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By A. S. Venkatadri, H. B. Bell

The equilibrium sulfur distribution between molten iron and Ca0-Mg0-Al203 slags containing iron oxide was investigated at 1550°C. The results were used to derive the iron oxide activities at low iron oxide concentrations in the slag by combining the sulfide capacity data obtained from gas-slag work with the free energies of both the sulfur solution in iron and the iron oxide formation in slag. The derived ferrous oxide activities were compared with values based on Tem-kin's kin's and Flood's ionic models. One difficulty in using these models is that the nature of the aluminate ion in slag is uncertain. Nevertheless, such indirect methods, in particular, those described in the present paper, are of value because of the difficulty of measuring small amounts of oxygen in liquid iron in equilibrium with slag. It is shown that these methods confirm the consistency of thermodynamics data on liquid iron and slags. It is well established that decreasing the iron oxide activity in the slag increases the desulfurization of molten iron at constant slag basicity. This effect is most pronounced at the very low iron oxide activities, characteristic of blast furnace slags. Yet a precise quantitative determination of the significance of low iron oxide contents in slag in blast furnace desulfuri-zation is not possible for the following reasons: a) difficulty of separation of iron "shots" from the slag, and b) errors in chemical analysis of small amounts of iron oxide in slags. In view of these obstacles, one must resort to indirect methods of calculating iron oxide activities. EXPERIMENTAL TECHNIQUE The apparatus for providing the sulfur equilibrium data has been described previously1 and was similar to that used by ell' in connection with the study of slag-metal manganese equilibrium. The procedure consisted of: a) melting about 50 g of Armco iron in a magnesia crucible in a platinum furnace, b) adding a mixture of about 15 g of lime-alumina slag and varying amounts of Fe2O3 and CaS, and c) maintaining the temperature at 1550°C for more than an hour in an atmosphere of argon to enable the sulfur equilibrium to be attained. Several melts were made using lime-alumina slags with basic composition 55, 50, and 45 pct lime. During the experiment the temperature was controlled manually using a Pt/10 pet Rh-Pt thermocouple. After the experiment, the Power was shut off and the flow rate of argon was increased to freeze the melt as quickly as possible. The analysis of sulfur in the metal was carried out by the oxygen combustion method3 using uniform drillings from the top and bottom of the metal button. After crushing and grinding and removal of any iron particles with the aid of a hand magnet, the slag was analyzed for sulfur by the CO2 combustion method.4 The E.D.T.A. method was employed for the analysis of lime5,6 and magnesia,= the ceric sulfate method7 for the analysis of slag iron oxide, and the perchloric acid dehydration method5 for the analysis of silica. The remaining amount was taken to be Al2O3 precipitation with ammonium hydroxide in several preliminary melts had confirmed the propriety of using this simple procedure. RESULTS The activity of iron oxide in binary, ternary, and more complex slags has been the object of numerous investigations, and the two experimental methods for its determination are: 1) Equilibrating the metal with the slag in question and measuring the oxygen content of the metal. The ferrous oxide activity is then given by aFeO L%OJSat where [%0]sat is the oxygen content of the metal in equilibrium with pure iron oxide slag. This method was used by Chipman et al.8,9 2) Equilibrating the slag in iron crucibles with known partial pressures of H2/H2O or CO/CO2 mix-tures.10-12 This method is limited to temperatures between 1265" and 1500°C. The very low oxygen content of the melts in this investigation made it impossible to derive the ferrous oxide activity by the first of these methods. Therefore, the iron oxide activities were computed by means of: Sulfide capacity data from the gas-slag work" Temkin's concept14 Flood's approach15 a FeO from Sulfide Capacity. The method of calculating the aFeO involves the sulfide capacity of the slag (c,), the sulfur distribution coefficient (Ls), the free energy of dissolution of sulfur in iron, and the free energy of formation of iron oxide in the slag. Bell and Kalyanram13 have investigated the sulfur absorption characteristics of lime-alumina slags containing magnesia by the Carter-Macfarlane method16 (based on comparing the sulfide capacity of the slag in question with that of a standard slag of unit lime activity) and have derived lime activity values. The relation between sulfide capacity and their lime activity a'CaO is given by: Cs= 3—: Xa'CaO at 1500°C

Jan 1, 1970

By Luiz C. Correa da Silva, Robert F. Mehl

A. D. Le Claire and R. S. Barnes (Atomic Energy Research Establishment, Harwell, Didcot, Berks., England)-—This much awaited paper admirably confirms that the Kirkendall effect is a true diffusion phenomenon and likely to be found in all diffusing systems. The most likely explanation put forward so far to account for the shift of interface is that the two components of the system, diffusing in opposite directions, do so with unequal rates so that there is a net loss of material from that half of the diffusion zone rich in the more rapidly diffusing component. This loss is accompanied, and at least partly compensated for, by a closing up or decrease in volume of this latter half of the diffusion zone and an expansion of the other half so as to tend to keep constant the overall volume per atom. This is manifest as a movement of the original interface. If this is a true picture of what is taking place then there are at least two important matters requiring further study."1—The quantitative relating of the observed shift with the independently measured separate diffusion coefficients of the two diffusing species."2—A detailed study of the mechanism and characteristics of the closing up process."We would like first to make a few remarks pertinent to these topics. In connection with the first of these, it is a pity that more and detailed measurements were not made on the Au-Ag system, the only one for which the separate diffusion coefficients of the two species have been measured.'" One of us (A. D. Le C.) has calculated from Johnson's results the shift to have been expected in samples D.2 and D.3. Darken4 showed that the velocity v with which the markers move is related to the separate diffusion coefficients Dau, Dag, by the eauation:"dN"v = (Dag — Dau "dx"dN"where .is the concentration gradient at the mark-ax"ers. Under certain conditions,4, 20 it can also be shown that:"Xm"v = "2t"where x, is the total marker shift after time, t:"dN". . xm = 2t (Dag — Dau) [9]"dX"Johnson measured Dag and DAu in a chemically homogeneous alloy and so his reported figures represent the true or ideal diffusion coefficients"; the same quantities in eq 9 represent the actual diffusion coefficients as would be measured in the presence of a chemical concentration gradient, so we need to multiply Johnson's reported values of Dag and Dau by the"1 before insert-dlogN "ing them in eq 9. 7 is the activity coefficient of Ag at the concentration prevailing near the markers which we shall assume to be - 50 pct. The values of the thermodynamic factor for N = 0.5 and the temperatures at which D.2 and D.3 were annealed were obtained from thermodynamic data quoted by Darken.' aN/ax was computed from the coefficient of inter-diffusion of Au and Ag given by Johnson on the assumption that in the samples D.2 and D.3, the concentration distance curve could be represented by the standard equation:""No is the original difference in concentration between the two halves of the couple, and + is the error or probability function."aN/ax at x = 0 is then given by:"adN/dx "2/nDt"and we assume that this represents the concentration gradient at the markers, although it is probable that the figure is slightly high."When all the appropriate quantities are inserted in eq 9, we find that the expected shifts are: for D.2, 0.0134 cm and for D.3, 0.0119 cm."The agreement between these results and those

