Search Documents

By C. P. Lawhon, J. P. Simpson, W. M. Evans

Data obtained under controlled test conditions using a microbit drilling machine showed that oil emulsified in water muds may either increase or decrease the drilling rate, depending upon drilling conditions. A low-viscosity oil such as diesel fuel can give drilling rates in limestone almost equal to that of water. Data obtained for water emulsified in oil muds showed little decrease in the drilling rate in water-saturated cores as the water percentage of the mud was increased above the 5- to 10-percent range. Changes in drilling rate were found to be dependent upon the oil or water concentration of the mud and upon the type of formation drilled. Changes in static filtration on paper (API filtrate) did not correlate with filtration while the mud was circulated across rock. INTRODUCTION Oil additions to water muds have been reported to increase drilling rates, provide hole stability and improve filtration control. Eckel' showed that water-base emulsion muds used in the West Texas area increased drilling rate with increasing oil concentration up to 15 percent oil by volume, but drilling rate decreased at a concentration of 20 percent by volume. Based on laboratory tests using water muds to drill shale, Cunningham and Goins' reported that drilling rates increased and tendency for the bit to ballup decreased with the addition of oil. Percentage increase in drilling rate varied with the particular formation. They showed oil additions to improve drilling rates ap proximately 75 percent in Vicksburg shale and as much as 150 percent in Miocene shale. Each investigation showed an optimum oil content for the particular formation. Most data that indicated improved filtration control due to oil additions were based on static API Eltrates through paper rather than dynamic filtration through permeable rocks. Some types of dynamic test give a better representation of filtration down-hole while drilling and might be more likely to show some correlation with drilling rate. Static filtration would be important, of course, in relation to hole stability and formation damage. This laboratory's drilling tests, conducted on water-raturated Berea sandstone, indicated that improvements in drilling rate were not evident with increasing oil concentration in water-base muds. Investigation also showed similarity between oil-emulsion (water-in-oil) muds and water-emulsion (oil-in-water) muds while drilling these formations. In Lueders limestone high concentration of water-in-oil muds and high concentration of oil-in-water muds provided the same relative drilling rates. In Berea sandstone there was a large reduction in relative drilling rate with both the oil and water muds that contained low percentages of emulsified fluid. Dynamic filtration rates of water muds on rock did not always decrease with increasing oil percentages even though the static API filtration rates on paper did decrease. Data observed in laboratory drilling of limestone and sandstone indicate that improvements in field drilling operations when water- or oil-emulsion muds are wed may not be the result of increased drilling rates but of improved hole conditions. In some cases, actual drilling rates might be slower but improved hole conditions will result in less total time on the hole. DEFINITIONS Mud pressure—Pressure of drilling fluid as measured after leaving the drilling chamber. This is considered as the approximate mud pressure just past the bit and at the face of the formation. Terrastatic pressure—Pressure representing weight of overburden. Formation pressure—Pressure of formation fluid as measured at outlet of drilling chamber. This is considered as approximate pressure of fluid in the pores of the formation. Differential pressure—Difference between the mud pressure and formation pressure. Relative drilling rate, percent—Drilling rate with experimental fluid divided by drilling rate with water times 100 equals percent. LABORATORY EQUiPMENT AND TESTING PROCEDURES The drilling equipment has been described in previous publications The microbit drill is a closed system (capacity, approximately 7 gal) that can be pressurized to 15.000 psi and heated to 500F. Main components are a drilling chamber, filter-heater, rotary-drive and variable-speed cir-

forated, allowing the completion of the removal of wash water. When discharged into the washed nut bin, the coal is moist but carries so little water as to not be objectionable to the trade, nor to give any difficulty from freezing during the coldest weather. The rock and bone from the primary jigs is elevated to a 15-ton bin by means of a single strand scraper conveyor 40 feet center to center operating on a 45 degree incline, carrying 12" x 5" scrapers every two feet. This conveyor travels at a speed of 100 feet per minute and has a capacity of 17 tons per hour. From this bin, this material falls into the third or rewash jig similar in all respects to the first two, which discharges the rock waste directly into a 15-ton refuse bin below and the bone into a short dewatering conveyor which delivers into a similar 15-ton bin from which the bone is taken to the powerhouse. The oversize and water from the shaker screen, the water from the dewatering conveyor for both the washed nut and bone, and the sludge and wash water from the three jigs, are delivered by launders to the first compartment of a three-compartment settling tank. Most of the coarser broken coal is deposited in this tank, from which is it continually removed by a bucket elevator carrying 8" x 5" perforated buckets operated on a 60 degree incline at 200 feet per minute, capable of delivering 25 tons per hour to the 50-ton washed coarse slack bin. The water passes successively through the three compartments of the settling tank and from thence through a six-inch pipe to a centrifugal pump, circulating 900 gallons per minute against a 32-foot head. A four-mesh screen 30" x 72" in the third compartment of the settling tank removes the chips of wood, paper, and the other trash, which otherwise would accumulate in the water. Water is provided from the camp water system, deriving water from the well located in an arroyo bed. During the summer months just passed, the water used, has been 108 gallons per ton of raw nut, or 146 gallons per ton of washed nut. The water meter had not been installed last winter, but it is estimated that operating at capacity, the washery will be found to require only about 75 to 100 gallons per ton of raw nut. It has not been found necessary, nor advisable, to attempt to dry the sludge from the settling tank, nor to save the water from leakage of the tanks and bins. The sludge from the jigs is washed into the settling tank and the sludge from the settling tank is washed through a tile drain to the arroyo. The jigs, shaker screen, circulating pump, washed slack elevator, and the rock handling conveyor, are all driven from line shafts driven by one 40 H. P. motor, each jig driven through a clutch. The belt conveyor and the washed nut conveyor, have separate motor drives of five and seven and a half H. P. respectively. The washer is housed in a corrugated iron building, which is partially heated by steam coils. One attendant is required for operation, regulating the feed of the jigs, the supply of water, removal of the rock, and oiling and maintaining the machinery. The rewash jig is operated only intermittently. About eleven per cent by weight of raw nut is removed as waste and four per cent goes to the washed slack bin. No control analyses of the products have been made; the efficiency of the plant being determined only by the physical appearance of the products; but the washery has been a source of pride and satisfaction to all those connected with it. As mentioned before, it has caused no interruption of operation and it has assisted materially in creating an unprecedented demand for ALAMO nut. MR. CHARLES: If there are any questions, I shall be pleased to endeavor to answer them. MR. LITTLEJOHN: Mr. Charles, do I understand it is the nut only that is washed there? MR. CHARLES: Yes, sir. MR. LITTLEJOHN: What did you say the size was? MR. CHARLES: Through three inch round perforations, retained on

