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By E. Buehler, H. J. Levinstein

The temperature ranges in which the three inter-metallic phases in the Nb-Sn system form have been determined and the composition and structure of two of the three phases has been established. The kinetics of the formation of Nb3Sn in cored wire samples has been studied in the temperature range of 800° to 1050°C. From 800°to 950°C the rate of formation increases by four orders of magnitude. The rate-controlling step for the formation process in this temperature range appears to be the diffilsion of tin through NbSn. At higher temperatu~es a change occurs in the mechanism of the formation process such that up to a temperature of 1050°C the rate of formation of Nb3Sn does not increase above the rate observed at 950°C. For temperatures helow 950°C the current-carrying capacity of the wire increases with increased percent reaction reaching a maximum value when the formation process is 90 to 95 pct complete. The maximum current-carrying capacity obtainable in this temperature range is independent of the temperature. Above 950°C tlze current-carrying capacity obtainable in the wire decreases with increasing temperature of formation. A model is proposed which accounts for the ohserved behavior. RECENTLY, Buehler et a1.l reported the results of an investigation of the process variables which influence the superconducting properties of Nb3Sn-cored wire. These results indicated that at least four variables affect the properties of the manufactured wire. These include composition, particle size of the starting powder mix, temperature of heat treatment, and time of heat treatment. In order to understand completely the role of these variables, it is necessary to have an accurate knowledge of the phase equilibria in the Nb-Sn system. At the present time, phase-equilibrium diagrams for the Nb-Sn system have been published by a number of investigators.2-5 The diagrams differ as to the number of phases present, the composition of the phases, and the temperature range of stability of the phases. The present investigation was undertaken in order to resolve these differences. Since the investigation of Buehler et al. demon- strated that the length of time at the temperature of heat treatment affected the superconducting properties of Nb3Sn, it is apparent that it is necessary to understand the kinetics of the formation process as well as the equilibrium conditions before a complete understanding of the system is possible. As a result, the kinetics of formation of the various phases in the system were also studied in this investigation. EXPEFUMENTAL PROCEDURE Diffusion couples and sintered powdered compacts were employed in the phase-diagram investigation. The diffusion couples were made by filling 1/8-in.-ID monel-sheathed niobium tubes with tin. The monel sheath was employed to facilitate drawing.' The tubes were then drawn to a tin-core diameter of 32 mils. Samples approximately 3 in. long were then cut from the drawn composite. The tin was drilled out of the ends to a depth of 1/4 in. and niobium-wire plugs were inserted into the ends and peened over. The monel was removed by etching in concentrated nitric acid, after which the samples were sealed in evacuated quartz bulbs and heat-treated in a resistance-wound tube furnace. The samples were quenched into ice water upon removal from the furnace. The diffusion couple samples were examined metallographically employing a chemical etching solution consisting of 10 ml of saturated chromic acid per g of NaF. In addition, two anodizing solutions were used for phase-identification purposes. The first was the picklesimer7 solution; the second consisted of equal parts by volume of 30 pct H2O2 and concentrated NH4OH to which 1 g of NaF was added per 25 ml of solution. The anodizing conditions for the second solution were 2 v and 100 ma with a tin cathode. The powdered compacts were made by pressing previously mixed powders of 99.9 pct pure Sn and 99.6 pct pure Nb supplied by the United Mineral Co. into cylinders 3/8 in. in diameter by 1/2 in. long. The cylinders were then sealed in quartz tubes and heat-treated in the same manner as the diffusion couples. The samples were examined metallographically and by X-ray diffraction techniques. Since it was desirable to be able to correlate the kinetic data with current-carrying capacity, the type of specimen chosen for this part of the investigation had to be a compromise between the optimum system for studying kinetics and one which was suitable for making current-carrying capacity

Jan 1, 1964

By John W. Bell

In the introduction to an excellent pamphlet, John Gross' makes the following statements: Although marked progress has been made along mechanical lines, the theory and conception of underlying principles have not advanced so rapidly. This lack of advance in theory may be attributed to the unfortunate situation resulting from the controversy as to whether the Rittinger or Kick law is applicable to crushing. Many pages of the technical literature are burdened with theoretical discussions in favor of one or the other of these laws, which have tended to cloud rather than to clear the atmosphere. Realizing the situation, the Milling Committee of the American Institute of Mining and Metallurgical Engineers, through its secretary, E. A. Hersam, studied the milling industry and, because of the apparently hopeless lack of agreement in the Kick versus Rittinger dispute (5, 13, 14, 16, 18. 19. 21, 22, 23, 24, 30, 34). concluded that a foundation lor the theory of crushing was of primary importance. The numbers in the paragraph quoted refer to papers listed by Mr. Gross in his Bibliography on Crushing and Grinding.I One is obliged to infer that these papers show "hopeless lack of agreement in the Kick versus Rittinger dispute." No. 22 is a paper by Arthur 0. Gates2 and No. 23 is one by the writer.3 Employing the subject matter contained in papers Nos. 22 and 232,3 the writer will show that their authors formulated identical conclusions, based solely on experimental evidence. Exactly the same defect in the Stadler hypothesis was described in each of the two papers, although entirely different experimental methods were employed in uncovering it. Both of the authors, independently, formulated the conclusion that Rittinger's was a true hypothesis and Stadler's false. The evidence in a third paper4 will be employed to prove that Stadler's hypothesis, when examined experimentally, is worthless. Stadler's Hypothesis Worthless It is the writer's opinion that the evidence available in 1915 and the corroborating evidence in 1916 was amply sufficient to eliminate the need for any further consideration of Stadler's hypothesis. Certainly the evidence produced in 1918 dealt this hypothesis its coup de grace. It follows, therefore, that in the year 1918 there was only one credible hypothesis left—the Rittinger hypothesis. Gates' Opinion What information is available in Mr. Gates' paper?2 His conclusions are not consecutively summarized, none the less they are perfectly clear. On page 876, Gates says, and it is a very significant utterance: But my results show, among other things. that many more of Stadler's energy units are obtained per foot-pound-applied in coarse than in finc crushing. This suggests a doubt as to the correctness of his unit, since one would expect a foot-pound-applied to produce the same number of "energy units," whether the feed and resulting product were coarse or fine. When Rittinger's theory is applied, the number of mesh-tons (my unit of surface produced) is