Jan 1, 1952

NEW MEMBERS The following list comprises the names of those persons who became members during the period July 10, 1919, to August 10, 1919. BALL, C. LEONARD.. Cons. Engr., Suffern Co., Inc., 135 Broadway, New York, N. Y. BARRY, CHARLES W Box 502, Idaho Springs, Colo. BATTLE, JOEL ALLAN, JR., Min. Engr., U.S. Bureau of Mines, Room 2114, Interior Bldg., Washington., D. C. BEER, GUIDO, Compagnia. Italian, Dir Bronzi Speciali, C. I., B. S. La Direzione, Italy. BITLER, WILLIAM F., Management of Coal Properties, The Provident Life & Trust Co. of Philadelphia, 409 Chestnut St., Philadelphia, Pa. BLOOM, SETH W., Chief Engr,, Northwestern Min. & Exchange Co., 130 E. Sribner Ave., Du Bois, Pa. BOYDELL, W. Guy B., Min. Engr., Tul Mi Chung Mine, Care Seoul Min. Co. Whang Hai Do, Chosen. Korea. BRYAN, RUSSELL R.., Met., Sunnyside Min. & Mill. Co., Eureka, San Juan Co., Colo. CHIAPELLA, STEPHEN EUGENE 323 W. 30th St., Los Angeles, Cal. CONWAY, EDMUND JOHN, Exploration Engr., Granhy Consolidated Min., Smelt & Power Co., Ltd., Anyox, B. C., Canada. DEMOREST, DANA J Prof. of Met., The Ohio State Univ., Columbus, Ohio. EIDEMILLER, H. N., Geol., Benjamin C. Neely, Min. Lands & Leases, Crystal Falls, Mich.

Jan 9, 1919

By W. R. Johnson, M. Hansen, John M. Parks

AS part of a research project sponsored by the Signal Corps Engineering Laboratories, which had the objective of obtaining a magnet wire of good conductivity and low temperature coefficient of resistance, a comprehensive literature survey, supplemented by experimental work, revealed that a linear relationship exists for solid-solution alloys between the electrical conductivity, K, and the temperature coefficient, a, as expressed by the equation: k = a/ß where ß is constant for the solvent metal and a - per°C. tR0 It has long been known that the electrical conductivity at a given temperature and the temperature coefficient of resistance of binary alloys are related to their constitution by the LeChatelier-Guertler rules, as illustrated by Figs. 1 and 2: Rule 1—In alloy systems consisting of a heterogeneous mixture of two phases, the electrical conductivity and temperature coefficient vary as a straight line, if the composition of the alloys is given in volume percentage, Fig. 1. Rule 2—In solid solutions, the electrical conductivity and temperature coefficient are always lower than those of the solvent metal, and usually a considerable decrease occurs with the first small percentage additions of the solute metal, Fig. 2b. If the two components form a continuous series of solid solutions, the electrical conductivity and temperature coefficient curves take the form of a U-curve, Fig. 2a. That some kind of proportionality exists between electrical conductivity and temperature coefficient of resistance is implied by the LeChatelier-Guertler rules and by study of data such as those given by Smith and Palmer,' Fig. 3. Dellinger2 in 1910 first recognized this relationship in a number of commercial copper wires, ranging in conductivity from 94 to 100.7 pct I.A.C.S. He gave the ratio of temperature coefficient to the percentage of conductivity as a constant, C = 0.003939. A year later, Lindeck observed that the linear relationship was valid for a wider range of conductivity in "various sorts of copper," and concluded that the product of resistivity and temperature coefficient was 6.78x10-5 1.5 pct. Since then, this relationship seems to have been entirely ignored. Conductivity-Temperature Coefficient Relationship If the electrical conductivity of copper solid-solution alloys with phosphorus, silicon, arsenic, antimony, aluminum, nickel, manganese, and iron is plotted against the temperature coefficient of these alloys, the diagrams in Figs. 4 and 5 are obtained. Similar data were found with copper-rich solid solutions containing magnesium, cobalt, and titanium,'" as shown in Fig. 6. In all cases, a linear relationship exists. The point representing the highest

Jan 1, 1952

By A. E. Beasley, Ike McKinney

Scale is a broad term which includes many types of mineral deposits which have limited solubility in water. These mineral components precipitate when combinations of scale-forming cations and anions exceed their solubility. Scale deposits are tightly bound to each other and to the metal surfaces of a water system. Precipitates that do not readily adhere to each other or to metal surfaces are known as sludges. Sludges are easily removed from a system by flushing. For example, a sludge is formed in the internal treatment of boiler waters with orthophosphates where the calcium is purposely precipitated as hydroxyapatite. Calcium phosphate would have a tendency to adhere to the boiler tubes except for the addition of tannins or lignins. These sludge conditioners maintain the precipitated calcium phosphate as a sludge which can be readily removed by boiler blowdown.