Jan 1, 1926

By G. W. P. Rengstorff, H. B. Goodwin

A method is described for purifying iron in batches of 150 Ib or more. Oxygen, carbon, nitrogen, and sulphur are removed from flakes of electrolytic iron by treatment in wet and then dry hydrogen. A special consumable-electrode arc furnace is used to remove hydrogen and to melt the flakes into ingots. A LTHOUGH iron and steel have been made and used for hundreds of years, there are still wide gaps in the knowledge of these metals. One reason for this is that the true properties of the base metal, iron, are not well known, simply because really pure iron has never been readily available for research purposes. Commercial iron, and even the "pure" irons which are readily available, are really complex alloys of iron with oxygen, nitrogen, hydrogen, carbon, sulphur, silicon, and other elements. With such materials, it has not been possible to prepare steels and other iron-base alloys in which all elements are present in exactly controlled amounts. It is an almost impossible task to determine the separate effects of each element or the intereffects of several elements unless alloys can be prepared containing only the desired elements. The ability to make controlled alloys of low impurity content is of far more than academic interest. It will assist in the study of such practical problems as the brittle failure of ship hulls or high pressure gas pipelines, determination of the factors which affect the deep-drawing properties of steels, the improvement of magnetic and electrical properties, the phenomenon of aging, and many others. In 1949, the American Iron and Steel Institute asked Battelle Memorial Institute to prepare high purity iron on a larger scale than had been attempted up to that time. The work was directed toward the preparation of iron as low as possible in carbon, oxygen, nitrogen, hydrogen, and sulphur because these are the contaminating elements of major interest in many research investigations on iron-base alloys. The initial goal was to prepare iron with not more than a few thousandths of one percent of each of these impurities. The purpose was to set up a "bank" of high purity iron on which researchers could draw when a supply was needed and which could be replenished from time to time as the stock became depleted. Of several possible purification methods, heating in hydrogen was selected as the most promising for the removal of both carbon and oxygen from solid iron. Metallic impurities are not removed by hydrogen. Electrolytic iron was chosen as a starting material because it is the most readily available form of iron low in metallic impurities. Decarburization and desulphurization were obtained by annealing in wet hydrogen at relatively low temperatures. The optimum temperature, as found by previous investigators,' is about 1400°F. This treatment also removes nitrogen. Deoxidation is favored by dry hydrogen and higher temperature. There is evidence from previous work that an anneal at 2200°F in dry hydrogen will deoxidize the iron, reduce the nitrogen content, and reduce the sulphur content. These facts suggested the use of a two-stage process: treatment in wet hydrogen followed by treatment in dry hydrogen. To carry out the purification process in a reasonable time, it was necessary that the iron be in thin pieces. Flakes of electrolytic iron were used. Because most research requires that the iron be in massive form, it was nccessary to melt the purified iron to consolidate it into large pieces. For this work, it was decided to prepare ingots weighing at least 15 lb by using a cold hearth arc-melting process in which the iron was melted in an inert atmosphere of argon or helium. This method of melting was selected because the water-cooled copper crucible is not wet by the iron and does not contaminate it as a refractory crucible would. Because the crucible is also the ingot mold, contamination from mold materials was also eliminated. Contamination from electrodes was avoided by making them from purified electrolytic iron. The melting procedure finally developed was an adaptation of the Kellogg electric ingot process.' Two batches of purified iron weighing about 100 Ib each in ingot form were prepared with analyses as shown in Table I. The remainder of this paper describes the procedures in more detail. In general, the process con-

Jan 1, 1956

By Henry R. Piehler

Continuous seven- and nine teen -filament close-packed silver-steel filamentary composites mere tested in tension. For purposes of comparison, the tensile behavior of the composite was predicted from the measured properties of the individual com-ponents. It was assumed that the axial strain is the same in both components and that the contribution of each component to the composite flow stress is proportional to its volume fraction. Good agreetnent was obtained between the observed and predicted tensile behavior. However, the composite elongation at fracture was about twice that observed when the individual steel wires were tested alone. Composites in which the filaments were widely spaced failed by the consecutive fracture of the filaments. In composites with closely spaced filaments, a composite instability preceded frachcre. These effects are explained in terms of a lateral restraint to the necking of the filaments which develops in the deforming composite. TWO-COMPONENT or composite materials are increasingly being developed and used as structural materials. Of all the composite geometries used, the filamentary configuration has proved to be the most successful. Polymer-bonded fiber-glas, the most common of the filamentary composites, has been investigated most extensively to date. One explanation of the behavior of fiberglas1 suggests that the load transfer between the glass fibers and the polymer matrix occurs primarily through friction. Bond separation between the fibers and the matrix is presumed to occur at very low stresses. Subsequently, only frictional bonding can provide for the transfer of load from the matrix to the fibers. The force normal to the fiber-matrix interface which gives rise to this friction is assumed to arise from the matrix shrinkage which occurs during solidification. The behavior of metallic filamentary-composite materials would be expected to differ from that of fiberglas in several significant aspects. Residual stresses resulting from differences in thermal contraction can be kept to a minimum by proper heat treatment. A strong wetted bond is formed between the two phases. In brazed joints,2 for example, the interphase bond is sufficiently strong that the weaker material will fail before separation occurs at the interface. Most metal filaments can undergo appreciable amounts of plastic deformation before failure. Failure by plastic instability or necking frequently occurs in metallic filaments, but not in glass fibers tested at room temperature. Differences between the behavior of fiberglas-polymer and metallic filamentary composites have indeed been observed in composites containing various types of metallic filaments in a silver matrix.3,4 At strains of the order of 10-2 pct, all the deformation was accommodated by the silver matrix. Hence, the strength of the composite depended only on the fiber concentration and not on the nature of the fiber. At higher strains, the strength of the composite increased when filaments with higher work-hardening rates were used. Surface slip line observations on a silver-mild steel composite that had been stretched 4 pct showed that an appreciable amount of deformation occurred in the filaments. Work on tungsten-copper filamentary composites5 has shown that the ultimate tensile strength for varying filament fractions followed a linear mixture rule. Assuming that the axial strains in both filaments and the matrix are equal, this linear mixture rule can be expressed as: The subscripts c, f, and m refer to the composite, filaments, and matrix, respectively. A and V are the area and volume fractions of each component. sc and of are the ultimate tensile strengths of the composite and the filaments. sm is the flow stress of matrix at a strain equal to the elongation at failure of the filaments. However, the tungsten filaments can undergo only a limited elongation before they fracture without an appreciable reduction in area. A composite containing more ductile filaments might indeed deviate from this linear mixture rule for the ultimate tensile strength, since filament failure by necking might be arrested by the matrix. SPECIMEN PREPARATION Specimens were prepared from 0.8 pct carbon steel piano wires of 0.015 in. initial diameter. The wires were given a thin nickel flash and a silver plate varying in thickness from 0.015 to 0.007 in., depending on the filament fraction desired. In order