Jan 1, 1943

By John W. Bell

In the introduction to an excellent pamphlet, John Gross' makes the following statements: Although marked progress has been made along mechanical lines, the theory and conception of underlying principles have not advanced so rapidly. This lack of advance in theory may be attributed to the unfortunate situation resulting from the controversy as to whether the Rittinger or Kick law is applicable to crushing. Many pages of the technical literature are burdened with theoretical discussions in favor of one or the other of these laws, which have tended to cloud rather than to clear the atmosphere. Realizing the situation, the Milling Committee of the American Institute of Mining and Metallurgical Engineers, through its secretary, E. A. Hersam, studied the milling industry and, because of the apparently hopeless lack of agreement in the Kick versus Rittinger dispute (5, 13, 14, 16, 18. 19. 21, 22, 23, 24, 30, 34). concluded that a foundation lor the theory of crushing was of primary importance. The numbers in the paragraph quoted refer to papers listed by Mr. Gross in his Bibliography on Crushing and Grinding.I One is obliged to infer that these papers show "hopeless lack of agreement in the Kick versus Rittinger dispute." No. 22 is a paper by Arthur 0. Gates2 and No. 23 is one by the writer.3 Employing the subject matter contained in papers Nos. 22 and 232,3 the writer will show that their authors formulated identical conclusions, based solely on experimental evidence. Exactly the same defect in the Stadler hypothesis was described in each of the two papers, although entirely different experimental methods were employed in uncovering it. Both of the authors, independently, formulated the conclusion that Rittinger's was a true hypothesis and Stadler's false. The evidence in a third paper4 will be employed to prove that Stadler's hypothesis, when examined experimentally, is worthless. Stadler's Hypothesis Worthless It is the writer's opinion that the evidence available in 1915 and the corroborating evidence in 1916 was amply sufficient to eliminate the need for any further consideration of Stadler's hypothesis. Certainly the evidence produced in 1918 dealt this hypothesis its coup de grace. It follows, therefore, that in the year 1918 there was only one credible hypothesis left—the Rittinger hypothesis. Gates' Opinion What information is available in Mr. Gates' paper?2 His conclusions are not consecutively summarized, none the less they are perfectly clear. On page 876, Gates says, and it is a very significant utterance: But my results show, among other things. that many more of Stadler's energy units are obtained per foot-pound-applied in coarse than in finc crushing. This suggests a doubt as to the correctness of his unit, since one would expect a foot-pound-applied to produce the same number of "energy units," whether the feed and resulting product were coarse or fine. When Rittinger's theory is applied, the number of mesh-tons (my unit of surface produced) is

