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By N. Mungan, F. W. Smith, J. L. Thompson

Adsorption of polymers and transport, rheology and oil recovery efficiency of their solutions were studied in the laboratory to evaluate the use of polymers in waterflood-ing. While a tenfold mobility reduction was obtained with polymer concentrations as low as 0.05 per cent by weight, the mobility reduction depended on the type of polymer, molecular weight, salinity and pH of water, crude oil and capillary properties of the porous media. Choice of a suitable polymer and a workable concentration will have to be tailored for each application. Little reduction in the residual oil saturation can be expected from polymer flooding. Improvement in the volumetric sweep efficiency is possible hut the extent of the improvement can best be evaluated by properly designed field testing. Some aspects of the field use of polymer floods are discussed. INTRODUCTION Waterflooding is a simple, inexpensive secondary recovery method and is being used widely. Innumerable laboratory studies have been made to unravel the fundamentals of the displacement of oil by water and to find the ways of most efficient oil recovery. These studies and a great many field case histories have revealed that the prime cause of poor oil recovery is the inefficient and incomplete sweep of reservoir volume by the injected water. Sweep efficiency is affected by many factors of which the mobility ratio is an important one. Mobility ratio M is defined here as the ratio of water to oil mobilities: M = (k»/y,r)/(k,JJJJ........(1) In Eq. I, the permeabilities are the effective permeabilities and depend on fluid saturations and, hence, change during the different depletion stages in a flood. A wide practice is to use the effective water permeability at residual oil saturation and the effective oil permeability at interstitial water saturation in Eq. 1. If the mobility ratio is greater than one, the mobility ratio is unfavorable and water, being more mobile than oil, would finger through the oil zone resulting in poor oil recovery efficiency. If the mobility ratio is favorable (one or less) the displacement of oil by water occurs more or less in a pistonlike fashion. In some waterfloods. the mobility ratio is unfavorable and any additives by which the mobility of water can be decreased would favor more efficient oil recovery. The thing to bear in mind, however, is whether or not the improvement in oil recovery is sufficient to more than pay out the cost of the additives needed. For example, materials like sugars, alcohols and glycerine reduce water mobility by thickening the water, but the cost of material requirement precludes any field application. For an additive to be useful in water-flooding, it must bring about a large reduction in water mobility at low concentrations; it must be adsorbed only negligibly; and it must not completely plug up the formation. Some synthetic organic polymers have shown promise of meeting these requirements and have been used in the field.'-W owever, no in-depth studies of the rheological, adsorption and oil displacement characteristics of polymer solutions have been reported. The present work is a study of these properties. EXPERIMENTAL In this work, concentrations are given on a weight per volume basis; 0.5 per cent concentration means 0.5 gm of polymer is dissolved in enough water (or NaCl solution) to make 100 ml. A bactericide, usually 0.1 to 0.2 per cent by volume of 38 per cent formaldehyde solution, was used in the polymer solutions. The NaCl solution was 30,000 ppm. Some properties of the polymers studied are given in Table I. Physical properties of all cores used are in Table 2. Flow behavior of polymer solutions was studied by three consecutive flow tests in cores. First, water (or brine) was injected at constant rate of about 1 ft/D to obtain the water mobility. Then, filtered polymer solution (prepared in water or brine) was flowed through the core. Since the rate was constant, increase in the pressure drop across the core reflects decrease in the mobility. Finally, the core was flooded with water (or brine) to study recovery of mobility. The Alundum cores which were used in

Jan 1, 1967

By D. L. Sikarskie, B. Paul

A theory is presented for the static penetration of a single rigid wedge into brittle material. The material considered is one which exhibits both crushing and chipping phases in the penetration process. If the wedge angle and three parameters are specified, the theory predicts forces and associated penetrations during both the crushing and chipping phases. For certain ranges of the parameters agreement with the limited experimental data available is promising, except for the initial phase of the penetration process where refinements on the proposed theory are required. The theory also predicts that for certain values of the wedge angle and other known parameters, the chipping process does not occur and penetration is due entirely to crushing. When viewed in detail, the drilling of rock by percussive means involves, among other things, system dynamics, actuating forces, dynamic stress levels and the actual penetration mechanism of the bit into rock. If rock drills are to be significantly improved, a thorough understanding of the entire system would be highly desirable. In this paper, one aspect of the system, namely the mechanism of penetration of the bit, will be studied in detail. It has been found1 that for the velocities encountered in percussive drilling (of the order of 20 fps) a static analysis adequately describes the penetration process, at least for some rocks. Hence, we will only be concerned with describing analytically the static penetration of a single wedge shaped tool. It will further be assumed that the wedge is long enough to permit a two-dimensional analysis. Numerous authors have studied the static penetration of a wedge into rock. The following papers give some of this work and provide additional references to other work. Cheatham2,3 has assumed the rock to behave plastically and has obtained force-penetration equations for both Coulomb-Mohr and parabolic yield criteria. Evans and Murrell4 have studied the penetration of two types of coal and have found equations relating the penetration characteristic (P/dSc) to wedge angle for the various strength coals tested. race' attempted to find a correlation between hardness as determined by indenting the material and other mechanical properties and concluded that the results of such a test are generally inconclusive. His paper however contains a very extensive bibliography on the indenting of many different materials. Gnirk6 also has a fairly complete literature review on the static penetration of rock, of which he makes use in his indexing studies. A wide range of behavior is found in the wedge penetration of different rocks under different external conditions. For example, a rock that is essentially elastic-brittle at standard pressure may become elastic-plastic at a high confining pressure.7 It has also been observed4. " that some rocks will merely be crushed and indented by a wedge, whereas others will crack and form chips, furthermore the existence or non-existence of chips depends in great measure on the geometry of the indentor, type of rock and the depth of penetration. Hence, to attempt a theory which embraces all possible behavior is not practical at present. We, therefore, confine our attention to predicting the force-penetration characteristic and volume removal behavior for a type of rock which exhibits both crushing and chipping phases in the penetration process. Such behavior is characteristic of the harder rocks such as granites and represents a more difficult problem than the behavior of softer rocks such as coal and certain sandstones. In this preliminary study an attempt will be made to describe only the essential features of this complex penetration process. A qualitative description of these essential features is obtained with the aid of Fig. 1.1, where a wedge of vertex angle 28 is shown at some intermediate stage of the penetration process. As the wedge advances, the rock is fragmented (i.e. crushed) in some local region surrounding the wedge, the shape of this region being unknown. Simultaneous with the fragmentation in this local region, essentially elastic stresses are assumed to be building up in the surrounding rock. When a certain penetration level, di+1, is reached, the stresses along some surface are sufficient to cause failure and a chip is thus formed. The process now repeats, i.e., a crushing phase followed by the formation of a chip.

