Search Documents

By B. C. Raynes

IN the early part of 1952, under the auspices of the U. S. Atomic Energy Commission, Horizons Inc. undertook an investigation dealing with the preparation of high purity thorium metal in order to develop an economically competitive production process for this metal based on a recovery of the metal by a fused salt electrolysis, since a survey of the literature of thorium chemistry indicated that electrolytic methods had not received much attention, despite the consideration that electrochemical production methods often offer attractive commercial potentialities. Thorium metal has been prepared by methods which fall into four general categories: 1) reduction of halides or double halides; 2) reduction of the oxide; 3) thermal decomposition of halides; and 4) electrolytic methods. Some of the important results obtained by various investigators since about 1900 in recorded attempts to prepare pure thorium metal are summarized in Table I. A bibliography of pertinent literature is included in this paper. Thorium is strongly electropositive and possesses a great affinity for oxygen and nitrogen. As a result the prospects for the production of high purity thorium from aqueous media or oxygen bearing compounds are remote. The most promising and profitable area of investigation for production of thorium metal lies in fused salt electrolysis. Thorium has been produced previously by this technique from halide salts in fused alkali chloride eutectic mixtures. Until recently, however, the lack of known large uses for thorium has inhibited the investigation of these methods. The basic problem in an investigation into fused salt production methods for thorium is to develop a suitable fused salt system for the economic preparation of thorium. The first portion of the work in these laboratories was a small scale investigation of the electrolysis of potassium thorium fluoride, KThF5, under a variety of conditions. High purity thorium was prepared in this manner, but the process did not appear to offer the simplest and most attractive continuous commercial operation. The work reported here relates to an all-chloride system employing thorium chloride as the cell feed. ThCL4 was produced as an anhydrous material stabilized in molten sodium chloride. This product, further diluted in NaCl, was subjected to electrolysis. The electrolytic process has been studied in cells capable of holding up to 50 lb total salt charge. Ductile, pure thorium metal has been reproducibly obtained in this operation. Considerable experimentation was carried out in the preparation of ThCL as a cell feed free from moisture, oxides, and other impurities. Thorium was cathodically deposited as a coarsely crystalline powder interspersed with residual bath salts. Aqueous procedures for separating and recovering the metal were developed. The thorium metal powder obtained has been evaluated with respect to its hardness, chemical purity, and certain other physical properties. Preparation of ThC1,—Thorium chloride, and the chlorides of some other metals (aluminum, beryllium, tantalum, zirconium, etc.) cannot be obtained from aqueous solution by direct heating and evaporation. Evaporation and heating of a solution of thorium chloride yields a hydrated salt or partially hydrated salt, and finally Tho,. Anhydrous thorium chloride is obtained by forming a hydrated ammonium chloride complex salt in acidified water solution, dehydrating this compound, and finally decomposing the double salt and subliming the ammonium chloride component. Various methods for the preparation of anhydrous thorium chloride, in accordance with this concept, were investigated as indicated in Table I1 from hydrated thorium chloride (ThCl, . 3H2O), and from thorium oxycarbonate (ThOCO,). In the method found most satisfactory for this work, thorium oxycarbonate was dissolved in an excess of concentrated HC1 to give a clear yellow solution. At least 2 mol NH,Cl were added to the solution per mol of contained thorium. Ammonium thorium chloride hydrate was crystallized from solution by cooling and saturation with HC1. The resultant complex, (NH,Cl),ThCl;xH,O, was dehydrated by evaporation at 130° to 150°C and thoroughly dried at about 250°C. The dried ammanium thorium chloride was then mixed with sodium chloride in proportions to form NaThCL or to produce a ThCL4-NaCl mixture with a given thorium content. The ammonium chloride was sublimed off at temperatures above 500°C in an inert atmosphere furnace to give an anhydrous chloride source electrolyte, essentially free of Tho, and of NKC1.

Jan 1, 1958

By Carrol M. Beeson

Reasons are given for using a Boyle's-law porosimeter in conducting core analysis for either routine or research purposes. Among other things, it is pointed out that such a porosimeter permits the measurement of all basic properties on the same sample, thereby eliminating the sources of error inherent in the use of adjacent samples. References are made to investigations of gas adsorption on various porous materials, to show that the use of helium in Boyle's-law porosimeters reduces to negligible proportions the error due to the adsorption or desorption of the operating gas. Two Boyle's-law instruments are described. which permit accurate and rapid measurements of porosity. Schematic sketches and explanation:; are included, along with derivations of equations required in performing precise determinations. Summaries of data obtained during calibration are tabulated and analyses of the data are resented as indications of the precision and accuracy of each device. Comparisons are also shown for measurements made with each of the instruments on the same test pieces and cores. INTRODUCTION An accurate porosimeter, operating on the principle of Boyle's law. is of considerable value in the analysis of cores for either routine or research purposes. This is due primarily to the fact that the measurement of porosity with such an instrument leaves the sample free of contamination by any liquid. When used in conjunction with an extraction apparatus' for determining oil and water saturations, a Boyle's-law porosimeter permits the measurement of all basic properties on the same sample. This eliminates the sources of error inherent in the use of adjacent samples, or the necessity of determining porosity after all other properties have been obtained. Large errors may result from combining measurements made on adjacent samples in order to obtain a single property. This type of error is definitely involved when oil and water are measured with one sample, and the pore vo1ume is measured with an adjacent one. Furthermore, the source of error would be present to some extent, even if the analyst could choose the samples so they were truly adjacent from a geological standpoint. The use of adjacent samples in routine core analysis also necessarily decreases the probability of correlating core properties. For example, the chance of correlating the "irreducible" interstitial-water saturation with permeability, is bound to be greatly reduced by measuring these properties on "adjacent" samples. For research purposes, amplification is scarcely required concerning the greater flexibility of a method for measuring porosity which leaves the core free of contamination by any liquid. Even under those circumstances which require that the core be saturated with a liquid, a previous measurement of porosity with a gas is useful in determining the degree of saturation that has been attained in the process. Furthermore, for comparable accuracy, porosity usually may be determined more rapidly with a gas than with a liquid. This advantage of the Boyle's-law instrument is most outstanding when the determination time is compared with that required in obtaining porosity by evacuation of the core followed by saturation with a liquid of known density. Several porosimeters which operate on the principle of Boyle's law have been described2,3,4,5,6,7 in the literature. No comparison will be attempted between those instruments and the ones described herein. Before helium gas became readily available, Boyle's-law porosimeters were subject to an appreciable error due to the adsorption of the operating gas on the surface of the core solids. There is considerable direct and indirect evidence in the literature to support the contention that the adsorption of helium on porous solids is negligible at room temperature. In discussing the use of Boyle's-law porosimeters, Washburn and Bunting2 stated that "for most ceramic bodies dry air is a satisfactory gas, but hydrogen will be required in some instances. Helium could, of course, be employed for all types of porous materials at room temperatures or above." Howard and Hulett8 obtained evidence that the adsorption of helium was negligible at room temperatures, even on activated carbon ; for the density measured with this gas was unaffected by changes in pressure or by changes in temperature from 25 °C to 75 °C. For oil-well cores, Taliaferro, Johnson, and Dewees" obtained lower porosities with helium than with air, but apparently did not study helium adsorption. From the work of these investigators, it follows that the use of helium in Boyle's-law porosimeters reduces the error due to gas adsorption to negligible proportions. This makes it possible to construct instruments which permit the determination of porosity with (1) a high degree of accuracy, (2) with great rapidity, and (3) without contamination. THE KOBE POROSIMETER The fundamental design of the Kobe Porosimeter was developed by Kobe, Inc., which firm built about 12 of the instruments during 1936 and 1937. Since that time, seven or eight more have been constructed with their permission, making a total of about 20 that have been put into operation.

