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By David Turnbull, J. H. Hollomon, J. C. Fisher

Understanding of the diffusion problem has recently been furthered by the analysis of Birchenall and Meh1.l They pursued the problem of the variation of the diffusion coefficient with composition for non-ideal solid solutions. Their analysis follows the tradition of Wagner,l Jost, Dehlinger, and Darken & who assumed the net flux of diffusing material to be proportional to the gradient of a quantity related to free energy. The basic assumption in Birchenall and Mehl's formulation of the problem is that the net flux of diffusing material is proportional to a thermodynamic activity gradient. To estimate the applicability of the derived relations, they corrected the diffusion coefficients of carbon in austenite by utilizing Smith's6 activity data for carbon, and the diffusion coefficients for zinc in copper with activity data computed from the vapor pressure measurements of Har-greaves.' The corrected coefficients for carbon were virtually independent of carbon concentration. For the diffusion of zinc in copper a moderate variation of diffusion coefficient with concentration remained after the correction. The problem of diffusion can be formulated in another way than that used by Birchenall and Mehl. The method is that of chemical rate theory and has been used by Eyring and his coworkers8,9 as well as by Eyring and Zwolinskilo in a discussion to Birchenall and Mehl's paper. As yet the method has not been applied to substitu-tional solid solutions. On the basis of their assumptions, Eyring and Zwolinski derived a relation between the diffusion coefficient and activity that is identical with that of Dehlinger and Darken but which does not correct for the variation of the diffusion coefficient with concentration as well as does the relation derived by Birchenall and Mehl. It was thought that the theory of diffusion would be more complete if the inconsistency between the two analyses could be rationalized and if diffusion in substitu-tional alloys were analyzed on the basis of the concepts of the chemical rate theory. Chemical Rate Theory According to the theory of absolute reaction ratess the reaction +..... +X, Eq I is viewed as taking place in two steps. First the reactants A1, A², . . . A; combine to form an activated complex M with which they are in equilibrium: A1 + A1+ . . . + A=M. Eq 2 Second the activated complex decomposes to give the products XI, XZ, . . . Xi: M?X, + X²+ . . . +Xi Eq g It has been showns that the number of activated complexes decomposing per unit volume per unit time is given by the expressiont kT -h CM † The transmission coefficient has been taken as unity.

Jan 1, 1949

By H. N. Treaftis, J. W. Cahn

THE previous determinations of the solvus of tin in solid lead disagree with one another by as much as 40°C or almost 10 at. pct. Even determinations that appear to be careful differ considerably in both the solubility and its temperature coefficient. Recent kinetic workl -3 on the rate of precipitation of tin from lead-tin alloys and thermodynamic work4 on the heat of solution of tin in lead have given some insight into the time necessary to reach equilibrium in this system. As this time is longer than that used in almost all previous determinations of the solvus, these determinations are questionable. Since the interpretation of recent kinetic results requires accurate values of the equilibrium solubility the present work was undertaken. DISCUSSION OF PREVIOUS RESULTS The methods used in previous studies may be placed into three classes: 1) Several alloys covering a range of compositions are allowed to reach "equilibrium" at a certain temperature.5-7 Some property, such as the X-ray lattice parameter of the lead-rich phase or the re- sistivity of the alloy, is then measured as a function of composition. The solubility limit for that temperature is taken to be that composition at which a discontinuity in the property occurs. However, the recent kinetic work has shown that tin precipitates in two stages. The first stage is rapid but leaves the lead still supersaturated. The second stage is very slow, and it seems from the equilibration times quoted by the investigators of the solvus that the end of the first stage of precipitation was usually mistaken for equilibrium. This is especially true at temperatures below 100°C where the first reaction is still quite rapid (from minutes to months), but where the second stage is so slow that very long holding times are required to reach equilibrium. Alternatively micrographic work8 on several alloys of different compositions seems to have given good results if done carefully. 2) The beginning of precipitation in a homogenized alloy is measured as it cools slowly8-10. Since reactions in solids undercool easily, such determinations will always give too low a temperature for the solvus. 3) Some property of an alloy is measured as a function of temperature while the alloy is above the solvus.5,9,11 The range of temperature can usually be extended slightly into the two phase region. Then the alloy is precipitated at a much lower temperature and slowly reheated. The solvus is taken to be the lowest temperature where the property of the reheated alloy is equal to that previously determined for the homogeneous alloy. Usually one also expects a discontinuity at the solvus in the temperature variation of the property for the reheated alloy. The difficulty in this method is the sluggishness of the dissolution process, and this method may give too high a solvus temperature. EXPERIMENTAL The phase boundary or solvus temperature was determined by a modification of method 3 for a series of chemically analyzed high-purity alloys, ranging from 5.1 to 26.4 at. pct Sn. The resistance, as a function of temperature, of a sample of homogenized alloy (which could easily be undercooled) was compared with the equilibrium resistance which that alloy sample attained after precipitation at room temperature followed by long isothermal anneals at various temperatures. Before each anneal the sample was rehomogenized and reprecipitated. The solvus temperature could be located to within 1°C as the intersection of the resistance vs temperature curves for the homogenized and equilibrium alloys. No attempt was made to locate the phase boundary more accurately since the limiting factor was the precision with which the alloys could be analyzed. This precision was ±0.1 wt pct Sn and corresponds to an error of 1 deg in temperature. This use of isothermal anneals differs from some of the previous investigations in which method 3 was used with baths of slowly rising temperatures. It was found early in the investigation that solvus temperatures tended to be high if the latter method was used even at extremely slow heating rates. For example a

