Figs. 1 and 2. REFERENCES 1. Carpenter and Spencer: "Measurements of Compressibility of Consolidated Oil Bearing Sands," U. S. Bureau of Mines, R.I. 3450, (1940). * * *

Jan 1, 1952

By Charles R. Austiuon, Carll H. Samans

It has been known for several years1 that certain alloys of the Konal type, containing commercial cobalt (99.32 per cent Co and 0.42 per cent Ni) and varying amounts of ferrotitanium, exhibit very high tensile strengths at 600°C. However, their proportional limits and yield pints are relatively low. published data' for the alloys quenched in water from 950°C. and then tested at 600°C. are summarized in the upper section of Fig. I. Similar specimens that were aged at 650°C. for 72 hr., after quench and prior to testing at 600°C., gave the result; shown in the: lower section of Fig. I. In the present work the investigation of the properties of these materials has been extended by a study of the tensile deformation characteristics in moderately longtime tests at 600°, 700' and 800°C. after quenching from various solution temperatures. In addition, some metallographic studies have been made to correlate with the deformation tests, and to obtain information on the quasi-binary system cobalt-Fe2Ti. The material, very kindly furnished by the Westinghouse Electric and Manufacturing Co. in the form of hot-swaged rods of 3/16-in. diameter, analyzed as shown in Table 1. The alloys, when originally made up,' were based upon an iron-titanium compound, Fe3Ti, as indicated by the work of

Jan 1, 1941

By Carll H. Samans, Charles R. Austiuon

It has been known for several years1 that certain alloys of the Konal type, containing commercial cobalt (99.32 per cent Co and 0.42 per cent Ni) and varying amounts of ferrotitanium, exhibit very high tensile strengths at 600°C. However, their proportional limits and yield pints are relatively low. published data' for the alloys quenched in water from 950°C. and then tested at 600°C. are summarized in the upper section of Fig. I. Similar specimens that were aged at 650°C. for 72 hr., after quench and prior to testing at 600°C., gave the result; shown in the: lower section of Fig. I. In the present work the investigation of the properties of these materials has been extended by a study of the tensile deformation characteristics in moderately longtime tests at 600°, 700' and 800°C. after quenching from various solution temperatures. In addition, some metallographic studies have been made to correlate with the deformation tests, and to obtain information on the quasi-binary system cobalt-Fe2Ti. The material, very kindly furnished by the Westinghouse Electric and Manufacturing Co. in the form of hot-swaged rods of 3/16-in. diameter, analyzed as shown in Table 1. The alloys, when originally made up,' were based upon an iron-titanium compound, Fe3Ti, as indicated by the work of