Jan 1, 1943

By J. Campbell

Various models are discussed for the evaluation of the negative pressures which may occur in solidifying materials which exhibit various deformation modes: elastic-plastic, Bingham, viscous, or creep flow. The inadequacy of the previously proposed elastic-plastic solution for solidifying metals is revealed by comparison with the more reliable creep results which are given graphically for aluminum, copper, nickel, and iron. The maximum tensions experienced in the liquid phase of solidifying spheres ranging in size from large castings to submicron powders are in the range from —10' to —105 atm for these metals. THERE has been much recent interest in the negative pressures associated with the volume change on solidification and in the possibility of the occurrence of cavitation. Considering the freezing of a highly supercooled liquid, an attempt to evaluate the stresses in the liquid ahead of the rapidly moving solidification front has been made by Horvay1 on a microscale and by Glicksman2 on a macroscale. In a casting of a wide freezing range alloy, the pressure differential due to viscous flow of residual liquid through the pasty zone has been discussed by Piwonka and Flemings,3 In a previous publication4 the author has attempted to estimate the negative pressure occurring in the residual liquid of a spherical casting, employing an elastic-plastic model to describe the collapse of the solidified shell under the internal tension. An earlier model assuming a rigid shell was shown to be inaccurate by many orders of magnitude. The elastic-plastic model is critically reviewed here, and other models are developed which are thought to be more closely related to metals and other materials near their melting points. The spherical geometry (Fig. 1) is chosen because the highest shrinkage pressures would be developed, although the analyses are readily adaptable to cylindrical geometry. A parallel sided casting experiences little internal tension because of the relatively easy dishing inward of the sides. (This commonly observed phenomenon has previously been attributed solely to atmospheric pressure.) Furthermore, small regions of confined liquid in a large solidified volume of a casting approximate reasonably well to spherical geometry. ELASTIC-PLASTIC MODEL The author has shown4 that as solidification proceeds the internal hydrostatic tension builds up until the elastic limit of the shell is exceeded. At this point the internal pressure is closely -2Y/3. Subsequently a plastic zone spreads from the inner surface toward the outer surface of the shell. When the whole casting is deforming plastically a rather more generalized analysis taking account of the externally applied pressure PA + 2y/b gives the internal pressure as: P = Pa + 2y/a + 2ys/b - 2 Y In(b/a) [1] The 2y/a and 2ys/b terms result from the tendency of the liquid-solid and solid-vapor interfaces to shrink, reducing their energy, and thereby helping to collapse the solid phase and compress the liquid phase. The 2y/b term would be important only for powders. The last term arises because of the plastic restraint of the solid, resisting collapse and so effectively expanding the residual liquid. From Eq. [I] it is easily shown that there is a minimum in the pressure at the radius amia= y/Y [2] which is of the order of 103K for the metals aluminum, copper, and iron, and corresponds to the minimum pressure Pmin = 2 Y[l-ln(bY/y [3] The results of a fully worked out elastic-plastic solution are given in a previous reporL4 The main criticism which may be leveled at this analysis when applied to metals at their melting points is the strong dependence of the yield stress on the strain rate. The strain rate varies with both solidification conditions (e.g., whether chill-cast or slowly cooled) and during solidification, as is indicated in the following section. Thus an appropriate choice of Y is very arbitrary. Before proceeding to a discussion of models which are strain-rate-dependent, it is necessary to evaluate the strain rate as a function of the rate of solidification. SOLIDIFICATION RATE Various empirical relations have been deduced5 for the rate of thickening of the solid shell by pour- out tests on partially solidified spheres. These, however, are unsatisfactory for our purposes since they become very inaccurate when the liquid core is very small. A theoretical approach is therefore necessary, and some solutions are set out below. Making the assumptions of constant surface temperature of the casting during freezing, no superheat, and a material freezing at a single temperature, Adams8 deduces the approximate solution: which becomes when b » a: Employing a semiempirical approach vallet6 finds:

Jan 1, 1969

By Matsubara, A.

THE problem of the equilibrium between iron, carbon, and oxygen was first carefully investigated by E. Baur and A. Glaessner,1 who determined the equilibrium conditions of the two reactions Fe304 + CO ? 3FeO + C02 (1) FeO + CO ? Fe + C02 (2) within the range of temperature of 350 to 900° C. The next series of investigations was made by R. Schenck and his co-workers,2 who sought to check the results of Baur and Glaessner's work within the range of 550° to 700° C. and to elucidate the conditions of formation of iron carbide. The equilibrium conditions at the higher temperatures, however, are generally understood to be much more complicated, owing chiefly to the formation of solid solutions between iron, its oxides, and carbide; nevertheless their determination is of much more practical importance than those at the lower temperatures. It is well known that each of the reactions is reversible; equilibrium is established when the partial pressure of oxygen in the gaseous phase has become equal to the dissociation pressure of magnetic oxide in equation 1 and that of ferrous oxide in equation 2. These equilibria are subsequently designated by "the Fe304-FeO equilibrium" and "the FeO-Fe equilibrium," respectively. As the Fe304-FeO equilibrium has three phases with three components, it must be bivariant. But the reaction involves no pressure change in the gaseous phase, hence the final composition of the latter is practically unaffected by pressure. To know, the equilibrium conditions, the compositions of the gaseous phase at different temperatures must be determined. At the higher temperature, however, iron and its oxides dissolve one another in various proportions forming solid solutions; in many cases the content of oxygen in the solid phase becomes a new independent variable.