Jan 1, 1965

By Kenric C. Owen

INTRODUCTION Situated 23 miles east of Pretoria the Premier Mine started diamond production in 1903. Two years later it produced the largest diamond yet discovered, the 3 106 carat Cullinan stone. For the period to 1932 when the mine was closed down due to economic circumstances, open cast mining was practised using inclined rope haulage traction and by this time had produced 48.5 million carats of predominantly industrial quality diamonds from 148 million tons of ore. In 1945 it was decided to re-open the mine using underground mining methods. A system using long hole benching was devised (Hodgson and Sewel 1960). This system was later modified but still forms the basis for approximately fifty percent of production. Following the successful introduction of block caving on associated diamond mines in the Kimberley area (Gallagher and Loftus 1960) this mining method was introduced to the Premier Mine in the late 60's and now accounts for nearly 50% of production. This paper will discuss block caving at Premier Mine in the light of our experience and discussion will be directed to the main geological and structural features of the orebody and host rocks and the related constraints imposed on the mining methods. Reference is made to the long hole benching mining method for comparative purposes. GENERAL DESCRIPTION OF OPERATIONS The ore from the block caving and bench mining areas gravitates via ore passes to a twin haulage, 500m below surface. Electric 13 tonne locomotives, each hauling a train of 10 Granby type cars, deliver the ore to two 42" x 48" (1.06m x 1.22m) jaw crushers. The ore is reduced in size to minus 0.15m before being hoisted to the treatment plant on surface. Hoisting is done with 12.5 tonne bottom discharge skips in a five compartment rectangular shaft using two 3 240 H.P. semi automatic Ward Leonard winders. A small single drum service winder operates in the other compartment. Men and materials travel in a separate shaft in a 5,4m x 2,8m cage operated by a Koepi winder. These two shafts are also the main intake airways to the mine. The two main extraction fans capable of 250 m3/s at 3,2 kPa are situated on surface and are connected to the underground workings by an incline and a network of air passes and return airways. GEOLOGY Although there are numerous occurrences of kimberlite bodies in the district, the Premier Mine kimberlite pipe is the only economic orebody. It is roughly oval in shape with surface dimensions of 900m on the long axis and 450monthe short axis. The surface area is 320 000 m2. The kimberlite has intruded a massive body of felsite and norite which is intersected by a number of faults. The contact between the kimberlite and host rock is clear cut and dips inward at an average angle of 80°. Cutting across the pipe and the country rock is a 75 metre thick gabbro sill, the top of which intersects the pipe below the 347m level and dips at 15' to the north west. The kimberlite has been metamorphosed a distance of some 20m both above and below the sill contacts. Age measurements on biotite from the gabbro date the sill as 1 115 million years, thereby providing a minimum age of the pipe. (Pre Cambrian). All other pipes in South Africa are of Cretaceous age (60 million years). A simplified geological plan and section of the Premier Mine orebody is shown in Figure 1. It is thought that the kimberlite intruded in at least three distinct phases. The kimberlites of these different phases can be distinguished most easily by their characteristic colour. BROWN KIMBERLITE. This is the oldest kimberlite and forms a crescent shape in plan on the south eastern side of the pipe. In depth it increases in relative area. Although the brown kimberlite carries the highest diamond grade in terms of carats per ton all the various kimberlites in the Premier pipe are economic to mine.

Jan 1, 1981

By W. O. Philbrook, R. S. Kaplan

Rates of oxidation were studied for levitation-melted samples of Fe-C, Fe-Si, Fe-C-Si, Fe-C-P, Fe-C-Mn, and Fe-C-S alloys oxidized by mixtures of either 5 or 10 pct O2, in helium at several temperatures in the range 1850o to 2050°C. The concentrations of the oxidized elements decreased linearly with time. Mass transport in the gas phase was found to be the rate-controlling step. Ilowever, a mulliple -film model was necessary to account for the flux of iron and manganese vapor counter to the oxygen flow. THE advent of the basic oxygen and spray-refining processes of steelmaking has generated considerable interest in the kinetics of reactions between oxygen-bearing gases and liquid iron alloys. The object of this research was the determination of the role of mass transport in the gas and metal phases and of surface chemical reactions in the overall oxidation process. Of the reactions for elimination of elements dissolved in liquid iron, the oxidation of carbon has been investigated most extensively. Studies by Fuji and Ura,1 Fuji,' and Gunji et a1.,3 done with pilot-scale basic oxygen furnaces, indicated that mass transport of gaseous oxygen was rate controlling when the metal carbon content was greater than 0.15 to 0.30 pct. When the carbon content was less than this critical amount, diffusion of carbon dissolved in the iron was thought to be rate limiting. L. A. Baker et a1.4,5 levitated samples of iron-carbon alloys and oxidized them in CO-CO2, CO-C02-He, and O2-He atmospheres at 1660°C. These investigators found that the metal carbon concentration decreased linearly with time and their samples exploded when the carbon content fell below about 0.8 pct. They concluded that the rate-limiting step was the transfer of oxidant to the gas-metal interface. A model based on this rate-limiting step predicted decarburization rates within a factor of two of those experimentally observed. The explosion of the samples was attributed to a shift in rate-controlling step from gas-phase mass transport to transport of carbon dissolved in the metal. L. A. Baker and R. G. ward6 and R. Baker7 used freely falling droplets to investigate oxidation kinetics. In both papers, the authors speculated that flame fronts may have been partially responsible for the lack of better agreement between experiment and theory. Swisher and Turkdogan8 oxidized liquid iron having an initial carbon content of 0.97 pct with CO-CO2 and CO-C02-Ar mixtures at 1580°C. They concluded that a surface reaction was the rate controlling step. Iron-silicon alloys have been oxidized by R. Baker7 and Filipov and Martynov.9 R. Baker 7 also studied iron-carbon-silicon alloys falling as liquid droplets through oxygen. He found that the rate of both carbon and silicon oxidation varied inversely with the drop radius. When the initial silicon concentration was greater than 6 pct, the samples cooled during their fall. Manganese oxidation has been studied by R. Baker,7 and by Filipov and Martynov.9 ward10 investigated the loss of manganese from liquid iron under vacuum. He found that mass transport of manganese vapor was rate limiting in argon atmospheres of 0.02 torr to 700 torr pressure. Iron-sulfur alloys were desulfurized with H2-He and H2-Ar mixtures by Peters et al.11 A model based on the transport of H2S from the gas-metal interface into the bulk gas gave fair agreement between the predictions of the model and the experimental results. EXPERIMENTAL TECHNIQUE Essentially, the technique consisted of using helium-oxygen gas mixtures to oxidize levitated samples of liquid binary and ternary iron-base alloys. The fused silica reaction tube is shown in Fig. 1. The coil design is similar to that of L. A. Baker et al.4'5 A Tef-lon-sheathed, ferritic stainless steel lifter (B) and an alumina pedestal (C) were used to support the sample in the coil prior to levitation and for the recovery of the sample. Samples were inserted into

