Search Documents

By B. L. Averbach, Morris Cohen, S. A. Kulin

The martensitic transformation can be initiated by elastic stresses at temperatures above M. in a steel containing 20 pct Ni and 0.5 pct C. Shear strains and normal tensile strains acting on a potential habit plane promote the transformation but compressive strains oppose it. THE strain sensitivity of the martensitic transformation has long been recognized. It is now well known that martensite formation can be induced by plastic deformation at temperatures below, and not too far above, the M, point.' However, the exact role of elastic vs. plastic strains and of the concomitant stresses has proved to be a very elusive matter. Many investigators2-' of the steel hardening reaction have made use of the stresses resulting from volume changes to account for such observations as the existence of retained austenite and its variation across the section of a bar, the change in the amount of retained austenite with quenching rate, and the self-stopping nature of the transformation when the cooling is stopped. The effect of applied strain as an independent variable has been studied in 70 pct Fe-30 pct Ni alloys by Scheil7 and McReynolds.8 Some data are also available for lithium and Li-Mg alloys,9 Cu-Zn,10 Cu-Sn and Cu-A1 alloys," and aus-tenitic stainless steels."-" It has been found that martensite formation can be induced isothermally, even at temperatures above M,, by mechanical deformation of the parent phase. The competitive nature of plastic yielding by slip and by the martensitic reaction has been depicted by Scheil.7 Basically, Scheil postulated that: 1—at temperatures not too far above M, (where austenite is less stable than martensite), a critical resolved shear stress (within the elastic range) is required to promote the transformation to martensite; 2—at and below M,, the austenite lattice becomes mechanically, as well as thermodynamically, unstable and shears over spontaneously into martensite without the application of external stress; and 3—at temperatures sufficiently far above M8, the critical resolved shear stress for martensite formation increases to a level above that required for slip, and plastic flow then supersedes the transformation when external stress is applied. Scheil's concepts were tested by McReyno1ds8 ho found no change in the elastic moduli (measured both statically and dynamically) of 71 pct Fe-29 pct Ni alloys in the vicinity of the M, temperature. Since the moduli did not approach zero or become negative on cooling to M,, it was concluded that the austenite lattice does not become mechanically unstable at M2, as postulated by Scheil. McReynolds also reported that M, is not raised by elastic stresses. Accordingly, plastic deformation was considered to stimulate the transformation by generating martensite nuclei in the distorted regions of the parent phase. The above issues with regard to the role of applied stress require clarification, if a basic understanding of the martensitic transformation is to be obtained. For example, in the reaction-path theory,'"," it is postulated that strain embryos exist in the austenite that provide part of the activation energy for the nucleation process. These embryos are visualized to be regions of localized strain in which the atoms in the austenite lattice are displaced part way along the path to their ultimate positions in the martensite. Consequently, it would

Jan 1, 1953

The Library of the above-named Societies is open from 9 A.M. to 10 P.M., except on holidays. It contains about 70,000 volumes and 90,000 pamphlets, including sets of technical periodicals and the publications of scientific and technical societies. Members of the Institute, with few exceptions, are forced to spend a portion of their time in localities isolated from sources of information. To these the Library, through its Library Service Bureau, can render valuable service through correspondence; letters requesting information will receive especial attention. The Library is prepared to furnish references and photographic copies of articles on mining and metallurgical subjects; to determine the existence of mining maps, and to furnish general information on the geology and mineral resources of all countries. All communications should be made as definite as possible so that the information received may be what is desired and not include collateral matter which may not be of interest. The time spent in searching for such collateral matter will be saved, and the information will be sent more promptly and in more usable shape.

Jan 7, 1917

By Richard P. Hight

Abrasives include the substances, natural or artificial, that are used to grind, polish, abrade, scour, clean, or otherwise remove solid material, usually by rubbing action but also by impact (pressure blasting for example). They do not include abrasive tools, for instance, lathe tools and files--or polishing agents such as waxes, which act by filling pores. Detergents and cleaners whose action is chemical rather than physical are omitted al- though some chemical-action polishes and cleaners may also contain solid abrasives, for example, many automobile and metal polishes. General Considerations The most important physical properties of materials that qualify them for use as abrasives are hardness, toughness (or brittleness), grain shape and size, character of fracture or cleavage, purity or uniformity. For making bonded abrasive products such as grinding wheels, additional important factors are stability under high heat and bonding characteristics of grain surfaces. The economic factors of cost and availability are always important. No one single property is paramount for any use. For some uses extreme hardness and toughness are needed, as in diamonds for drill bits; for others, the factors of greatest importance are hardness and ability to break down slowly under use, to develop fresh cut- ting edges when grains become worn-for example: in garnet for sandpaper neither highly cleavable or friable grains nor extremely tough grains are wanted. For still other uses, great hardness is objectionable; for example, abrasives for dentifrices and for glass-cleaning soaps. For the most efficient use in the more critical applications, the different types of abrasives are rarely completely interchangeable; thus, while crushed quartz and garnet are both used in sandpaper, the papers are not at all interchangeable in their use applications. In the last analysis, the choice of a high grade abrasive depends upon the quality and quantity of work done by the abrasive per unit of cost. Initial cost of an artificial abrasive may be much greater than that of a natural abrasive but the artificial abrasive may do so much better work than the natural one, and do it so much faster that the ultimate cost will be less. It is for this reason that artificial abrasives have largely replaced natural abrasives. Abrasive Value Mineralogical hardness or "scratch" hardness as expressed in Mohs' scale is an important property in evaluating abrasive materials, but, as noted before, it is only one of several essential properties. The mineral hardness of pure crystal almandite garnet is about 7.5, but if the crystal is crossed by incipient fracture planes, or if it contains inclusions of other minerals, the apparent or useful hardness may be much lower. While the quartz grains in a sandstone have a hardness of 7, the bond holding the grains together may be so weak that the stone is valueless as a commercial abrasive. In artificially bonded wheels and stones, the hardness, strength, and character of the bond are fully as important as the hardness of the abrasive grains. Thus, in an overall consideration of abrasive hardness of loose abrasive grains, both "scratch" hardness and toughness must be considered. In naturally or artificially bonded abrasive stones, bond characteristics are a third factor, which is most important. The problem of abrasive hardness is further complicated by the inadequacies of methods of testing hardness and of expressing relative values. The Mohs' scale is inadequate both because the methods of testing are very crude and