Jan 1, 1965

By V. Koump, T. F. Perzak, R. G. Olsson

The rate of dissolution of recrystallized alumina in molten iron oxide in equilibrium with iron at 1450°C was studied by rotating alumina disks in the melt. The samples were rotated from 1 to 12 min at speeds from 54 to 3270 rpm. It is concluded from the experimental results that the process is limited by diffusion in the liquid boundary layer. The interdiffusion coefficient for the dissolution of alumina disks in pure molten iron oxide was estimated to be about 3 xl0-5= sq cm per sec. THE erosion of refractory materials is of considerable importance in iron- and steelmaking processes. Since many refractories contain alumina, this investigation was undertaken to develop a further understanding of the erosion mechanism. Shurygin et al.1-3 have investigated the rate of dissolution of alumina in molten silicates and molten fluorides by rotating alumina disks in various melts. The rates were reported to be limited by diffusion in the liquid boundary layer. In the present investigation the rate of dissolution of alumina in molten iron oxide in equilibrium with iron was studied in a similar manner; alumina disks were rotated at different speeds in molten iron oxide at 1450°C. The relationship between the rate of dissolution of the flat surface of the disk and the speed of rotation was used to determine whether the process is limited by diffusion in the liquid boundary layer or by some chemical reaction mechanism. APPARATUS AND EXPERIMENTAL PROCEDURE A schematic diagram of the experimental apparatus is shown in Fig. 1. The iron oxide melts were contained in 2-in.-diam high-purity iron crucibles that were centered in a cylindrical graphite susceptor. Prior to each sequence of experiments, sufficient reagent-grade ferric oxide was added to a crucible to form approximately 350 g of molten iron oxide; the depth of the melt was about 11/2 in. To prevent excessive erosion of the crucible, about 70 pct of the required iron was added to the crucible in the form of iron powder. The mixture was melted in an atmosphere of purified argon by induction heating with a 250-kc generator. After the oxide was molten, a Pt/Pt-10 pct Rh thermocouple at the exterior of the crucible was calibrated against an iron-sheathed thermocouple immersed in the melt and was thereafter used to regulate the melt temperature. All experiments were conducted at 1450°C with a probable error of 10°C. The alumina disks were constructed from pure re-crystallized alumina having a density of 3.7 g per cu cm (porosity approximately 6 pct). For each disk sample a 1-cm-diam alumina cylinder of known length (0.9 to 1.0 cm) was cemented into a ground seat at the end of a 1.27-cm-OD centerless ground alumina tube. The ends of the tube and cylinder were flush and served as the disk surface. When mounted in the apparatus the alumina tube was guided by tungsten carbide bearings and rotated by a variable-speed motor. The bearing and drive assembly could be raised and lowered in order to allow the sample to be quickly moved in and out of the melt. At the start of an experiment, a sample was preheated for several minutes directly above the melt, and then immersed in the middle of the melt to a depth of a in. and rotated for 1 to 12 min at speeds of 64 to 3270 rpm. The speed of rotation was measured by a hand tachometer. At the start and completion of each experiment, a melt sample was withdrawn with a cold copper rod and the alumina content was determined by chemical analysis. During individual experiments the alumina concentration of the melt changed by the order of 0.25 wt pct. Average melt compositions for individual experiments were used in the subsequent computations and were in the range between 0.12 and 4.3 wt pct alumina. The extent of dissolution was determined by sectioning the end of the sample and measuring the final length of the alumina cylinder with a microscope. Since the exposed end of the cylinder, i.e., the disk surface, was etched in a manner characteristic of this geometry, a number of measurements were made on

Jan 1, 1969

By T. P. Floridis, J. H. Young

The need for close control of the phosphorus content of steels has led to numerous investigations on the equilibria of the dephosphorization reactions. Winkler and chipman1 have established the general conditions for effective dephosphorization of steel. They are high slag basicity, high oxygen potential, and low temperature. Other investigators have made additional contributions to the understanding of the dephosphorization process. The current status of the understanding of the dephosphorization of steel is concisely presented by Bodsworth2 and by Ward. The investigation reported in this communication was undertaken with the purpose of establishing the effect of additions of barium oxide and calcium fluoride on the dephosphorizing capacity of slags. Esin and Gel'd4 proposed that barium oxide, being more basic than calcium oxide, should cause an increase in dephosphorizing capacity when added to steelmaking slags, or when used as a substitute for calcium oxide. Derge5 has also proposed that in the future conventional slags might be replaced by BaO-Al2O3 slags. There is, however, no experimental evidence confirming the effect of barium oxide on the dephosphorizing capacity of slags. The effect of calcium fluoride on the dephosphorization of steel is not clearly understood. It is generally recognized that additions of calcium fluoride are beneficial. It is not clear, however, whether calcium fluoride affects the equilibrium of the dephosphorization reaction, or whether it simply causes an increase in the fluidity of the slag and, consequently, faster approach to equilibrium. The experimental procedure consisted in equilibrating synthetic molten slags with liquid copper at 1550°C under a gas stream containing argon, hydrogen, and water vapor. In all experiments the argon to hydrogen ratio was approximately 4:1, and the hydrogen to water ratio was 5.42:l. Molybdenum crucibles were used as containers for the slag and metal. Under the above-described conditions of temperature and composition of atmosphere, there was no observable attack of the crucibles by the metal, slag, or atmosphere. Copper was used instead of iron, because iron attacks molybdenum. The equilibration was made in a tubular furnace consisting of a recrystallized alumina tube. The alumina tube was heated by electrical resistance. A Pt-40 pct Rh wire winding was used for most runs. A silicon carbide tubular resistor was also used for some runs. Temperatures were measured with a Pt-Pt-Rh (10 pct Rh) thermocouple and kept constant within ±5°C. Equilibrium was approached from both sides, i.e., by adding the phosphorus either as oxide in the slag or as a phosphorus-rich alloy of phosphorus and copper. The holding time at the equilibrium temperature was 6 hr. At the end of each run the crucibles were rapidly cooled and removed from the furnace. The slag and metal were separated and analyzed. The experimental results are shown in Table I. The phosphorus content of the slag is expressed both as percent phosphorus pentoxide and as percent phosphorus. The basicity ratio is computed by dividing the number of moles of basic oxides-oxides of barium, calcium, magnesium, and sodium—by the number of moles of acidic oxides- oxides of aluminum, phosphorus, and silicon. Calcium fluoride is not included in the computation of the basicity ratio; i.e., calcium fluoride is assumed to be neither basic nor acidic. The distribution ratio of phosphorus—percentage of phosphorus in the slag divided by the percentage of phosphorus in the metal- is plotted in Fig. 1 against the basicity ratio. The results indicate that slags containing barium oxide have greater dephosphorizing capacity than slags containing calcium oxide. The high dephosphorizing capacity of slags containing sodium oxide and the low dephosphorizing capacity of magnesia-containing slags which already have been reported in the literature2 are confirmed by the results of this investigation. It appears that calcium fluoride has a beneficial effect on the distribution of phosphorus between slag and metal in acid slags only. Although the obtained distribution ratios between the phosphorus contents of slag and copper are not directly applicable to the dephosphorization of steel, they are sufficient for evaluating the effect of slag additions on the dephosphorizing capacity of slags in general. An increase in the ratio of distribution of phosphorus between slag and metal indicates lowering