Jan 1, 1950

By A. E. Bibb, J. R. Fascia

Single-crystal wafers of zirconium have been exposed to 680°F neutral water. The single crystals were of known orientation and weight-gain data as a function of crystal orientation were obtained. These data show that all the crystal faces studied obeyed a cubic rate law out to the time of transition whereupon the crystals corroded at an approximately linear rate. The time to transition varied from 114 days for (1074) crystals to about 325 days for the (2130) faces. The epitaxial relationship be-tween metal and monoclinic oxide was found to be (0001) H (111) and [1120] 11 [101]. A black tight adherent oxide layer was formed on the crystals in the pretransition range. This black oxide was found to be monocrystalline. The white corrosion product produced after transition was found to be polycrys-talline but highly oriented. X-ray line-broadening studies found that the black oxide was a highly strained structure whereas the white oxide was relatively strain-free. These results indicate a strain-induced re crystallization or fragmentation accompanies the change from protective black oxide to nonprotective white oxide. ZIRCONIUM alloys have been used quite extensively in high-temperature aqueous environments. Alloy additions can be made to commercial sponge zirconium which enhance the corrosion resistance of the zirconium in both water and steam media, which raise the tolerance limit for certain impurities detrimental to corrosion resistance, and which reduce the amount of free hydrogen pickup during corrosion. The development of the corrosion-resistant zirconium alloys has been a long and tedious job involving trial and error methods. This technique has been necessary because of a lack of fundamental data and hence understanding of the corrosion mechanisms. The objective of the work described herein was to provide some fundamental data with respect to the aqueous corrosion of zirconium crystals as a function of the orientation of the exposed surfaces. Hg. The zirconium chunk was then cooled to below the transformation temperature (862°C) and reheated to 1200°C for 8 hr. The ultimate size of the zirconium grains increased with the number of cycles. Rapid or even furnace cooling through the transformation temperature produces a considerable amount of substructure which was intolerable in corrosion experiments as it would be in the study of any crystallographically dependent property. It was found that a high-temperature a-phase anneal for approximately 4 days reduced the substructure below the limits detectable by visual or X-ray means. Crystals so produced were carefully cut from the massive zirconium chunk and oriented by standard back-reflection Laue techniques. The crystals were then mounted in a goniometer head and, by using the three degrees of freedom available, slices on the order of 0.015 to 0.020 in. were cut parallel to any desired crystal plane. These slices were then carefully polished on both sides to produce smooth flat faces, pickled to remove about 0.002 in. per face, annealed for 1/2 hr at '750°C in a vacuum of approximately 10"5 mm Hg, flash pickled, and checked for orientation. The pickling solution was 45-45-10 vol pct HN0,-H20-HF and continuous agitation was provided to eliminate pitting of the slices. Any slice that was not within 2 deg of the desired orientation was discarded, and any evidence of substructure as indicated by the Laue spots was also grounds for discarding the sample. Thin slices were used for the corrosion tests because weight gain per area data could be obtained with only a minimum area exposed to the corrosive media that was not of the desired orientation. The thin single-crystal slices were of irregular shape and as a result the areas were determined by placing a crystal inside an inscribed square of known area, enlarging a picture of this assembly about X5, and tracing both the enlarged square and crystal with a planimeter. The zirconium used to produce these single crystals was crystal-bar grade, a typical analysis of which is given in Table I. An oxygen analysis on prepared crystals gave a concentration of 205 ppm. The hydrogen concentrations are believed to be less than 15 ppm due to the dynamic vacuum anneal given each crystal. Typical nitrogen values for zirconium treated in this manner are about 10 to 20 ppm. RESULTS AND DISCUSSION Single-crystal wafers have been exposed to de-oxygenated, deionized water in static autoclaves.