Jan 1, 1970

By P. G. Winchell, A. J. Heckler

An experimentally simple method for determining the effect of alloying elements on the activity of carbon is validated in Fe-Ni-C austenite. The technique consists of the equilibration of carbon between specimens of different nickel contents within a sealed silica capsule. The attainment of carbon equilibrium within each capsule is evidenced by: 1) in each capsule specimens of the same nickel content attained the same final carbon content regardless of their initial carbon contents, 2) in every capsule the final carbon content was reached for most nickel contents by carburizing and by decarburizing. The activity of carbon attained within each capsule was calculated from the carbon content of a binary Fe-C alloy placed within the capsule, and from the activity coefficient of carbon in the Fe-C system as found by Smith for CO/CO2/C equilibrium. The activity of carbon in Fe-Ni-C austenite determined by this method at 1000°C agrees with prior work by Smith, who used mother method. The measurements are extended to 800°and 1200°C. The activity coefficient of carbon 7c, in Fe-Ni-C austenite is given by: where xC is the ratio of carbon to metal atoms and XNi is the ratio of nickel to metal atoms and where the standard state is chosen such that yC = 1 as xc approaches zero in Fe-C alloys. This equation appears to be valid for xni < 0.3, and 1073° < T<1473°K. ThE activity of carbon in Fe-C austenite has been measured by smithL at 800°, 1000°, and 1200°C. Smith has also studied the effect of nickel on the activity A. J, HECKLER and P. G. WINCHELL are Graduate Student and Associate Professor of Metallurgical Engineering, respectively, School of Metallurgical Engineering, Purdue University, Lafayette, Ind. This paper is based on a thesis submitted ty,to Purdue University, in partial fulfillment of the requirements for the degree of M.S. in Metallurgical Engineering which A. J. HECKLER received from Purdue in January 1962. Manuscript submitted August 13, 1962. IMD of carbon in austenite at 1000°C. In both these studies the activity of carbon was fixed by a flowing CO-C02* *Gas mixtures of hydrogen and methane were also used in Ref. 1 but these results are not incorporated in Ref. 2 or in the present study. gas mixture. In the present work, Smith&apos;s results for Fe-Ni-C austenite are confirmed and extended to 800" and 1200°C by a different experimental technique. EXPERIMENTAL PROCEDURE In essence the experimental technique consisted of enclosing specimens of various nickel contents in an initially evacuated silica capsule and annealing the capsule until carbon equilibrium was attained among the enclosed specimens. The carbon activity obtained within the capsule was determined from the final carbon content of the binary Fe-C alloy included in each capsule and the results of smith.&apos; In order to evaluate this method the absence of nickel transfer between specimens must be established and the attainment of carbon equilibrium between samples must be assured. The absence of nickel transfer was demonstrated in the case of an originally pure iron sample which was annealed at 1200°C in a capsule with a 27.3 at. pct Ni alloy. The final nickel content of the iron specimen was less than 0.1 at. pct, a change which has a negligible effect on carbon activity. The attainment of carbon equilibrium was demonstrated within every capsule and in over half the results by achieving the same final carbon content in a sample which carburized during equilibration and in a sample of the same nickel content which decarburized during equilibration. The base Fe-Ni alloys were vacuum melted from Ferrovac E or electrolytic iron and Mond or electrolytic nickel. The samples were rolled and/or swaged and their carbon content adjusted to the desired pre-equilibration level either by methane-hydrogen carburization or by direct carbon transfer from a graphite source in a sealed silica capsule. As mentioned previously, high-carbon and low-carbon samples were prepared for most nickel levels in each capsule. The specimens were cleaned and

Jan 1, 1963

By H. Macpherson

Durhm has a well earned reputation for supplying some of the finest coking caals in the world. The caals, in general, vary in rank from 301 to 501/2. Durham has traditionally produced foundry coke for the major proportion of the foundries in Great Britah. Durham coals can be described as clean, soft coals, which yielded, with the old hand methods of coal getting, low ash small coal because the extraneous shale was normally harder than the coal and occurred in larger pieces. Under these conditions, with a plentiful supply of cheap labor, it used to be sufficient, at most collieries, to hand clean the large sizes of coal which could then be remixed with the untreated small coal to produce carbonization coals, ready for the coke ovens, at under 5 pct ash. With the introduction of mechanical methods of coal mining, the coal gradually required more cleaning. The first method adopted to resolve this problem was the introduction of pneumatic dry cleaners for the small coal. Although such machines had little effect on the fine coal (say below 1/8 in.), they could clean the intermediate sizes of coal. This, coupled with hand cleaning the larger sizes above 1-1/2or 2 in., resulted in a combined run-of-mine mixture below 6 pct ash, capable of maintaining the quality and reputation of the cokes produced. In more recent years, the intensification of mechanization and power loading, coupled with gradual exhaustion of the cleaner seams, has created the need for a more complete method of coal cleaning. This particularly applies in the fine sizes (say below 1/50 in.) which normally vary, under present day conditions, between 15 and 35 pct ash and are much too dirty to be included in the raw state in a carbonization mixture. This pronounced change has been accelerated because legislation controlling the dust conditions of mine airs for the prevention of pneumoconiosis has resulted in tk~e extensive use of water underground and a consequent increase in moisture content of the run-of-milie output. The presence of damp fine coal decreast the efficiency of prescreening and dry cleaners, so that this type of preparation for low ash coking coals is decreasing, although it is still used satisfactorily for industrial coals in the medium ash range. Table I shows the gradual increase in mechanization, the reduction in manpower, the increased use of explosives per ton of coal extraction, and the increase in the proportion of coal cleaned by mechanical means in Great Britain. Although similar figures are not available for Durham Div. until after the date of nationalization of the coal industry, it is probable that the increase in mechanical cleaning, particularly by dry cleaners, was more marked in the Durham collieries than elsewhere in the country. As dry clealiers were replaced by coal washeries in the Gritish ccal industry, no special attempts were made to recover the slurry, with the result that large outflows of dirty water were allowed, deposits of slurry came in to lagoons and neighboring streams, and a proportion of fine material was lost from the coking coal. This position, coupled with the higher moisture of the washed coking coal, resulted in adverse effects on coke oven throughputs and coke quality. It is now realized that the natural coal fines are an essential ingredient of coking coals in obtaining the correct coke structure in metallurgical cokes. This, together with economic pressure, led to the introduction of flocculation and filtration plants for the recovery of slurries, and later, when the ash contelits of the filter cakes were too high, to the introduction of froth flotation equipment. After this position had been reached, the tailings from the froth flotation pIants were, in many cases, still allowed to constitute an undesirable effluent. Recent legislation on river pollution has changed this picture; it is now necessary to provide a circuit which is completely closed so far as solids are concerned. The gradual increase in the coal cleaned by wet methods and froth flotation in Durham Div, is shown in Table 11. It is now an accepted feature of new Washeries that. froth flotation should be an integral part of the washing process from the initial installation of the plant.