Jan 1, 1961

H. H. Kellogg (Columbia University)—The accurate measurements of the equilibrium gas ratios for the reaction: Pb(1) + H2S = PbS(c) + H2 [I] reported in this paper are a distinct contribution to the literature, and the authors are to be congratulated. I wish to comment, however, on the correlation of the data which is presented. The authors show a straight line correlation of log H2S/H2 vs 1/T, Fig. 1, and are satisfied with this for calculation of ?Fo even when extrapolated to low temperature (427 °C). Heat capacity data for the constituents of this reaction are available (at least to 900°K), however, and ACP for reaction [I] is finite and positive in the temperature range studied. Simplification of the heat capacity equations yields: ?CP= 2.71 + 1.65 x 10-3T (298°-900°K) This positive value of ?CP should result in a small but noticeable curvature of a plot of log K vs 1/T. That the experimental data fail to show such a curvature may be traced to another oversimplification of the author's treatment of their data. They assume that the activity of liquid lead is unity for all temperatures, so that

Jan 1, 1961

By Paul R. Dingess, Edward H. Hare, Douglas C. Brockie

Mining in the Tri-State district of Missouri, Kansas, and Oklahoma has been nearly continuous from about 1848 until the present day, although the major activity was from about 1880 to 1955. The district, which has produced over $2 billion in zinc and lead concentrates, ranks as one of the greatest mining districts in the world. Unlike other Mississippi Valleytype deposits in the United States, which occur in Cambrian and Ordovician limestones and dolomites, the Tri-State district ores occur in Mississippian limestones containing abundant chert. Zinc is 5 to 6 times more abundant than lead. In the Picher Field, the principal sub-district which has accounted for 61 percent of the total district production, most of the ore has been mined from the single horizon, M bed. Most ore bodies, other than those of the "Sheet Ground" or blanket-type, are in large, essentially flat-lying breccia zones and have a definite mineral zonal pattern. An irregular, generally elongated central dolomitic core is surrounded progressively outward by the main ore run, the jasperoid zone, the muddy or shaly and bouldery zone, the sparry calcite limestone zone, and the fossiliferous, dominantly crinoidal, limestone zone. Some of the zones may be absent or nearly so and may overlap to some extent with an adjacent zone. Although the district has been studied by many authors, much controversy still exists about such items as genesis, paragenesis, and time of emplacement. These subjects are discussed in the paper.

Jan 1, 1968

By H. E. Cline, T. H. Alden

A study zvas made of rate-sensitive plastic deformation and superplasticity in alloys of lead and tin. These alloys (lead, PO-19 pct Sn, Sn-38 pct Pb, Sn-2 pct Pb, tin) were extruded, aged at room temperature, or melted and resolidified to produce a variety of ~nicrostrnctures. Flow stress us strain rate data were obtained frorn tension tests for strain rates between 10-6 and 1 min-1. The curve log o .us log £ was S-shaped jor fine-grained materials and approxinzately linear for coarse-grained nzaterials. At constant grain size, the behavior was relatively insensitive to conposition. High rate sensitivity (d log o/d log k) and superplasticity occurred at intermediate strain rates in fine-grained materials and are believed to be associated with a transition with strain rate in the mode of plastic flow. This transition was shifted to higher strain rates with increasing temperataire or decrensing grain size. The high rate rneclzanisrn is presunzed to be slip, while rnetallographic evidence sug-gests that the low rate lnechanism is pain boundary sliding. PEARSON' discovered that extruded eutectic alloys of Pb-Sn and Bi-Sn could be elongated as much as 2000 pct in tension. The ability for stretching decreased with aging time or annealing to increase the grain size. At high strain rates, or if the material was in the cast condition, normal ductility was observed. Following deformation of the extruded Pb-Sn eutectic at low rates, Pearson observed an equiaxed granular structure on an initially flat surface, while rapid straining produced elongated grains. He attributed the large deformation in the extruded alloys to the persistence of extremely small grains to a temperature sufficiently high for inter granular flow. Avery and backofen2 measured the strain rate sensitivity of the flow stress, m = d In old In 6, in the Pb-Sn eutectic and established a correlation between m and the tensile elongation. In the extruded eutectic alloy the strain rate sensitivity was 0.1 to 0.2 at rapid rates and the elongation was small, while at low rates m increased to 0.4 to 0.6 and superplastic elongation was observed. They also noted a grain size effect. In the case of the cast Pb-Sn eutectic the strain rate sensitivity remained at 0.1 over the range of strain rates of their experiment (3 x 10"3 to 2 min-I). These authors suggested that diffusional (Nabarro-Herring) creep was the mechanism by which deformation occurred at low strain rates, while climb-controlled creep occurred at high rates. Two predictions of this model are that, at low strain rates, the strain rate sensitivity approaches 1, i.e., Newtonian viscosity, and that the strain rate at constant stress varies as D/L2, where D is the coefficient of self-diffusion and L the grain size. More recently, a mechanical and microstructural investigation of the dilute superplastic alloy, Sn-5 pct Bi, has been done.3 The results show that the high strain rate sensitivity is associated with a transition with strain rate of the mechanism of plastic flow. At low strain rates, grain boundary sliding and its associated accommodation processes were evident, while at high strain rates quasi-uniform slip was concluded to be the dominant deformation process. The following experiments were performed to extend our knowledge of the phenomena of superplasticity to a larger range of strain rates, compositions, temperatures, and microstructures in the Pb-Sn alloy system. The question of why a cast structure does not exhibit viscous behavior although it appears to have a fine microstructure2 was investigated.