Jan 1, 1964

By J Price, M. R. Geer, H. F. Yancey

COAL mine operators recognize coal as an abrasive material, because the wear of drilling, cutting, and conveying equipment is reflected as a cost item for replacement of parts. Similarly, industrial consumers of coal experience abrasive wear on all coal-handling equipment. Operators of pulverized fuel plants are doubtless most keenly aware of the abrasiveness of coal, because under the high contact pressures developed between coal and metal in pulverizers, abrasive wear is increased many fold. Moreover, experience in operating pulverized fuel plants has demonstrated that some coals are much more abrasive than others. Hardgrove' stated that maintenance costs entailed by the wear of grinding elements is often a more important variable than the cost of the power required to pulverize different coals. Craig2 also reports that one coal may cause pulverizer parts to wear several times faster than another. It is apparent, therefore, that those concerned with pulverizing coal could profitably employ a method for estimating the abrasiveness of different coals, just as they utilize standard tests for thermal value, grindability, and ash-fusion temperature to assist in selecting the most suitable and economical coal to use in a particular plant. The objective of this investigation was to develop a test procedure that would be suitable for general use in estimating the abrasiveness of coals. However, few, if any, of the standard tests now used for evaluating the properties of coal are the product of a single investigation or the result of a single investigator's efforts. Rather, in each case, a testing procedure was devised by one investigator, used by others on a wider variety of coals, and finally refined completely as the result of the joint efforts of a number of interested people. Thus, the test procedure for estimating abrasiveness developed in the course of this work may not be refined sufficiently in its present form for general use, but it may serve as the starting point from which an acceptable test procedure can be developed. The method has been used thus far on only about a dozen coals, and there has been no opportunity to attempt a correlation between experimental results and actual plant experience. Only wider use of the procedure by other investigators and correlation with plant experience can determine to what extent the method will have to be modified to render it suitable for general application. Test Method Although the literature contains no record of an attempt to devise a method for estimating the abrasiveness of coal that could be used industrially, several investigators have tested properties of coal that are closely related to its abrasiveness. The abrasiveness of a material generally is considered to be related to its hardness, and hardness tests for coal have been employed by Heywood,' O'Neill," and Mathes. Also, the resistance of coal to abrasion, a property that presumably is related to the abrasiveness of coal, was measured by Heywooda and by Simek, Pulkrabek, and Coufalik.2 11 these investigators tested only individual pieces of coal. Since coal is a heterogeneous material having components of varying properties, tests of this type can yield results having little more than academic interest. Only a test method that utilizes a representative sample of coal can give results that are useful industrially. The abrasion tests used for various other materials have been considered for adaptation to testing the abrasiveness of coal. The tests used for metals,7-9 paving and flooring,'" and rubber," cannot be used because coal is not sufficiently abrasive.~ The present experimental work was begun before World War II and was conducted by three research fellows"'" working under a joint agreement between the University of Washington and the Bureau of Mines. After a great deal of preliminary work with a variety of apparatus and materials, a test procedure was developed which consisted of rotating a test disk 2Yz in. diam in a steel mortar containing the coal sample. The shaft carrying the test disk at the lower end and a 100-lb load on the upper end was free to move vertically. The bed of coal in the mortar was kept fluid by low-pressure air admitted through a port near the bottom of the mortar. Measurable wear on an Armco iron disk could be obtained in this test procedure, but, despite extensive efforts to eliminate them, several major disadvantages remained in this test method. First, with most coals the amount of wear on the iron disk did not exceed a few milligrams. Second, a single type of disk was not applicable for all coals. A smooth iron disk gave satisfactory results with both bituminous and sub-bituminous coals, but hardly any wear with anthracite or coke. A disk having studs or projections gave more satisfactory abrasion losses with anthracite and coke and presented no operating difficulties with free-burning bituminous and sub-bituminous coals. It could not, however, be used with caking coals because these coals formed a

Jan 1, 1952

By Arthur M. Miller

FROM the time of its establishment in 1933, the Tennessee Valley Authority has been active in the field of phosphates. Under the T.V.A. Act it has a broad Congressional mandate to guide a unified development of the resources of the region for the long-range benefit of the people. As one phase of this function, it is directed to co-operate with farmers in the experimental large-scale use of improved fertilizers and development of better fertilizer practices. Following careful study, it was concluded that the objectives of this phase could best be attained by soil rebuilding through the use of phosphatic fertilizer and lime in an improved farm management sys- tem. This activity was launched through a program of test and demonstration on farms and simultaneous technical investigations to develop new and improved phosphatic fertilizers. Phosphorus has since become a keystone of the Authority's resource development and conservation program. Human effort is being conserved by phosphate utilization on the farm, and mineral conservation has been promoted by technical developments in phosphate mining and manufacturing operations.

Jan 1, 1944

By Philip D. Wilson

FEAST and famine-or, chronologically, famine and feast-have characterized the aluminum supply program during 1943. Fortunately for the war effort the famine phase is over and aluminum production is now in the happy position of being abundantly able to supply all the requirements of the armed services plus a monthly surplus which is building up a substantial stock pile as a reserve against any contingencies. But the present condition of oversupply cannot be attributed to the super-efficiency of the aluminum production program which was designed to take care of the over-all requirements of the war with little or no margin of safety. The present more than comfortable situation is due primarily to the fact that the armed services generally have not consumed anything approaching the amount of aluminum which their requirement estimates indicated.

Jan 1, 1944

By C. K. Leith

THE outstanding fact of the mineral world today, at home and abroad, is the surplus of current production, and particularly of capacity for production, over current requirements. This is not by Any means a new condition, but never before has it loomed up in such' menacing form. - Those of us who have devoted most of our professional efforts to the discovery and development of 'new mineral supplies now suddenly find ourselves with the job apparently accomplished, waiting for some one else to find an outlet for excess mineral production before we can further. The management of the industry is in much the same boat. The psjrcho16gy of the industry has been so grooved in the direction of acquisition of, minerals that at the present moment the mineral industry confronts the new problem of surplus in more or less of a daze.

Jan 1, 1931

By Zay Jeffries

OF the new production of non-ferrous metals in 1930 gold will rank first in value. We usually think of copper as the most important non-ferrous metal. The copper industry as a whole, that is, adding copper production to copper fabrication, is the largest non-ferrous metal industry. Prior to the world war; however, gold led in value of new metal produced. During the war copper passed gold in value, but gold regained its position during the 1921 depression. For the past several years copper has again passed gold, but in 1930 gold promises again to regain the lead. The gold producer has at times been called a social parasite, largely because we ' cannot eat or drink gold, or because we cannot use it for clothes or for the construction of buildings. Let us briefly examine this accusation.