Jan 1, 1962

By H. Dykstra

Calculated wellbore pressures were obtained for parameters of radilcs ratio and permeability. In all cases bur two, after-production was allowed to occur for one day. The calculated pressure build-up data were compared with actual pressure build-up data from a condensate well. The paper discusses the comparison, gives reasons for, inability to match calculated (2nd actual data, and presents conc1usions derived from the comparison. INTRODUCTION Considerable information has been published on the decline in wellbore pressure for oil and gas fields resulting from production of fluids. Considerable information also has been published on pressure build-up for oil fields, but relatively little has been published for gas and condensate fields. Perrine&apos; summarized the equations derived for pressure build-up in oil wells and showed how the different methods could be applied. On the other hand, very little theoretical information has been published on pressure build-up in gas or gas-condensate wells.2-4 Tracy,&apos; by pointing out the similarity between the equation describing oil wellbore pressure decline and the equation describing gas wellbore pressure decline, showed how methods of pressure build-up analysis could be applied to a gas well. In analyzing pressure build-up data for gas or gas-condensate wells, it would be very desirable to compare actual pressure build-up data with calculated pressure build-up data. Such a comparison would lead to a better feeling for the quantitative picture of gas-well build-up curves and would help to establish a degree of confidence in a given build-up curve. This paper discusses the comparison and presents conclusions made from it. Calculated wellbore pressures are given for parameters of radius ratio and permeability. In all cases but two, after-production was allowed to occur for one day. The work was done in an attempt to evaluate the reserves of a gas-condensate field. As will be discussed later, it was not possible to make an evaluation. METHOD OF CALCULATION The method used for solving the depletion and pressure build-up behavior for a gas-condensate well was that developed by West, Garvin and Sheldon.5 or the IBM 704 computer program used, it was assumed that liquid condensing out of solution would have only a minor effect on the flow behavior. Therefore, the field was treated as having single-phase flow, with the gas saturation S, remaining constant at unity minus the connate-water saturation Sw. As will be discussed later, this may not have been a good assumption. It also was assumed that oil production could be considered as equivalent gas production by using a conversion factor based on an analysis of the liquid produced. An outer boundary condition of no-flow was assumed. BASIC DATA The data required for the study were reservoir properties, fluid properties and production data. Reservoir properties included the following: thickness h, 179 ft; porosity, 0.194; connate-water saturation, 0.43; gas saturation, 0.57; permeabilities k, 1.0, 0.5, 0.25 and 0.15 md; radius ratios re/rw, 800, 1,000 and 2,000; wellbore radius rw, 5 in.; initial reservoir pressure P, 6,529 psia; and reservoir temperature, 272°F. The selection of permeabilities was based on core-analysis data showing an average air permeability of about 2 md. With a relatively high connate-water saturation, the average effective gas permeability would be about one-half, or less, of the air permeability. The selection of radius ratios was based partly on the observed rapid decline in wellbore pressure during production and partly on the fact that the well was believed to be located in a relatively small fault block. Reservoir fluid properties were obtained from a reservoir fluid study on a recombined sample of gas and condensate. Gas formation-volume factors were calculated from pressure-volume measurements made at reservoir temperature. Gas viscosities were calculated by the method of Carr, et al,G from an analysis of the re-combined sample. These data are shown as a function of pressure in Table 1. The production schedule from the gas-condensate

By Dale A. Vaughan, Oliver M. Stewart, Charles M. Schwartz

A. U. Seybolt (General Electric Research Laboratory)—The authors should be commended for adding some important information to our knowledge of the solubility of interstitial elements in metals. It is becoming increasingly evident that the effect of even traces of such elements have very far-reaching effects upon the mechanical properties of the body centered cubic metals. Those who have worked in this area know that the accurate determination of the small solid solubility limits in systems of the type reported by the authors is a quite difficult task, and it is therefore not surprising that frequently the results of different workers are not in agreement. It is instructive, and usually helpful, to plot the solubility results on log weight or atomic percent -1/T coordinates to find out if a straight line is obtained. A straight line is expected because in systems displaying solubilities of the order of 1 to 3 at. pet or less, Henry&apos;s law is usually obeyed—or at least well enough obeyed so that the deviation from linearity is not very appreciable. If Henry&apos;s law is obeyed, one canthen use the Van&apos;t Hoff Equation in the form In N = ?H/RT + C, where N is mole fraction, at. pet, or wt pet for small values, and AH is the partial molal heat of solution of the solute. R and T have the usual significance, and C is an integration constant. If one plots the reported nitrogen solubility values as indicated above, the three points fall reasonably well on a straight line. The oxygen values for the two upper temperatures fall very closely to the nitrogen values as shown in the authors&apos; Fig. 15. However, the value at 500°C departs widely from the straight line established by the data at 1500" and 1000°C. It is, of course, true that one cannot place too much emphasis on the significance of a line established by only three points, but in the absence of reasons for anticipating deviations, data exhibiting wide departures from linearity should at least be examined closely. Fig. 16 shows the log at. pct -1/T plots for the authors Ta-O and Ta-Ndata including a solid circle point at 500°C and 1.8 at. pet for Ta-O, which is simply extrapolated from the two higher temperature points. In addition, the data of R. P. Elliott9 for Nb-O are shown. These points were picked off his curve and are not very exact, but as can be seen they line up well on a straight line. It is interesting, and probably significant, that the slope of Elliott&apos;s results is not far from those of Vaughn, et al. This is probably to be expected because one would anticipate that the partial molal heats of solution of oxyten in these two very similar metals should be not too far apart. AH for Ta-O is about -1900 cal per mol, while for Nb-O it is near -2300 cal per mol. Hence, this lends some support to the thesis that the point at 500°C for Ta-O is much too high. The data of Gebhardt and Preisedanz10 are also plotted, and it is seen that their data while lying on a linear plot, have an appreciably steeper slope. The possible reasons for this will not be discussed here except to point out that their pressure-composition data show anomalies which suggest that they may have been dealing with a different equilibrium from that being discussed. There is another consideration which would also suggest that the solubility at 500°C is lower than shown. The solubility values were obtained by the classic method of first establishing a lattice parameter-composition curve. This the authors did, and there is probably little doubt that it is quite accurate. Such a plot is generally almost error-free because it has a self-correcting feature in that any deviation from linearity makes a data point immediately suspect, and subject to confirmation. Unfortunately, this is not true with respect to the actual solubility values. These are obtained ordinarily by taking an alloy containing more solute than is soluble at some temperature and then thermally