Jan 2, 1921

By H. I. Aaronson, C. Wells

THIS is a preliminary report on a detailed metal- lographic investigation of the bainite reaction in a plain carbon hypoeutectoid steel. In view of the current interest in the bainite reaction and of the controversies which still exist about even the basic phenomenology of this mode of transformation, it was considered desirable to present a summary of the more important results obtained to date prior to the completion of this investigation. The steel used contained 0.29 pct C, 0.76 pct Mn, 0.25 pct Si, 0.005 pct P, and 0.007 pct S. The alloy was homogenized for 48 hr at 1250°C. Individual specimens were then austenitized for 30 min at 1300°C and isothermally transformed for various times at temperatures above and within the bainite region, ranging from 775" through 500°C at intervals of 25°C. These specimens were carefully examined on a research metallograph; a few specimens of especial interest were also studied electron microscopically.' Bainite may be defined as the aggregate structure resulting from the precipitation of carbides from supersaturated ferrite which formed by nucleation and diffusion-limited growth. Two groups of experimental observations made during the present study provide support for this mechanism of the bainite reaction: 1—at 625°C, partial conversion of pro-eutectoid ferrite to bainite began after more than 99 pct of the austenite had decomposed and 2—the precipitation of bainitic carbides occurred only within the ferrite phase. The proeutectoid ferrite and the bainite reactions in the steel studied were found to be morphologically continuous. Following the classification scheme of Mehl and Dube,2 three principal morphologies of proeutectoid ferrite were identified in the temperature region (625" to 550°C) in which the two reactions blend—grain boundary allotriomorphs," * Grain boundary allotriomorphs are crystals which nucleate at and grow preferentially along matrix grain boundaries. Widmanstaetten side plates, and intragranular plates. Carbide precipitation converted these morphologies into their bainitic equivalents with increasing isothermal reaction time. Conversion took place more rapidly as the reaction temperature was reduced. The replacement of supersaturated ferrite by bainite, however, did not occur uniformly even within individual austenite grains and was noticeably incomplete at higher transformation temperatures, e.g., 625° to 575°C. The ferritic and bainitic forms of a given morphology thus were frequently found to coexist, often inextricably intermixed, in a given specimen. At 625" and 600°C, the conversion of ferrite to bainite was clearly seen to have occurred entirely by the nucleation of carbides at ferrite/ferrite boundaries, as shown in Fig. 1. The nature of the loci at which carbides formed at lower temperatures was often difficult to ascertain with a light microscope, although the alignment in rows of many of the carbides, illustrated in Fig. 2, suggested that nucleation had again occurred at grain boundaries or subboundaries within the ferrite. Application of the electron microscope confirmed this deduction for bainitic structures formed at these temperatures, as shown in Fig. 3. The dense black appearance of bainite formed at very low reaction temperatures in higher carbon steels3 indicates, however, that isolated lattice defects within ferrite crystals prob-

Jan 1, 1956

By W. E. Curran

For years the geographical isolation of the Southern iron-ore district from the great producing centers in the North and East enabled it to meet its conditions and solve its own problems without regard to the practices and policies of other districts, but during the past few years distances have been shortened, practices and wages are being standardized, .and these changing conditions have brought new problems to the South.

Jan 1, 1937

By A. W. Ross, William Marsh Baldwin, T. S. Howald

The related subjects of preferred orientation, directionality in physical properties, and earing tendencies of wrought metal strip have attracted the attention of metallurgists to such an extent that in the past 20 years hundreds of researches have been published on this one general problem. The anisotropy of tensile strength and elongation have been exhaustively studied in their relationship to the occurrence of ears in cups drawn from strip'-~O.~g and, to a lesser extent: yield strength7."-l7 and stress-strain curves'5 have been investigated. Despite the tremendous fund of knowledge thus accrued, no simple quantitative correlation of directionality and earing tendencies has yet been found. In a sense, this is not surprising. The formation of ears in a drawn cup clearly is a special phase of the general study of metal flow; in particular (as will be brought out in the course of this paper), ears are due to anistropy in the rates of deformation of the metal in the radial, circumferential, and "thickness" directions of the original blank. It would be difficult to effect a correlation between caring tendency and a property that may be completely independent of the flow of metal, or at best related to metal flow in an exceedingly complex fashion. Yet, it is this correlation that has been attempted; tensile strength and elongation are attributes of metal rupture. a phenomenon that has quite admirably been shown to be distinct from the phenomenon of metal flow,21 while yield strength and stress-strain

Jan 1, 1946

By William Marsh Baldwin, T. S. Howald, A. W. Ross

The related subjects of preferred orientation, directionality in physical properties, and earing tendencies of wrought metal strip have attracted the attention of metallurgists to such an extent that in the past 20 years hundreds of researches have been published on this one general problem. The anisotropy of tensile strength and elongation have been exhaustively studied in their relationship to the occurrence of ears in cups drawn from strip'-~O.~g and, to a lesser extent: yield strength7."-l7 and stress-strain curves'5 have been investigated. Despite the tremendous fund of knowledge thus accrued, no simple quantitative correlation of directionality and earing tendencies has yet been found. In a sense, this is not surprising. The formation of ears in a drawn cup clearly is a special phase of the general study of metal flow; in particular (as will be brought out in the course of this paper), ears are due to anistropy in the rates of deformation of the metal in the radial, circumferential, and "thickness" directions of the original blank. It would be difficult to effect a correlation between caring tendency and a property that may be completely independent of the flow of metal, or at best related to metal flow in an exceedingly complex fashion. Yet, it is this correlation that has been attempted; tensile strength and elongation are attributes of metal rupture. a phenomenon that has quite admirably been shown to be distinct from the phenomenon of metal flow,21 while yield strength and stress-strain