Jan 1, 1930

By Jei Y. Choi, Paul G. Shewmon

The surface self-diffusion coefficient of copper (D,) has been measured between 847° and 1069 "C for six different orientations. These were the(111), (110, (100, and three higher index surfaces. The activation energy for Ds (designated Q s) was found to be about 49 kcal per mol for all six surfaces, and Do about 2 x 104 sq cm per sec. At any temperature Ds varied by no more than a factor of three over these orientations. It is shown that, if the free energy of a surface atom is uniquely determined by its number of nearest neighbors, it follows from the Principle of microscopic reversibility that Qs should have the same value for all surface orientations, and Ds should vary little with orientation. This model also suggests that for clean fee metals Qs ~ 2/3 AH, (heat of vaporization). This is true for copper. ALTHOUGH it has been appreciated for several decades that atoms can diffuse more rapidly on a surface than through the bulk of a crystal, it has only been in the last few years that reliable values of the surface self-diffusion coefficient (Ds) have become available. Tracer studies of Ds had been attempted prior to this period, but when a tracer is placed on a surface, an ever increasing fraction of it is drained off into the lattice. The correction for this loss involves a very difficult, and as yet unperformed calculation. Those who have worked with tracers have not corrected for this loss.1, 2 Thus their results indicate that Ds is greater than the self-diffusion coefficient in the lattice (Dl), but it has not been established that they give quantitative data on Ds. A procedure which avoids the problem of tracer loss is to study the rate of mass-transfer under the effect of surface tension. If the surface asperity being studied is very small, the mass transfer occurs entirely by surface diffusion. The kinetics at which a grain boundary groove forms on an initially plane surface is a well-studied case of this type. The smoothing of a slight scratch in an otherwise flat surface is another procedure that has been studied. If these grooves are up to 20 to 30 µ in width, the dominant mechanism for mass transfer is surface diffusion (at least in the case of metals with low vapor pressures), and the widths can easily be measured with an interference microscope. Of these two, mass-transfer techniques only in the case of grain boundary grooving has a rigorous mathematical treatment been given. This was done by Mullins.3,4 His analysis predicted that in the case of copper in an atmosphere of an inert gas, surface diffusion should be the dominant transport mechanism. This analysis gave an equation for the groove profile and predicted that the width of the groove would increase as (time)1/4. Mullins and Shewmon showed that both of these predictions agreed with experiments.5 Thus the validity of the values of Ds given by this procedure seems to be well established. Gjostein has used copper bicrystals and the grain boundary grooving technique to determine Ds and the activation energy for surface selfdiffusion (9,) in the [001] direction on surfaces ranging between the (100) and (110) planes.= He reported that Qs = 41 kcal per mole and Do = 6.5 x 102 sq cm per sec for all orientations studied. Since the results did not change with the dew-point of the dry hydrogen atmosphere or the type of refractory tube used, he concluded that the surfaces were clean, or at least that the results were not influenced by any impurities chemisorbed from the atmosphere. The work reported here reproduces and extends Gjostein's study in that D s and Q s were determined for copper over a wider range of orientations. To study the effects of impurities, two purities of copper were used as well as cathodic etching to remove any possible electropolishing film. Gjostein postulated that the diffusing atoms on a surface near a low index plane are the few atoms which are adsorbed on the smooth region between ledges or steps in the surface. A more rigorous derivation of the equation relating Ds to the concentration and jump frequency of these adsorbed atoms is given here. Using this treatment, our empirical observation that Q s and D s are essentially the same for all surface orientations can be shown to follow from the assumption that the free energy of a surface atom is uniquely determined by its number of nearest neighbors. The studies of D s using the scratch technique have been carried out by Blakely and Mukura on nickel,' and by Geguzin and Oveharenko on copper. The latter study using copper gives values of D s roughly

Jan 1, 1962

By F. C. Farnham

THERE has been very little, if any, uniformity in the reference datum used for magnetometer surveys. It has been the practice to choose a base station at which the magnetic field is assumed to be normal and call the difference in field strength between a given station and this base the anomaly at the given station. For small-scale surveys latitude and longitude corrections may or may not be applied, but for large-scale surveys such corrections usually are applied. The United States Coast and Geodetic Survey maps showing lines of equal magnetic intensity are commonly used to determine the normal latitude and longitude variation by scaling values from the map for given points and computing the change per mile north and the change per mile east. This method has been quite satisfactory for isolated surveys, but when two surveys originating at different base stations were extended until they joined, difficulty arose, not only because of discrepancies between base-station values, but also because of differences between the latitude and longitude correction factors used for the separate surveys. It is the purpose of this paper to describe a reference datum for magnetometer surveys which, it is believed, will eliminate most of the difficulty arising from this source. In order to be satisfactory, a general datum for magnetometer sur-veys should be as close as possible to the observed field and still he based on some assumed distribution of magnet poles, in order that the "normal" value of any component of the field for any given point may be computed to as many significant figures as desired. Such a field has been com-puted, and a comparison of the intensity of its vertical component with the average vertical intensity for the United States as shown by the U.S.C.G.S. map of lines of equal intensity for 1935 is shown in Fig. 1.

Jan 1, 1939

By E. S. Machlin

An extension of the thermodynamic theory has been made for the case of irreversible growth processes occurring by the motion of an interface. The theory is applicable to such diverse phenomena as diffusion, growth in recrystallization, continuous grain growth, growth of carbides, etc., growth of eutectoid products, growth in solidification, recovery, "slipless" flow, etc. THE publication of a recent book1 has served to focus attention on a very powerful means of treating certain irreversible processes. This method which has been formally described as the thermodynamic theory of irreversible processes is applicable to processes which involve an approach to equilibrium and for which the deviations from equilibrium are small. The irreversible processes can be classified into three groups: chemical reactions, transport processes (diffusion, heat and electrical flows), and relaxation phenomena involving a degradation of internal energy to more stable states. The limits of applicability of the theory can be precisely defined1,2 for each type of irreversible process. For example, in a chemical reaction at constant temperature and pressure, the Gibbs free energy released per mol in the process should be less than the thermal energy, RT. Another type of irreversible process, which sometimes involves a combination of the first two of the above-mentioned groups, is treated in this paper. This process is one characterized by the motion of an interface separating two regions having different values of free energy and may be briefly described as a growth process. Prigogine2 and Herring3 have treated special cases of this type of process. Previous conscious applications of the theory in metallurgy have been limited to the field of diffusion, one of the transport processes. Darken,4 Bardeen,5 Prigogine2 and others have made significant contributions in this respect. Some other applications of the theory are described in this paper. The Theory The thermodynamic theory of irreversible processes is based on the work of Onsager,6 DeDonder,7 Prigogine2 and others. A resume of the theory has been given by Prigogine2 and DeGroot.1 A brief description of the theory follows, although for a complete understanding the reader is urged to read the references. It is first assumed that the change in entropy, even for a system removed from equilibrium, is given by dS = [dU + pdV - Si µi, dn, - Sk Pk dxk]T-1 Using this expression, the irreversible entropy production in the system is calculated by subtracting the contribution to the change in entropy of the system by transfer of heat, work, or matter from the surroundings. Thus, for example, the irreversible entropy production of a system at constant temperature and pressure is given by dtS = — — dG (DeDonder7) Now it has been shown by Prigogine,2 DeDonder,7 and DeGroot1 that the rate of irreversible entropy production diS/dt, when calculated in the manner suggested, can be written as a sum of products of conjugate forces XK and fluxes Jk, i.e., d,s/ = Sk Jk Xk [I-1] dt The assumption is next made that a linear relation exists between a given flux and the forces, obtained from Eq. I-1, i.e., Ji = Sk Lik Xk (i = 1, 2, . . . n) [I-2] Generally, there is a degree of freedom in choice of the fluxes and forces. However, for all the choices consistent with Eq. I-1 the Onsager8 relations, based on the principle of microscopic reversibility, namely, Lik = Lki, are valid. The coefficients Lik, depending upon the choice of the conjugate fluxes and forces, may be more or less dependent upon the parameters defining the state of the system. In general, the proper choice of fluxes and forces utilizing Eq. I-1, makes the coefficients Lik independent of time. Also, because many of the three classes of irreversible phenomena have already been treated,1,2 a proper choice can be made by analogy. In any case, the validity of Eq. 1-2, from whatever choice made using Eq. I-1, must be tested by experimentation. The theory, thus, comprises the following steps: 1—The irreversible entropy production is calculated to yield Eq. I-1. 2—The terms in Eq. I-1 are grouped