Jan 3, 1973

By R. E. Ogilvie, E. T. Peters

The X-ray Kossel-line method has been used preaioz~sly for measuring lattice parameters to accuracies of 1 part in 100,000.5 A second application of this method is described for determining the crystallographic orientation of a randomly positioned single-crysta1 spherical volume that can he as small as 50 µ in diameter, within accuracy limits of ±1/2 deg. The theory, experimental procedure, and interpretation of Kossel-line patterns and an experimenta1 verification of the predicted orientation relationship of the cph k and fee a Cu-Si phases are presented. This orientation relationship can be described as (111)a, (00.1)k; [110]a [11.0]k. In addition, the lattice parameter of the a phase was found to he a. = 3.62154 ± 0.00014Å. The Kossel-line method when used in conjunction with electron microanalysis is shown to he capable of providing a complete chemical and structural analysis of a given crystal. THE most easily accomplished methods for determining the orientation of a single crystal are variations of the Laue X-ray diffraction method. Although certain materials can be oriented to within ± 1 deg accuracy by observation of exterior macroscopic features, such as etch pits, cleavage faces, or growth features, the Laue method is generally preferred for routine laboratory application. Both back-reflection and transmission patterns are coordinated by appropriate reference charts and are plotted in terms of reflection plane poles (normals) on a stereographic projection. Orientation is deduced by relating the pole distribution (which is fixed by the crystallographic symmetry of the specimen) to two specified external reference directions. The Laue method has several limitations. 1) Orientation can rarely be determined to better than ±l deg accuracy. Principal errors involve inaccuracy in specimen-to-film distance, measurement confidence of individual Laue spots, and stereographic plotting. 2) Because of the indeterminacy of the X-ray wave length diffracted to a given spot, it is not possible to determine supplementary crystallographic data, such as interplanar spacings and lattice parameters. 3) The method is generally limited to specimens of cubic symmetry or to specimens of high symmetry and known structure. 4) The relatively large cross-sectional area of the incident X-ray beam generally precludes the measurement of relative grain orientation in a polycrystalline material.* _____ Several of these limitations can be overcome by application of the Kossel-line method, which has been previously employed for precision lattice-parameter determinations.'-= For this method, a point source of divergent monochromatic X-rays is generated within the crystal by means of an incident electron beam. The divergent X-rays which fulfill the Bragg law are diffracted by the specimen and are recorded on a film placed either in transmission or back reflection. Analysis of the film yields a direct measurement of orientation and lattice-spacing values to an accuracy of ±1/2 pct. As analyses can be obtained from spherical specimen volumes as small as 50 µ in diameter, the method provides a means for structural analysis of second-phase or impurity precipitates within a given matrix. The primary limitation of the Kossel-line method is the requirement for an electron microanalyzer or similar apparatus capable of producing a finely focused electron beam. This paper is designed to present the theory, experimental procedure, and geometrical interpretation of Kossel patterns. The experimentally determined orientation relationship between the k and a phases occurring in the Cu-Si system and a precision measurement of the a lattice parameter are presented as a practical application of the method. THEORY OF KOSSEL LINES Divergent X-ray beam photography utilizes an effective point source of characteristic X-rays which, when diffracted from a single crystal, form numerous diffraction and absorption cones that are recorded on film.7 The cones generated from a source lying within the crystal are called Kossel lines.' Although the X-ray scattering from a divergent point source contained within a crystal is described in terms of Laue dynamical theory,9 the directions of the diffracted spectra can be ade-

Jan 1, 1965

By R. T. DeHoff, F. N. Rhines

The problem of determining the number of particles of a phase distributed randomly in unit volume c an opaque matrix from measurements made on random plane sections is closely investigated. A formalized derivation for the general case is presented. Applications of this formal result are made to specific types of aggregates dispersed in a matrix; circles, particles with flat circular ends, cylinders, and constant shape aggregates of ellipsoids of revolution. Quantitative measurements of the average geometric properties of these aggregates are developed. In 1953 R L. ullman' developed a technique for determining, from measurements made on random plane sections, the number per unit volume, Nv, of particles imbedded in an opaque matrix. Using meas urements previously developed for volume fraction, vV,' and surface area per unit volume, .SV,= he was able to determine average volume, average surface area, and average dimensions of particles, independent of size distribution, for spheres and circular disks,' as well as for uniformly sized cylinders of any axial ratio.4 The technique is mathematically rigorous for the cases studied. Recent studies of this problem have yielded rigorous solutions for the general case of cylinders, permitting evaluation of NV independent of size distribution and with all axial ratios intermixed. Generalization to shapes having flat, circular ends has been deduced. A solution has also been obtained for the ellipsoid of revolution, independent of size distribution, but requiring a constant axial ratio in the generating ellipses. In the following derivations, as in Fullman's work, it is assumed that the problem is purely a combination of geometry and probability theory,that is,eithe the particles to be measured are imbedded randomly in the matrix, or a sufficient number of random plane sections are taken to make the sample representative. A relationship exists between the number of par- ticles of a given size and shape that may be situated in unit volume (Ny) and the number of intersections a random plane can be expected to make with these particles (Na). It is the purpose of the following section to derive this relationship. The probability of Intersecting Convex Bodies. Consider a convex, closed surface, that is, one for which no two surface normals point in the same direction, situated at some arbitrary position and orientation in a cube of material that is one unit long at each edge. It is not necessary to assume that this surface is symmetrical. Let planes be constructed in the cube parallel to the top face and at random distances from it. Those planes which lie between the two planes which are just tangent to the top and bottom of the surface will intersect it. The probability that a plane will intersect the body may be defined as the limit of the fraction of planes that lie between the two tangent planes as the total number of planes constructed becomes infinite. This fraction, in the limit, is equal to the distance between the two tangent planes, DV, divided by the total length over which planes are constructed, which has been taken as unity. If the body is now rotated to a new orientation, applying the same argument, the probability of intersection is again numerically equal to the distance between tangent planes. Let DV ($, 0) be defined as the distance between tangent planes of a convex body as a function of orientation, Fig. 1. The probability, Pr, of intersecting the body with a randomly oriented and randomly positioned plane, is then equal to the average value of DV (0, $) over all possible orientations. It may be easily shown that for a system of spherical coordinates the probability of finding an orientation between Q and Q + de, $ and $ + d$ is (1/4n) sin $ dB d$, so that This relationship may be applied to each body in an aggregate of convex bodies. In particular, if the bodies in an aggregate are classified according to size and shape, and the ithsuch class is considered, Eq. 111 may be applied to this entire class, the probability of intersecting any body in this class being