Jan 1, 1968

By G. Caetani

I. INTRODUCTION. WE owe to the courtesy of Mr. R. M. Raymond, Manager of the El Oro Mining & Railway Co., Ltd., the permission of publishing in this paper the results of a series of experiments and tests made in view of determining the economical limit to which the fine grinding of the ore by tube-mills could be carried on. For the sake of clearness, the following definitions are given of certain terms used in this paper, as well as of the units and screens in the experiments. Slime : In a general way " slime" is that mill-product, of which from 90 to 95 per cent, will pass a 200-mesh screen (0.067 mm. aperture), and which is treated as one class of material in the El Oro cyanide-plants. As a screen-product, slime constitutes all material that *ill pass a 200-mesh, screen. In sizing, the following products are distinguished:- Coarse Sand : That material remaining on a 100-mesh (0.111 mm. aperture) screen. Fine Sand : That passing through. 100-mesh and remaining on a 200-mesh (0.067 mm. aperture) screen. Slime: That passing through 200-mesh. Fines, which pass through 200-mesh and settle in 30 seconds, and silt, which does not settle in 1 minute. Sand-index : The number proportional to its total fineness considered from the economical point of view, as explained on page 93. Absolute extraction : The percentage of values actually brought into solution. Actual extraction: The percentage of values actually brought to the ziuc-boxes. Units : Dollars, U. S. Currency; pounds; and short tons (2,000 lb.). Gold is valued at $20.67, and silver at $0.50 per ounce. Screens : In the sizing-tests the screens used were:¬ Mesh (per 1 in.), . 24 30 40 60 80 100 150 200 250 Aperture (mm.), . 0.740 0.515 0.424 0.250 0.159 0.111 0.090 0.067 0.058 Strengths of solution : Strengths are expressed in the percent- . age of KCN contained, though the sodium cyanide, which is

Jan 1, 1906

By H. C. Fiedler

Heats of high purity iron containing 3.1 pct Si and be -tween 0.0003 and 0.0295 pct N were prepared by vacuum melting ad then pouring while in a nitrogen atmosphere with the pressure between 0 and 90 psi. Strip from a heat with 0.0184 pct N underwent complete secondary recrystallization during the final anneal. Heats with less nitrogen had too few Si3N4 particles to restrain normal grain growth, and the heat with higher nitrogen had too many particles to allow complete secondary recrystallization. In the hot-rolled structure, Si3N4 precipitates only at the grain boundaries, with the consequence that annealing after hot-rolling diminishes the ability to subsequently undergo secondary recrystallization. In contrast to this behavior, ALNprecipitates uniformly in the hot-rolled structure. Under 1 atm of nitrogen, Si3N, in 3.1 pct Si-Fe dissociates between 900" and 950°C; the solubility of nitrogen increases from 0.0010 pct at 900" to 0.0030 pct at 1200°C. The solubility of nitrogen in Si-Fe has been the subject of many investigations. Corney and Turkdogan1 heated a 2.83 pct Si alloy in nitrogen and found the solubility, under 1 atrn of nitrogen, to be 0.0019 pct at 900°C. They claimed that Si3N4 did not form in the alloy above 705°C in 1 atrn of nitrogen. Fryxell et al.2 heated samples of 3.25 pct Si-Fe containing 0.0025 pct N over a range of temperatures and then analyzed for total nitrogen by vacuum fusion and for nitrogen in solution by a modified Kjeldahl technique. At 900°C, they reported the solubility of nitrogen in equilibrium with Si3N4 to be 0.0011 pct. pearce9 found the solubility of nitrogen at 900°C under 0.95 atrn of nitrogen to be 0.0017 pct in a 3.06 pct Si alloy. He reported that Si3N4 does not form above 770°C in 1 atrn of nitrogen. Although internal friction measurements have given somewhat higher values for the solubility,4-6 if the solubility of nitrogen is as low as has been reported by most investigators, and if Si3N4 is stable up to at least 945°C at 1 atrn pressure of nitrogen as reported by Seybolt,7 a small amount of nitrogen in properly processed Si-Fe should be effective in promoting secondary recrystallization. The requirement is that in the final heat treatment there be enough small, well-dispersed particles of Si3N4 to restrain normal grain growth. Fast8 has obtained secondary recrystallization by nitriding high-purity 3 pct Si-Fe after hot-rolling to a thickness of 0.118 in., followed by processing to 0.012 in., and annealing. A large amount of nitrogen, 0.076 pct. was introduced during the nitriding heat treatment, but he has since reported9 that "a few hundredths of a percent" is sufficient. Small amounts of aluminum10 or vanadium" nitride are capable of promoting secondary recrystallization. Heats containing as little as 0.010 pct A1 or 0.042 pct V and from 0.006 to 0.009 pct N underwent complete secondary recrystallization at final gage, whereas heats with lesser amounts of aluminum or vanadium did not.l2 To be reported is the behavior of nitrogen in high-purity 3.1 pct Si-Fe, and the relation of this behavior to the ability to undergo secondary recrystallization. PROCEDURE Ingots weighing 1 lb were made by vacuum melting high-purity electrolytic iron (A104, Glidden Co.) and high-purity silicon (Monsanto Co.). The latter was used in preference to ferrosilicon to insure a low aluminum content. The design of the melting furnace permitted pouring with the furnace atmosphere either below or above atmospheric pressure. Accordingly, at the completion of melting, nitrogen was admitted to the desired pressure and the heat then immediately poured. The ingots were sound, with no indication of porosity. In Table I are listed the heats investigated, the nitrogen pressure at pour, and the nitrogen and oxygen contents as determined by vacuum fusion with a platinum bath at 1850°C, a procedure which insures measurement of the total nitrogen.13 In addition, all heats contained 3.1 pct Si and not more than 0.002 pct C, 0.003 pct S or 0.005 pct Al. It was subsequently found that the quantity of nitrogen contained in the heats in Table I does not necessarily represent that obtained under equilibrium conditions. For example, the ingot poured immediately after 1 atrn of nitrogen was admitted to the chamber contained 0.0093 pct N, whereas an ingot poured 3 min after the nitrogen was admitted contained 0.021 pct N and another poured after a 6-min delay contained 0.029 pct N. While some bleeding of the hot top occurred in the latter instance, the ingot when examined in cross section appeared sound. The ingots were heated to 1325°C in hydrogen and rapidly rolled to 0.080 in. in 3 passes. The roll speed of the final pass was reduced so as to increase the quenching effect of the rolls. The hot-rolled pieces were processed both as-hot-rolled and after heating for 3 min at 900°C in hydrogen. After cold-rolling to 0.026 in., the strips were heated for 2 min at 900°C in hydrogen, then cold-rolled to the final gage of 0.012 in. The loss of nitrogen in going from the ingot to cold-rolled strip was no more than 10 pct. The final heat treatment, which was for the purpose of develop-