Jan 1, 1954

By A. H. Heim

A method and apparatus for measuring gas porosities of rocks are described. The apparatus can be assembled from commercially available components. In principle, measurements are made by volume substitution at constant pressure. The maximum error is not more than 0.3 porosity per cent. Typical results are given. INTRODUCTION Determining the porosity of rock samples is one of the most important and yet most varied types of measurement in core analysis. Among the many techniques devised are the so-called "gas porosity" methods. An old and well known example is the Washburn-Bunting method.' The U. S. Bureau of Mines2-' described and later improved the apparatus for a now widely used method generally known as the "Boyle's law" method. In the present form of the Washburn-Bunting method,' the volume of air in the pores of a rock sample at atmospheric pressure is extracted and then collected in a graduated burette at atmospheric pressure. The volume of air is read directly as the pore volume of the sample. The absolute error in reading the collected volume of gas is independent of the total volume; thus, the relative error is larger when the volume is small, as it is for rocks of low porosity. In addition, the sample after measurement contains mercury, which limits its use for other analyses. The Bureau of Mines (or Boyle's law) method measures directly the solids volume of a sample from which the pore volume and porosity are derived, using a separate measurement of the bulk volume. Gas at a few atmospheres pressure is introduced into a sample chamber of known volume containing the rock sample. The pressure is accurately measured. Following, the gas is expanded into a burette at 1 atm, and the gas volume is read directly. From the initial pressure p, and the final pressure p2 and volume v,, the initial gas volume v1 is calculated using Boyle's law; that is, p1v1 = p2v2. Volume v, minus the volume of the empty sample chamber is the solids volume of the sample. The accuracy of the method is limited, unless corrections are made, by deviations of the gas from the "ideal" gas-law behavior assumed in the simple form of Boyle's law. The purpose of the present paper is to describe a method for measuring the gas porosity of a rock which avoids many of these difficulties. Gas volumes are measured directly with the same accuracy as the bulk volumes. Pressures of at least an order of magnitude larger than those of previous methods are employed to insure rapid penetration of the gas into the sample. While special equipment may be built to apply the method, the porosimeter may be constructed as well from commercially available components. For simplicity, the apparatus described will be referred to as the "Constant-Pressure gas porosimeter". THE CONSTANT-PRESSURE METHOD Fig. 1 shows schematically the arrangement of components comprising the present Constant-Pressure porosimeter. Briefly, the method is one of volume substitution and may be considered a null measurement. Omitting (for the present) some of the operational details, the method of measurement consists of the following three steps. 1. After evacuation, the volume of the measuring system (a ballast chamber, a manifold, two gauges and their connections) up to the sample chamber is filled with gas to a high pressure (- 1,000 psi). A sample of the gas at this pressure is trapped in one side of a sensitive differential pressure gauge to serve as the reference pressure for subsequent steps. 2. The evacuated sample chamber containing the rock sample is opened to the measuring system. As the gas expands into the chamber, the resulting decrease in pressure unbalances the differential pressure gauge. 3. The pressure is restored by means of a mercury volumetric pump. The volume of mercury injected exactly equals the free or void volume of the sample chamber (volume of empty chamber minus the solids volume of the rock within). From the injected volume and the known empty chamber volume, the solids volume is obtained and the porosity calculated. The pressure and the volume occupied by the gas are the same before and after opening the sample chamber. Expansion and compression of the gas are incidental operations and do not enter into the calculation of porosity. By the pressure balancing or nulling, the free volume of the sample chamber is merely substituted by an equal and measured volume of mercury. Since the measurements are at constant pressure, there are no compressibility corrections necessary for the sample chamber.

By F. B. Plummer

PRODUCING operations abroad during 1940 were shrouded in the fog of war. Little, if any, concrete information is available, and the data that issue from the belligerent countries are too frequently distorted for military purposes, for the volume of supply of gasoline and fuel oil has become an important strategic secret. Despite this lack of information signs indicate the spread of a slow paralysis which is gripping producing operations in foreign countries. Only in the Caribbean area are developments proceeding normally and even there the destruction of the Western European market is being seriously felt. This creeping paralysis is being brought about partly by the serious shortage of materials so necessary for drilling and other producing operations such as steel, machinery, and the like-together with a scarcity of that prime munition of war-money. Markets too have been curtailed by the operation of exchange control as all exchange is needed to support war efforts. As a result, gasoline is tightly rationed in all belligerent countries. The growing casualties in shipping are fast restricting the water-borne trade in petroleum, but have had a local stimulating effect in some areas where the risk is less or where water-borne transport can be efficiently used as for instance Trinidad and Egypt. The type of product needed for war effort, particularly the great demand for aviation gasoline, has changed the schedules of .refinery operations. As a result of all these influences the world oil picture outside the United States- has vastly changed during the year.