Jan 1, 1975

By Benjamin L. Miller, Charles H. Breerwood

From earliest recorded times, limestone has been employed in the industrial life of peoples of all sections of the world where it exists. It is widely distributed and therefore has been available in almost every country and has been employed for a variety of purposes. Its earliest use was for buildings, since it is more easily quarried and dressed than most other kinds of rocks and so could be utilized by early inhabitants, poorly equipped with tools. The next use was in the manufacture of lime, which was employed by the ancients in mortar. These two uses of limestone are still all important, but they have been overshadowed in scores of regions by literally hundreds of new applications for raw limestone or products made from it. Anyone familiar with modern manufacturing processes can quickly call to mind many industries in which limestones are essential, and new uses are continually coming to notice. Any enumeration would probably be incomplete and soon out of date. Origin of Limestone Disregarding details and unusual types concerning which often there is insufficient evidence and considerable difference of opinion, limestones have been formed by the precipitation of calcium carbonate from solution through the action of organisms, both plants and animals, or in a limited number of instances by chemical reactions without the intervention of living forms. Some of the organisms extracted the calcareous material in order to build up hard structures, either as bony skeletons or as coverings (clams, snails, etc.), whereas others in their life functions emitted substances that resulted in the precipitation of the soluble constituents outside the organisms themselves. In some instances the organisms utilized only calcium carbonate but in some cases other compounds as well were precipitated. Various materials have been found in the hard parts of animals, and for that reason it is almost impossible to find a pure natural limestone; that is, one composed entirely of CaCO3.

Jan 1, 1938

By Charles H. Breerwood, Benjamin L. Miller

From earliest recorded times, limestone has been employed in the industrial life of peoples of all sections of the world where it exists. It is widely distributed and therefore has been available in almost every country and has been employed for a variety of purposes. Its earliest use was for buildings, since it is more easily quarried and dressed than most other kinds of rocks and so could be utilized by early inhabitants, poorly equipped with tools. The next use was in the manufacture of lime, which was employed by the ancients in mortar. These two uses of limestone are still all important, but they have been overshadowed in scores of regions by literally hundreds of new applications for raw limestone or products made from it. Anyone familiar with modern manufacturing processes can quickly call to mind many industries in which limestones are essential, and new uses are continually coming to notice. Any enumeration would probably be incomplete and soon out of date. Origin of Limestone Disregarding details and unusual types concerning which often there is insufficient evidence and considerable difference of opinion, limestones have been formed by the precipitation of calcium carbonate from solution through the action of organisms, both plants and animals, or in a limited number of instances by chemical reactions without the intervention of living forms. Some of the organisms extracted the calcareous material in order to build up hard structures, either as bony skeletons or as coverings (clams, snails, etc.), whereas others in their life functions emitted substances that resulted in the precipitation of the soluble constituents outside the organisms themselves. In some instances the organisms utilized only calcium carbonate but in some cases other compounds as well were precipitated. Various materials have been found in the hard parts of animals, and for that reason it is almost impossible to find a pure natural limestone; that is, one composed entirely of CaCO3.

Jan 1, 1938

By D. G. Westlake

Resistance was measured as a function of temperature, 77° to 350°K,for niobium with hydrogen concentrations up to 3.76 at. pct. Cooling curves exhibited a discontinuity in slope that was attributed to the initiation of hydride formation. A thermal hysteresis was explained in terms of diffusion and the effects of mechanical constraint on nucleation and growth. The heat of solution of hydrogen in saturated Nb-H solid solution was 2. 737 * 0.045 kcal per g-atom, including an unknown stress contribution. The critical ternperatures for hydride formation during cooling and for embrittlement are correlated but not coincident. This, too, has been explained in terms of mechanical constraint and stress-itlduced tratzsfomtation. Nb-H alloys undergo a ductile-brittle transition with decreasing temperature.'-3 Similar behavior has been noted for v-H.1,5 For the latter system, there is evi-dence6 suggesting coincidence of the temperature of minimum ductility and the critical temperature T, for initiation of metal hydride precipitation during cooling. A decrease in ductility due to the presence of brittle hydride particles is readily explainable. The fact that ductility begins to decrease at some temperature higher than T,4,5 has led us6 to suggest that precipitation may be strain-induced locally during tensile testing. Wood and Daniels' have reported that a plot of temperatures for 10 pct reduction in ductility vs hydrogen concentration in niobium is not coincident with, but parallels, the solvus.7,8 They believe this indicates a correlation of precipitation and embrittlement. Unfortunately, the two reported solvuses 7,8 to which Wood and Daniels refer are not in agreement with each other. Furthermore, neither solvus was determined experimentally: each was a plot of calculated solubilities. Thus. neither is highly dependable for determining whether embrittlement coincides with initiation of hydride precipitation. Longson 9 studied phase relations in the Nb-H system between 77° and 473°K by dilatometry. Comparison with metallographic observations convinced him that discontinuities in the slopes of his dilatometric plots were coincident with the initiation of hydride precipitation. Plotting the logarithm of the hydrogen concentration vs the reciprocal of the temperature at which precipitation was initiated during cooling, he obtained a straight line shown in Fig. 1. Walter and chandler,'' using X-ray techniques to detect the for mation of a second phase? have obtained three experimental points in the temperature range 295° to 338°K which fall within Longson's experimental error for this plot. A similar plotg of temperatures at which dissolution was completed during heating was a parallel line shifted toward higher temperatures. A straight-line plot was obtained, also, for the temperatures of the ductile-brittle transitions,9 but it was shifted toward still higher temperatures. Longson calculated an activation energy of 2.980 * 0.300 kcal per mole for the hydrogen embrittlement mechanism, compared with 3.180 * 0.400 kcal per mole for hydride formation. Despite this agreement, he concluded, "It seems unlikely that embrittlement results from hydride formation..." because hydrogen embrittlement was observed at temperatures above the solvus. It is our contention that embrittlement is correlated with precipitation of the hydride.6 Because only Longson has investigated Nb-H phase relations at sub-ambient temperatures, we deemed it advisable to re-determine the temperature dependence of the solubility using the resistometric technique already proven successful for the V-H system.6 Coincidence of our solvus with temperatures for embrittlement would