Jan 1, 1941

By R. K. Datta

Eluropium -activated yttrium vanadate, excited by short- and long-wavelength ultraviolet radiations, shows enzission lines near 6100A, the principal ones correspondirzg to transitions of EU+3 ions from 5Do to the F2 energy level. The ~neclmlallistns of absorption and etnissiorz of this phosphor have been empirically studied. The absorption is caused by two separate processes in the matrix. The phosphor YVO4:Eu and tlie matrix YVO, haue essentially the same resectance spectra in the region 2500 to 4000if. There are two broat ah~o?~ption bands: natnely, around 2600 and 3600A regions. Whet? compared with the reflectance spectra of the constituent oxides, namely, Y2O3, V205, Eu2 03, the absorption bands of the tnatvix and the phosphor in the short- and long-wavelength ultraviolet regions can be interpreted as due to charge-transfer processes involving i) Y-O and ii) 17-0, respecti~~ely. The excitation spectrum' of the phosphor has two broad bands with peaks at about 2600 and 3600A regions. U can be postulated that enevgy absorbed under short- crud long-wavelength ultraziolet excitatzon, respectzcely, by Y-0 and V-O parts of the niatrix is transferred by radcatio~zless process to EU+3 ions. Thzs postulate can empirically be proved on the basis of the spectra of the systems (YVO4,-YPO4,):Eu. PO? ~ons do not have' any appreciable absorption in the short or long uv regions. When P0't3 ions are substitlited for v0i3 ions in YVO,:Eu phosphors, the absorption and excitation in the lo~zg uv region are gradually reduced. Ailoreover, the £«+3 emission under 3650A excitation is decreased zuitlz increase in PO^ content, lt~lzereas the emission under 253711 excitation remains esserztially constant with as IILUCIL as 60 mole pct of YPO, in YVO,:En. EUROPIUM-activated yttrium vanadate (YV04:Eu) is a well-known phosptor.'-3 When excited by cathode rays, 2537, or 3650A radiations, YV04:Eu emits typical narrow-band spectrum of EU'3 fluorescence in the region of 5900 to 7100A, a very strong maximum occurring at about 6190A. This emission is considered to be due to 5Do — 7F2 transition of excite: EU*3 in 4f state. Moreover, the emission under 3650A excitation increases with temperature markedly. Because of these properties, YV04:Eu phosphor finds wide application in industries, namely, in color television tube, laser, and high-pressure mercury-vapor lamps. It is the purpose of this paper 1) to present the empirical study of the mechanism of absorption and excitation of YV04:Eu phosphor by ultraviolet radiation, and 2) to offer an explanation for the process of emission. It should be mentioned that a theoretical discussion on the mechanism of absorption in terms of the crystal or ligand field theory is beyond the scope of this paper. Empirical studies presented here are based primarily on spectroscopic and crystal-chemical investigations. EXPERIMENTAL i) Preparation of Materials. The synthesis of vanadate phosphorinvolves preparation of (Yi-.tEuj^Oj, blending the mixed oxide with an oxidic compound of vanadium, such as V205 or NH4V03, and firing the mixture at about 1000°C for several hours when YVO4:Eu forms as a primary phase. (Y1-xEux)203 compositions are prepared by coprecipitation of oxalates, and igniting them at about 1000°C. The vanadium compound is added in excess of the stoichiometric proportion for fluxing purposes. The charge is cooled, ground, and the excess of vanadium is removed by a hot wash (-80°C) of alkali or ammonia. Y(VP)04:Eu samples are prepared by mixing (Yi-xEux)203 with stoichio-metric proportions of (NH4)2HP04 and the vanadium compound. The mixtures are prefired at 700" to 800°C for 1 or 2 hr, then ground and refired at 1150°C. The firings of the phosphors are done in silica crucibles, and the homogeneity of the final products checked by X-ray diffraction analysis. ii) Spectroscopic Measurements. Diffuse reflectance sqectra of the samples within the range 2500 to 7000A are obtained by using CaF2 as standard in Cary Recording Spectrophotometer, Model No. 14. The emission spectra from phosphor plaques, excited under different ultraviolet sources, are obtained by a direct-recording spectroradiometer4 adapted with a grating monochromator with nearly constant dispersion. Maximym sensitivity in the spectral region from 2500 to 7000A is obtained with a quartz-windowed, S-20 response p$otomultiplier. The total' band pass is kept about 30A. The spectra are calibrated against the light from a standard tungsten filament lamp reflected from a magnesium-oxide plaque. Brightness data given throughout this report $re measured from the height of the main peak (6190A) of the emission spectra. The excitation spectra are measured using sodium salicy-late as standard. RESULTS AND DISCUSSION The diffuse reflectance spectra of both pure and activated YV04, along with their constituent components, are shown in Fig. 1. YVO4 shows two broad absorption bands, namely, around 2500 and 3600A, respectively. Since there is little difference between the reflectance spectraoof YVO4 and YVO,:Eu in the uv region (2500 to 4000A), it can be postulated that excitation of the phosphor is mainly due to absorption by the matrix, i.e., YVO4. The question, now, is whether the matrix (Yv04) is excited as a whole, or different components are responsible for the two absorption bands. The characteristic absorption spectra of molecular ions involving transition metal ions, both in aqueous solutions and in crystals, are due to electronic transi-

Jan 1, 1968

By J. W. Onuscheck

The oxygen-fuel oil burner lance is a very useful tool at the Monessen B.O.F. It increases the overall flexibility of the operation. An additional 15,000 to 20,000 ingot tons can be produced at a given hot metal supply. It helps overcome sporadic drops in hot metal thermal values and/or supply. It results in increased yield, in particular, on high carbon heats where much yield was lost on reblow triggered slag reactions. The burner has also been adopted as a standard tool to aid burning in new vessel linings. Overall, steelmaking performance has improved with the use of standard preheat practice. Scrap charges up to 50 percent have been used routinely in times of extreme hot metal shortages, but the performance is weak in some categories. Development of a single step oxy-oil process is in progress. In this process, scrap and hot metal are charged as in the normal B.O.F. practice, but fuel oil is fired with the refining oxygen.