Jan 1, 1970

By Russell A. Carter

Seven years of rising silver prices have effectively revived an historic Idaho mining district and given it a new lease on life. Initial production earlier last year from the DeLamar open-pit silver mine in southwestern Idaho ushered in a new era of mineral production in a region that has weathered boom-and-bust cycles reaching back the better part of a century.

Jan 1, 1978

By Ed Van Eeckhout

As part of a U.S. Bureau of Mines-sponsored project on the utilization of "stiff" backfill to minimize potential rock burst hazards, a finite element study was undertaken to predict stresses and displacements around a stope mined up from the 5400 level of the Sunshine mine, Kellogg, Idaho. This stope was to be backfilled using a high-modulus fill. In preparation for that configuration, certain instrumentation was installed near the 5400 level to monitor stress changes. Due to untenable economics, only 2 cuts of the stope were ever made. This paper presents the results of the instrument readings taken during the first cut and compares them with the numerical predictions, as well as presents the modeling results of closure and fill stresses in the stope if it had been mined.

Jan 1, 1984

By D. Turnbull, J. H. Hollomon, J. C. Fisher

UNDERSTANDING of the diffusion problem has recently been furthered by the analysis of Birchenall and Mehl.1 They pursued the problem of the variation of the diffusion coefficient with composition for non-ideal solid solutions. Their analysis follows the tradition of Wagner,2 Jost,3 Dehlinger,4 and Darken,' who assumed the net flux of dif¬fusing material to be proportional to the gradient of a quantity related to free energy. The basic assumption in Birchenall and Mehl's formulation of the problem is that the net flux of diffusing material is proportional to a thermodynamic activity gradient. To estimate the applicability of the derived relations, they corrected the diffusion coefficients of carbon in austenite by utilizing Smith's' activity data for carbon, and the diffusion coefficients for zinc in copper with activity data computed from the vapor pressure measurements of Hargreaves.7 The corrected coefficients for carbon were virtually independent of carbon concentration. For the diffusion of zinc in copper a moderate variation of diffusion coefficient with concentration remained after the correction. The problem of diffusion can be formulated in another way than that used by Birchenall and Mehl. The method is that of chemical rate theory and has been used by Eyring and his coworkers8,9 as well as by Eyring and Zwolinski10 in a discussion to Birchenall and Mehl's paper. As yet the method has not been applied to substitutional solid solutions. On the basis of their assumptions, Eyring and Zwolinski derived a relation between the diffusion coefficient and activity that is identical with that of Dehlinger and Darken but which does not correct for the variation of the diffusion coefficient with concentration as well as does the relation derived by Birchenall and Mehl. It was thought that the theory of diffusion would be more complete if the inconsistency between the two analyses could be rationalized and if diffusion in substitutional alloys were analyzed on the basis of the concepts of the chemical rate theory. CHEMICAL RATE THEORY According to the theory of absolute reaction rates8 the reaction [A,+A2+ ... +.A;->X,+X2 +...+X; EqI] is viewed as taking place in two steps. First the reactants A1, A2, . . . A[i] combine to form an activated complex M with which they are in equilibrium; [A, + A2 + .. . + Ai = M. Eq 2] Second the activated complex decomposes to give the products X1, X2. . .. X[j]; [M->X1+X2+ ... +.X;. Eq3] It has been shown8 that the number of activated complexes decomposing per unit volume per unit time is given by the expression† [kT]