Jan 1, 1970

By Arnulf Muan, Carlos Landolt

Equilibria involving Cu-Pt alloys, copper oxides, and atmospheres of known ox2gen pressures have been determined at 1000' and 1200 C. The data obtained have been used to calculate activity-composition relations in the alloys. A moderate negative deviation from ideality is found. At high copper concentrations, the results of the present study are in good agreement with those of previous investigators, whereas at low copper concentrations the activities obtained in this investigation are slightly higher than those reported previously. The present study is part of a research program dealing with the determination of phase relations and thermodynamic properties of copper-containing systems at high temperatures. The information available for such systems is very scanty, particularly for copper oxides and their combinations with other oxide components. Platinum is commonly used as a container in studies of oxide equilibria. To evaluate quantitatively the extent of reaction between the oxide and the container, a knowledge of activity-composition relations in Cu-Pt alloys is necessary. Such data are not available for Cu-Pt alloys in the temperature range of particular interest in the present research program, and particularly for alloys low in copper. Studies of various aspects of the systems Cu-Pt and Cu-0 have been reported in previous literature. The system Cu-Pt is known1 to form a continuous solid-solution series above 812.C, whereas ordered phases are present in certain composition ranges at lower temperatures. Thermodynamic data for the system have been reviewed by Hultgren et al.,' who presented free energies of mixing at 65Oo C, mainly derived from electromotive force cell measurements by Weibke and Matthes.3 Enthalpies of mixing at 640°C have been obtained by Oriani and Murphy4 with liquid tin calorime-try. Their results differ considerably from those derived from the temperature dependence of the data of Weibke and Matthes. Thermodynamic data for the disordered alloys have been obtained by Assayag,5 and more recently by Schmahl and Minzl,6 by Myles and Darby,7 and by McCormack, Myers, and Saxer.8 The two latter sets of data7'' became available after the present study was completed. In the system Cu-0+ two oxides are stable at high temperatures, CuO and CuzO+ each having only minor deviations from stoichiometry. Equilibria in the liquidus temperature region of the system Cu2O-CuO have been studied by Roberts and systemsmyth,9'10CuzO-CuO by Vogel and ocher,I1 by Osterwald,12 and recently the the present authors.13 The system is of the eutectic type with a eutectic temperature of 1083.C The composition of the eutectic liquid corresponds to Xcu0 = °.44, and the oxygen pressure of the coexisting gas phase is Po2 = 0.55 atm.13 Equilibrium oxygen pressures for coexistence of solid CuO and solid Cu2O have been determined by Schmahl and Muller,l4 by Gadalla, Ford, and white,l5 by Bidwell,16 and recently by the present authors.13 There is reasonably good agreement among the various sets of data. Free energies of formation of Cu2O(s) from the elements have been derived by Tretyakov,17 by Bidwell,16 by Kiukkola and wagner,18 by Pal'guev and Neuimin," and by Steele and Alcock,20 There is particularly good agreement among the latter three1'-20 sets of data. THEORETICAL BASIS Consider a subsolidus isothermal section of the system Cu-Pt-0, as shown in Fig. 1. Two phase as-

Jan 1, 1970

By Robert A. Rapp, Jan E. Verfurth

From the measurement of internal-oxidation band widths in Ag-In and Cu-A1 alloys, products for the solubility No and the diffusivity Do of oxygen in silver and apparent NODo products in copper have been obtained over a range of temperature. The NODO products for silver are in agreement with the product of the individually determined No and Do values of Eichenauer and Müller. Although interstitial diffusion of oxygen in silver is expected, the temperature-independent factor Do of the diffusion coefficient does not agree well with the theory of Wert and Zener. For Cu-A1 alloys internal oxidation does not follow the expression derived for ideal kinetics, since the apparent NODo product calculated from internal-oxidation measurements is a function of the alloy content in the specimen. Thus, unequivocal values for No or DO or even the product NODO in copper are not available from the literature. RELIABLE values for the saturation solubility NO and diffusivity DO of oxygen in fcc metals are lacking and difficult to determine, partially because internal-friction measurements are not applicable. Permeability experiments and Sieverts7-type adsorption -desorption methods3 have met with difficulty; however, Eichenauer and Müller4 have recently reported on the solubility and diffusivity of oxygen in silver as determined by the latter technique . Rhines, Johnson, and Anderson,5 and independently Meijering and Druyvesteyn,' introduced the possibility of deriving values for the product NODO in a metal from measurements of the widths of internal-oxidation zones (subscales) formed during the internal oxidation of alloys. In addition to these authors, several other investigators7-9 have made such measurements in various silver and copper alloys at various temperatures, mostly using me- chanically polished specimen surfaces. The purpose of this investigation was to determine over a range of temperature the calculated products NODO in silver and copper from systematic measurements of the widths of internally oxidized zones in Ag-In and Cu-A1 alloys, using specimens with electro-etched surfaces. Consider the internal oxidation of a dilute solid-solution alloy in which the base metal is not oxidized. If diffusion of oxygen is the rate-controlling step, then the depth 5 of the internal-oxidation zone is given by where y is a dimensionless parameter and t the oxidation time. Based on the solution of the diffusion equation, wagnerl0 has shown that under certain conditions several mathematical simplifications may be used in the evaluation of y, so that Eq. [I] may be expressed for the case that y « 1, and y(Do/DB) 1, where N(so)the is the equilibrium solubility (mole fraction) of oxygen in the solvent metal for the given oxidizing atmosphere, is the mole fraction of the solute metal in the bulk alloy, 4 is the diffusivity of the solute in the base metal, and v is the ratio of oxygen atoms to solute atoms in the precipitated oxide BO,. Rearranging Eq. [2] Maak' has derived an expression analogous to Eq. [3] for the case that an external-oxide scale, in addition to an internal-oxidation zone, is formed. For this combined external and internal oxidation for the case that 5/2 where 5 is the distance of the internal-oxidation front from the original external s.urface, and X is the distance of the external oxide/metal interface from the original external interface. The function F is defined by the expression

Jan 1, 1964

By J. A. Hren, G. Thomas

A high-temperature stage has been used to study precipitation and dissolution in thin foils of Al-20pct Ag alloy directly in the electron microscope. The results show that the aging characteristics are similar to those observed for bulk materials, and in addition, direct evidence is presented for clustering at the solid solution temperature. The limit of solubility of G. P. zones is-350°C. The heterogeneous precipitation, the growth and dissolution of ?&apos;have been studied in detail. Growth of ?&apos; parallel to the basal planes, occurs by continuous motion of inter -facial partial dislocations. Growth stops at intersecting particles due to formation of sessile a/6 <110> interfacial dislocations. Growth normal to the habit plane occurs by the spontaneous nucleation of partial dislocations on alternate (111) planes and the thickening rate is --10-3= times the lengthening rate. The precipitates dissolve in layers and the final product is a whole a/2 <110> dislocation . The nucleation -growth -dissolution processes are thus completely reversible. Kinetic data obtained from the dissolution rates of ?&apos;particles enable the diffusion coefficient to be determined and the activation energy is found to be 37.5(±4) kcal mol-1, which is that expected for dzffusion of silver in aluminum. The velocity of the interfacial dislocations is thus dependent solely on the rate of diffusion of silver atoms. RECENTLY it was demonstrated that a high-temperature stage could be effectively used in the electron microscope to follow directly the processes of precipitation and dissolution in thin foils of A1-4 pct Cu alloy.&apos; These experiments also provided kinetic data which enabled the diffusion coefficient to be estimated. This new development of electron metallography opens up many fruitful areas of research and it was decided to investigate the aging behavior in thin foils of A1-20 pct Ag alloy, particularly the mechanism of heterogeneous precipitation (i.e., precipitation on lattice defects). This system was chosen because the aging characteristics of bulk specimens are now well known,2"7 and because we wished to obtain more details of the role played by partial dislocations and stacking faults in the nucleation growth and dissolution of the hcp ?&apos; phase. This is of interest for the general case of fcc-- hcp transformations. Part of the A1-Ag phase diagram is shown in Fig. 1. The use of a high-temperature stage also enables a study to be made of the clustering process (formation of G. P. zones) and to determine the structure of the solid solution prior to the usual quenching and aging procedures. It is also possible to obtain kinetic data from measurements of the rates of dissolution of precipitate particles. Unlike the results of previous experiments on A1-4 pct CU 1 where much of the initial precipitation occurred on the foil surfaces, the results on the A1-20 pct A1 alloy were identical to those reported for bulk specimens6,7 and no surface precipitation was ever observed. Thus, it was possible to follow the aging sequence: G.P. zones — ?&apos; — ? directly in the thin foils. This paper is concerned with the formation and dissolution of zones and the ?&apos; phase, and no attempt has been made so far to follow the mode of discontinuous precipitation of ?. I) EXPERIMENTAL DETAILS The high-purity A1-20 pct Ag alloy was prepared by the Aluminum Co. of America in the form of 0.001-in.-thick sheets. These were cold rolled with intermediate anneals to a thickness of 0.0004 in.,