Jan 1, 1946

By F. W. C. Boswell, R. L. Cunningham, H. M. Weld

Chemical analysis shows the partition of the magnesium addition between the metal and the graphite is independent of whether the graphite is in the form of nodules or flakes. The bright central spot observed in nodular graphite polished sections is shown to be due to the structure of the nodules. DURING the past few years numerous papers have been published on the production1-7 and heat treatment" of nodular cast irons. However, very little information is available on the structure of the nodules and the reason for their formation. It would appear that an explanation of the phenomenon of nodulation must await a detailed knowledge of the nature of the nodule. Disagreement exists among various workers on such a fundamental point as to whether or not a nodule actually contains a microscopically visible, nongraphitic nucleus.9-11 Work was initiated with a view to obtaining definite information on this and other aspects of the problem. Chemical Separation and Analysis Microscopic appearance had indicated9-11 that a nongraphitic core might exist in nodules (Fig. 1). It appeared that a chemical comparison of separated nodules and flake graphite would be profitable, for if the core is nongraphitic a relatively large amount of certain elements would be found in the nodules as compared to the flake. This comparison could best be made by obtaining nodules and flake from the same melt of cast iron, part of which had been in-noculated with a suitable addition reagent for the formation of nodules. A 300 lb melt was produced. About half of this was innoculated in the ladle with an Fe-Si-Mg alloy to produce nodules and cast into keel blocks; the remaining half of the melt had silicon added in an effort to compensate for the silicon in the innoculant used in the other half of the melt and this was cast into similar keel blocks. The analyses of the resultant irons are given in Table I. Nodules and flake were chemically extracted from 2 kg samples of metal as described in the appendix. While this method dissolved the iron and chromium carbides, it did not dissolve the titanium, vanadium, and molybdenum carbides. These latter carbides could have been removed by nitric acid, but in other experiments it was found that it attacked pools of metallic iron entrapped in the nodules which had, until the nitric acid treatment, been protected from the attack of the sulphuric, hydrochloric, and hydrofluoric acids. It will be shown in the next section that entrapped iron exists in nodules but not in flake. On microscopic examination many tiny irregular particles were observed to accompany both the nodules and the flake. These were identified by tabling a sample of nodules from which a sufficient fraction was obtained for X-ray analysis. A good pattern of titanium carbide was obtained indicating that this was the predominant compound present. Since it was not possible to determine how completely the carbides could be removed mechanically and since their removal from flake is much more difficult, it was decided not to resort to any separation as this would render further comparisons more difficult. The samples were ashed in a combustion

Jan 1, 1953

By S. Skowronski

The melting of cathode copper, ususally containing 95.98+ per cent. • Cu, would appear to be a simple matter. Owing to the well known affinity of copper for sulfur, however, so much sulfur is absorbed by the copper during the operation that a long and expensive refining process is required to remove it, and the final product is inferior in purity and lower in electrical conductivity than the original cathode copper. The furnace operation, as now conducted, includes the following stages: 1. Charging the cathodes into the furnace. 2. Melting the cathodes. 3. Oxidizing period—saturating the copper with cuprous sub-oxide and bringing the metal to the condition known as "set copper;'' this is now done by blowing air into the molten bath of metal. 4. Reduction period, otherwise known as "poling," whereby the oxygen previously added is removed by covering the molten bath completely with coke or charcoal and introducing large poles of green wood; this reduces the cuprous sub-oxide, bringing the copper to the "tough pitch" stage ready for casting. 5. Casting Period. Many experiments have been made to obviate the long periods of oxidation and subsequent reduction, with no success. While the copper first cast will be good, as indicated by the set surface of the bars, it is impossible to hold it to the "tough pitch" condition, and long before the whole charge has been poured the copper will become "overpoled," entailing numerous difficulties. Sulfur has always been blamed by the furnace men as the reason why this refining process is necessary, yet the literature on the subject does not sufficiently emphasize how small a proportion of sulfur will ruin copper for practical purposes. The sulfur absorbed by copper during the melting period comes from two sources: (1) the sulfate left on the cathode sheets in the tank houses; (2) the fuel. The percentage of sulfates on the cathodes is variable, and depends on the care taken in washing the cathodes after removing

Jan 1, 1919

By John W. Cahn

Tile avevage value of the mean curvature of surfaces in a specimen can be precisely delermined by sitrlple measurements performed on random sections or on 1 vojectiotzs of these surfaces. For surjaces enclosing particles, the quanlity is sllown to be velated to the probable tlurrrhev ot particles intevcepted by a random platne and, under certain conditions, to the perimeter of their Projected image and to the increuse in surjace area when the particles grow. Many of the velalionsl~ips are valid for any shape or size of the particles. THE recent growth of the field of stereology or quantitative microscopy is largely the result of the discovery of a limited number of rigorously defined geometrical parameters that can be precisely measured on random sections or projections of a structure without assumption about particle shape.' Such parameters have been the volume fraction and surface area and line length in a unit volume. The present paper introduces the average of the mean curvature of surfaces in a volume, and shows that it can be rigorously measured by counting methods alone. AVERAGE CURVATURE ON A PLANE Consider a curve y = v (x) on the xy plane. The curvature Kp in the plane at any point is given by Kp = (dZy/dx2)/[1 + (dy/dx)2]3/2. The average curvature along the curve may be defined as Kp = (1/L) fKpdl |1] where dl = [(dx)' + {dy)2]1/2 is the length of an element of the curve and .(dl = L is the total length of the curve. The integral on the right-hand side of Eq. [l] will be called the total curvature, It is dimensionless and readily evaluated by substituting d = arctan (dy/dx) to give ah which is the change in direction of the tangents to the ends of the curve, Fig. 1. Hence, Kp = (1/L)(?h) [2] It can also be seen that Eq. [2] is applicable in the limit of sharp corners. Even though the curvature is infinite at a corner, f Kpdl remains integrable and equal to the change of angle. The signs of the quantities Kp and dl are arbitrary and, if the areas adjoining the curve are equivalent, there seems to be no compelling reason to fix the signs. For a closed curve, however, it becomes worthwhile to use the signs to distinguish among different types of areas or phases enclosed. For such a closed curve AO = t2r and As a convention, we shall take the direction of the integration along the curve in such a way that the area or phase under consideration (henceforth called a) is kept to the left side of the curve, Fig. 1. Then Kp is positive where the curve is concave and negative where the curve is convex. For a closed curve Ad - +2n if the curve encloses a, and Ad = —2n if the curve is surrounded by a. PLANAR SECTIONS OF THREE-DIMENSIONAL STRUCTURE OF ISOLATED a PARTICLES Consider next a planar section of a microstructure containing particles of a in a matrix. We place no restriction on shape of connectedness of these particles, and begin by considering the curvature of only the boundary between a particles and matrix' Clumps of contiguous a particles are then treated as a single a particle. The two-dimensional section will show in a unit area na simple closed curves enclosing a particles and nh closed curves of holes, in-