Jan 1, 1962

By T. A. Rickard

The history of this State is that of one generation. Thirtysix years only have elapsed since the birth of that beneficent industry whose footsteps were the first to traverse the wilderness of the prairies and penetrate the solitude of the mountains. So soon is history made. The men who halted on the rolling plain where Denver now stands and gazed westward at the snow-clad ranges in eager questioning of their possibilities of golden wealth, have lived to see a noble city built where once their camp-fires burned, and have participated in the discovery of a magnificent series of productive mines amid the mountains which seemed at that time the Ultima Thule of their pilgrimage. To those who investigate the workings of our complicated mining and metallurgical industries, the story of their evolution from humble beginnings will appear an instructive romance. The record that tells it presents features common to the growth of modern mining regions, but also bears aspects peculiar to

Jan 1, 1897

By Steve H. Carpenter, Henry E. Otto

The explosive welding of metals is dependent upon the production of a jetting action caused by the collapsing of one metal plate against another. Successful welds are generally accomplished if the yield strength of the metals is in the range of 10,000 to 90,000 psi and the sonic velocity of the metal is greater than the detonation velocity of the explosive if direct contact explosive is being used.&apos; Should the detonation velocity exceed the velocity of sound in the metal it may still be possible to obtain the jetting action and a good weld. However, in most cases where a high detonation velocity is used complications arise because of reflected shock waves which tear the bond apart as fast as it is put together.&apos; Explosive welding of lead presents several problems since its yield strength and sound velocity are very low. Various values have been published3-5 for the velocity of sound in lead ranging from 2000~ to 23004 m per sec. Most of the high-order explosives have detonation velocities on the order of 6000 to 8000 m per sec, which precludes their use. The dynamites have a lower detonation velocity of around 2800 m per sec which is still somewhat too high. Lower-order explosives such as ammonium nitrate (1070 m per sec) must be used to weld lead in the as-received condition if the explosives are used in direct contact. Rather than use low-order explo&apos;sives it was decided to alter the sonic velocity of the lead. The sonic velocity is directly related to the modulus of the material according to the following expression: Fig 1—Interface of explosive weld of lead to steel. Lead is on top As-polished Magnification 75 times as well as the yield strength. Bolling et al. 6 show that the shear modulus of lead single crystals increases from about 0.72 X1011 dynes per sq cm at 300°K to about 0.98 X1011 dynes per sq cm at 0°K, an increase of approximately 3 5 pct. This gives an increase in the sonic velocity of around 700 m per sec. Hence, the sonic velocity of lead at cryogenic temperatures is approximately equivalent to the detonation velocity of the low-order dynamites. We have obtained high-quality lead to steel explosive welds using a 40 pct dynamite in direct contact with the lead. Prior to detonation the lead was chilled with liquid nitrogen (78°K) to increase the strength and sonic velocity. Welds were made while the lead was cold. Specimen sizes were 3 by 6 in. A preset angle of 5 deg with a 0.10-in. standoff at the base was the geometrical setup used. The amount of explosive used for optimum welding of an 1/8 -in. -thick lead sheet to a steel plate was found to be 7 g per sq in. A PETN sheet explosive line wave generator was used to insure a linear detonation front through the dynamite. A photomicrograph of a lead-steel weld is shown in Fig. 1. The typical wave effect that constitutes a good explosive weld is present. When tested in shear, the weld failed in the lead, indicating that the bond is stronger than the lead base metal. Higher-order explosives were also tried without success. We believe this indicates the importance of matching the detonation velocity and the sonic velocity for successful explosive welding. Note Added in Proof. High quality explosive welds of lead to steel have recently been obtained at ambient temperature using a low velocity (1000 M per sec) free running dynamite. The weld interface obtained is comparable to Fig. 1. &apos;S. H. Carpenter, R. H. Wittman, and R. J. Carlson: Proceedings of the First International Conference of the Center for High Energy Forming, Syracuse University Press, syracu.se, N. Y., in press. &apos;A. HI Holtzman and G. R. Cowan: Welding Risearch. Council Bull., No. 104, April, 1965. &apos;Metals Handbook, 8 ed., p. 1062, Metals Park, Ohlo. &apos;J. M. Walsh, M. H. Rice, R. G. McQueen, and F. L. Yarger: Phys. Rev., 1957, vol. 108, pp. 196-216; &apos;L. V. Al&apos;tshuler, K. K. Krupnikov, B. N. Ledener, V. I. Zuchikhin,

Jan 1, 1968

By C. F. Rust

Experimental evidence is presented showing that reproducible formation resistivity factor measurements and resistivity index determinations on reservoir core samples map be made utilizing either the two- or four-electrode methods. Equipment is described which permits the application of either technique to the core specimen without loss of time and with a minimum amount of effort. Since electrical resistivity measurements on reservoir rocks are important not only in electric log interpretations, but also in the study of fundamental rock parameters, it was considered desirable to compare the applicability of both techniques of resistivity measurement. INTRODUCTION The techniques employed in the measurement of electrical resistivity on reservoir rocks, as practiced in the petroleum industry, may be reduced to two fundamental methods: one utilizing two electrodes only, usually referred to as the two-electrode method; the other using two additional electrodes and commonly known as the four-electrode method. In the former, the core sample whose resistivity is to be measured is mounted between two electrodes, usually metal discs, which serve to pass a current of known magnitude through the saniple. The potential drop across the sample, measured between these same two electrodes, and the core dimensions furnish the necessary data to compute he resistivity of the sample. In the four-electrode technique the end plates, again usually ol metal, still serve as current electrodes. Additional probes or electrodes dispersed along the sample are utilized to measure the potential drop. Both methods are used in practice1,2 and it is the purpose of this paper to compare the two techniques as applied to the determination of formation reiistivity factors and the resistivity index exponent n, in Archie&apos;s empirical equation I = p/po = Sw 11. To evaluate the two techniques it is desirable to point out the experimental precautions which must be taken to insure reliable results. It is evident from the electrode arrangements of the two- and the four-electrode methods that, for a given sample, the volume of sample included by the four-electrode method is less than the volume included by the two-electrode method. One of the prime difficulties associated with the two-electrode method is the possible occurrence of an abnormally high resistance between the electrodes and the brine-saturated sample, which results in erroneous resistivity values for the core sample itself. Attempts to alleviate this difficulty meet varying degrees of success. Methods used in the past employ such absorbent materials as brine-saturated Kleenex: chamois, or felt. A technique described by Morgan, Wyllie, and Fulton,1 appears to be more satisfactory. Their method consists of spraying or painting the end areas of a core sample with conductive silver paint. This technique reduces contact resistances between the porous medium and the electrodes to a value which is generally negligible as compared to the resistance of the sample itself. In the four-electrode method these requirements are not as stringent since separate probes are used to measure the potential difference acrozs a portion of the sample. In this case, contact resistance occurring at the current electrode; are of no consequence. and those appearing at the potential