Jan 1, 1963

By H. Guyod

The response of the Guard Electrode sonde (LL3) and the Laterolog (LL7) can be mathematically computed only for cases that do not represent realistic conditions. A resistance network analogue that simulates a number of typical—although idealized—formations was used instead to obtain, for both devices, a large number of resistivity logs and current distribution maps. From these data, charts were prepared for estimating true resistivities under a number of conditions. Some of these charts and current distribution maps are presented. INTRODUCTION Two main benefits are expected from a resistivity log: (1) obtaining geological information for mapping and other purposes, and (2) obtaining petrophysical data, based on true rock resistivity. The geological information can be derived from any resistivity curve having sufficient vertical detail, but true rock resistivities frequently are difficult to determine with desired accuracy because we do not have sufficient interpretation data. This is particularly true for the records given by the Laterolog tools. The object of this paper is to throw some light on the factors affecting the responses of these tools so that better resistivity data can be obtained from Laterologs. LATEROLOGS Laterolog measuring systems are of two types: the LL3 sonde, frequently called "Guard", and the LL7 sonde. Both measure the resistance between a single exploring electrode placed in the borehole and a faraway return electrode whose influence will be assumed here to be negligible. Although the principles of these tools have already been outlined,1-3 it is desirable to review them briefly in this article. LL3 Fig. 1, left side, represents a long cylindrical, vertical current electrode placed in a medium of uniform resistivity. The current leaving the center section of the electrode flows essentially along horizontal lines, delineating a surface having the shape of a biconcave lens. It is the elec- trical resistance offered to this particular group of current lines that is measured by the Guard tool. This is done in practice by having a long cylindrical electrode consisting of three sections physically and electrically separated by thin insulating washers, as shown in the center of the figure, and keeping the three sections at the same potential. It is obvious, for all practical purposes, that the current and potential distributions about this electrode are the same, as if we had a continuous electrode of same dimensions. Because the three sections are electrically separated, the resistance seen by the center section E can be independently measured. This section will be called the exploring electrbde, or E electrode. Its height generally is from a few inches to 1 ft. The outer sections are the guards G, which are several feet long. The combined length of the three sections is from 10 to 12 ft for the tools currently used in the petroleum industry. Let V denote the potential difference between E and the faraway return electrode, and I be the current flowing between these two electrodes. The resistance (Re) seen by the exploring electrode is VII, and the corresponding apparent resistivity is Ra = k(Re),............(1) where k is the tool calibration factor. The previous description establishes that the Guard tool uses that central portion of the sonde from which, in a uniform medium, the current follows essentially horizontal paths. When the formation being logged is fairly uniform, and when its resistivity is of the same order as

Jan 1, 1965

By Nicholas J. Grant, Rolf Nordheim, Bill C. Gissen

The system Cb-Re was examined in detail utilizing pure metals, careful melting techniques, and heat treatments. Metallographic and X-my methods were utilized for phase identification. In addition to soli-dus determinations, the composition limits and mode of formation of the intermetallic compounds 0 and X were determined. The binary constitution diagram Cb-Re has been the subject of a number of investigations.&apos;-7 Two intermetallic phases have been described and tentative diagrams have been proposed. It was the aim of this investigation to obtain a complete and more accurate diagram through the use of purer alloys and improved techniques. The diagram worked out by Knapton7 was published after our experiments were concluded. EXPERIMENTAL METHODS The starting materials were Re powder of 99.95 pct purity, supplied by the Chase Brass and Copper Co., and Cb rondelles of 99.6 pct purity, supplied by the Electro Metallurgical Co. Typical analyses are given in Table I. The alloys were prepared from compacted Re powder and Cb rondelles; for critical compositions master alloys were used. The melts varied from 5 to 50 g and were melted nonconsumably in an Heraeus arc furnace, under ti-tanium-gettered laboratory grade argon. It was necessary to invert the buttons and remelt, followed by crushing and further remeltings, the number of which depended on the nature of the fracture of the alloy. The weight of each alloy was carefully checked after each melting operation. It was found that significant weight losses occurred only when loose Re powder was used. These losses amounted to a maximum of 3 wt pct in such instances, but did not occur after the charge was once molten, regardless of the composition. Typical loss of weight after 4 remelts, including crushing, amounted to 0.2 wt pct. Oxygen pickup during successive melting cycles did not appear to be significant, since the weight gain values never exceeded 0.01 wt pct. Control of the composition of the alloys was not too difficult; however, the problem of homogenization was a far greater one. Optimum alloying conditions were finally achieved by a combination of master alloy production and repeated crushing and remelting cycles. The compositions of the alloys utilized to determine the constitution diagram are listed in Table 11. The weight balance method was used ultimately as the sole analytical method, since repeated checks indicated that it was accurate to 0.2 pct, if the weight losses were small. The results were double-checked by a metallographic study of the homogeneity of the samples, since this was presumed to be the more serious factor. Heat treatments at 1200°C or lower were accomplished by sealing the specimens in Vycor tubes, heating in a Globar furnace, followed by air cooling. This was considered to be an adequate quench because of the very low temperatures involved. For temperatures of 1200" to 1900°, alloys were homogenized and heat treated in a tungsten-filament resistance vacuum furnace. From 1900" to 2750" a tantalum-tube resistance furnace was utilized, operating under a vacuum of 105 mm Hg. The temperature measurements up to 1200" were made by means of platinum-platinum 10 pct Rh thermocouples, with an accuracy of 5°C. For temperature measurements greater than 1200°C, optical pyrometers were used. They were calibrated against a standardized instru-