Jan 1, 1972

By B. C. Allen

Liquid surface tensions of copper and 18 Group IV-A to VIII transition metals (Ti, Zr, Hf, V, Cb, Ta, Mo, W, Re, Ru, Rh, Pd, Os, Ir, Pt, Fe, Ni. Co) have been measured by the static pendant-drop and dynamic drop-weight methods on the same rod sample. The drops were formed by electron-bombardment heating in high vacuum. Application of necessary corrections enabled determination of surface tensions to k2 pct and agreement between methods to * 1 to 4 pct for all the metals studied. Evidence is presented that the liquid surface was well screened by metal vapor, suggesting negligible adsorption of gaseous impurities and that the surface tensions measured are characteristic of the metals involved. Correlations between liquid surface tension and melting point, molar volume, heat of vaporization, and atomic number are presented and discussed. Temperature coefficients of surface tension were calculated using Eötvös' law. SURFACE tension and interface energies of metals are the result of incomplete atomic coordination resulting in a force perpendicular to the boundary, tending to minimize its area. These energies are important in many phases of metallurgy, including microstructure, sintering, joining, electronic emission, and lubrication, which in turn affect many physical and mechanical properties of metals. Liquid surface tension refers to the interface between the liquid and its own vapor or nonreactive atmosphere, and is considered a physical property of the liquid. Since equilibrium shapes can be readily obtained with liquids, the units of surface tension (force per length) and interface energy (energy per area) are interchangeable. Thermo-dynamically, the surface tension ?LV is given by the change in free energy F with surface area A at constant pressure P, temperature T, and composition N: for commercially important refractory metals, vanadium, columbium, tantalum,13,14 molybdenum,14 and tungsten,l5 and none for the rare platinum-group metals and rhenium. Measuring the surface tensions of transition metals is difficult because of their high reactivity and melting points. Of the many techniques available,16-18 the pendant-drop 19-21 and drop-weight methods17,22 are considered superior because they can be modified to eliminate persistent sources of contamination such as supports and capillaries necessary in the popular sessile drop, capillary rise, and maximum-bubble-pressure techniques. The necessary modification is to melt a drop on the tip of a vertical rod, which provides support through a solid of the same composition.13,15 The object of the work was to study the surface-tension behavior of copper and transition metals, having reasonably low vapor pressures. Liquid surface tension of each pure metal was systematically determined by using a combination of the static pendant-drop and dynamic drop-weight methods on the same rod. Liquid drops were formed by electron-bombardment heating in high vacuum. EXPERIMENTAL WORK As indicated in Table I, the metals studied were high purity and generally were obtained in rod form. The exceptions were titanium and zirconium, which were machined from crystal bars, and molybdenum (tot 11, osmium, and ruthenium, which were sintered and arc cast into rods. All the metals were ground or swaged to desired sizes between 1- and 7-mm diam, and centerless ground round and smooth to a finish better than 50 µ in., rms. Each rod was thoroughly cleaned with steel wool, degreased, acid etched, and dried. In a typical run, the rod was vertically clamped in a modified floating-zone electron-bombardment furnace designed after Calverley23 and Carlson.24 The specimen was outgassed and maintained positive at several kilovolts in a dynamic vacuum of 10-5 to 10-7 mm. The bottom end was enclosed by a tantalum pillbox and heated by electrons emitted from a hot concentric tungsten filament mounted on a movable bracket. The bombardment power was slowly raised until melting was observed. Power requirements ranged from 30 w for copper to 1300 w for 4-mm tungsten. The stabilized and out-gassed drop of near-maximum size was photographed at 4. 1X on panchromatic film at desired time inter-

Jan 1, 1963