Jan 1, 1948

By D. Harrington

ONE of the main functions of the United States Bureau of Mines is to obtain and disseminate information that will promote safety in and around mines, and the health and safety of employees engaged in mining. Serious health and safety conditions arising out' of contamination of air in metal mines by dust, fumes from explosives and fires, and absorption of oxygen by timber and other causes, led the Bureau of Mines to cooperate with the United States Public Health Service in the study of dust occurrence and ventilation in metal mines in various parts of the country. Dr. A. J. Lanza, of the U. S. Public Health Service, and Edwin Higgins, mining engineer of the U. S. Bureau of Mines, in 1915, made a detailed study in the mines around Joplin, Mo., their reports1 are now available. In 1916, 1917, and 1918, a similar study was made in the Butte, Mont., region by Doctor Lanza and D. Harrington, mining engineer of the Bureau of Mines; the reports of this investigation will be available soon. In 1919, the study was continued in some of the Arizona mines by D. Harrington, of the Bureau of Mines, and G. E. McElroy and Dr. R. A. Koronski, of the U. S. Public Health Service, the underground work being completed in June, 1920; these reports are now being prepared for publication. In the spring of 1920, the scope of the work was extended, with D. Harrington in charge as supervising mining engineer, and short studies made in the mines of the Coeur d' Alenes in Idaho and around Oatman, Ariz. It is hoped soon to extend the work into mines of California, Nevada, Colorado, Michigan, and Minnesota, and ultimately to other states should the mining companies be willing to cooperate.

Jan 2, 1921

By Charles H. Fulton

IT is assumed that the word "college" for the present purpose signifies technical school or technical department of a college or university. About ten or fifteen years ago, and more recently in some instances the contact between the technical school and the industry, as represented by the operating companies, was very limited. The school made no effort to place its graduates in the industry and the graduate's first position was obtained by his own or his friends' efforts; the friend often was a professor. The industries, or the operating companies, seemingly had little interest in the training of the technical graduates they employed or in seeking to discover their personal characteristics and fitness for the work. In the public mind there was little relation between technical training and industry. Such training was in the field of education; industry was in the field of business; and the interrelationship was not a matter of common knowledge or concern.

Jan 1, 1929

By E. S. Machlin, W. R. Yankee

IN a previous study1 of the effect of heating com-mercial titanium in air on its subsequent friction coefficient against other metals, as well as itself, it was found that the friction coefficient markedly decreased from a value of about 0.7 to about 0.3. A tentative explanation was given that surfaces normally produced at room temperature are not contaminated sufficiently to prevent seizing or welding of the titanium to the softer mating metals. The latter tend to cleanse themselves during rubbing over the harder titanium. It was thought that the lack of a contaminant protective film on the titanium was due to the high solubility of titanium for oxygen and nitrogen and hence an inability to form a contaminant oxide or nitride. This explanation requires the ratio of the surface absorption rate to the diffusion rate to become much lower at room temperature than it is at high temperatures. In order to check the phenomenon further, commercial titanium specimens were nitrided or oxidized at 800°C for 20 hr in flows of prepurified N2 and 01, respectively, at about 1/2 in. H2O above atmospheric pressure. Friction runs were made in argon using a freshly cut copper hemisphere (cut in argon) on surfaces cut successively into the diffusion layers in the titanium (cut in argon) using the techniques described in a previous publication.' DPH values (100 gram load) were made as a function of depth into the diffusion layer using a Tukon tester. Also, micrographs were taken at separate cross sections to indicate the diffusion layers. The results obtained are presented in Figs. 1 and 2, which show the "static" friction coefficient vs hardness for the nitrided and oxidized specimens, respectively. A separate measurement of the friction coefficient of clean copper vs iodide titanium also was made. From results reported in the literature' giving the oxygen and nitrogen contents as functions of the hardness, cross plots were made showing the friction coefficients as functions of the amount of interstitial solute. These plots are given in Figs. 3 and 4. From micrographs of the diffusion layers and the phase diagrams, it was deduced that the data in Figs. l through 4 correspond to the single phase a region. The points observed on the compound regions have been excluded from the figures. It is apparent that nitrogen or oxygen in solution in the a titanium markedly affects the friction coefficient against a softer mating metal. Discussion of Results These results are extremely interesting from both a practical and theoretical viewpoint. The theoretical implications will be discussed first. According to Bowden, the friction coefficient should be given to a good approximation by the relation where a is the fraction of contact area that has welded, a is the shear strength of weaker component, and H is the hardness of softer component. Using this relation alone, it is difficult to understand the results because none of the terms should be affected by a variation in the oxygen or nitrogen content of the harder and stronger metal, titanium. Even if the ratio of S/H for titanium is used in Eq. 1, the ratio has been shown to be independent of oxy-gen or nitrogen content.' If a more rigorous equa-tion is used combining Eq. 1 and a result given pre-viously" for the case where welding is absent, then the relation obtained is µ = a S/H + (1-a) a W aß/H where a is constant and Waß is the work of adhesion between the two metals comprising the friction couple. This relation states that if a is less than 1/2 or so, variation in the work of adhesion Waß between copper and the titanium should affect the friction coefficient markedly. It is reasonable to expect that the work of adhesion will depend on the oxygen or nitrogen content of the titanium. Available data4 show that clean metals and oxides have much lower works of adhesion than the same metals against the