Jan 1, 1962

By Donald E. Grimes

In conjunction with Inland Steel&apos;s development of lead-bearing steels possessing improved machin-ability because of tellurium and/or selenium additions, it was decided to determine liquidus and solidus temperatures in the Pb-PbTe-PbSe sub-ternary system. With the exception of alloys in the PbTe-PbSe system, it is believed that no previous study of this subternary has been performed. Thermal analysis was employed in a general survey of the subternary. In addition to PbTe, PbSe, and pure lead, ten ternary compositions were selected at intervals of ten at. pct. Sixty-gram alloys were prepared by sealing an appropriate mixture of the elements in quartz crucibles with a central thermocouple-well under a vacuum of less than 10 p. All three elements were 99.999+ pct pure with only trace impurities detected by spectroscopic examination. After the alloys had been heated at least 20°C above the liquidus in a Kanthal furnace, cooling and heating curves were obtained. Two or more cooling curves were employed both for the determination of each alloy liquidus and for the solidus of those al- loys containing greater than 50 at. pct Pb. Cooling rates were 0.5° to 3.5°C per min during the 5 min immediately prior to the start or end of solidification. For those ternary alloys containing 50 at. pct Pb, the solidus was determined from heating curves. Temperatures were measured with a Pt/Pt-10 pct Rh thermocouple which was calibrated in the same apparatus against the freezing points of zinc (A. D. MacKay—99.999 pct), antimony (A. D. MacKay-99.999 pct), and copper (ASARCO—99.999+ pct) both before and after the experimentation. The only interruptions in the continuous strip-chart recording of the temperature occurred for brief periods at significant points of interest when direct readings were made with a Rubicon Type B potentiometer sensitive to * 1 µv. The average liquidus and solidus temperatures obtained in this investigation are listed in Table I together with probable errors based on the accuracy of the thermocouple calibration and the reproduci-bility of the data. No chemical analyses of the alloys were performed because the synthetic or as-charged compositions were felt to be reliable. The melting points obtained for PbTe (924.7° ± 0.7°C) and PbSe (1084.0° ± 0.6°C) compare favorably with recent findings of other investigators.&apos;-&apos; As indicated in Table I, both the liquidus and solidus temperatures increase as selenium replaces tellurium for a constant atomic percent lead. As a result, the ternary liquidus and solidus temperatures for a given percent lead lie between the corresponding binary temperatures published in the literature. It should be noted that those ternary alloys containing 50 at. pct Pb exhibit a relatively narrow liquid-plus-solid region (<80°C) when compared with alloys containing greater than 50 at. pct Pb. Alloys with 60, 70, or 80 at. pct Pb not only have a much wider liquid-plus-solid region (>500°C) but also exhibit considerably lower and approximately constant solidus temperatures which thus form a virtually isothermal solidus "plane" slightly below the melting point of pure lead (327.3°C). For these alloys

Jan 1, 1965

SEC. 1. The membership of the Institute shall comprise seven classes, namely: 1. Members; 2. Honorary Members; 3. Senior Members; 4. Associates; 5. Junior Members; 6. Rocky Mountain Members; 7. Junior Foreign Affiliates. All shall be equally entitled to the privileges of membership, excepting that no member of any class whose residence shall be outside of the United States of America, except those residing in Mexico and Canada, shall be entitled to vote. SEC. 2. Members: A person to be eligible for election or transfer into the class of Member must be at least 27 years of age and must have had at least six years&apos; employ¬ment in the practice of engineering, mining, geology, metallurgy, or chemistry, during at least three years of which he must have held positions of responsibility in one or more of these fields. This shall not apply to Rocky Mountain members. SEC. 3. Honorary Members: Each candidate for Honorary Membership must be recommended by at least ten Members and must be elected by ballot at a meeting of the Board of Directors by the unanimous vote of the Directors present; provided, how¬ever, that the number of Honorary Members shall at no time exceed twenty. Such election shall automatically act as a transfer of such member from any other class of membership to which he may belong. SEC. 4. -Senior Members: The Directors may in their discretion place on the Honor Roll of Senior Members and transfer from any other class of membership other than Honorary Membership the name of any Member or Associate who has reached the age of seventy years and who has paid dues for thirty years, and for good reasons in special cases may vary the age or number of years. SEC. 5. Junior Members: A person to be eligible for election to the class of Junior Member must be qualified through education or experience to hold a subordinate position in engineering, mining, metallurgical, geological or chemical work. He shall be not more than 33 years of age at the time of election. SEC. 6. Associates: A person eligible for election or transfer into the class of Associate shall be one, who, in the opinion of the Committee on Admissions and the Board of Directors, is suitable for such election or transfer by reason of his interest in or connection with mining, geology, metallurgy, or chemistry. SEC. 7. Rocky Mountain Members: Membership in a special class of life member¬ships without annual or other dues and without right to receive the printed literature distributed to other members or the right and privilege of wearing the official badge of technical members, is given to all members of the Rocky Mountain Club at the time of consolidation. These special Rocky Mountain memberships shall be claimable by any member of the Rocky Mountain Club, not already a member of the Institute, availing himself of the privilege within ninety days after mailing of notice to him, by the Secretary of the Institute. SEC. 8. Junior Foreign Afliate: Upon appropriate action by the Board of Direc¬tors and with its approval, members in good standing of any technical society having its headquarters outside of the United States of America, Canada, or Mexico,