Jan 1, 1968

By M. Otogawa

TsunashiRo Wada, honorary member of the Institute, died at his residence, Ushigome, in Tokyo, on Dec. 20, 1920, at the age of sixty-four; he was born on March 15, 1856, at Obana in the province of Wakasa. An expert mineralogist, lithologist and geologist, he identified himself throughout his life with the development of the mining interest of this country. Perhaps the most noteworthy of his meritorious services in the public sense was the extension of the Imperial Steel Works at Yawata, anticipating the grim fate that hurled Japan. into a war with Russia in 1904. Educated in the Imperial University of Tokyo by foreign professors, he studied especially mineralogy, lithology and geology. In 1875 he was appointed assistant professor in the Imperial University of Tokyo, and in 1878 entered the service of the Home Department. From 1880 until 1893, Mr. Wada was Director of the Imperial Geological Survey of Japan, during which time he practically laid the foundation of the geological investigation work in Japan. In 1884, he made a trip to Europe by government order to attend the international Congress in Berlin, visiting en route several countries of Europe and America. While Director of the Survey, he was also, from 1880 to 1885, lecturer, and from 1885 to 1891, professor of mineralogy and lithology in the Imperial University, and, from 1889 to 1893, was Director of the Imperial Mining Bureau of Japan. In this capacity, he revised the mining laws of Japan, thus laying the foundation of Japan's mining administration. In 1894, he was again appointed lecturer in the Imperial University of Tokyo; in 1895, appointed Technical Adviser on Mines to the Imperial Household Department of Japan; and, in 1897, appointed President of the Imperial Steel Works, which was completed in 1900 with the expenditure of $10,000,000. In this capacity he did a great deal to promote the iron and. steel industry of this country. We owe him the ore-purchase contract with the Daiya iron mine in China, which remarkably facilitated the extension of the iron works in later days. The victory of the Russo-Japanese war must be said to be due to his merit in no small measure. He resigned the presidency of the Imperial Steel Works in 1901. In 1899, Mr. Wada visited America and several countries of Europe by government order; in 1902, he traveled through north and middle China doing exploration work and studying the geology of the country, accompanied by mining engineers and geologists. From 1896 to 1908, Mr. Wada was president and honorary member of

Jan 1, 1922

By M. Otogawa

TsunashiRo Wada, honorary member of the Institute, died at his residence, Ushigome, in Tokyo, on Dec. 20, 1920, at the age of sixty-four; he was born on March 15, 1856, at Obana in the province of Wakasa. An expert mineralogist, lithologist and geologist, he identified himself throughout his life with the development of the mining interest of this country. Perhaps the most noteworthy of his meritorious services in the public sense was the extension of the Imperial Steel Works at Yawata, anticipating the grim fate that hurled Japan. into a war with Russia in 1904. Educated in the Imperial University of Tokyo by foreign professors, he studied especially mineralogy, lithology and geology. In 1875 he was appointed assistant professor in the Imperial University of Tokyo, and in 1878 entered the service of the Home Department. From 1880 until 1893, Mr. Wada was Director of the Imperial Geological Survey of Japan, during which time he practically laid the foundation of the geological investigation work in Japan. In 1884, he made a trip to Europe by government order to attend the international Congress in Berlin, visiting en route several countries of Europe and America. While Director of the Survey, he was also, from 1880 to 1885, lecturer, and from 1885 to 1891, professor of mineralogy and lithology in the Imperial University, and, from 1889 to 1893, was Director of the Imperial Mining Bureau of Japan. In this capacity, he revised the mining laws of Japan, thus laying the foundation of Japan's mining administration. In 1894, he was again appointed lecturer in the Imperial University of Tokyo; in 1895, appointed Technical Adviser on Mines to the Imperial Household Department of Japan; and, in 1897, appointed President of the Imperial Steel Works, which was completed in 1900 with the expenditure of $10,000,000. In this capacity he did a great deal to promote the iron and. steel industry of this country. We owe him the ore-purchase contract with the Daiya iron mine in China, which remarkably facilitated the extension of the iron works in later days. The victory of the Russo-Japanese war must be said to be due to his merit in no small measure. He resigned the presidency of the Imperial Steel Works in 1901. In 1899, Mr. Wada visited America and several countries of Europe by government order; in 1902, he traveled through north and middle China doing exploration work and studying the geology of the country, accompanied by mining engineers and geologists. From 1896 to 1908, Mr. Wada was president and honorary member of