Jan 1, 1941

By T. M. Kegley, J. H. Frye, D. L. McElroy, M. L. Picklesimer, E. E. Stansbury

Measurements of rate of growth, thermodymmic quantities, and partitioning of Mn are reported for high-purity eutectoid Fe-C and Fe-C-Mn steels for the auistenite-pearlite reaction. Evaluztion of the cotnstants of a derived-rate equation with these data indicate that Mn additions cause the decrease observed by increasivg the activation energy and apparent activation entropy or the movenment of complexes at the interface. A diffusion-controlled mechanism is not required. Appreciable partitioning of Mn to cementite occurs entirely behind the austenite-pearlite interface for more than 30°C of subcooling. ThE growth of pearlite from austenite has been extensively studied over a period of years. but the rate-controlling step in the process is not known nor is the mechanisrn of the effect of alloying elements understood. A comprehensive review of the subject has been given by Mehl and Hagel. The present study has been concerned with further considerations of the effects of alloying elements on the rate of growth of pearlite. Analytical relatioriships for the rate of growth of pearlite have been considered by Zener.2 Turnbull,3 Machlin,4 Cahn.5 Frye,6 and Frye et a1.7 The derived expressions in each case involve the free energy of the transformation. the interlamellar spacing. and some rate term of the nature of the diffusion coefficient. mobility or frequency of occurrence of some rate-determining step. The treatments. of course. differ in detail. Further consideration is given in the present paper to the equation of Frye, Stansbury. and McElroy which was derived from modified absolute rate theory without in any way specifying the mechanism of the reaction. This equation is r=c ? T ? F exp -?E*/RT [1] where r = rate of growth in mm/sec c = a constant AT = equilibrium transformation temperature minus actual transformation temperature "C ?F = free energy per mol of austenite minus that of pearlite ?E* = activation energy R= gas constant ?F in Eq. [1] is computed from the following: ?F=?H?T/To - ?T' dT' ?T' ?CdT"/T" [2] To To where AH is the enthalpy per mol of austenite minus that of pearlite at the equilibrium temperature, To, and AC is the difference in specific heat between austenite and pearlite per mol. Subsequently, Darken, Fisher, and Galligan8 have reported that a layer of ferrite separates pearlite from austenite at the growing interface (i,e., the advancing face of Fe3C is in contact with ferrite, not austenite) and the ratio of the thickness of this layer to the spacing of the pearlite has not been found to vary with alloy content or transformation temperature. This observation does not require any alteration in the above equation: however, it may require that a different significance be attached to the factor, AT. The AT term appears in Eq. [I] as a consequence of a factor for the amount of growth per complex transformed at the interface.* It is based *This is not the sole reason for expecting such a relationship. See Ref. 7._______________________________________________________ on a l/2 ?T dependence of the interlamellar spacing. Zener2 has developed a theory which leads to Soa 1/?V where So = the pearlite interlamellar spacing. This relation is as consistent with the data on interlamellar spacing as other relationships, although, as pointed out by Mehl and Hagel,1 the data are not sufficiently precise to consider the relationship as confirmed. The work of Darken, Fisher, and Galligan8 requires that the above be written where f = the thickness of ferrite layer between austenite and pearlite. The present paper is concerned with iron-carbon-manganese eutectoid alloys and reports experimental measurements of the following kinds: 1) the effect of

Jan 1, 1961

By R. S. Rickard, M. C. Fuerstenau

Anodic polarization curves for iron dissolution and cathodic polarization curves for copper deposition and ferric and hydrogen ion reduction were studied. These results were used to predict the relative rates of the reactions: The rates of the first two reactions were found to be first order with respect to the reacting ion, and the rale-controlling step was diffusion of the ions to the callzode surface. The rate of hydrogen ion reduction in an oxygen-free solution is dependent on the reciprocal of the square root of the hydrogen ion activity. In solutions containing oxygen, the rate of hydrogen reduction becomes dependent on the square root of the partial pressure of oxygen. At equal concentrations copper precipitation occurs about twice as fast as ferric ion reduction. In an air-saturated solution containing 0.01 M cupric ion at pH 2, the rate of hydrogen ion reduction zs about 10 times slower than that of copper precipitation. At pH values below 3, the rate of hydrogen reduction in oxygen-free solutions is very slozu. COPPER cementation has been utilized industrially for many years as a means of recovering copper from aqueous solutions. There are many different types of cementation plants, but all simply provide a means of contacting iron with relatively dilute copper solutions. In the past little or no attention has been paid to rates or mechanisms of the reactions involved. As a result, this and other studies'-3 have been undertaken recently to establish the important parameters in this system. The reactions involved in copper cementation by iron are: Since transfer of charge is involved in every case, these reactions should be considered from an electrochemical point of view. In any electrochemical system involving electrolytic conduction, passage of electrons necessitates ion transfer to the respective electrodes according to Faraday's law. The current in the system will be proportional to the rate of ion transfer, and, therefore, when the current in the galvanic cell is known, the rates of the reactions involved can be determined. Galvanostatic electrode measurements5" are applicable for these electrochemical studies, in that with this technique polarization curves (current density vs electrode potential) are established by impressing a constant current through an electrode and measuring the electrode potential. Once the current density, electrode potential, and reacting area are known for each reaction in this cementation system, the rates of the iron-consuming reactions can be determined. EXPERIMENTAL MATERIALS Several metal electrodes were used in this investigation; they are shown in Table I. Solutions were made with reagent-grade salts and conductivity water. Air, nitrogen, and oxygen were employed. All of these gases were saturated with water and degreased prior to use. EXPERIMENTAL PROCEDURE The experimental work was divided into two general areas. The first area involved galvanostatic measurements, which were used to determine the rates of reactions as a function of various parameters. The second area comprised actual cementation experiments to check the rates predicted from the electrode measurements. Galvanostatic Electrode Experiments. Polarization curves were obtained using a standard galvanostatic technique5'= with the apparatus shown in Fig. 1. The various electrode polarization experiments were run the same way except for changes in solution composition, polarity, and type of measured electrode. The general procedure involved the following steps: 1) a solution was made 0.5 M in sulfate ion and to the desired cation concentrations; this solution was placed in a constant-temperature bath and saturated with the desired gas; 2) the electrodes were cleaned and placed in the electrode holder; 3) the previously cleaned apparatus was assembled and immersed in a constant-temperature water bath (temperature controlled to ± 0.05"C); 4) the electrode was then positioned; the solutions were introduced, and the polarization meas-

Jan 1, 1969

By Nick Holonyak

Halogen vapor-transport synthesis of Ga(As,-,Px) and its preparation into laser junctions are described. Electrical and optical properties of Ga(As,-,PX) laser junctions are discussed. The present limitations in these properties are related to material proble?vzs and the very early state of development of Ga(As,-,PX), and are discussed in this context. Inhonzogeneity problems, fluctuation of As :P ratio, and problems with deep-level contaminants are described and related to Ga(As,-,PX) junction performance. Laser junctions are demonstrated which operate to wavelengths as short as 6470 A (77°K). The prospect that Ga(As,-,P,) will operate to wavelengths perhaps 100A shorter is mentioned. IN this paper we wish to describe some of the more important features of almost 1 year of experience in the preparation and properties of Ga(As,-,P,) p-n junction lasers. Because much data so far available are far from complete, some of the results still must be considered tentative and subject to correction and revision as work on Ga(As,-,P,) crystal problems progresses. Although the electrical, optical, and device properties of Ga(As,-,P,) junction lasers are understandably of considerable interest, the work to date points out that by far the most serious problems extant and those deserving first attention are problems involving the growth, doping, and perfection of Ga(As,-,P,) crystals. One of the most formidable of these is to grow Ga(As,-,P,) sufficiently free of deep levels, either due to contaminants or to structural imperfections, to allow fabrication of laser p-n junctions which can be cooled and not suffer from "freeze-out" of carriers on deep levels (and consequent double-injection behavior). In addition to the problems of growing crystals adequately free of deep levels and generally of the highest perfection, so that the best possible laser junctions can be realized, the further goal remains of increasing the phosphorus content well beyond 40 pct in an attempt to determine the practical lower wavelength limits of laser action in the Ga(As,-,P,) system. Even though the laser junctions prepared in Ga(As,-,P,) are of importance in their own right, we have considered them at this point mainly a means to study the growth and crystal problems of the material. It can be concluded that the laser junctions now available are almost completely limited by the purity and structural deficiencies of Ga(As,-,P,) crystals, and cannot be fairly compared with, for example, GaAs p-n junction lasers until Ga(As,-,P,) crystal growth has been more extensively developed. The basis for the statements above will become evident in the following sections which describe Ga(As,-,P,) crystal and junction preparation, and laser-junction properties. G(As,-,P,) CRYSTAL GROWTH As previously reported,2 we have found it convenient to employ the halogen vapor-transport process3 for synthesizing Ga(As,-,P,) crystals for use in laser junctions. Commercially available GaAs and Gap, separately prepared by halogen vapor tranport, are sealed in the desired ratio in a quartz vessel with a quantity of column-VI donor and a small quantity of metal halide which supplies the halogen for transport. The sealed ampoule, as shown in Fig. 1, is heated at a temperature in the range from 1025" to 1100°C at the position of the source GaAs and Gap. The GaAs and Gap are simultaneously vapor-transported and deposited as Ga(As,-,P,) at one end of the ampoule