Jan 1, 1937

By C. H. Samans, G. F. Tisinai

HARDENING and embrittlement of the ferritic chromium stainless steels at temperatures near 885 °F have been known for a long time.&apos; However, no satisfactory explanation has been given. Both ordering and precipitation hardening have been suggested. Fisher, Dulis, and Carroll2 discovered a chromium-rich body-centered-cubic precipitate in embrittled alloys. Subsequently, Williams&apos; and Wright4 also have found evidence of this body-centered-cubic constituent. William&apos;s hardness, electrical resistance, and magnetic studies led to his proposal of a new constitutional diagram for the Fe-Cr alloys. The new feature of this diagram is the eutec-toidal decomposition, below about 970°F, of the s phase into two stable body-centered-cubic solid solutions, one rich in iron and the other rich in chromium. An observation of Heger5 that the amount of s phase has increased and the amount of chromium-rich body-centered-cubic phase decreased in the interval 5000 to 32,600 hr at 900°F, even though the alloy increased in hardness, casts some doubt on this diagram. If precipitation hardening causes the embrittlement, the precipitate probably is always coherent with the matrix, since no evidence of overaging has been reported. It cannot be stated positively, however, that Fisher&apos;s body-centered-cubic constituent is the embrittling phase. According to Preston&apos;s data,6 such a chromium-rich phase should have a parameter less than about 0.5 pct larger than that of the iron-rich matrix lattice. Moreover, the constitutional relationships whereby Fisher&apos;s constituent forms, and whether it is stable, metastable, or a transition phase, are not yet completely clear. The recent studies of Wright4 and of Lommel,7 as well as the earlier studies of Becket8 and of Hochmann,9 have shown that 885°F hardening occurs in relatively pure Fe-Cr alloys. No evidence of its occurrence or absence in chromium itself has been reported. The rate of hardening in high purity alloys seems appreciably slower than that in alloys containing larger amounts of impurities (chiefly carbon and nitrogen). This may be due merely to the absence of hardening and straining effects from precipitated carbides and/or nitrides. These observations on high purity alloys make it seem unlikely that 885 °F hardening is caused by a constituent containing other than iron and chromium atoms, e.g., carbides and/or nitrides. Wright,4 Lommel,7 and Lena and Hawkes10 emonstrated the accelerating effects of a finely dispersed precipitate of (probably) chromium nitride on the hardening reaction. This appears to be evidence that lattice straining increases the rate of nucleation of the hardening constituent. Some new observations on 885°F hardening are reported here. They show an effect of preheat treatment that should contribute to a better understanding of the 885°F hardening phenomenon. They also clarify a discrepancy which exists in the literature. Some investigators have reported most rapid hardening at 885", whereas others have reported it at 930°F. The present work also shows that 885°F hardening does not occur in electrolytic chromium, and that any long range ordering type of reaction affecting any sizeable part of the volume is unlikely. Materials Studied Table I shows the currlposition of the alloys used in this investigation. In these alloys carbon and nitrogen are present in roughly similar amounts. Presumably both elements precipitate, as carbides and/or nitrides, during the heat treatments given.

Jan 1, 1958

By E. A. Elevatorski

Wollastonite, named after William H. Wollaston, an English chemist, is a calcium metasilicate, CaSiO3. It has a short history as an industrial mineral. The earliest production of wollastonite is reported to be from a deposit near Code Siding, located north of Randsburg, Calif. At this locality small tonnages of wollastonite were quarried during 1933-34 and 1938-41, and processed into mineral wool. This operation was largely experimental and virtually no United States production was again reported until the 1950s when a large deposit near Willsboro, N.Y., was developed by the Cabot Corp. A processing plant was placed on-stream in 1953, with nearly continuous production to date, and it is currently operated by Interpace Corp. Since 1958, wollastonite deposits in the Little and Big Maria Mountains of Riverside County, and in the Panamint Range of Inyo County, both in California, have operated intermittently for production of both ornamental and commercial wollastonite. During 1973, the United States was the major producing country, furnishing about 75% of the world&apos;s output. Recent production also has come from Finland, Mexico, and Kenya. Small amounts have been shipped intermittently from India, USSR, New Zealand, Republic of the Sudan, Republic of South Africa, and South-West Africa. The principal use of wollastonite is in the manufacture of ceramics, especially wall and floor tiles. Other uses are for paints, fillers, adhesives, reinforcing agents, plastics, fluxes, and glazes. Mineralogy Pure wollastonite, CaSiO3, has the composi¬tion of 48.3 % CaO and 51.7 % SiO,. However, it is seldom found in the pure state due to the ease with which it takes into solution the metasilicates of manganese, magnesium, iron, and strontium. Predominantly, wollastonite occurs as a contact metamorphic deposit forming between limestones and igneous rocks. Commonly associated minerals are garnet, diopside, epidote, calcite, and quartz. It has a specific gravity of 2.8 to 3.0, and hardness of 4.5 to 5 on Mobs&apos; scale. When pure, it has a brilliant white color, but with impurities it may be grayish or brownish. Luster is vitreous to pearly. Melting point of wollastonite is about 1540° C. Wollastonite occurs in coarse-bladed masses, rarely showing good crystal form. It is usually acicular or fibrous, even in the smallest of particles. The most unique property of crushed and ground wollastonite is its cleavage. Fragments of crushed wollastonite tend to be needle-shaped, imparting a high strength, and this property is the basis for many of its uses. The fiber lengths are commonly in the ratio of 7 or 8 to 1, length to diameter. Some crystals of wollastonite fluoresce under short-wave or longwave ultraviolet light, or both; colors ranging from yellow-orange to pink-orange. Specimens may also show phosphorescence. The brightness of wollastonite is a property of considerable importance to the paint industry. Material, 99% pure, with a size of -325 mesh, has a General Electric reflectance rating of 92 to 96%. Chemically, wollastonite is inert and this property makes it useful as a filler and reinforcing agent. There are two polymorphs of calcium silicates: wollastonite, a low temperature form, and pseudowollastonite, a high temperature form. Inversion of wollastonite to pseudowollastonite occurs at about 1120° C, resulting in an increase in the coefficient of expansion and a color change. Pure white wollastonite, on inversion, may change to a cream tint, or various shades of red or brown. The color change is thought to be due to the presence of iron and strontium.

Jan 1, 1975

By N. J. Grant, K. M. Zwilsky

A series of copper-alumina dispersion strengthened alloys were prepared using three different copper and two different alumina powder sizes. Improvements in strength of up to ten times that of pure copper were found in room-temperature as well as elevated-temperature stress-rupture tests. Conductivity values remained from 70 to 90 pct that of pure copper. The best alloys were based on the finest metal powder (1 p) and contained from 7.5 to 10-0 vol pet of 0.018 or 0,033 p alumina. DISPERSION strengthening of metals consists of strengthening a metal matrix by the addition of oxides or other refractory constituents, followed by strain hardening, in order to reinforce the base material and extend its temperature range of application. Since the discovery of SAP by lrmannl and Von zeerleder2 in 1949, many investigators have reported data obtained on a variety of metal-inert oxide alloys.3-7 The present work deals with the mechanical mixing of copper and alumina powders. While several techniques of introducing the second phase have been investigated to date, mechanical mixing so far has been recognized as the simplest, least expensive, and most universally applicable technique that can be used to obtain an ultrafine dispersion of inert particles. In the present case, the effects of changing the metal particle size, the oxide particle size and the volume percent of oxide were investigated. This work is an extension of a previous study.6 EXPERIMENTAL PROCEDURE The starting materials were three different grades of copper powder and two different alumina powders. The three metallic powders were -74 µ(- 200 mesh) electrolytic copper powder consisting of irregular equiaxed particles having a normal screen distribution and analyzing 99.5 pct Cu, and two powders having a 5-µ and 1-µ particle size, average, respectively. The latter powders were produced by the hydrogen reduction of purified sulfate solutions at elevated temperature and pressure and were furnished by the Sherritt Gordon Mines, Ltd. The alumina used was obtained from Godfrey L. Cabot Co., under the trade name of Alon C, one batch of powder having a particle size of 0.018 µ, the other a particle size of 0.033 µ. The crystal structure of these alumina powders was found to be cubic gamma. Each batch of powder was mixed in a Waring Blendor for a total of 15 min, followed by a low-temperature reduction in hydrogen and vacuum compacting in cylinders which were hydrostatically pressed at 35,000 psi to give a compact that could be handled conveniently. Six of the compacts were hydrogen sintered at 900°C while the remaining four were sintered at 1000°C. Subsequently, all compacts were hot extruded at 760°C with a reduction of area ratio of approximately 20 to 1. Evaluation of alloys included density and resistivity measurements, room-temperature tensile tests, stress-rupture tests at 450°C plus one other temperature per alloy, hardness tests, microstruc-tural examination, X-ray analysis of the dispersed phase after dissolving the metal phase, and oxidation studies on two of the alloys. A vacuum-melted, wrought copper rod was tested together with these alloys for comparison purposes. RESULTS Table I is a summary of the compositions, sintering temperatures, densities and conductivity values of the ten alloys prepared. All alumina additions are given in volume percent, and will be referred to as