Jan 1, 1962

By Frank A. Herald

Through the generous cooperation of the authors of the papers in this chapter, a great wealth of fundamental data is being made available. The same plan of securing and submitting data will be carried forward next year, with the hope of making a nearer approach to complete presentation of the data contemplated in the plan. In order to conserve space, we are printing below such footnotes as have general application to Table 1 in the papers in this chapter: Footnotes to Column Headings Table I In areas where both oil and gas are produced, unless gas is marketed outside the field, such areas are included in column headed "Oil." Manufacture of casinghead gasoline and carbon black is interpreted as outside marketing of gas. Production per acre is determined by dividing into the number of barrels of oil the sum of the number of acres assigned to "Oil" plus such number of acres of the total assigned to "Oil and gas" as represents the portion thereof occupied by oil. Wells producing both oil and gas are classified as "Poducing oil only" unless gas from them is marketed off the lease. W. water; G. gas; A, air. Bottom-hole pressures are preceded by "e." All other figures represent pressures at casinghead with well closed. P, paraffin; A, asphalt; M, mixed. 0 Cam, Cambrian; Ord, Ordovician; Sil, Silurian; Dev, Devonian; Mis, Mississippian; MisL, Lower Mississippian; MisU, Upper Mississippian: Pen. Pennsylvanian; Per. Permian; Tri, Triassic; Jur. Jurassic; CreL, Lower Cretaceous; CreU. Upper Cretaceous; Eoc, Eocene; Olig, Oligocene; Mio. Miocene; Pli. Pliocene. 6, sandstone: SH, sandstone, shaly; Ss, soft sand; H, shale; L, limestone; LS, limestone. sandy; C, chalk; A, anhydrite; D, dolomite; Da. arkosic dolomite; GW, granite wash; P, serpentine. Figures are entered only for fields where the reservoir rock is of pore type. Figures represent, ratio of pore space to total volume of net reservoir rock expressed in per cent. "Par" indicates that the reservoir rock is of pore type but said ratio is not known by the author. "Cav" indicates that the reservoir rock is of cavernous type; "Fis," fissure type. A, anticline; AF, anticline with faulting as important feature; Af, anticline with faulting as minor feature; AM, accumulation due to both anticlinal and monoclinal structure; H, strata are horizontal or near horizontal; MF, monocline-fault; MU, monocline-unconformity; ML, monocline-lens; MC, monocline with accumulation due to change in character of stratum; MI, monocline with accumulation against igneous barrier; MUP, monocline with accumulation due to sealing at outcrop by asphalt; D, dome; Ds, salt dome; T, terrace; TF, terrace with faulting as important feature; N, nose; 9, syncline. Information will be found in text as indicated by symbols: A, name of author, other than above. who has compiled the data on the particular field; C, chemical treatment of wells; G, gas-oil ratios; P, proration; U, unit operation; R, references; W, water; 0. other information.

Jan 1, 1934

By Donald L. Johnson

REVIEWS on the applications of optical ellipsometry to the study of polycrystalline metal surfaces and oxidation-corrosion processes have been presented by Kruger and Hayfield, and white.' In view of the ability of this method to measure differences in film thicknesses to below 10A, ellipsometry was used to study nitrogen chromium surface reactions during the early stages of growth. Chromium specimens in the form of a vapor-deposited film on glass substrate were exposed to purified nitrogen for selected time increments at 700°F. This temperature was selected because it gave the best combination of exposure time and thickness change. Ellipsometer readings were taken immediately after exposure to determine polarizer and analyzer angles using monochromatic light at 5000A.2 After each set of readings was obtained, the specimens were exposed for an additional increment of time in nitrogen and a new set of readings taken. Film thickness was computed from LUCy's3 equation for nonabsorbing thin films. In Lucy's derivation, two equations for computing thickness were obtained. Peterson and Bashara4 have discussed the validity for using one of these equations when an independent value of the refractive index is used. The film was assumed to be Cr2N (Ref. 5) and was determined to be optically isotropic. Optical isotropy was determined by rotating the films about the surface normal and noting that the azimuth and phase difference did not change. Since Cr2N is reported to be hexagonal, it is assumed that optical isotropy results from randomly oriented grains of very small size. The thickness was computed using refractive indexes varying from 1.6 to 2.0. The maximum variation in computed thickness over this range for a given exposure was 20 pct. The data reported are based on a refractive index of 1.8. Reference readings on the metal surface were taken just prior to nitrogen exposure. No attempt was made to deoxidize or denitride the metal surface after vapor deposition, although specimens were observed to gain approximately 2A per day in air at room temperature. Twelve experimental exposures were made on a single sample over a total accumulative time of 132 min. Additional experiments over longer time intervals were made to determine the effect of heat up and cool down during and after exposure. As a result of these experiments, the thickness computed for each exposure was increased by 4A. Time profiles based on the linear law are similar to the oxidation profiles for many metals.' The rate of accumulation of the nitride film is rapid at first and slows down as the film thickness increases. The parabolic law x2 =k1t +k2 [11 gives a straight line in Fig. 1; therefore, it is concluded that the kinetic behavior is parabolic. Sey-bolt and Haman5 reported similar results for CrlN on chromium at 1000°C although the order of the thickness was much greater (10-3 cm). Analysis of thickness data based on other values of refractive index shows that the curves are shifted vertically but retain the same shape. According to Mott,7 it is expected that for thin films k2 is zero in Eq. [I]. Since the plot in Fig. 1 is linear through the origin, k2 is zero and the parabolic nature of the film growth is further indicated. The parabolic rate constant, calculated from the slope in Fig. 1, is 4.4 x 10-16 sq cm per sec. The corresponding work (+) required to bring an electron from the metal into the oxide is estimated to be 1.5 ev.7 The author thanks professor N. M. Bashara and D. W. Peterson, Electrical Materials Laboratory, University of Nebraska, for making the ellipsometer available and providing technical assistance. The Electrical Materials Laboratory is supported by the office of Naval Research, NONR 3718 (01). This work was partially supported by the Engineering Experiment Station and the Mechanical Engineering Department, University of Nebraska.