Jan 1, 1964

By Robert D. Pehlke, Robert G. Blossey

The solubility of nitrogen in liquid binary and ternary Fe-Ni-Co alloys has been measured by the Sieverts' method between 1550°and 1700°C. Solubility data and standard free energzes and enthalpies of solution for nitrogen in the alloys are presented. Interaction parameters are discussed and presented for binary and ternary alloys. MOST of the studies of nitrogen solubility in liquid metals have been directed toward the dilute alloys of iron. Several of these investigations have included measurements of the nitrogen solubility in Fe-Ni al10s'- and in Fe-Co alloys.435 There has been some work, however, that has extended across the e-i-" and F-CO" binaries. This investigation was undertaken to determine the nitrogen solubility in both binary and ternary alloys of the Fe-Ni-Co system. It was also hoped that the differences between earlier studies might be resolved. EXPERIMENTAL METHOD This investigation was made using a Sieverts' apparatus described previously." The nickel (99.85 pct) and cobalt (99.9 pct) were obtained from Sherritt-Gordon Mines, Ltd., and the iron (99.95 pct) was Fer-rovac-E obtained from Crucible Steel Co. Recrystal-lized alumina crucibles were used throughout the entire investigation with no evidence of crucible-melt reaction. Melt temperatures were measured with an optical pyrometer and the temperature scale calibrated against the melting points of the three pure metals. The emissivity of the melt was assumed to be a linear function of composition for all alloys, as has been shown for Fe-Ni alloys.lZ The emissivity of the pure metals at 1600°C were taken as 0.43 for iron, 0.44 for cobalt, and 0.45 for nickel. Using these emissivities, the trans mis sivity of the system was found to be 0.51 i 0.01. The Sieverts' method was used for this study and followed the procedures outlined previously.l' The individual metals were weighed to give about 100 g of alloy. The alloys were melted in the crucible under a partial pressure of argon. The system was evacuated, and the "hot volume" was measured with argon. To avoid the errors caused by vaporization, the melt was held under vacuum only long enough to ensure that all of the gas in the system had been removed. The influence of any small amount of vaporization on the "hot volume" was shown to be negligible by measuring the "hot volume" after a run. This measurement agreed with that made at the start of the run within the implicit error, 0.2 cc, caused by the limitations in accurately reading the buret. The solubility-pressure relationship was measured in the pure metals and in several alloy compositions throughout the ternary system. These measurements were made by admitting measured amounts of nitrogen to the system, and then determining the equilibrium nitrogen pressure above the melt. This method has the distinct advantage of higher accuracy, particularly at lower pressures, than measurements made by withdrawing gas from the system to reduce the pressure after determining the solubility at 1 atm nitrogen pressure. This latter method has a practical lower limit of about 0.4 atm where an increased error is encountered because the buret must be emptied to permit further measurements at lower pressures. By determining the relation between apparent solubility and pressure, it was possible to make a good estimate of the initial nitrogen content of the metal from the intercept of the solubility curve extrapolated to zero pressure.11 DISCUSSION The solubility data corrected to 1 atm nitrogen pressure are summarized in Table I. The reported solubility has been corrected for the initial nitrogen content of the alloys. The initial nitrogen contents fell between 0.0002 and 0.0010 wt pct, and were lower in the iron and nickel than in the cobalt. Sieverts' law was obeyed in all alloys at pressures up to 1 atm. Examples of this behavior are shown in Fig. 1. The reaction for solution of nitrogen is Taking the standard state as 1 wt pct N in the alloy and the reference state as nitrogen at infinite dilution in the alloy, and noting the adherence to Sieverts' law, K becomes the solubility of nitrogen in the alloy at 1 atm pressure. Thus the solubility data of Table I were used directly to calculate the standard free energy for the solution reaction. These results are also presented in Table I. The enthalpy of solution is also summarized in Table I as calculated from a form of the van't Hoff relation: Iron-Nickel System. The data for the solubility of nitrogen in liquid Fe-Ni binary alloys is presented in Fig. 2 along the with data of aito, Schenck et al.,' and Humbert and 1liott.l' The data for studies of nitrogen solubility in Fe-Ni alloys containing less than 20 pc t i'- are not presented in Fig. 2, although they are in good agreement with the present work. The results of this study are in good agreement with Schenck

Jan 1, 1967

By C. M. Marquardt

Tramp iron and steel moving on a conveyor belt cause small currents to be generated in a coil situated in a strong magnetic field, which are converted to an alternating current and are amplified. The output voltage from the amplifier fires a thyratron with a relay in its anode circuit, which actuates a howler and simultaneously drops a spot of marker material on the belt.