Jan 1, 1955

By R. W. Armstrong, D. H. Feisel

Self-diffusion in pure crystalline solids has been described through extension of the Cohen and Tum-hull volume -fluctuation model originally proposed for diffusion in simple liquids. It is shown, for a number of crystalline solids, that the self-diffusion coefficient, D, obeys the relationship where a is the lattice spacing, v the Debye frequency, Z' the lattice-volume fluctuation per atom required for a diffusion jump, and (?V/Vo) the relative increase in the lattice volume resulting from thermal expansion between O°K and the temperature under consideration. The calculated value of Z' is dependent upon the difiusion mechanism and the lattice geometry. ThE need for an increased understanding of mass-transport processes in crystalline solids has resulted in much research to determine rates of self-diffusion.' For several metals (e.g., copper, silver, and iron), the experimental values of the self-diffusion coefficient, D, have been determined over a large interval of temperature and the accuracy of D has been investigated through repeated experiments. Also, a number of empirical and theoretical diffusion studies have established a rational basis for understanding the D values for the different elements.2"6 The empirical diffusion analysis by Sherby and simnad6 supplied the main stimulus for the present study. Sherby and Simnad, reviewing the self-diffusion data for a substantial number of pure crystalline solids, suggested that sufficient data were available to establish with some certainty the apparent intrinsic material properties which influence D. Without explicit regard for any mechanism of diffusion, these investigators obtained an empirical relationship for D which correlated the self- diffusion coefficient for each element with the melting temperature, crystal structure, and valence of the particular element. Their analysis is only unsatisfactory in that the effect on D of crystal structure is not very clear and the valence to be assigned to an element is not always straightforward. The present study is an attempt, from a very different viewpoint from that of Sherby and Simnad, to establish a basis for understanding the self-diffusion coefficients for crystalline solids. This analysis was undertaken for the purpose of developing a general expression for D which would explicitly depend on the mechanism of diffusion. The main result of the study is that diffusion in crystalline solids may be described in terms of a volume-fluctuation model which was originally proposed by Cohen and Turnbull7 to describe diffusion in simple liquids. The model appears to be useful for predicting self-diffusion coefficients in crystals. The following sections describe the volume-fluctuation model for diffusion, the application of this model to crystals, and the resultant agreement with experimental data. 1) THE VOLUME-FLUCTUATION MODEL FOR DIFFUSION Cohen and Turnbull7'8 developed their model for liquid self-diffusivity for the purpose of describing certain properties of liquids, glasses, and the liquid-glass transition. A hard-sphere model for the liquid structure is used. In this model, the size of a spherical molecule or atom is fixed for all temperatures by the interatomic spacing at the absolute zero of temperature. At any temperature above O°K, the atom is viewed as being contained within a larger spherical cage defined by the interatomic spacing of the atoms at that temperature. A random distribution of varying cage sizes is assumed to exist in the liquid. An individual diffusion jump occurs when the free volume of an atom (the volume of the cage containing the atom minus the volume of the atom) is large enough for the atom to jump out of its cage. With this physical picture of diffusion in liquids, Cohen and Turnbull derive the following equation for self-diffusivity: D=Doe-yv*/vf [1] where Do is the product of three factors which are the diffusion-path geometry, the diffusion-jump distance, and the velocity of the diffusing atom, v*

Jan 1, 1964

By AIME AIME

WINFIELD SCOTT MORRIS, known from Coast to Coast within the petroleum industry as "Buck" Morris, is and has been for several years an outstanding man in the Petroleum Division of the A.IM.E., so it is most natural to have him as the Chairman of the Division. "Buck" has been such a vociferous promoter of everything TEXAS that most of his friends believe him to be a "Longhorn" by birth-but the records show he was born at Wilmington, N. C., on July 29, 1901. He worked his way through college and graduated from the University of North Carolina in 1924 with a B.S., followed by a C.E. in 1927. His graduation thesis was entitled "De¬sign of a Modern Oil Refinery."