Jan 1, 1967

By Richard H. Siller, Rex B. McLellan

A model for interstitial solid solutions has been considered in which a repulsive Potential exists between interstitial atoms in the solvent lattice. It has been shown that this model is consistent with the thermodynamic Properties of certain interstitial solid solutions. The model is then applied to the calculation of the variation of the diffusivity of carbon in au-tenite with composition. Although the energy levels at the saddle point, and thus the absolute values of dif-fusivity, cannot be calculated, it is shown that by taking the repulsive interactions between the diffusing atoms into account the functional form of the dependence of diffusivity on solute concentration can be derived. ThE composition dependence of the diffusivity, D, of carbon in austenite at a given temperature is well-known.'-3 smith3 tried to reconcile the observed composition dependence of D at 1000°C with the previously observed4 composition dependence of carbon activity using equations for D derived by arken5 and Fisher, Hollomon, and Turnbull,6 but was unsuccessful. In this paper we shall modify the approach of Fisher et al. by considering the "blocking" model7 for interstitial solid solutions, based on concept due to Speiser and Spretnak,' in which a repulsive potential exists between interstitial solute atoms in the solvent lattice, causing a certain number of interstitial sites to be "blocked" from occupancy by further solute atoms. We shall thus be able to describe the intimate relationship between the composition dependence of carbon diffusivity, a kinetic phenomenon, and the composition dependence of carbon activity in austenite. THEORY Consider for convenience one-dimensional interstitial diffusion in an fcc lattice in the [loo] direction. Fig. 1. Assume that solute atoms occupy octahedral sites only.7,9'10 These octahedral sites are located on {lOO} planes a/2Å apart. A solute atom, A, occupying an octahedral site on a {100 } plane denoted by 2, has twelve nearest-neighbor octahedral sites: four on plane 1, four on plane 2, and four on plane 3. Diffusion occurs when there is a net flux of solute atoms, through an imaginary plane shown with dashed lines, from plane 2 to plane 3. Fisher et al6. use the concept of activated complexes, as given in the theory of absolute reaction rates." They show that the number of solute atoms per cubic centimeter per second which pc — Fig. 1-Diagram showing the arrangement of octahedral sites (x) in the fcc lattice. pass in the direction of diffusion from activated to new interstitial position is: ?where C is the concentration of the solute in atoms per cubic centimeter, l/m + is the fraction of new interstitial positions corresponding to motion in the forward diffusion direction (transmission coefficient), ?F* is the free-energy difference between the activated complex and the reactants when each is in its standard state at the temperature of the reaction (independent of temperature and composition in the case of carbon in austenite), y is the activity coefficient of the solute species, and, finally, ym is the activity coefficient of the activated complex (assumed constant). The flux of atoms moving in the forward direction through an area of 1 sq cm perpendicular to the direction of diffusion is therefore: m+ Ym l ' atoms per second where is the distance between planes. The blocking model states that a nearest-neighbor octahedral site of a given solute atom has a probability, f, of being inaccessible to other solute atoms. The number of available sites for diffusion on a given plane will, therefore, depend on f, which is constant, and Nu, the number of solute atoms on that plane. The effect is to have more available sites in the diffusion direction, thereby increasing the net flux of solute atoms. This is reflected in the transmission coefficient, l/m. To calculate the transmission coefficient for solute

Jan 1, 1970

By G. V. Sullivan, B. E. Davis, T. O. Llewellyn

The Bureau of Mines, US Department of the Interior, conducted studies to recover phosphate from four dolomitic southern Florida deposits not currently mined. The samples contained 5.8-10.2% P205 and 1.7-4.8% MgO. Chemical analyses of sized fractions indicated that no pebble concentrate, +1.2 mm (+14 mesh) could be produced from these samples. A scheme was developed that consisted of desliming, grinding, scrubbing, and redesliming the ore to produce a flotation feed. Conventional one-step fatty acid fuel oil batch flotation tests on the samples resulted in concentrates containing 29.0-31.3% P205 at flotation recoveries ranging from 72.4 to 96.1% of the flotation feed. The MgO content of the concentrates ranged from 0.47 to 1.36%. Continuous flotation of the Manatee No. 2 sample indicated that commercial-grade phosphate concentrates analyzing 31.3% P205 and 0.55% MgO could be produced with a flotation recovery of 89.9%. The MgO content of concentrates obtained from the Manatee No. 1 and Hardee samples was 1.20 -1.36 %, respectively. Leaching with aqueous SO2 reduced the MgO content of these phosphate concentrates to 0.5 and 0.8%, but with a concomitant loss in phosphate recovery of about 10%.

Jan 1, 1985

By AIME AIME

LOCAL COMMITTEES. EXECUTIVE.-W. A. Lathrop, Chairman; R. V. Norris, Secretary; S. D. Warriner, Treasurer; Irving A.. Stearns, W. J. Richards, H. S. Drinker, C. D. Simpson. GENERAL RECEPTION.-Irving A. Stearns, Chairman. Archibald, James, Jr., Pottsville. Lawall, E. H., Wilkes-Barre. Ashley, H. H., Wilkes-Barre. Lentz, W. 0., Mauch Chunk. Ayres, WV. S., Hazleton. Lewis, Albert, Bear Creek. Beard, J. T., Scranton. Loomis, W. H., Jeddo. Bridgman, J. C., Wilkes-Barre. Markle, Alvan, Hazleton. Bunting, Douglas, Wilkes-Barre. Markle, John, Jeddo. Chase, F. M., Wilkes-Barre. Neale, J. B., Minersville. Coroner, Eli T., Scranton. Norris, R. V., Wilkes-Barre. Cote, E. B., Jr., Drifton. Oliver, Paul A., Oliver's Mills. Davies, W. H., Hazleton. Owens, W. D., Pittston. Davis, H. G., Dorranceton. Pardee, 1. P., Hazleton. Dodge, W. F., Wilkes-Barre. Quin, R. A., Wilkes-Barre.