Jan 1, 1922

DISCUSSION, M. Cohen presiding A. H. Geisler and D. L. Martin (GeneTal Electric Research Laboratory, Schenectady, N. Y.)—We were rather interested to note the author's conclusion that the cubic to tetragonal transformation may be of the second order, for we have been able to show that the order-disorder transformation in an analogous alloy system is a first-order transformation with a discon-

Jan 1, 1952

By C. Schlumberger

THE object of this paper is to describe the adaptation of electrical resistivity measurements to the particular case of exploration in which the surface is an expanse of water (river, lake, sea). Water in itself does not constitute an obstacle to electrical exploration. It is merely an overburden, which is fluid instead of being solid, and as a consequence the routine of the measurements has to be modified. Also, in many instances, the liquid under consideration is highly conductive (salt water). This introduces an additional difficulty into exploration work, and has to be overcome by the geophysicist. We do not propose to discuss here the basic principles of electrical resistivity measurements, which have been dealt with in various previous papers,1 but will simply recall the two fundamental techniques which govern its field application: 1. Horizontal exploration, or method of the resistivity map, in which a series of electrical measurements are carried out at various stations, keeping the same electrode spacing. Thus, a horizontal layer of the subsoil, of a practically constant thickness, is explored. 2. Vertical exploration, or "vertical sounding?2 method, in which a series of measurements are made with increasing electrode spacings at one or several stations. In this way, the apparent resistivity is deter-

Jan 1, 1934

By Nestor Torres-Acuña, Fathi Habashi

Metallic copper of purity equal to commercial electrolytic copper is deposited during the anodic dissolution of technically available white metal, Cu2S, in m acidic solution of' copper(II) sulfate as electrolyte and copper sheets as cathodes. The process may be applied on commercial scale since it has the advantage of by passing the converting and poling steps, decreasing pollution problems due to SO, and recovering the sulfur of the white metal in the elemental form. The anodic dissolution is believed to take place in three steps: The working conditions that lead to 98 pct cathodic current efficiency are: 30 gpl Cu2+ and 100 gpl H2SO4 in electrolyte, current density 1.0 amp per sq dm, and tetnperature of bath 40°C'. DURING the smelting of copper, nickel, lead, and zinc sulfide ores, large amounts of sulfur dioxide are produced. Because the release of this gas in the atmosphere causes pollution problems, many attempts were made in the past for its recovery either in liquified form or processed to sulfuric acid. Although these two forms of sulfur are the usual forms that are consumed by the chemical and metallurgical industries, their storage and transport usually raise economic problems. It was realized, long ago, that a process by which sulfur can be recovered directly in the elemental form would be most attractive. Elemental sulfur is easily stored and transported, and is readily converted to SO2, H2S, or H2SO4 when needed. Processes aimed to recover the metals from their sulfide ores, and at the same time by-product sulfur in the elemental form, were recently reviewed.' As early as 1882, Marchese2 patented a process in which a matte having the composition: Cu 15, Pb 14, Fe 41, and S 25 pct was electrolyzed. According to cohen3 the process was applied on a pilot scale by the Aktiengesellschaft fur Bergbau-, Blei-, und Zinkhiitten-betriebe at Stolberg, Rheinland, Germany. The process was unsuccessful, however, owing to the contamination of the electrolyte during electrolysis. Studies in this field were reported by Bernfeld4 and Egli.5 Borchers et a1.6-8 developed the process further by using white metal (Cu 78.2 pct, S 19.6 pct) instead of the matte, and a pilot plant was operated by the Mansfeldschen Kupferschiefer Co. at Eisleben, German~.~ It appears, however, that the process never went into commercial operation. Further studies in this direction were carried out by Russian workers.10-23 The International Nickel Co. of Canada erected a pilot plant at Port Colborne in 1951 to apply the process to nickel matte which is essentially pure nickel sulfide."'- 26 Full-scale plant went into operation at the Thompson Refinery in Manitoba in 1964.27 In this method nickel sulfide matte is melted and cast into anodes analyzing 76 pct Ni and 20 pct S with small amounts of copper, cobalt, and iron. These anodes are then electrolyzed in an aqueous solution of NiS04 at pH 4. Further work on this method was reported in the literature.28-31 In this paper, experiments on the anodic dissolution of white metal in aqueous copper sulfate solution are reported. EXPERIMENTAL White metal, Table I, obtained from The Anaconda Co., was cast in form of anodes 10 by 7.5 by 1 cm, Fig. 1. The anodes are mechanically strong and do not break easily; when polished they gave a shiny gray metallic appearance. From the chemical composition shown in Table I, it can be seen that the atomic ratio Cu:S corresponds approximately to the formula CU2.06S. The copper in excess to the formula Cu2S is most probably present as a separate phase since metallic copper could be seen under the microscope, Fig. 2. Fig. 3 shows the X-ray diffraction pattern of white metal which matches fairly well with that of reagent-grade Cu2S.