Jan 1, 1962

By Donald A. Brobst

The minerals barite (BaSO4) and witherite (BaCO3) are the chief sources of the element barium and its compounds needed for many industrial processes and products. Barite, the principal ore mineral, is found the world over and is abundant and widely distributed throughout the United States.3 Witherite is much less common than barite, though more desirable in many ways as a raw material for the production of barium chemicals. England is the chief producer of witherite. Witherite is not mined in the United States at the present time, but it has been mined with barite from a deposit at El Portal, California. Barite is also called barytes, tiff, cawk, or heavy spar. Ordinarily it is a heavy mineral that crystallizes in the orthorhombic system. It is colorless, white, or gray, and transparent to opaque. In some deposits barite is black, yellow, brown, red, green, or blue because of included impurities. The streak is white and the luster vitreous to resinous or pearly. The specific gravity of pure barite (65.7 pct BaO and 34.3 pct SO3) is calculated to be 4.5, but inclusions and impurities in natural barite may reduce this value considerably. Well-formed crystals are generally tabular and have three cleavages. The barite of many deposits, however, has an uneven fracture and an apparent cleavage caused by separation along planes between successively deposited layers. The hardness is 2.5 to 3.5 on Mohs&apos; scale. Commercially the terms "hard" and "soft" are used to refer to ease of grinding. Barite is relatively insoluble in water and acid, and thus can be used as a chemically inert material. Witherite, the natural carbonate of barium (77.7 pct BaO and 22.3 pct CO2), crystallizes in the orthorhombic system. The fracture is uneven and the luster is vitreous to resinous. The hardness is 3 to 3.5. The specific gravity of the pure mineral is calculated to be 4.29. It is transparent to opaque. The color is ordinarily white, gray, yellow, brown, or green. Geology and Distribution of Deposits Workable deposits of barite are widely distributed throughout the world in many geologic environments in sedimentary, igneous, and metamorphic rocks. Most deposits can be classified into three main types: (1) vein and cavityfilling deposits; (2) bedded deposits; and (3) residual deposits. 1. Vein and cavity-filling deposits are those in which barite and associated minerals occur along faults, gashes, joints, and bedding planes, and in breccia zones and solution channels. They also occur in various collapse and sink structures in limestone. Sharp contacts of the veins and cavity fillings with wall rocks are common. Barite cements fault and collapse breccia by replacement of the matrix or by filling voids. Large-scale replacement of the wall rocks beyond ore-controlling structures is rare. Barite in vein and cavity filling deposits is generally dense, "hard," and white to gray. Associated minerals are fluorite, calcite, ankerite, dolomite, quartz, and many sulfide minerals, especially pyrite, chalcopyrite, galena, and sphalerite. Gold, silver, and rare earth minerals occur with barite in some deposits in the western United States. Barite is also a gangue mineral in metallic ore deposits but production as a byproduct from such deposits will be affected by many economic factors. The host rocks are igneous, sedimentary, and metamorphic rocks of pre-Cambrian to

Jan 1, 1960

By L. Guttman, C. S. Barrett, J. S. Bowles

THE transformation from the face-centered cubic (Al) to the face-centered tetragonal (A6) structure in certain alloys of the indium-thallium system reported in the preceding paper1 exhibits many interesting crystallographic and metallo-graphic features, most of which presumably are similar to those of other cubic to tetragonal transformation such as, for example, the one which occurs in the chromium-manganese system,2 the one which, judging by microstructures and X-ray pat-terns,3 probably occurs in the copper-manganese system, the ones accompanying ordering in FePt,4 Copt,&apos; and AuCu,5 and the transformation near 115°C in barium titanate.6,7,8 If, as mentioned in ref. 1, the transformation is second order, the phases in equilibrium do not differ in composition, and it is both possible and likely that the mechanism is a diffusionless one. The present paper reports the results of a detailed study of the indium-thallium transformation and presents a theory for the atomic movements of the transformation which accounts for the observations. Experimental Crystallography of Transformation Markings The transformation from cubic to tetragonal in the indium-thallium alloys produces microstruc-tures of the type illustrated in fig. 1. These structures are observable either as relief effects produced on a smooth surface by the transformation, or after polishing and etching. These microstruc-tures are markedly similar to those found in copper-manganese alloys: iron-platinum alloys," and barium titanate,7,8 where it has been demonstrated that the lamellae are parallel to the (101) planes of the original cubic crystal. That the observed lamellae in indium-thallium alloys are also parallel to the (101) planes was proved by the following analyses performed on single grains in polycrystal-line samples containing 20.75 atomic pct T1. A study of the microstructures of a number of specimens revealed the fact that in many specimens the transformation markings continued unchanged in direction across the (111) interfaces of annealing twins. This at once demonstrates that the lamellae are parallel to a plane that is common to both parent and twin orientations, i.e., a plane in the zone <112>. This conclusion is compatible with the lamellae being parallel to (101) planes. To make a more complete determination of the habit plane of the lamellae, two grains were selected in which annealing twins ({Ill) twins) had been present in the high-temperature modification (cubic). The traces of the annealing twins, and of the transformation markings in both parent and twin crystals, were plotted together in stereographic projection, and a parent-twin pair of orientations was found that accounted for all lamellae as (101) planes. The projection of one of these twinned grains is reproduced in fig. 2. In view of these results the probability of there being another solution for the habit plane remote from (101) is very small, but to explore the possibility that the habit plane deviates slightly from (101), a more precise analysis was undertaken. In this, the orientation of a grain in the cubic modification was determined from a Laue back-reflection photograph taken with the sample at 90°C. The traces of the lamellae that formed in this grain on cooling were plotted in the stereographic projection