Jan 1, 1952

By N. A. McLeod

BALL wear in wet grinding mills has been the subject of considerable discussion in the last few years. Its importance to millmen is obvious in view of the fact that ball wear may cost from 2 to 4¢ per ton of ore for the more fortunate operators and many times this cost when a refractory ore must be reduced to a fine state of comminution. Consequently, any factual information that may be obtained on the nature of ball wear may be applied to introduce changes leading to lower ball consumption and therefore also to lower costs. In 1940, while employed with the Britannia Mining and Smelting Co., Britannia Beach, B.C., I had occasion to investigate factors that might affect ball consumption. We performed a number of tests, which will be briefly described. These tests originated as a result of changing from a 3 1/2-in. ball to a 2-in. ball of different type of manufacture and were motivated by the desire to obtain the best possible type of 2-in. ball. Our testing was helped by the fact that the company operated a one-ton electric furnace, so that it was quite easy to make steel changes. It should be emphasized at the beginning that these tests produced results that in their general application to milling should be interpreted qualitatively rather than quantitatively. As will be evident in the description of the method used in testing, the balls were subjected to an intermittent batch grinding treatment, which may have produced results in rate of steel wear that may not have an accurate correlation with steel consumption in full-scale mill operation. However, with this fixed and rather arbitrary method of testing, results were obtained that may be of some interest and may stimulate further work on this subject. Unfortunately, owing to pressure of war work, our tests, which we had intended to repeat on a continuous grinding operation, had to be discontinued. METHOD OF TESTING Tests were made in a small cylindrical mill, rotating at 72 r.p.m. Internal dimensions of the mill were 10 1/2-in. dia. by 9 in. The cylindrical inner surface was lined with rubber and the two ends were formed by steel plates. A charge of 2000 grams dry feed and 2000 c.c. of water was added every 2 hr., the mill being drained of pulp before the addition of each charge, by tilting and sluicing with water. The mill was run on afternoon and night shift for daily periods of about 15 hr. total grinding time, and each test lasted from 60 to 150 hr. This batch method of testing involved a higher average pulp temperature in the mill, which undoubtedly affected comparative results in some of the tests. HARDNESS OF BALL VS. WEAR In these tests, special "eutectoid" steel balls were used, some of which were chill-cast and quenched, some sand-cast and quenched, and some sand-cast and annealed to a dead soft condition. The results obtained, using as mill feed an ore containing considerable free quartz and

Jan 1, 1945

By R. F. Hehemann, Darrell W. Smith

The kinetics of alloying- in W-5 rot pct Re powder compacts were investigated at temperature about the upper limit for the formation of the x phase, such that a single intermediate phase was involved in the process. The rates and directions of motion of the a-o and o-b interface were assessed as functions of tinze at the sintering teri7peraticve by quantitative izetallog-ralhic techtziques. The iiotion 01 these interjuces could be specified approxitnate1.y by u Parabolic )-ate law and deviations from this ,rate law were attribuled to a complex interaction between surface dif&apos;fusion and volume diffusion during the initial stages of sintering. WHEN binary or more complex alloys are produced by sintering compacted blends of elemental powders, a complication is encountered which does not arise in the sintering of pure metals. In addition to concern for grain size and densification, the rate of inter diffusion of the component elements must be considered. The general problem of alloying during sintering has been treated by numerous investigators.&apos;-7 These investigations have been concerned only with systems that form continuous series of solid solutions and a concentric-sphere diffusion model4 provides a useful description of homogenization in these stems.&apos; Some controversy remains, however, over the contribution of surface and grain boundary diffusion to the homogenization process. Heckel% ePorts that homogenization can be described by volume diffusion at all temperatures, whereas other invetiators&apos;&apos; recognize the importance of surface and grain boundary diffusion, particularly at lower temperatures. Analysis of the homogenization process in partially miscible systems is complicated by the motion of the interfaces separating the individual phases. A simple analytical solution does not exist for such finite systems with spherical symmetry. It was the purpose of this work to examine the kinetics of the formation and dissolution of an intermediate phase in a binary system through an assessment of the motion of the interfaces separating this phase from the terminal solid solutions. PROCEDURE The W-Re system is an example of a partially miscible binary system and was selected for study because of its current importance in refractory-metal technology. The equilibrium phase diagram, Fig. 1, shows that the o phase will be formed by interdiffu-sion between tungsten and rhenium. At temperatures between approximately 2125" and 282O°C, the o phase will appear as the only intermediate phase in the diffusion system. In this work, a mixture of elemental powders containing 5 pct Re was employed. In such a mixture, the rhenium particles will be distributed randomly in a tungsten matrix. During sintering, a o-phase layer will form at the W-Re interface. The development and subsequent disappearance of the o phase are controlled by the relative rates and directions of motion of the 0-0 and a-p interfaces. The motion of these interfaces can be inferred from quantitative metallographic measurements of the average radii of the o shells surrounding rhenium particles. Elemental tungsten and rhenium powders of commercial purity were employed in these investigations. The rhenium powder was spheroidized from +200 mesh agglomerates by plasma-arc spraying and was then classified to yield a powder composed of essentially

Jan 1, 1967

By A. H. Daane, J. F. Haefling

BECAUSE of the wide use of platinum in industry and research, the physical properties of this metal, including its vapor pressure, have been studied in some detail.&apos; The other members of the palladium-platinum group of metals have not been studied as extensively, and only qualitative information is available on the vapor pressure of palladium. Data given in literature by Vines1 and Brewer2 on the vapor pressure of palladium are based on the qualitative observations by Holborn and Austin3 and Crookes4 on the rate of volatilization of palladium filaments in various atmospheres. The general observation that palladium is the most volatile metal of the palladium-platinum metal group was corroborated by Bell, Love and Normand who studied the separation of isotopes of the platinum-group metals by a mass spectrometric method. We have measured the vapor pressure of palladium using the Knudsen effusion technique. In this work, the effusion vessel was suspended from a quartz-fiber microbalance into an induction furnace, and the amount of vapor effusing from the vessel was determined by direct weighing of the vessel during the measured heating times. This technique has been described in a report from this laboratory." The vapor pressure of palladium was calculated from these measurements using the equation P...... = 17.14 -W- (77m)&apos;u [1] a t where ? is the weight loss in grams of vapor of molecular weight m from a vessel having an orifice of a sq cm, during t sec. The derivation of this equation from kinetic theory has been described in a previous report from this laboratory: as well as in texts discussing the kinetic theory of gases.%" Test Vessel—In the search for a suitable material for the effusion vessel, it was found that tantalum reacted with palladium metal to form intermetallic compounds, and graphite was readily dissolved in palladium metal to form what appeared to be a liquid phase at a temperature several hundred degrees below the melting point of palladium. On cooling, the graphite gathered into spherical balls in the palladium, with crystals extending radially from the center of these balls, some of which were a millimeter or more in diameter. However, palladium metal vapor did not attack the graphite vessel, so graphite could be used where it did not contact condensed palladium. Tungsten did not appear to react with palladium vapor or molten palladium at its melting point, but it was not convenient to use a tungsten-vapor pressure vessel because of the difficulty of fabricating this metal. Since the vapor-pressure range to be studied (10 2 to 10 &apos; mm) did not appear to extend above the melting point of palladium, a combination of tungsten and graphite served to provide a very satisfactory effusion vessel. The lower half of the graphite vessel was lined with some strips of tungsten foil and the sample of palladium consisting of a coil of sheet was placed in the tungsten liner; in this way, no contamination of the palladium by carbon occurred. Procedure After outgassing at 1500C, the tungsten-lined graphite effusion vessel was loaded with 300 mg of