Jan 1, 1969

By M.A. Hunter

This paper gives the results of an investigation of the specific resistance and temperature coefficient of the electrical resistance of nickel and its important alloy, monel metal. For most of the pure metals, the temperature coefficient of resistance is approximately 0.004 per degree centigrade at 20" C. Nickel and iron, however, are exceptions. This property is important as it gives us good material for the construction of thermometers and other instruments involving electrical control. A summary of information on this subject has been publishcd by the Bureau of Standards.l The present experiments antedate this publication by several years and as the information obtained is not contained in it, the results of the experiments arc published as additional information. Electrical Properties of Pure Nickel It is generally conceded that the lowest values for electrical resistance are obtained in the purest metal. In the case of nickel, the best material obtainable is electrolytic nickel, which contains approximately 99.80 per cent. nickel, 0.15 per cent. iron, and 0.05 per cent. copper. Any cobalt that may be present is included in the nickel figure. If the elcctrolStic sheet has been deposited without intermission, it is possible to cut a section from the sheet and roll it into wire without melting. By this means a nickel wire may be obtained that is uncontaminated by any of the impurities always taken up by nickel during melting. Two samples of nickel wire obtained from different electrolytic nickels had the follolving electrical resistance and temperature coefficient of electrical resistance: Specific Temp. CofEE. Sample MateRial ReSISTance peR Deg. C. NO. 1 Electrolytic nickel.................... 7.55 0.00550 NO. 2 Electrolytic nickcl ................... 7.60 0.00553 * Rensselacr Polytechnic Institute. Director of Research, Driver-Harris Co. Russell Sage Laboratory, Rensselaer Polyt,ecllnic Institute. 1 U. S. Bureau of Standards, Circular 100 (March, 1921).

Jan 1, 1923

By M. A. Hunter

This paper gives the results of an investigation of the specific resistance and temperature coefficient of the electrical resistance of nickel and its important alloy, monel metal. For most of the pure metals, the temperature coefficient of resistance is approximately 0.004 per degree centigrade at 20" C. Nickel and iron, however, are exceptions. This property is important as it gives us good material for the construction of thermometers and other instruments involving electrical control. A summary of information on this subject has been publishcd by the Bureau of Standards.l The present experiments antedate this publication by several years and as the information obtained is not contained in it, the results of the experiments arc published as additional information. Electrical Properties of Pure Nickel It is generally conceded that the lowest values for electrical resistance are obtained in the purest metal. In the case of nickel, the best material obtainable is electrolytic nickel, which contains approximately 99.80 per cent. nickel, 0.15 per cent. iron, and 0.05 per cent. copper. Any cobalt that may be present is included in the nickel figure. If the elcctrolStic sheet has been deposited without intermission, it is possible to cut a section from the sheet and roll it into wire without melting. By this means a nickel wire may be obtained that is uncontaminated by any of the impurities always taken up by nickel during melting. Two samples of nickel wire obtained from different electrolytic nickels had the follolving electrical resistance and temperature coefficient of electrical resistance: Specific Temp. CofEE. Sample MateRial ReSISTance peR Deg. C. NO. 1 Electrolytic nickel.................... 7.55 0.00550 NO. 2 Electrolytic nickcl ................... 7.60 0.00553 * Rensselacr Polytechnic Institute. Director of Research, Driver-Harris Co. Russell Sage Laboratory, Rensselaer Polyt,ecllnic Institute. 1 U. S. Bureau of Standards, Circular 100 (March, 1921).

Jan 1, 1923

By S. C. Sun, T. Chao

The reaction of gaseous sulfur trioxide with different aluminum-bearing minerals for the conversion of their alumina content into water soluble sulfates has been investigated. Theoretical considerations indicate that this reaction is thermodynamically feasible and that preferential sulfatization can be accomplished. The five minerals tested were gibbsite, boehmite, diaspore, kaolinite, and halloysite. In general, over 90% sulfatization could be achieved in 1 hr when using sodium sulfate as an additive at a temperature between 500° and 600°C. It was found that sulfates of the light alkali and alkaline earth metals exhibited some effectiveness in promoting the sulfa-tizing reaction. Selective sulfatization of alumina in a mixture of calcined halloysite and ferric oxide was accomplished. The gas-solid type of sulfatizing reactions have become increasingly important in recent years for the treatment of the oxides of such nonferrous metals as cobalt,' nickel,' manganese,3 zinc, and copper.4-6 Similar reactions were attempted in the present investigation for the recovery of aluminum from the low grade aluminous ores. Unlike the Bayer process in which silica is a serious contaminant, or the acid processes whereby iron usually causes difficulties, the reactions between gaseous sulfur trioxide and various aluminous minerals could hopefully be selective for aluminum. THEORETICAL CONSIDERATIONS Reactions between aluminum-bearing minerals and gaseous sulfur trioxide have been shown respectively in Table I and Fig. 1 to be thermodynamically favorable for temperatures below 1000°K approximately. Calculations of the thermodynamic functions were where ?G, ?H, ?Cp and ?S are changes in free energy, enthalpy, constant-pressure specific heat, and entropy of the system under consideration, respectively; T is the absolute temperature, R the universal gas constant, and K the equilibrium constant. Thermochemical data so far available for these calculations were based on sources given by T. Chao.7 In Table I, the free energy values indicate that reactions between the gaseous sulfur trioxide and

Jan 1, 1968