Jan 1, 1968

By R. F. Mehl, C. E. Birchenall

SINCE Maxwell1 first considered the self-diffusion process in 1872 its importance in the kinetic theory of matter has been recognized. Until the discovery of isotopes in 1913, a direct measurement of this quantity seemed impossible. The only information that could be gathered indirectly was for gaseous systems for which the kinetic theory was well developed. When methods of direct observation be-came available, investigations on self-diffusion were carried out in condensed phases. In metals these data are presumably of potential importance in the study of recovery, recrystallization, creep, sintering, and related phenomena. Following the pioneer work of Von Hevesy2 and his collaborators, who determined the rate of self-diffusion in lead with the naturally occurring thorium B isotope, several metals have been investigated. Pb, Ag³, Au.6,5, and Cu6,7,8,9 are examples of isotropic crystals existing in only one phase modification. Anisotropy of diffusion has been demonstrated in Bil6 and Znll. This paper is a study of a single metal in two allotropic forms and also of self-diffusion in a body-centered cubic lattice. Despite the fact that the measurements in each of the papers cited on self-diffusion in copper seem to be internally consistent to about 10 to 15 pet, the curves reported by different authors differ by factors of 2 to 4 at the same temperatures. This uncertainty may account, in part, for the failure to establish a successful correlation between the self-diffusion rates and other physical characteristics of the metals. No satisfactory theory of metallic self- diffusion has as yet been proposed to account for all the existing data and to permit estimation in other metals. Experimental Part: Two units of radioactive iron were used in these experiments, each a mixture of Fe53 and Fe59 (12). Fe53 decays by K electron capture and the emission of an X ray with a half life of about 4 years. Fe59 emits two beta spectra, one with a maximum energy of 0.26 Mev, the other 0.46 Mev, and gamma rays of 1.1 and 1.3 Mev, with a half life of about 44 days. They were present in nearly equal concentration initially. The composite half life started at about 50 days and increased as the Fe59 decayed, leaving Fe55 relatively more abundant. After aging a year, the half life was too long to measure significant decay in a month. The absorption properties also changed with time. Because of the importance of the absorption coefficient in the diffusion calculations, it was necessary to determine this quantity frequently over the period during which these experiments were carried out. This correction was unsuspected at the time of publication of notesl3 on this work and accounts for the discrepancy in alpha iron and for part of the discrepancy in gamma iron.* * The data in the present paper supersede those given in the notes entirely. In one note the scale of log D was inadvertently reversed. In addition to the correction for the drift in absorption coefficient, the D values for gamma iron at low temperatures were high owing to insuficient correction for diffusion occurring during heating and cooling through the high temperature part of the alpha range at a rate much slower than that employed in the runs reported here. The high temperature alpha rates are much higher than the low temperature gamma rates and correspond to large equivalent times at these temperatures. These experiments were discarded and new measurements taken. Independent experiments with the same activity units indicated a radioactive contaminant in the iron, but exhaustive attempts to isolate and identify it chemically failed. These experiments? indicate † These experiments will be discussed in a later publication from this laboratory. that the contaminant represented only a trace of little importance in the diffusion results. The active iron was plated from an iron chloride solution. Enough of the solution was dropped on a 1% in. square of filter paper to wet it thoroughly.

Jan 1, 1951

By Q Liu, P D. Katsabanis

The energy output of crushed AN/FO, crushed AN/FO mixed with Aluminum (5%, 6.4% and 9.4% A1 by mass) and a commercial emulsion explosive has been measured using a detonation calorimeter. The charges had a diameter of 10 mm and were heavily confined by a 11 mm thick copper shell. In order to achieve stable detonation glass microballoons were used in the explosives so that the density of the AN/FO charges would be around 1.1 g/cc. The charges were detonated in vacuum and the detonation products were analyzed using gas chromatography. It was found that energy values were very close to calculated values obtained by ideal detonation codes.

Jan 1, 1993

By C. R. Kuzell

The Editor desires to call attention to the charts in the paper of the above title which were published in the August Bulletin on pages 2190 and 2191. It was impracticable to include in the Bulletin. charts of sufficient size to be used as working diagrams for the direct determination of operating values, but the Institute is prepared to furnish copies of these charts on a large-size scale, at a moderate cost, to those who desire to have them for this purpose. CORRECTIONS Page 2185, line 3. For "is accessory apparatus" read "in accessory. apparatus." Page 2188. Substitute for lines 11 and 12: Nitrogen, oxygen, carbon monoxide, Cp = 6.50 + 0.0010T Hydrogen, Cp = 6.50 + 0.0009T