Jan 1, 1959

By R. A. Deju, R. B. Bhappu

Further information on the surface characteristics of the silicate minerals was obtained by experimentally correlating the oxygen-silicon ratio of the silicates with their electrokinetic properties. Specifically, the behavior of the minerals in an electric field was investigated using zero point of charge as a parameter. A modified electrophoresis cell was used for the determination of electrophoretic mobilities. It was shown that there is an increase in the zero point of charge with increasing oxygen-silicon ratio in the silicates. Finally, a chemical interpretation was presented to describe the surface phenomena observed in the experiments. In recent years great interest in surface chemistry has produced a number of methods to study the surfaces of minerals and to observe the phenomena occurring at their interfaces. One such method is discussed in this paper. A rather complete review of the surface characteristics of the oxide minerals has been undertaken by parks,&apos; but, a similar study has not been made for the silicate minerals. Two previous papers by the authors2&apos;3 attempted to remedy this situation. In these papers it was demonstrated that the reaction between the silicate mineral particles and acidic water involves mainly an exchange of metal ions for hydrogen ions on the surface of the solid, leading to an increase in pH of the aqueous phase. Also, the degree of reaction was found to depend on the oxygen-silicon ratio of the silicate structure, being least for the quartz and greatest for the olivines. A hypothesis was then set forth explaining that upon the fracturing of a silicate mineral, the oxygen-metal bond (which is almost entirely ionic in character) will break more easily than the stronger oxygen-silicon bond. This results in the exposure of unsatisfied oxygen sites on one hand and active, exchangeable cations on the other. These active sites on the fractured surfaces are then available for reaction with the hydrogen ions in acidified aqueous solution. Thus, an increase in degree of adsorption of hydrogen ions occurs as the oxygen-silicon ratio increases due to the presence of a larger number of active sites on such minerals. A correlation between oxygen-silicon ratio and electrokinetic properties will be further pursued in this paper from both the theoretical and experimental points of view. Efforts will then be made to present a chemical interpretation of surface phenomena observed in the experiments. It is believed that this study may supply pertinent information on the behavior of silicate minerals in froth flotation systems. ELECTROKINETIC STUDIES Equipment: In a previous paper,2 Deju and Bhappu described a simple method for determing the zero point of charge using a potential across a cata-phoresis cell and observing particle movement by means of a Rayoscope* optical system. This setup is simple in design and operation and extremely reliable. With care, reproducible results within 1.5% accuracy may be obtained. A new setup has been developed, based partly on the design by Zeta-Meter Corp.4 and partly on previous cells used at the New Mexico Bureau of Mines. This new, modified cell is shown in Fig. 1. Although

Jan 1, 1967

By C. S. Yust, C. S. Morgan

ThIS note reports the observation of masses of dislocation etch pits around the weld necks of small single-crystal particles of calcium fluoride sintered to a cleaved face of a larger CaFz crystal. Crystal particles in the -50 +I00 mesh size range were placed on freshly cleaved CaFz surfaces and heated at 1250°C for 30 min in a tantalum container in an argon atmosphere. The sintered specimens were then etched at room temperature for 40 to 50 min in a 2 pct sulfamic acid solution which is a selective etch for dislocations in caF2.&apos; Figs. 1 through 3 show the masses of dislocation etch pits observed around weld necks after etching. In some cases, particles were gone after removal of the specimens from the furnace although weld necks were readily visible. In other instances, no etch pits formed around a weld neck. A possible cause of concentrations of dislocations on the crystal surface is mechanical deformation of the base crystal when particles are dropped on it. If such a deformation does occur, it would be much smaller than that caused by the light punching of a crystal with a sharp instrument which results in large concentrations of etch pits. However, crystals deformed by punching with the sharp instrument and annealed at the conditions of these experiments (1250°C for 30 min) before etching showed no concentrations of dislocation etch pits. It is obvious that dislocations from the much smaller deformations, possibly created when particles are placed on the surface, would also anneal out. Etching of large crystals which had particles placed on them in the usual manner but which were not heated showed no dislocation concentrations such as shown in Fig. 1. The magnitude of dislocation etch-pit concentrations did not vary with extensive variation of the cooling rate. The appearance of many of the etch-pit clusters is typical of a well-annealed condition, indicating that the dislocation concentrations formed before the specimen temperature was lowered. Therefore, it is evident that thermal stresses in the neck area did not create the deformation indicated by the presence of the dislocations. The possibility exists that the etch-pit concentrations at places where particles had been removed may be the result of deformation accompanying the fracture of the sintered bond. That this is not so was demonstrated by breaking off particles around which no etch pits occurred. Re-etching never resulted in the large concentrations observed at sintering sites. The stress available to effect material movement during sintering of two particles will depend on the geometry at the contact point but can easily exceed the macroscopic yield stress in CaFz systems. It appears that the plastic deformation observed results from sintering or simply from the weight of the small particles. It has been previously argued that plastic flow makes an important contribution to the initial densification of oxides having the fluorite crystal structure.2p3 If plastic deformation occurs, it would begin as soon as the temperature is sufficiently high

Jan 1, 1967

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 W. E. Brigham, P. W. Reed, J. N. Dew