Jan 1, 1950

By B. B. Rath, Hsun Hu

In wedge-shaped bicrystals of zone-refined aluminum it is observed that (111) pure tilt boundaries migrate under the driving force of their own inter-facial free energy. The boundary velocity is a power function of the driving force. The driving force exponent decreases with decreasing angle of misorien-tation. For example, at 64O°C, the exponent decreased from 4.0 for a 40 deg to 3.2 for a 16 deg tilt boundary. An evaluation of the driving force acting on the boundaries during their motion indicates that for low driv-forces, up to about 2 x l03 ergs per cu cm, the velocity is relatively independent of misorientation, whereas at higher driving forces a 40 deg tilt boundary exhibits the highest velocity. The measured activation energy for boundary migration approaches that for bulk self-diffusion at low driving forces, decreasing from 33 to 27 kcal per mole as the driving force is increased from 1 x l0 to 5 x l03 ergs per cu cm. These results are compared with current theories of grain-boundary migration. In previous experimental studies of grain boundary migration the driving force has been limited to a difference in stored energy across the boundary. This stored energy has been introduced into the crystal either by prior deformation1-3 or by grown-in lineage structure. A part of the energy stored in the deformed crystal is released by recovery either prior to or concurrently with grain boundary migration, thus introducing an uncertainty as to the magnitude of the driving force responsible for grain boundary migration. The grown-in lineage structure, though thermally stable during annealing, neither provides conditions under which different levels of energy may be stored in the imperfect crystal nor provides a control of orientation difference across the migrating boundary of a growing grain. Furthermore, because of variation in the lineage structure, it is difficult to determine accurately the energy stored in the imperfect crystal. Several investigations of grain boundary migration during normal grain growth have also suffered from difficulties in estimating the driving force because of uncertainties in the principal radii of curvature.~ In the present investigation the velocity of pure tilt boundaries in zone-refined aluminum bicrystals of selected orientation (40, 30, and 16 deg around the [Ill] tilt axis) has been measured in the absence of a dislocation density difference across the moving boundary, thus eliminating the previous experimental difficulties. The driving force for boundary migration is derived from a gradient of the total interfacial free energy of the migrating boundary in wedge-shaped bicrystals. A similar method was attempted by Bron and Machlin in a study of grain boundary migration in silver. However, they found that one of the crystals was deformed and consequently the motion of the boundary was partly due to a difference of stored energy across the boundary. The observed behavior of boundary velocities as affected by the driving force is examined in the light of the predictions of the current theories of grain boundary migration.7"10 The effect of boundary misorientation on velocity is compared with the theory of " which is based on a dislocation core model for high-angle boundaries. EXPERIMENTAL METHOD Seed-oriented bicrystals of zone-refined aluminum, 2.5 cm wide, 0.5 cm thick, and 12 cm long, containing tilt boundaries with a common (111) axis, were grown from the melt in the direction of this axis. Spectro-graphic analysis, reported earlier,'' indicated the purity of the crystals to be 99.999+pct. Three such bicrystals containing 16, 30, and 40 deg tilt boundaries were used. Wedge-shaped specimens were prepared from these bicrystals by spark cutting followed by electrolytic polishing. The angle of the wedge was usually 40 deg and the specimens were usually 0.25 cm thick. The intercrystalline boundary was located within 0.2 to 0.5 cm from the tip of the wedge. Fig. 1 shows a section of an oriented bicrystal containing an outline of a wedge-shaped specimen. The crystallographic directions shown in Fig. 1 represent the orientation of one of the crystals (the larger section of the bicrys-tal); the orientation of the other crystal differs only by rotation around the common [lil] axis. The parallel faces of the wedge always corresponded to the common (171) planes in both crystals, whereas the orientation of the side faces varied, depending on the misorientation angle. The bicrystal orientations were determined

Jan 1, 1970

By R. Schuhmann, J. Th. Overbeek, P. L. De Bruyn

THE technique of concentrating valuable minerals from lean ores by flotation depends upon the creation of a finite contact angle at the three-phase contact, mineral-water-air. If the mineral is completely wetted by the water phase, contact angle zero, there is no tendency for air bubbles to attach themselves to the mineral. However, when the contact angle is finite, the surface free energy of the system, water-air bubble-mineral particle, can be diminished by contact between the bubble and the particle, and if not too heavy the mineral will be levitated in the froth. With a few exceptions, all clean minerals are completely wetted by pure water. Thus the art of flotation consists in adding substances to the water to make a finite contact angle with the mineral to be floated, but to leave the other minerals with a zero contact angle. The contact angle concept and experimental measurements of contact angles have played important roles in flotation research for several decades.'-" Nevertheless, there remain unanswered some basic questions as to the scientific significance of the contact angle and the nature of the processes by which flotation reagents affect contact angles. The contact angle is a complex quantity because the properties of three different phases, or rather of three different interfaces, control its magnitude. Considering the interfaces close to the region of ternary contact to be plane, the relation among the contact angle and the three binary interfacial tensions is easily derived. The condition for equilibrium among the three surface tensions, Fig. 1, or the requirement of minimum total surface free energy leads to Young's equation, Eq. I: ysa — ysl = yLA cos 0 [1] According to this equation, the contact angle has one well-defined value. Actually it is found in many experiments that the value of the contact angle depends on whether the air is replacing liquid over the solid (receding angle) or the liquid is replacing air (advancing angle). The receding angle is always the smaller of the two.4 Two explanations have been offered for this experimental fact. According to some investigators,5-8 roughness of the surface causes apparent contact angles that are different for the receding and the advancing cases although the actual local contact angle may be completely determined by Eq. 1. The other explanation involves the hypothesis that the solid-air interface after the liquid has just receded is different from the same interface when no liquid has previously covered it.1,4 Adsorption of constituents of the air or liquid might play a role here. In this discussion the difference between advancing and receding contact angle will be neglected and plane surfaces where Eq. 1 describes the situation will be considered. But there is still a fundamental obstacle to the application of Young's equation. The surface tension of the liquid (rla) can easily be determined, but the two surface tensions of the solid (rsa and ySL) cannot be measured directly. Eq. 1, however, is not without value. By contact angle measurements it is possible to establish how ysl — ysl varies with the addition of solutes to the liquid phase. Also, Eq. 1 affords a convenient starting point for calculating net forces and energy changes involved in the process of bubble-particle attachment.1,2 . If for the moment surface tension of the liquid (yLa) is considered a constant, an increase in ysa — ysL, will tend to decrease the contact angle. A decrease in ySA — ysl, corresponds to an increase of the contact angle. In cases where ySA — ySL > yLa the contact angle is zero; it will only reach finite values when ysa — ysa has been decreased below YLA. Thus on the basis of Young's equation and contact angle measurements alone, it can be learned how flotation reagents affect the difference Ysa — ysl, but no conclusions can be drawn as to the effects of reagents on the individual surface tensions ysa, and ysL, not even as to signs or directions of the surface tension changes resulting from reagent additions. A quantitative relationship between the surface tension or interfacial tension and the adsorption occurring at a surface or an interface is given by the Gibbs equation, which for constant temperature and pressure reads dy = — 2 T, du, [2] where dy is the infinitesimal change in surface tension accompanying a change in chemical potential

Jan 1, 1955