Jan 9, 1914

By John H. Hollomon, C. Zener

It is commonly recognized that a given material may be described as ductile or brittle only with reference to the conditions of test. Thus under the usual test conditions quartz is brittle, but under high pressures it is ductile. Salts that are brittle at room temperature become ductile at elevated temperatures. Pitch, brittle with respect to rapid loads, flows at low rates of loading. Pearlitic steel, ductile under the usual conditions of test, may be embrittled under the proper conditions of combined stresses, temperature, and rate of loading. Earlier Investigations A clear analysis of the conditions necessary for plastic flow and for fracture was first given by LudwikI1 who introduced two types of stress, the "flow stress" and the "stress at fracture." These stresses may refer to tensile or to shear stresses, or, in fact, to any type of stress. Ludwik considered these two stresses to be independent of one another, functions of the conditions of test and of the prior history of the material. For the purpose of analysis. both a Flow stress and a stress at fracture can be envisaged as functions of strain over the entire range from zero to infinite strain. Thus, the material is brittle if the stress at fracturc is less than the flow stress and ductile if the reverse is true. According to Ludwik's analysis, the problem of determining the effects of combined stresses, of temperature and of strain rate upon the behavior of metals reduces to a problem of determining the effect of these variables upon the flow stress and upon the stress at fracture. In the present paper, methods are described for determining the effects of two of these variables, temperature and strain rate, and examples are given of the dependence of tlow stress and stress at fracture, upon these two variables. The effect of combined stresses will be discussed in a succeeding paper. The flow stress may be determined from a load-diameter curve. Load-diameter curves were obtained over a wide range of temperature and over the limited range of strain rates obtainable with the lever-type Riehle machine used. The curves were then converted to an extremely wide range of strain rate by making use of the equivalence of the effects of changes in strain rate and changes in temperature, previously proposed2 and demonstrated3 by the authors. According to this principle of equivalence, strain rate e and temperature T affect the flow stress only through a single parameter-p of the form: p = eeQ/RT 111 In this equation, R is the gas constant (2 cal. per gram mol per deg. C.), and Q is a heat of activation, which varies from material to material, and may depend upon the strain, but not upon the strain rate or the temperature. There is associated with every value of p a flow-stress curve. article of strain rate and of temperature that give the same p have the same flow-stress curve. Therefore, merely by changing the temperature of test, the effect of changing the strain rate may be obtained. Thus, under isothermal conditions, the material will behave the same at

Jan 1, 1944

By K. A. Semlak, F. N. Rhines

NFILTRATION is a term used to designate that i- process by which the pores of a metal powder are filled with a relatively low-melting liquid metal through the action of capillary forces. This is accomplished in practice either by heating the porous body in contact with the solid infiltrant metal above the melting point of the latter, or by preheating the porous body separately and then dipping it into the liquid metal. The liquid, as it sweeps through the porous body, replaces the gases progressively, thus yielding a relatively dense product in a short time.' Liquid-phase sintering, which is related to infiltration, is a process by which a mixture of two or more metal powders is sintered at a temperature between the liquidus and solidus of the ultimate alloy.' According to Cannon" liquid-phase sintering can be divided into three stages which he calls liquid flow, accommodation, and solid sintering. The largest density increase occurs during the first stage, where the lower melting component melts and, driven by capillary forces, flows among the particles of the higher melting component, where, after dissolution of the bonds between the solid particles, it moves them into close packing. This happens so quickly that little has yet been learned of its mechanism. A study of the rate of capillary rise of a liquid metal in a higher melting metal-powder compact may be expected, therefore, to contribute not only to a firmer understanding of the process of infiltration as such but also to a more extensive knowledge of what occurs during the initial stage of liquid-phase sintering. Theoretical Basis In order to derive a mathematical expression of the rate of infiltration, it has been assumed that a powder compact consists of a great many parallel capillary tubes and that the rate of rise of a liquid in an average capillary channel represents the rise in the entire compact. For a straight capillary, assuming that Poiseuille's law obtains for the non-stationary state and that wetting is very rapid, Ligenza and Bernstein' have derived the following differential eauation of motion where h is the height of rise of the column of liquid at time t, R, is the radius and 1 the length of the capillary, t) and 7, the viscosities of liquid and air, respectively, p and p, the density of the liquid and air, respectively, y the liquid-gas surface tension, 0 the liquid-solid contact angle, and g the acceleration due to gravity. The term on the left of Equation [I] represents the rate of change of momentum of the contents of the capillary tube. On the right the terms represent, respectively, the forces due to a) surface tension, b) viscous resistance, c) gravity, and d) end-drag effect. Equation [I] is not amenable to explicit solution, but for a tube of sufficiently small radius, the rate of rise may be slow enough so that the rate of change of momentum and end-drag terms may be neglected. The validity of this simplification was established by Ligenza and Bernstein' by graphical differentiation of observed data obtained from organic liquids rising in glass tubes. The solution of this simplified case is:

Jan 1, 1959

By G. W. P. Rengstorff, L. E. Olds

High purity molybdenum ingots containing controlled amounts of a single impurity element (oxygen, nitrogen, or carbon) were prepared. These ingots were tested for ductility by bending test specimens at various temperatures. The relationship between the plastic behavior of the ingots and their chemical composition has been determined. MANY proposed applications for molybdenum require ductility at or near room temperature. At the present time, it is possible to obtain wrought molybdenum with considerable ductility only if special fabrication techniques are used to control the grain structure. Starting with are-cast or powder metallurgy ingots, the usual methods for obtaining ductility rely on fabrication procedures that result in fibered microstructures in the finished product. Recently, it has been found that the ductility of either powder metallurgy or are-cast molybdenum can be improved by uniform recrystallization of the metal to a very fine equiaxed grain structure.' The need for a fibered or a fine grained structure may limit the practical usefulness of molybdenum. For example, welding. which may be used in fabricating the metal, generally produces coarse grained structures that lead to brittleness. This applies, certainly, to currently available commercial molybdenum. Although commercial molybdenum is brittle when the grains are coarse, it has been shown experimentally that fine grained structures are not always essential for ductility. For instance, as-cast molybdenum with a coarse columnar grain structure is ductile if it is sufficiently pure.' Because high purity cast molybdenum has good ductility even when coarse grained, it is probable that the brittleness in coarse grained commercial molybdenum is caused by the impurity content of the metal. Although the general effects of impurities on the cold ductility of molybdenum have been known in a qualitative manner for some time, no quantitative evaluation of these effects has been available. The present investigation was made in order to determine more accurately the effects of oxygen, nitrogen, and carbon on the cold ductility of cast molybdenum. Oxygen has long been known to be detrimental to ductility, although the minimum amount which will embrittle molybdenum has been open to speculation. Parke and Ham" showed that ingots with oxygen contents above 0.003 pct could not be forged. Maringer and Schwope have described the embrittle-ment of molybdenum wire by oxygen. A discussion on the effects of heat treatment on the distribution of oxygen in molybdenum has been given by Perry, Spacil, and Wulff." Although nitrogen would also be expected to have harmful effects on ductility, no extensive work has been done previously to determine whether this is so. However, Tury and Krausz" found that wires presumably with less than 0.007 pct N were brittle. Carbon is added to commercial cast molybdenum for deoxidation. Parke and Ham" have shown that molybdenum containing as much as 0.06 pct C could be forged if the oxygen was kept below 0.003 pct. Also, Bruckart and others' found that the room temperature ductility of sintered molybdenum improved with carbon contents up to 0.84 pct. However, Rengstorff and Fischer' found that residual carbide particles in cast molybdenum apparently had an unfavorable effect on room temperature ductility.