By C. B. Alcock, L. I. Cheng

By the use of radiochemical methods for the study of the gas-liquid equilibria at low temperature, and for the determination of the sulfur contents of metal beads which had been equilibrated with H2S/H2 mixtures of known sulfur potential, it has been possible to obtain the liquid solubility and the free energy of solution of sulfur in liquid tin and lead at temperatures between 500°and 680°C. THE gas-liquid equilibrium method has proved in the past to be most successful in the determination of the thermodynamic behavior of dilute solutions of sulfur in liquid metals.1,2 One of the basic requirements for success with this method is that the volatility of both the metal and its lowest sulfide should be small, otherwise sulfide will be deposited at the cool end of the furnace, where it may react with the outgoing gases to form either sulfur-rich lowest sulfide or higher sulfides. The resultant value of the apparent equilibrium constant will then be lower than the correct one. This argument applies even at sulfur potentials below that in equilibrium with a separate condensed phase of the lowest sulfide at the reaction temperature, T. The mass of sulfide which is deposited at the cold end of the furnace, and hence the extent to which further reaction occurs with the outgoing gases, depends on the time taken for equilibrium to be reached between metal and gas. Since this will depend principally on the bulk of the metal phase which is used, one should clearly attempt to uie as small metal samples as possible. These considerations are important in the study of dilute solutions of sulfur dissolved in liquid tin and lead which both have moderately high vapor pressures as metals and form volatile sulfides. The limit on the size of the metal samples which may be used is set chiefly by the difficulties of analysis for very small amounts of sulfur. The oxygen or carbon dioxide combustion method, followed by iodimetric determination of the sulfur dioxide which is formed,has been found to be successful for the determination of small amounts of sulfur in copper, iron, cobalt and nickel.4 This method was unsatisfactory for sulfur dissolved in tin and lead, mainly because the sulfur dioxide was to some extent absorbed by the copious tin or lead oxide deposits which were formed on the walls of the combustion tube. Furthermore some of the sulfur was found to segregate on the surface of the beads as flaky sulfide crystals which would easily be lost in the transfer of a bead from a boat in the gas equilibration apparatus to one in the combustion apparatus. Oxidation in aqueous media to sulfate ion followed by precipitation as barium sulfate was, therefore, adopted as the analytical procedure. The gas-metal equilibrium experiments were all carried out with radioactive sulfur and thus the analysis involved the counting of barium radiosulfate. Furthermore the use of the radioisotope meant that the approach to the gas-metal equilibrium could be followed continuously by gas counting.&apos; The metal beads were held separately in glass crucibles during equilibration and were transferred from the furnace to the beaker for dissolution in nitric acid still in the crucibles, and thus the possibility of sulfur loss by detachment of the sulfide segregates was eliminated. The temperature range of this investigation was 500° to 680°C. EXPERIMENTAL APPARATUS AND METHOD The apparatus consisted of two furnaces placed in series in a gas recirculation system, Fig. 1. One furnace F1, which was vertical was used to heat the alumina crucible, A, holding six metal beads in separate glass crucibles. The beads weighed between 300 and 700 mg each. The crucible assembly was introduced and removed from the furnace mechanically under a stream of oxygen-free argon. The other furnace, F2, was horizontal and was used to heat a cobalt Co9S8 mixture, held in an alumina boat, and made with radiosulfur containing about 1/2 millicurie per g of sulphur. This mixture, which was finely powdered, was used as a source of known H2S/H2 mixtures6 for a given furnace temperature. The recirculation system also contained a gas re-circulation pump (P), an end window Geiger-Miiller counter (N)—placed downstream of F1 so as to monitor the H2S pressure in the gas leaving this furnace— a sample volume for chemical analysis of the gas phase (G), gas drying tubes (D), filling taps and other standard ancillary equipment. The gas sampling volume was principally used in the cali-

Jan 1, 1962

By D. Atkinson, C. Bodsworth, I. M. Davidson

A geometric model of interstitial solid solutions, which has been used previously as a basis for the prediction of carbon activities in Fe-C austenite, is shown to serve also for the calculation of nitrogen activities in Fe-N austenite. The model has been developed to enable predictions to be made of the activities of an interstitial element in the presence of two host atom species. The activities calculated via the model are shown to be in satisfactory agreement with the measured values in the austenite phase for carbon in Fe-C-Co, Fe-C-Cr, Fe-C-Ni, Fe-C-~n, Fe-C-Si, and Fe-C-V alloys and for nitrogen in Fe-N-Ni alloys. The effect of the second substitu-tional solute on the logarithm of the activity of the interstitial element is expressed as the product of a constant mad the atomic concentration of that solute. The constants so derived we related to the thermo-dynamic interaction coefficients which describe the effect on the activity coefficient of carbon of an added solute element. In recent years the thermodynamic activities of carbon and nitrogen in the single-phase austenite field have been determined for iron binary alloys and for several iron-base ternary alloys. In order to extend the use of these measurements, it is desirable to be able to predict with reasonable accuracy the activities of the interstitials at compositions and temperatures other than those which have been measured experimentally. In all the systems studied to date, the interstitial elements do not conform to ideal behavior. Hence, the available data cannot be extrapolated or interpolated using the simple thermodynamic concepts of solutions. Several models have, therefore, been formulated for the purpose of predicting the activity of an interstitial element in the presence of one species of host atom. These models can be divided into the geometric1"5 and energetic6-&apos; types. The former group is based on the assumption that at low concentrations the activity of the interstitial species is determined by a composition-dependent configurational entropy term and an excess free-energy term which is temperature-dependent but independent of composition. The purpose of this paper is to show that the treatment, based on a geometric model, can be extended to enable predictions to be made of interstitial activities in the presence of two substitutional host atom species. THE CONFIGURATIONAL ENTROPY OF MIXING ICaufman5 has shown that the configurational entropy, S,, for a binary solution comprising of a host atom species, A, and an interstitial species, I, can be expressed as: where NI is the atom fraction of the interstitial species, R is the gas constant, and (2 - 1) is the number of interstitial sites excluded from occupancy by the strain field around each added interstitial atom. The number of interstitial sites per host atom, p, is unityg for the fcc austenite solutions considered here. The configurational entropy of mixing for a ternary solution comprising two substitutional atom species, A and B, and one interstitial species, I, can be derived similarly. Let the number of atoms per mole of each of these species in the solution be represented by «a, ng, and nI. From geometric considerations, it is improbable that the addition of a few atom percent of a second host atom species will change the type of sites (i.e., octahedral) in which the interstitial atom can be accommodated in the austenite lattice. At higher concentrations (determined largely by the relative atomic radii of the atomic species present and any tendency to nonrandom occupancy of the host lattice sites) other types of interstitial sites may become energetically favorable. Restricting consideration to compositions below this limit, for 1 = 1 the number of suitable interstitial sites is given by (n + nB). However, if each interstitial atom excludes from occupancy (Z - 1) additional sites, the total number of sites available for occupation is reduced to (n + ng)/Z. The number of vacant interstitial sites is given by: The total number of recognizable permutations of the atoms must include the recognizable, different configurations of the A and B atoms on the host lattice. Assuming that these arrangements are purely random, and are not affected by the presence of the interstitial species, the total number of recognizable permutations in the ternary alloy is given by: The configurational entropy is obtained by expanding, using Stirling&apos;s approximation, and collecting like items, as:

Jan 1, 1969