Jan 1, 1944

By C. J. Fleisch, C. P. Clingerman

THE recent installation of a combination dust catcher, gas washer and precipitator at Carrie blast furnaces of the Homestead Steel Works has given very satisfactory results. The following description of the gas-cleaning installation is based on actual operating experience. When Carrie blast furnace No. 3 was rebuilt the decision was made to fine-clean all the gas produced by the furnace, because the management wanted fine-cleaned gas for fuel in the stoves and boilers. In order to keep the installation cost as low as possible, the gas-cleaning system was streamlined. All by-pass lines and goggle valves for bypass lines were eliminated from the system. A radical departure from the use of 8-in. tubes in the Cottrell-type precipitators was made by using 12-in. diameter tubes in a single compartment, the single compartment being divided into two units by a single partition wall in the top header. THE FURNACE PROPER A few of the characteristic points and dimensions of the furnace proper are: [Hearth diameter 26 ft. o in. Bosh diameter 29 ft. 1 3/4 in. Stock-line diameter 20 ft. o in. Large-bell diameter 114 ft. 8 in. Small-bell diameter 6 ft. 6 in. Height of furnace from center of iron notch to bottom of large bell, closed 94 ft. 4 in. Height of furnace from center of iron notch to main platform 105 ft. o in.] The furnace top is equipped with a McKee revolving distributor, the operation of which is electrically interlocked with the skips, bell hoists, and coke-weighing and charging apparatus through a Freyn automatic charging control. The gas leaves the furnace first through four offtakes, 5 ft. g in. in diameter, then through uptakes that are approximately 85 ft. high, which feed into a single down-comer that is 9 ft. in diameter. DUST CATCHER The primary dust catcher installed (Fig. I) may be described as a single-cone type. The inlet pipe at the top of the dust catcher is g ft. in diameter; it is flared to a conical shape as it extends down inside the dust-catcher shell, which is 35 ft. in diameter, 37 ft. high on the straight side, and has a conical top and bottom. The slope of the bottom is 50° with the horizontal. The cone-shaped pipe inside the dust-catcher shell is 42 ft. high and is 19 ft. 7 in. in diameter at its bottom lip where it releases the gas in-

Jan 1, 1943

By C.P. Clingerman

The recent iastallation of a combination dust catcher, gas washer and precipitator at Carrie blast furnaces of the Homestead Steel Works has given very satisfactory results. The following description of the gas-cleaning installation is based on actual operating experience. When Carrie blast furnace No. 3 was rebuilt the decision was made to fine-clean all the gas produced by the furnace, because the management wanted fine-cleaned gas for fuel in the stoves and boilers. In order to keep the installation cost as low as possible, the gas-cleaning system was streamlined. All by-pass lines and goggle valves for bypass lines were eliminated from the system. A radical departure from the use of 8-in. tubes in the Cottrell-type precipitators was made by using 12-in. diameter tubes in a single compartment, the single compartment being divided into two units by a single partition wall in the top header. The Furnace Proper A few of the characteristic points and dimensions of the furnace proper are: Hearth diameter.............. 26 ft. o in. Bosh diameter............... 29 ft. 1 3/4 in. Stock-line diameter........... 20 ft. o in. Large-bell diameter........... 14 ft. 8 in. Small-bell diameter........... 6 ft. 6 in. Height of furnace from center of iron notch to bottom of large bell, closed............ 94 ft. 4 in. Height of furnace from center of iron notch to main platform ...................... 105 ft. o in. The furnace top is equipped with a MC-Kee revolving distributor, the operation of which is electrically interlocked with the skips, bell hoists, and coke-weighing and charging apparatus through a Freyn automatic charging control. The gas leaves the furnace first through four offtakes, 5 ft. 9 in. in diameter, then through uptakes that, are approximately 85 ft. high, which feed into a single down-comer that is 9 ft. in diameter. Dust Catcher The primary dust catcher installed (Fig. I) may be described as a single-cone type. The inlet pipe at the top of the dust catchei is 9 ft. in diameter; it is flared to a conical shape as it extends down inside the dust-catcher shell, which is 35 ft. in diameter, 37 ft. high on the straight side, and has a conical top and bottom. The slope of the bottom is so0 with the horizontal. The cone-shaped pipe inside the dust-catcher shell is 42 ft. high and is 19 ft. 7 in. in diameter at its bottom lip where it releases the gas inside the dust catcher. The ratio of the area of the inside cone at its bottom lip to the

Jan 1, 1943

By C. P. Clingerman

The recent iastallation of a combination dust catcher, gas washer and precipitator at Carrie blast furnaces of the Homestead Steel Works has given very satisfactory results. The following description of the gas-cleaning installation is based on actual operating experience. When Carrie blast furnace No. 3 was rebuilt the decision was made to fine-clean all the gas produced by the furnace, because the management wanted fine-cleaned gas for fuel in the stoves and boilers. In order to keep the installation cost as low as possible, the gas-cleaning system was streamlined. All by-pass lines and goggle valves for bypass lines were eliminated from the system. A radical departure from the use of 8-in. tubes in the Cottrell-type precipitators was made by using 12-in. diameter tubes in a single compartment, the single compartment being divided into two units by a single partition wall in the top header. The Furnace Proper A few of the characteristic points and dimensions of the furnace proper are: Hearth diameter.............. 26 ft. o in. Bosh diameter............... 29 ft. 1 3/4 in. Stock-line diameter........... 20 ft. o in. Large-bell diameter........... 14 ft. 8 in. Small-bell diameter........... 6 ft. 6 in. Height of furnace from center of iron notch to bottom of large bell, closed............ 94 ft. 4 in. Height of furnace from center of iron notch to main platform ...................... 105 ft. o in. The furnace top is equipped with a MC-Kee revolving distributor, the operation of which is electrically interlocked with the skips, bell hoists, and coke-weighing and charging apparatus through a Freyn automatic charging control. The gas leaves the furnace first through four offtakes, 5 ft. 9 in. in diameter, then through uptakes that, are approximately 85 ft. high, which feed into a single down-comer that is 9 ft. in diameter. Dust Catcher The primary dust catcher installed (Fig. I) may be described as a single-cone type. The inlet pipe at the top of the dust catchei is 9 ft. in diameter; it is flared to a conical shape as it extends down inside the dust-catcher shell, which is 35 ft. in diameter, 37 ft. high on the straight side, and has a conical top and bottom. The slope of the bottom is so0 with the horizontal. The cone-shaped pipe inside the dust-catcher shell is 42 ft. high and is 19 ft. 7 in. in diameter at its bottom lip where it releases the gas inside the dust catcher. The ratio of the area of the inside cone at its bottom lip to the