Jul 1, 1911

By R. G. Ward, D. R. Gaskell

Using the maximum bubble pressure technique, the densities of iron silicates at 1410°C have been measured blowing helium, nitrogen, and argon. By ensuring equilibrium between the melt and the blowing gas with respect to oxygen potential and by minimizing tempcrature cycling of the furnace, iron precipitation in the melt has been prevented. Thus the previously reported effect of blowing-gas composition on the densities of the melts has been eliminated. Consideration of the oxygen densities of the melts gives an indication of the structural changes accompanying composition change. The density-composition relationship of iron oxide-silica melts in contact with solid iron has been the subject of several investigations1-7 and considerable disparities exist among the various results obtained. Of these investigations, all except one5 have employed the maximum bubble pressure method. In the most recently reported of these investigations1 the density-composition relationship obtained blowing nitrogen differed from that obtained blowing argon. The measured densities obtained under nitrogen were greater than those obtained under argon, the difference being a maximum at the pure liquid iron oxide composition and decreasing with increasing silica content. This observation rationalized the disparities existing among the results of the earlier investigations, showing that two lines, one for nitrogen and the other for argon, could be drawn to fit all the earlier results. No explanation for this phenomenon could be offered. Chemical analysis of rapidly quenched samples of melt for dissolved nitrogen, and direct weighing measurements, excluded solution of nitrogen in the melt from being the cause of the increase in density. The range of blowing gases was extended by Ward and Hendersons who measured the density of liquid iron oxide bubbling helium, nitrogen, neon, argon, and krypton. The measured density was found to decrease smoothly with increasing atomic number of the bubbling gas. The work reported here is a continuation of the program initiated by Ward and Sachdev7 to study the densities in multicomponent melts in which the iron oxide-silica system is the solvent. As such it is necessary to explain or eliminate the anomalous densities of iron silicates under different atmospheres, and the present rede termination was carried out towards this end. EXPERIMENTAL The maximum bubble pressure method of density determination was again employed and the experimen- tal apparatus used was essentially the same as that used by Ward and Sachdev.7 A molybdenum-wound resistance furnace heated an ingot iron crucible of internal diameter 1 in. containing a 2-in. depth of melt. The bubbling gas was blown through a 1/4 -in.-diam mild steel tube onto the end of which was welded a 2-in. extension of 1/4 -in.-diam ingot iron rod, drilled out to 5/32 in., and chamfered to an angle of 45 deg. The blowing tube was introduced to the furnace through a sliding seal and its position was controlled by a vertically mounted micrometer screw which allowed the depth of immersion to be determined with an accuracy of ± 0.01 cm. A Pt/Pt-10 pct Rh thermocouple was located below the crucible and temperature control was effected initially by means of an on-off controller and later by a saturable core reactor. The bubble pressure was determined by measurement of a dibutyl phthalate manometer using a cathetometer. PREPARATION OF MATERIALS Iron oxide was produced by melting ferric oxide in an inductively heated iron crucible in air. The liquid was quenched by pouring onto an iron plate. Silica was prepared by dehydrating silicic acid at 650°C for 12 hr. RESULTS Before any measurements of the density of a melt were made, the density of distilled water at room temperature was measured bubbling helium and argon. Both gases gave the density as 1.00 ± 0.01 g per cu cm which showed that the density of the manometric fluid (dibutyl phthalate) was not affected by contact with the blowing gas. With the furnace controlled by an on-off temperature controller an attempt was made to measure the density of pure liquid iron oxide by bubbling argon. The furnace atmosphere gas and bubbling gas were dried over magnesium perchlorate and deoxidized over copper turnings at 600°C. It was found that the pressure required to blow a bubble at a given depth increased slowly with time, and thus it was impossible to obtain a unique value for the density of the melt. Inspection of the blowing tube after removal from the furnace showed that rings of dendritic iron had precipitated from the melt onto the immersed part of the tube. This is shown in Fig. l(a) where the various "steps" correspond to different depths of immersion. The precipitation of iron was considered to be due to one or both of two possible causes: i) The composition of the liquid iron oxide is that of the liquidus at the temperature under consideration and can be expressed by the equilibrium

Jan 1, 1968

By G. Y. Chin, A. R. Von Neida

The relationship between crystalline texture and magnetic anisotropy in a Co-10 pct Fe alloy has been investigated by means of X-ray pole .figures, hysteresis-loop tracings, and magnetic-torque measurements. The cold-rolled texture of a sample after 95 pct thickness reduction is of the "brass-type", that is, (110)[112/. At 500°C the cold-rolled material recrystallizes fo a (311)[112] orientation, plus a minor (210) [001] component. This texture persists up to 1400°C, at which point it is replaced by a secondary recrystallization texture, (111)[112]. Magnetic-torque measurements show that the easy axis of magnetization lies along the transverse direction in the cold-rolled material and changes to the rolling direction after primary recrystallization. This change is also reflected in the hysteresis characteristic; whereas the B-H loop along the rolling direction is nonsqunre with a low value of residual induction (750 vs 19,000 gauss at saturation) for the cold-rolled material, the annealed sample exhibits a very square loop with a large value of residual induction (16,000 gauss). Theoretical torque curves calculated from the texture data on the basis of magnetocystalline anisotropy energy compare favorably with the observed torque curves. Values of the crystal anisotropy constant, K1, obbained from these comparisons are in good quantitative agreement with single-crystal data. Furthermore, both the torque amplitude of the poly crystalline material and the magnitude of K1 obtained with a single crystal show an identical temperature dependence over the range from —195° 10 +220°C. It is thus conclzided that the magnetocrystalline anisotrpopy erlergy is chiefly I-esponsible. for the nzagnetic allisotropy of textured Co-10 pct Fe alloy. THE results of a study on the relationship between crystalline texture and magnetic anisotropy of an alloy containing 90 pct Co and 10 pct Fe by weight are reported in this paper. The alloy has an fcc structure: a saturation magnetization of about 19,000 gauss,2 and a nearly zero value of magnetoatriction.3 puzey4 has reported a large crystalline anisotropy constant of -7.4 X 105 ergs per cu cm, indicating the (111) directions as the easy axes of magnetization. Hence, texture variations resulting from cold work and annealing are expected to introduce a magnetic anisotropy in the polycrystalline material through the alignment of these (111) easy directions. In the present study, magnetic anisotropy of both rolled and annealed strips was determined by magnetic-torque measurements and hysteresis-loop tracings The results were correlated quantitatively with calculations based on texture data obtained by the X-ray pole-figure technique. It is established that the magnetocrystalline anisotropy energy is indeed chiefly responsible for the magnetic anisotropy of textured Co-10 pct Fe alloy. EXPERIMENTAL Material Preparation. The alloy nominally contained 90 pct Co, 9.5 pct Fe, and 0.5 pct Mn by weight, the chief impurities being nickel, carbon, and silicon (less than 0.5 pct total). The cast ingot was rolled to strips 10 mils thick and slit to 1 in. in width. After strand annealing at 900°C in a hydrogen atmosphere, these strips were further cold-rolled to various thicknesses down to 0.25 mil (97.5 pct reduction), with samples collected for study of the development of texture and magnetic anisotropy as a function of thickness reduction. subsequently, samples cold-rolled from 100 mils to 0.25 mil were obtained, thus extending the thickness reduction range to 99.75 pct. In addition, 0.5-mil samples cold-rolled from 10 mils were selected