Jan 1, 1957

By Charles L. Thomas

A novel, highly sensitive, and reproducible nzetlzod for the determination of hydrogen in solid materials is presented. The procedure requires equilibration of the specimen with hydrogen gas, rapid quenching, and hot vacuum extraction of the dissolved gas with subse-quent quantitative analysis by mass spectroscopy. Good linearity is obtained for the Arrl~enius plots of the investigated metals. The advantages in the use of this method over that of Sieverts aye discussed. The solubility data for copper are in reasonable agveewzent with a considerable number of other inuestigations, wllile those fov silver are considerably lower than previously reported. The first known solubility data for gold are presented. Solubility equations and heats of MUCH of the data which are available on the solubility of hydrogen in various metals and alloys have been obtained by the classical Sieverts method.' The method involves the measurement of a decrease in pressure of a gas in a calibrated system, and the calculated contraction in volume is attributed to the solubility of the gas in the metal sample. The procedure requires several corrections, such as the solubility of the gas in the container walls and the diffusion of the gas through these walls, as noted by Steacie and .Johnson2 and others. In addition, errors may be incurred due to reactions between metal surface impurities, such as oxides, and the saturating gas. The precise calibration of the measuring system where large thermal gradients exist can present additional difficulties. Also, accurate volumetric measurements of small quantities of gas are difficult. Many of the objections to the Sieverts method were overcome on solid materials by Ransley and ~eufeld,~ who first saturated the metal with hydrogen and performed a subsequent extraction and measurement of the gas by chemical means. Eichenauer and pebler4 and Eichenauer, Kiinzig, and pebler5 measured the diffusion coefficient and solubility by following the degasification of a sample as a function of a rate of increase in pressure in a previously evacuated system. Here again, however, the procedure involves many of the corrections of the Sie-verts method. The present investigation deals with the solubility of hydrogen in solid copper, silver, and gold by a technique which eliminates many of the aforementioned corrections and possible errors. This procedure requires equilibration of the specimen with gas, rapid quenching, and hot vacuum extraction of the dissolved gas with subsequent quantitative analysis by mass spectroscopy. EXPERIMENTAL Two completely separate systems were employed to accomplish first, the equilibrium saturation of the sample and second, the extraction of the dissolved gas. Saturation Apparatus. The saturation apparatus, illustrated in Fig. l, consisted of a vertically mounted quartz tube with a three-way valve for vacuum or hydrogen near the top and an outlet near the bottom leading to a butyl phthalate seal. The bottom end of the tube was terminated with a joint accommodating an O-ring sealed "Asco Stirring Gland" (The Emil Greiner Co.). This gland facilitated movement of the thermocouple without introduction of air into the system. The upper portion of the tube (above the furnace) was water-jacketed. A Welsh 1405-B mechanical pump provided the necessary system evacu-

Jan 1, 1968

By C. Zener, John H. Hollomon

It is commonly recognized that a given material may be described as ductile or brittle only with reference to the conditions of test. Thus under the usual test conditions quartz is brittle, but under high pressures it is ductile. Salts that are brittle at room temperature become ductile at elevated temperatures. Pitch, brittle with respect to rapid loads, flows at low rates of loading. Pearlitic steel, ductile under the usual conditions of test, may be embrittled under the proper conditions of combined stresses, temperature, and rate of loading. Earlier Investigations A clear analysis of the conditions necessary for plastic flow and for fracture was first given by LudwikI1 who introduced two types of stress, the "flow stress" and the "stress at fracture." These stresses may refer to tensile or to shear stresses, or, in fact, to any type of stress. Ludwik considered these two stresses to be independent of one another, functions of the conditions of test and of the prior history of the material. For the purpose of analysis. both a Flow stress and a stress at fracture can be envisaged as functions of strain over the entire range from zero to infinite strain. Thus, the material is brittle if the stress at fracturc is less than the flow stress and ductile if the reverse is true. According to Ludwik's analysis, the problem of determining the effects of combined stresses, of temperature and of strain rate upon the behavior of metals reduces to a problem of determining the effect of these variables upon the flow stress and upon the stress at fracture. In the present paper, methods are described for determining the effects of two of these variables, temperature and strain rate, and examples are given of the dependence of tlow stress and stress at fracture, upon these two variables. The effect of combined stresses will be discussed in a succeeding paper. The flow stress may be determined from a load-diameter curve. Load-diameter curves were obtained over a wide range of temperature and over the limited range of strain rates obtainable with the lever-type Riehle machine used. The curves were then converted to an extremely wide range of strain rate by making use of the equivalence of the effects of changes in strain rate and changes in temperature, previously proposed2 and demonstrated3 by the authors. According to this principle of equivalence, strain rate e and temperature T affect the flow stress only through a single parameter-p of the form: p = eeQ/RT 111 In this equation, R is the gas constant (2 cal. per gram mol per deg. C.), and Q is a heat of activation, which varies from material to material, and may depend upon the strain, but not upon the strain rate or the temperature. There is associated with every value of p a flow-stress curve. article of strain rate and of temperature that give the same p have the same flow-stress curve. Therefore, merely by changing the temperature of test, the effect of changing the strain rate may be obtained. Thus, under isothermal conditions, the material will behave the same at

Jan 1, 1944

By C. G. Dunn

It is well known that plastic deformation alters many of the properties of a metal and subsequent heat-treatment partially or completely restores these properties.l In the deformed or strained state, the metal is unstable and tends to change toward a condition called a "strain-free state." The transformation occurs through recovery, recrystallization, and grain growth—processes that may take place singly or in combination. The distortion of the lattice of an individual grain of a metal in a state of strain may be rather complex in nature, because plastic deformation produces: (I) dislocations within mosaic blocks; (2) elastic variations of the lattice spacings; and (3) gross alterations throughout the lattice, especially along slip planes, along composition planes between a grain and its mechanical twins, and along boundaries of deformation bands. These gross alterations are of the nature of bent planes or rotated regions of the crystal lattice and are revealed by a spread in the orientation of the grain. Although we cannot describe these strains and their formation accurately because of insuffcient knowledge, we can, nevertheless, use the information as well as possible to obtain a better understanding of recovery processes. In recovery, the lattice of a grain is not made anew as it is in recrystallization, but is improved or mended in such a way that the basic structure remains unaltered: Until recatly observations were .that recovery produced no marked changes in the shapes of spots in Laue diffraction patterns, whereas recrystallization did, but now it is known for silicon ferrite2 that Laue spots may become quite sharp entirely through recovery. Consequently, the shape of Laue spots alone would not be a suitable test to distinguish between recovery and recrystallization. There is considerable evidence that the micro-structure usually does not change visibly during recovery. Absence of a visible change in the microstructure, therefore, provides a sufficient test of recovery in many cases. However, including this observation in a definition of recovery as a necessary condition (this is usually done) is unfortunate, because recovery may, as will become evident later, produce new grain boundaries that are visible not only in the microstructure but also in the macrostructure. For the present, therefore, let us say that a necessary condition for a process to be one of recovery is that the principal orientation or orientations of a deformed grain be essentially unchanged throughout the transformation toward the strain-free state. Several transformations may occur that fulfill this condition, and the nature of the distortion in a grain indicates what these must be if the lattice is to be mended in part or fully. Consequently, it will be convenient as well as