Jan 1, 1951

By David A. Sterling, Roger C. Malan

The Atomic Energy Commission is investigating the distribution of uranium and thorium in the Precambrian of the western United States and the relationship of time-space-facies patterns of uranium and thorium enrichment in the Precambrian, to the major resources of umanium in Mesozoic and Cenozoic continental clastic sediments. The results of preliminary studies in the southwestern. United States are summarized. Approximately 50% of the uranium resource of the Free World is in deposits of Precambrian age, principally in lower Proterozoic conglomerates in Canada and South Africa (Uranium Resources, Joint Report, ENEA and IAEA, 1967). Most of the uranium resource of the United States is in Mesozoic and Cenozoic continental clastic sedimentary rocks that fill intracratonic basins. The Atomic Energy Commission (AEC) is investigating the distribution of uranium and thorium in the Precambrian of the western United States and the relationship of time-space-facies patterns of uranium and thorium enrichment in the Precambrian to the major resources of uranium in the Mesozoic and Ce-nozoic host sedimentary rocks. This paper summarizes the results of preliminary studies of the Precambrian in the southwestern United States including New Mexico, Arizona, southern Nevada, and southern California (Fig. 1). The host rock provenances for the major uranium resources in epigenetic deposits of Mesozoic and Ce-nozoic age in the western United States were in areas of extensive Precambrian exposure along the eastern margin of the Phanerozoic geosynclinal belt (Fig. 2). Mesozoic continental clastic sediments in the Colorado Plateau contain about two-thirds of the uranium resource of the United States. These sediments formed from detritus derived from the Mogollon highland in the southwestern United States where the Precambrian was extensively exposed1-1 (Fig. 2). A genetic relationship may exist between this provenance and the major uranium deposits of the Colorado Plateau. The Pre- cambrian might be equally important in the genesis of uranium deposits whether the most important process in the formation of these deposits was the leaching of low-order intrinsic amounts of uranium from Precam-brian granite or from Mesozoic pyroclastics derived from syntexis of the Precambrian basement rocks.&apos; Precambrian Geochronology of the Southwestern United States The Precambrian geochronology of the southwestern United States is in an early stage of systematic study. Until recently, the only basis of correlation was through inconclusive field relationships. However, with the increased use of isotopic age dating, new data are becoming available for correlating regional and local events. As yet, there is no undisputed evidence of ages greater than 1.8 billion years (by) old in the southwestern United States. However, most geologists who have studied the region agree that volcanism and marine sedimentation of predominately eugeosynclinal facies took place in a northeasterly trending geosyn-cline prior to 1.7 by."&apos; Because of insufficient evidence for a pregeosynclinal continental crust, some researchers believe the geosyncline may have developed on oceanic crust.&apos; However, sediments metamorphosed to 1.7 by-old felsic paragneisses in the Panamint Range, California," and southeastward into southern Nevada are believed to have had a nearby continental provenance. The three Precambrian disturbances that are recognized in the southwestern United States are 1.6 to 1.8 by, about 1.4 by, and about 1.1 by-old (Fig. 3). In addition to plutonism, these disturbances are characterized by predominately lower-grade metamorphism. In this report, lower-grade metamorphic rocks include argillite, phyllite, slate, mica schist, and gneiss with relic sedimentary textures. Higher-grade metamorphic rocks, in this report, are recrystallized beyond megascopic recognition of the original rock type. Principal

Jan 1, 1971

By E. T. Turkdogan, L. S. Darken

Using the quadratic formalism, thermodynamic equations are derived for the composition dependence of the heat and entropy of mixing. The applicability of these equations is confirmed by available experimental data on the activities and heats of mixing for binary metallic systems of Group ZZB elements. In a recent paper arkeen&apos; introduced a quadratic formalism describing the composition dependence of the activity coefficient in the terminal regions of binary metallic solutions. That is, in the terminal region, which may extend to as much as 60 at. pct, the logarithm of the activity coefficient, log y,, of component 2 is a linear function of (1 - N,)&apos; where N2 is the atom fraction of component 2. Similarly, for the other component, log yl is a linear function of (1 - N,)&apos;. A number of iron-base binary liquid alloys were shown to obey this quadratic formalism. arkeen&apos; extended this formalism also to any corner of a ternary system and showed that the activity coefficients of the components 1, 2 and 3 (1 is taken as the solvent) can be represented by quadratic terms involving five parameters, four of the binaries and one for the ternary system. Numerous examples given by arkeen&apos; demonstrated the general applicability of the quadratic formalism to iron-base systems over a wide composition range. In this paper further examples are given of binary liquid systems (Group IIB elements, Zn, Cd, and Hg) and of several solid solutions, again demonstrating the appropriateness of this concept. A further purpose of this paper is to extend the quadratic formalism to the enthalpy and excess entropy of binary metallic solutions and to test the equations so found using available experimental data. QUADRATIC FORMALISM FOR HEATS AND ENTROPIES OF MIXING OF BINARY METALLIC SOLUTIONS The following equations, reproduced from Darken&apos;s paper, are for the two terminal regions of binary systems. at infinite dilution and a&apos;s are temperature dependent parameters to be determined from the experimental data. Although the quadratic formalism is an assumed representation of the data, Eqs. [I] to [4] are thermo-dynamically consistent with the Gibbs-Duhem relation and satisfy Raoult&apos;s and Henry&apos;s laws as limiting cases. As pointed out previously,&apos; the following form of the Gibbs-Duhem equation facilitates the integration in general but particularly in regions I and 11, where each of the derivatives is constant. The partial molar enthalpy of solution i, (and i; the value of i, at infinite dilution) are related to the activity coefficients y, and y," by the thermodynamic relation Differentiating Eq. [l ] with respect to 1/T and substituting the above thermodynamic relation gives for region (I) It is reasonable to assume that over a temperature range of experimental interest, the enthalpy of mixing is essentially independent of temperature, implying from Eq. [7] that the derivative da,,/d(l/) is also independent of temperature. On the basis of this argument, the temperature dependence of a has the form where £ and S have the units of enthalpy and entropy respectively; they are characteristic parameters for a terminal region of a binary system, e.g. for region (I), C12, S12 and for region (II), d:,,, S2,. Using this equation gives for dff ,/ d(l/), From Eqs. [7] and [9] an expre_ssion is obtained for the composition dependence of L,. Similar calculations are made for El and the results are summarized below for the two terminal regions. For region (I), The corresponding expressions for the molar heat of solution, AHM, are readily obtained from the above equations for the two terminal regions: For region (I),

Jan 1, 1969