Jan 1, 1965

By James Yancik

The Howe Coal Co. is mining the Oklahoma Lower Hartshorne bed which ranges in seam thickness from 38 to 42 in. and pitches approximately 7° to the northeast. The raw feed to the cleaning plant averages about 20% ash and 1.10% sulfur, being reduced in the cleaning process to 4.8% ash and 0.9% sulfur with a free swelling index of 8 or 8%. This coal rivals the Pocohantas seam in chemistry and coking characteristics but has better fluidity than the Pocohantas seam coal. The coal is presently being prepared for the Japanese steel market in an 85-tph pilot plant designed and constructed by Roberts & Schaefer. The cleaning-plant flowsheet is discussed in detail.

Jan 1, 1972

By Craig R. Barrett, Alan J. Ardell, Oleg D. Sherby

It is shown that the apparent activation energy for creep of pure poly crystalline metals increases with increasing temperature in the temperature range 0.5 to 1.0 of the absolute melting temperature. This increase is probably associated with the influence 0-f the elastic modulus on the creep rate. By accounting for the variation of Young&apos;s nodulus with temperature, the true activation energies for creep of pure cadmium and aluminuvl are shown to be equal to the activation energies for self-diffusion in these metals, within experimental error, at all temperatures above 0.5T,. New creep parameters are proposed for cmrelation of steady-state creep rate and time-to-rupture data. These are respectively, where u is the creep stress, E is Young&apos;s rrodulus, i,is the steady-state creep mte, t, is the time -to-rupture, and D is the self-diffusion coefficient [equal to Do exp (-QSd/RT)] . It has been established experimentally1 and theoreticallyZm4 that high-temperature creep of poly-crystalline pure metals is a thermally activated process and may be represented by the general expression where <, is the steady-state creep rate, A is a constant dependent on the internal structure of the material, f is some function of the applied stress (0) and test temperature (T), and D is the self-diffusion coefficient. If D is separated into its temperature-dependent and independent portions, then it is possible to rewrite Eq. [I] as where Qsd is the activation energy for self-diffusion. Assuming a simple Arrhenius-type relationship between creep rate and temperature at a given constant stress, the apparent activation energy for creep, Q,, is given by the expression It is obvious that if is not a function of temperature It has been shown that the steady-state creep rate for pure polycrystalline metals1 can be represented by where S is a constant, L is the grain diameter, E is the isotropic polycrystalline (unrelaxed) elastic modulus, and n is a constant equal to approximately 5 over a wide range of stress. The apparent activation energy for creep calculated from this expression at constant grain size and stress is given by

Jan 1, 1964

By T. H. Alden, H. W. Schadler

The strain rate dependence of the flow stress of the eutectoid Zn-Al alloy has been determined as a function of mechanical processing, microstructure, and temperature. The best superplastic properties result from the ultrafine, equiaxed structure produced by solution treatment and isothermal transformation at 0°C. Lamellar structures produced by isothermal transformation and coarse equiaxed structures produced by annealing also exhibit strain rate sensitivity in excess of 0.5, but at higher stresses and lower strain rates than the finest structure. Solution treatment and isothermal transformation eliminate the effect of prior processing history. Small composition variations in the binary alloy do not influence the mechanical properties. Below the eutectoid transformation temperature (.275C) increasing temperature lowers the flow stress at all strain rates. The data do not favor any of the present proposals for the mechanism of superplastic flow. ALLOYS of zinc and aluminum, near the eutectoid composition, have been investigated for: 1) the flow stress-strain rate and elongation behavior,1, 2) the transformation kinetics,3 and 3) structure,3"5 but the structure sensitivity of the mechanical properties is poorly understood. Using a near eutectoid alloy water-quenched from 380°C, Backofen et aL2 estab- high and increases with increasing strain rate. They found a correlation between strain rate sensitivity and tensile elongation as expected from the increased resistance to necking that a high strain rate sensitivity provides.296 The large elongation at high strain rates is attractive for metal forming. Since most other superplastic alloys7-l3 do not show high strain rate sensitivity at such a high strain rate (for the exception see Ref. 12) there is the possibility of a unique deformation mechanism for this alloy. The sensitivity of the mechanical properties of the eutectoid alloy to thermal history1 suggests a structure sensitivity that has not been demonstrated. Gar-wood and Hopkins3 identified a lamellar product for material transformed between 200" and 260°C. The size of the lamellae decreased with decreasing temperature. They also demonstrated that an unresolved transformation product formed below 200°C. A granular two-phase material was resolved for specimens quenched to below 150°C by Mitbauer and sauerwald4 who observed coarsening of the structure after annealing. The role of grain boundaries in superplastic deformation is suggested by the strong effect of grain refinement in encouraging this phenomenon at high strain rateS7-11, 13 and is emphasized in several proposals about rnechanism7, 8, 12 and in a theory14 of high-temperature deformation. Alden8 showed metallographic evidence that grain boundary sliding is occurring extensively at strain rates where m is large but less at high strain rates where normal plasticity is observed. Holt and Backofen10 have shown that sliding also oc-