Jan 1, 1947

By R. F. Mehl, B. Lustman

THE formation of intermediate phase layers in cementation processes has been subjected to extensive qualitative investigation though to relatively little quantitative study; this work has recently been fully summarized by F. N. Rhines.1 It is necessary here only to enumerate the general conclusions drawn concerning the kinetic laws governing the growth of intermediate layers and to state what is known concerning the structural changes accompanying the generation of phase layers. I. When the intermediate phase is protective in type-i.e., when its density is less than that of the base metal, so that a continuous coating is formed and maintained the isothermal growth of the phase follows a simple parabolic equation: X2 = kt [I] where X is the thickness of the alloy layer, k the reaction rate constant, and t the time. The applicability of this equation to diffusion processes is tested by plotting the square of the thickness versus time, or by plotting the thickness versus the square root of time; the resultant achievement of a straight line in such. a plot has been con¬sidered sufficient proof of the validity of this equation. Exceptions have been found where liquid phases are involved in the reaction, where the diffusion layer is cracked,2 and where thin semimetallic oxide and sulphide coatings are formed on metals.3 In the first two cases the thickness increases linearly with time, and in the latter it is a logarithmic function of time. 2. The rate of thickening varies with temperature according to the Arrhenius equation k = Ae-Q/RT [2] where k is the parabolic rate constant of Eq. I, or some other rate-descriptive function, A is the action constant, e the base of natural logarithms, Q the heat of activation, R the gas constant, and T absolute temperature. This equation has been found to be generally valid except when transformations occur during reaction in either the base metal or in the reaction layer; in such instances Eq. 2 is still applicable with different values for the constants A and Q above and below the transformation temperature. 3. All phases that are stable at the temperature at which diffusion occurs will appear in the interdiffusion of two components. In some cases certain of the phases may be too thin to be observed and identified easily. Nonequilibrium phases have never been noted in thick reaction layers; i.e., layers of a thickness that may be discerned microscopically. The relative, thickness of each phase in a diffusion layer is proportional to the concentration gradient and to the rate of diffusion in that phase .4 The reaction layers tend to have a

Jan 1, 1942

By C. G. Dunn

It is well known that plastic deformation alters many of the properties of a metal and subsequent heat-treatment partially or completely restores these properties.l In the deformed or strained state, the metal is unstable and tends to change toward a condition called a "strain-free state." The transformation occurs through recovery, recrystallization, and grain growth—processes that may take place singly or in combination. The distortion of the lattice of an individual grain of a metal in a state of strain may be rather complex in nature, because plastic deformation produces: (I) dislocations within mosaic blocks; (2) elastic variations of the lattice spacings; and (3) gross alterations throughout the lattice, especially along slip planes, along composition planes between a grain and its mechanical twins, and along boundaries of deformation bands. These gross alterations are of the nature of bent planes or rotated regions of the crystal lattice and are revealed by a spread in the orientation of the grain. Although we cannot describe these strains and their formation accurately because of insuffcient knowledge, we can, nevertheless, use the information as well as possible to obtain a better understanding of recovery processes. In recovery, the lattice of a grain is not made anew as it is in recrystallization, but is improved or mended in such a way that the basic structure remains unaltered: Until recatly observations were .that recovery produced no marked changes in the shapes of spots in Laue diffraction patterns, whereas recrystallization did, but now it is known for silicon ferrite2 that Laue spots may become quite sharp entirely through recovery. Consequently, the shape of Laue spots alone would not be a suitable test to distinguish between recovery and recrystallization. There is considerable evidence that the micro-structure usually does not change visibly during recovery. Absence of a visible change in the microstructure, therefore, provides a sufficient test of recovery in many cases. However, including this observation in a definition of recovery as a necessary condition (this is usually done) is unfortunate, because recovery may, as will become evident later, produce new grain boundaries that are visible not only in the microstructure but also in the macrostructure. For the present, therefore, let us say that a necessary condition for a process to be one of recovery is that the principal orientation or orientations of a deformed grain be essentially unchanged throughout the transformation toward the strain-free state. Several transformations may occur that fulfill this condition, and the nature of the distortion in a grain indicates what these must be if the lattice is to be mended in part or fully. Consequently, it will be convenient as well as

Jan 1, 1947

By H. W. Russell, Paul D. MILLER

IT is known that austenitic chromium-nickel steels that have free carbide in the grain boundaries are subject to intergranular corrosion. It is difficult to detect such a susceptible condition in a fabricated article because present test methods require a sample section for examination and in most cases this is difficult to obtain. The question of the nature and prevention of intergranular corrosion in austenitic stainless steels have been ably discussed by Bain and co-workers1-3 and by other investigators.4-10 The present methods of study subject samples to corrosive conditions in such reagents as the Strauss solution, a. mixture of copper sulphate and sulphuric acid. Such tests usually require at least 72 hr. to run. Various methods of measuring the degree of sensitization have been employed, such as the measurement of electrical resistivity, magnetic measurements, measurement of the degree of cracking produced on bending over a mandrel, and microscopic studies. The detection of carbides at the grain boundaries by metallographic polishing and etching methods is tedious and requires a skilled operator. A recent report on such methods of carbide detection is given by the American Society for Testing Materials Subcommittee VI of Committee A-10 11 and by Arness.12 The present investigation was undertaken to develop a simple test procedure for detecting carbide precipitation or susceptibility to intergranular corrosion. The test is designed for use in the plant and for the testing of fabricated structures. Carbide precipitation, the factor leading to susceptibility to corrosion, is produced by heating the alloy in the temperature range 800° to 1600°F., as in welding, in improper annealing or in service where such temperatures are met. The connection between such precipitation and susceptibility to corrosion has been thoroughly discussed, as has been the use of stabilizing addition elements to prevent precipitation. EXPERIMENTAL METHOD A small area of the steel under test is subjected to an anodic treatment in a cell that can be clamped onto a sample or an actual structure. The cell and electrical circuit used are illustrated in Fig. I. The cell C is lead, joined to the steel plate D and insulated from it by a short piece of rubber tubing E. The cell is forced tightly against the steel plate by a spring or clamping device. The seal formed by the rubber against the steel plate is sufficient to retain the liquid bath inside the cell. The spot treated can be made any shape desired, depending on the shape of the rubber gasket. The cell illustrated polishes a circular spot about 3/8-in. diameter. The bath consists of 60 per cent (by weight) sulphuric acid to which is added 5 ml. per liter of Glycyrrhiza extract (U.S.P.). The cell requires about 2 to 2.5