Jan 1, 1943

By Hermann Schmalzried, Carl Wagner

UPON heating a metal oxide or sulfide in H2, first only oxygen or sulfur is removed from the surface. Thus the metal/nonmetal ratio in the oxide or sulfide increases and the thermodynamic activity of the metal increases accordingly. For the formation of metallic nuclei, a certain super saturation is necessary, i.e., the activity of the metal must become greater than unity. Once nuclei of the metal have been formed, the supersaturation is supposed to decrease. Even under steady-state conditions of a reduction process, however, the activity of the metal inside an oxide or sulfide phase must be greater than unity in order to have a driving force for the individual steps of the reduction process. As an example, consider the reduction of Ag2S with a high mobility of cations and electrons. As shown schematically in Fig. 1, the reduction process involves the following steps:' 1) sulfur removal along the entire Ag2S surface in form of H2S, 2) migration of Ag' ions and electrons from the Ag2S surface to nuclei of metallic silver, 3) transfer of Ag+ ions and electrons from the Ag2S phase to the metal. For a finite rate of step 3, the activity of silver in Ag2S next to the Ag2S-Ag interface must be greater than unity. Moreover, for a finite rate of step 2, the activity of silver at the gas-Ag2S interface must be still somewhat greater. Theoretical considerations lead to the tentative conclusion that at least under steady-state conditions the supersaturation will be rather low.' To test this conclusion, the average activity aAg of silver in a Ag2S tablet about 2 mm thick with a diameter of 5 mm was followed as a function of time by measuring the electromotive force E of the cell Pt I Ag | Agl I Ag2S I Pt where AgI is used as a solid electrolyte in which only Ag+ ions are mobile. The activity aAg is calculated as aAg=exp(-EF/RT) Since the diffusion coefficient for transport of silver in Ag2S is very high (- 3 . l0-2 sq cm per sec),3 the average activity aAg is representative for both the bulk and the surface of the Ag2S tablet. Experiments were conducted at about 400°C. The cell was surrounded by an aluminum block in order to secure a uniform temperature and to eliminate thermoelectric effects. With the help of a potentiometer, first a potential of 0.16 v was applied to the above cell in argon in order to obtain a well defined initial state with a Ag/S ratio close to 2.000.~ Then the cell was disconnected from the potentiometer and a gentle stream of H2 was passed along the Ag2S surface. In view of the removal of sulfur in form of H2S, the electromotive force E decreased within 20 to 30 min to zero corresponding to a Ag/S ratio of 2.003 and became negative, indicating a value of aAg> 1. A representative plot electromotive force E vs time is shown in Fig. 2. The minimum of the electromotive force characteristic of the onset of

Jan 1, 1963

By M. E. Hassan, J. C. Calhoun, R. F. Nielson

An apparatus was constructed for the measurement of inter-facial tensions over a range of temperatures and pressures. This apparatus utilized the pendent drop method, and resembles in construction similar apparatus recently described in the literature and in use in some petroleum research laboratories. The interfacial tensions of benzene, propane, n-pentane, n-hexane. n-octane. and iso-octane against water were measured at temperatures ranging from 26" to 82" C and at pressures ranging from 1 to 204 atm. Values of interfacial tensions for the henzene-water system and their variations with temperature and pressure are generally in good agreement with value? of previous investigations. The data in all cases showed a slight decrease of interfacial tension with pressure at constant temperature in the range studied. The effect of pressure became less as the pressure was increased, with an indication of a reversal of the effect at higher pressures. There was a decrease of interfacial tension with temperature at constant pressure in all cases, as would normally be expected. This rate of decrease became greater the higher the temperature. A general equation is presented for the interfacial tensions as a function of presPurp and temperature over the range studied, and the constants calculated for each system. A definite trend was found in the effect of molecular weight on the interfacial tension at a given temperature and pressure, for the homologous series from propane to n-octane. Data for n-decane from the literature fitted well into this trend. INTRODUCTION It has been recognized for many years that surface forces play an active part in the production history of an oil reservoir as well as in determining the amount of unrecoverable oil. The magnitudes of these forces are governed by the values of the interfacial tensions. These vary greatly with composition, pressure, and temperature. The effect of composition is greater than that of pressure and temperature over the ranges normally encountered. In fact, because of the variety of compounds present in a crude, no attempt has yet been made to correlate crude composition with its surface tension or with its interfacial tension against water. The amount of dissolved methane greatly affects the surface properties of an oil, and there are "surface-active" compounds in crudes which have a much greater effect on boundary tensions than do equal amounts of hydrocarbons. The purpose of the present work was partly to contribute data that would eventually be used in correlations applicable

Jan 1, 1953