Jan 1, 1969

By R. T. Hukki, A. M. Gaudin

Previous work on the principles of comminution has shown: (I) that the surface produced is proportional to work input (Rittinger law,1a-3); (2) that there is regularity to the weight distribution of the fragments according to size.4-10 In this paper it is brought out that the surface on the fragments is distributed in definite and simple relation to size. The experimental work has involved: I. Construction of an apparatus capable of measuring the surface of mineral fragments independently of the chemical composition of the fragments and independently of the site of the surface; 2. Refining the methods available for measurement of particle size; 3. Designing and building a crusher capable of operating on very small quantities of mineral, if necessary on single crystals, and in such fashion as to minimize handling losses of material. Complete experiments have been carried out with massive quartz and individual quartz crystals. partial experiments, lacking surface measurements, have been made with glass spheres, galena, sphalerite, fluo-rite, salt and coal. Introduction The existence of regularity in weight distribution with size was noted many years ago, especially by A. 0. Gates;&apos; the subject was also studied in detail by one of us.6 In the latter paper it was shown that rocks can be divided into two classes: homogeneous rocks, which show no preferential breaking, and heterogeneous rocks, which show preferential breaking at the grain size of the rock. It was shown, furthermore, that the fragments obtained by rupturing a homogeneous rock occur (in the fine range) in such abundance as to permit the writing of a relatively simple equation to relate the weight retained on a screen to the screen opening. With screens of which the openings are in constant ratio, the weight retained, w, is related to the screen size x by the equation w = Cxm [I] In this equation C and m are experimental constants. A plot of weight retained against particle size is a straight line of slope m if the scales for x and w are both logarithmic. In the fine range, the slopes of the size-distribution graphs plotted according to the method described above vary within a limited range. An inspection of a number of size-distribution data by various experimenters indicates that the slope very seldom exceeds 1.0, but is usually greater than 0.7. More recently, schuhmann8 proposed a method of charting that has so many advantages of its own that it has been used primarily in this work. For fine particles Schuhmann has found that the data are represented by the equation (x)m k [2]

Jan 1, 1947

By A. M. Gaudin, R. T. Hukki

Previous work on the principles of comminution has shown: (I) that the surface produced is proportional to work input (Rittinger law,1a-3); (2) that there is regularity to the weight distribution of the fragments according to size.4-10 In this paper it is brought out that the surface on the fragments is distributed in definite and simple relation to size. The experimental work has involved: I. Construction of an apparatus capable of measuring the surface of mineral fragments independently of the chemical composition of the fragments and independently of the site of the surface; 2. Refining the methods available for measurement of particle size; 3. Designing and building a crusher capable of operating on very small quantities of mineral, if necessary on single crystals, and in such fashion as to minimize handling losses of material. Complete experiments have been carried out with massive quartz and individual quartz crystals. partial experiments, lacking surface measurements, have been made with glass spheres, galena, sphalerite, fluo-rite, salt and coal. Introduction The existence of regularity in weight distribution with size was noted many years ago, especially by A. 0. Gates;&apos; the subject was also studied in detail by one of us.6 In the latter paper it was shown that rocks can be divided into two classes: homogeneous rocks, which show no preferential breaking, and heterogeneous rocks, which show preferential breaking at the grain size of the rock. It was shown, furthermore, that the fragments obtained by rupturing a homogeneous rock occur (in the fine range) in such abundance as to permit the writing of a relatively simple equation to relate the weight retained on a screen to the screen opening. With screens of which the openings are in constant ratio, the weight retained, w, is related to the screen size x by the equation w = Cxm [I] In this equation C and m are experimental constants. A plot of weight retained against particle size is a straight line of slope m if the scales for x and w are both logarithmic. In the fine range, the slopes of the size-distribution graphs plotted according to the method described above vary within a limited range. An inspection of a number of size-distribution data by various experimenters indicates that the slope very seldom exceeds 1.0, but is usually greater than 0.7. More recently, schuhmann8 proposed a method of charting that has so many advantages of its own that it has been used primarily in this work. For fine particles Schuhmann has found that the data are represented by the equation (x)m k [2]

Jan 1, 1947

By W. R. Hibbard

IN ref. 1, on the basis of tension and torsion experiments with single crystals of a brass, the values given in Table I were obtained for elastic coefficients. It was pointed out by Zener that the values for the 71.2 pct Cu were not satisfactory, since they resulted in a negative value for the bulk modulus, namely —4.17X1012 sq cm per dyne. In reevaluating the data of this investigation, it was determined that the reason for this negative bulk modulus lay in the extrapolation of the reciprocal Young&apos;s modulus to the zero value of the orientation function shown in Fig. 5 of ref. 1. This extrapolation was reevaluated by the method of least squares (50 pct probability) and a new value of the coefficient S,, was determined as 18.9220.42X 10M sq cm per dyne in lieu of the value originally reported of 18.82x10 sq cm per dyne. This new value of S, leads to a new value of S, of — 9.43 X101" sq cm per dyne. The values of the other coefficients are unchanged. results. This value compares with the value of 12.3X10 sq cm per dyne reported by Schmid and Boas? The new results are summarized in Table 11. These results follow similar qualitative trends, previously published,&apos; relative to the effect of zinc content. However, the derived values of C11, C,, C,, and K are so sensitive to the uncertainty in the first decimal place of the S, values that they are probably not useful. This uncertainty must also apply to the previous results of Masima and Sachs," who obtained S, values from a similar extrapolation drawn wholly above their data points. Acknowledgments Advice and assistance on the statistical methods were obtained from R. W. Guard. The calculations were carried out by Miss E. Saacke.

Jan 1, 1958