Jan 1, 1941

By John F. Elliott, Robert D. Pehlke

The rate of reaction of nitrogen with liquid iron and with binary alloys of iron and Al, Cb, Cr, Ni, O, S, Si, and W were measured. The surface active elements, oxygen and sulfur, decrease the rate markedly. The other alloying elements have very little effect on the rate except when they function as deoxidizers, The rates of absorption and de-sorption were found to be equal. Several possible reaction mechanisms which may control the rate are considered. In order to describe completely the behavior of nitrogen in steelmaking processes, the mechanisms of mass transfer between the gaseous and liquid phases, nitrogen and iron, respectively, must be understood. A kinetic study to determine the nature of these mass transfer processes was undertaken, and the results of that investigation are presented in this paper. Specifically, the study was directed toward determining the influence of alloying elements on the rates at which pure nitrogen gas at constant pressure is absorbed and desorbed by liquid iron solutions: A previous paper1 reported measurements of the equilibrium solubility of nitrogen in liquid binary iron alloys. The experimental data are presented and discussed first and then several possible rate limiting mechanisms are considered. PREVIOUS RESEARCH The results of several investigations on the rate of absorption of nitrogen by liquid iron and iron alloys have been reported.2-14 There is little agreement on the rate coefficients among these studies because of the influence of geometry on the experimental system and of the purity of the liquid iron. The rate was found to be influenced by alloying content for the binary liquid iron systems: Fe-Al,2 Fe-C,4,6 Fe-Cr,4,5,8 Fe-Mn,5 Fe-Ni,5,8 Fe-O,9,10 Fe-O,9,10 and Fe-Si.2,6,7,11 Several investigators12"15 have reported that the rate of nitrogen absorption is increased in a reducing gas mixture and decreased in an oxidizing atmosphere. A mechanism for the retardation by oxygen of the absorption of nitrogen has been described by Naeser18 as the formation of an iron oxide film at the gas-metal interface. The film slows the absorption rate until it disolves in the metal, thus permitting nitrogen to enter the liquid iron. Karwat17 discussed the influence of oxygen in terms of the formation of gaseous molecules of nitrous oxide which represent a higher energy form than the nitrogen and oxygen or the oxidizing gas and consequently constitute an energy barrier for the process. Fischer and Hoffmann10 showed that the oxygen markedly reduces the rate of absorption of nitrogen, the rate constant being one order of magnitude smaller in liquid iron containing 0.15 to 0.24 pct 0 as compared to that in melts containing 0.001 to 0.02 pct 0. Although Chipman and Murphy2 reported that the rate of absorption of nitrogen in liquid iron was essentially independent of temperature, Eklund3 found that the rate increases strongly with increasing temperature as did Kootz4 and Saito.5,6 Karnaukhov and Morozov7 also reported a large temperature coefficient, but related it to increased stirring at higher power inputs in an inductively heated system. All of the authors above have treated their results assuming that the reaction is diffusion controlled, that the surface reaction is in equilibrium with nitrogen gas, and that a "first order" reaction takes place. Karnaukhov and Morozov7 and Humbert; who studied the rate of absorption in a closed system by observing pressure changes in the system as a function of time, concluded that their results best fit a diffusion-type analysis. This was further verified by von Bogdandy, Dick, and stranski18 and Fischer and Hoffmann10 who found the initial rate of

Jan 1, 1963

By R. D. Pehlke, J. V. Gluck

The limiting activity coefficient of zinc in a "binary " solvent has been described for several dilute ternary solutions by combining literature data from recent interaction studies in the terminal regions with thermodynamic data for the central regions. Results are discussed in terms of the Alcock and Richardson random solution model. The observed behavior agrees semiquantitatively with predictions using the model. RECENT efforts in the thermodynamics of dilute ternary liquid metallic solutions have been mainly concerned with the interactions between two dilute solutes, that is, the terminal region at an apex of the composition diagram.'-' A more general case is that of the behavior of a dilute solute over the full range of a ternary system, or, more specifically, the limiting activity of solute i as projected to the k-j binary side of the i-j-k composition triangle. An implication of this is that the interaction between i and j at the k apex should connect in some way to the interaction between i and k at the j apex. A model to characterize various types of expected behavior has been discussed by Alcock and Richardson.9,10 Such behavior can range from a simple linear relation for In yi over the 1-k binary to more complex curved relations which depend on various assumptions regarding the heat of solution in the j-k binary system and the presence or absence of clustering with solute i. Quantitative data to assess these concepts have been limited primarily to the cases of nonmetallic interstitial solutes in ferrous solutions. Alcock, Richardson, and various coworkers9-13 have discussed the behavior of oxygen, sulfur, silicon, or hydrogen in dilute solution over the range of iron + metal systems; however, the only data considered by them for substitutional nonferrous metallic solutions were the results of Elliott and Chipman concerning the activity of cadmium in the Pb + Sn, Pb + Bi, and Pb + Sb systems.9 These data were limited and did not cover the terminal regions in detail. An opportunity to extend the Alcock and Richardson considerations to the dilute solution of zinc in various "binary" solvents has been afforded by combining results of several of the recent investigations of ter-minal-region interactions with previous data from the literature for the same more concentrated solutions. RESULTS AND DISCUSSION The results of the analysis are shown in Figs. 1 to 5 where the log activity coefficient, (In yZn)xzn--o, is plotted vs the composition of the "binary" solvent. In these plots the end points are the values for In yzn in the appropriate binary solution with Bi, Pb, Sn, Cd, or In at the indicated temperature—usually 550°C (823°K). For the terminal regions the slopes were drawn using the first-order interaction parameters taken from various studies reported in the literature. The data points shown in the central regions were obtained by the short extrapolation to infinite dilution of the logarithm of the activity coefficient calculated from thermodynamic studies reported in the literature for the same systems. The sources of the data are indicated on each figure. Second-order effects were not considered. Reasonably smooth curves can be drawn to connect the central region with the terminal regions for the Zn-Pb + Bi system, Fig. 1, the Zn-Pb + Zn system, Fig. 1, and the Zn-Bi + Cd and Zn-Bi + Sn systems, Fig. 2. As shown in Fig. 2, where central region data are available from two independent investigations, the agreement is quite good. The Zn-Pb + Cd system does not appear to be as well behaved as the previous four, Fig. 3; however, this type of behavior has also been

Jan 1, 1970