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By J. T. Norton, N. J. Grant, A. M. Gervais

An investigation of the creep deformation of coarse-grained high-purity aluminum at temperatures approaching the melting point permitted the formulation of a theory of subgrain formation. Subgrain boundaries were found to be formed by two different processes: kinking and polygonization. Polygonization is considered as the main factor in subgrain formation. SINCE "slipless flow" was first discussed in detail by Hanson and Wheeler,' many studies have been undertaken to determine how metals deform at high temperatures. Several types of observations have been reported. Jenkins and Mellor,² working on the creep of mild steels and various grades of commercial irons, found metallographic evidence of a kind of substructure within the grains after deformation at high temperatures. Homes" observed after creep deformation of steel at high temperatures that the original X-ray spots were sharply divided into several small ones. The same phenomenon was reported by Hirst4 from his studies on lead and later by Crussard5 from his work on aluminum. The works of these investigators demonstrated beyond any doubt that the splitting of the X-ray spots was due to the fact that the grains underwent a division into subgrains during deformation at high temperatures. Since then, numerous experiments have been undertaken on aluminum in order to determine the mechanism of formation of subgrains. Research workers can be divided, for the purpose of discussion, into two different groups as regards thinking on subgrain formation. On one hand, based on the work on polygonization by Cahn,6 Guinier and Lacombe,7 Greenough and Smith," Crussard,10,11 and Servi, Norton, and Grant," it was concluded that subgrain formation was a consequence of the simultaneous effects, first, of inhomogeneous deformation which produced bending of the lattice, and second, polygonization. On the other hand, Wood and coworkers13-16 based their work on the results of an earlier report" which dealt with crystallite size and a fragmentation theory. It is interesting to note that while Greenough and Smith8 and Wood et al. performed similar experiments, their conclusions were quite different. Wood et al. did not recognize polygonization as a fundamental mechanism and said that aluminum, at the beginning of the deformation, fragmented immedi- ately into subgrains in order to permit deformation of the metal, the number of these subgrains being a function of strain rate and temperature. They concluded that deformation of grains occurred by flow along the subgrain boundaries. In view of the contradictory conclusions, it would appear that the data were not explicit enough to provide an unambiguous conclusion. It appears that the techniques by which most of the results were obtained, namely, X-ray work, were not enough by themselves to solve the problem. Another approach was needed. In the present research, therefore, an extensive metallographic study was planned to supplement the X-ray work. The importance of revealing the subgrain boundaries metallographically was realized, and this will explain the extensive development and use of etching techniques. In order that subgrains would be considerably larger and therefore more readily visible under a microscope, the creep experiments were performed at very high temperatures approaching the melting point of aluminum. Development of Experimental Technique Creep tests were run at constant load on high purity (99.995 pct) aluminum specimens having a very coarse grain size. None of the specimens was run to fracture. The specimens were originally round (diameter, 0.187 in.; gage length, 1 in.) and had parallel flats milled in the gage section to permit

Jan 1, 1954

By A. A. Rauth

In this paper, the author derives a series of formulas from basic principles and illustrates the application of these formulas to practical grinding charge problems. The paper establishes the nearly proportional relationship of mill power to charge level and shows how this relationship can be used to advantage in the design, manufacture and operation of grinding mills. The procedures outlined offer a rapid means of anticipating the power requirements for a given charge or determining makeup charges for a given power reading. The theories which have been developed concerning the dynamics of grinding have been motivated largely by the desire to derive workable formulas for the accurate determination of grinding mill power. This accurate determination has always been handicapped by the large number of variables to be considered, some of which are mill diameter, length, speed, liner design, grinding charge and material density, volumetric mill loading, internal friction, and charge size and gradation. In efforts to determine mill power, attempts have been made to utilize torque concepts. The formulas derived consider the grinding mass as a rigid body and utilize factors that are based on empirical data so that the movement of the charge within the mill is compensated for. These formulas are of principal interest to the mill designer since he is charged with the responsibility of analyzing all of the variables and from them predicting a mill size and a motor size which are compatible both with each other and with the grinding job for which they were intended. The mill operator, on the other hand, has an entirely different problem. The mill dimensions are already established and so is the driving motor. The operator's main concern is to obtain maximum performance from the mill he already has. For him, the many variables which perplex the mill designer are fixed values. Mill diameter, length and speed are set and, to a large extent, so are the conditions inside the mill from which the torque formula advocates derive their empirical data. It is conceivable that if the major mill dimensions which affect power demand are held constant, and if the variables influencing empirical factors are held fairly constant, as they are in an operating mill, then the only major variable remaining which affects power is the level of the charge itself. Under this condition.

Jan 1, 1970

By M. Cohen, D. J. Blickwede

Quantitative observations concerning the carbide phases in high speed steel are of importance for two general reasons: (1) the carbides, being inevitable constituents of the final structure, exert a direct influence on the properties of the steel; and (2) a substantial proportion of the total alloy content is tied-up in the carbides, and hence the extent of their solution on austenitizing governs the composition of the steel matrix. The latter relationship has a vital bearing on the response of the steel to tempering as well as on its performance in subsequent service. Accordingly, in the course of a long-term study of the behavior of high speed steels, the authors were confronted with the problem of securing quantitative data on the carbide phases. The obvious method for acquiring such information is to isolate the car-bides from the steel and subject them to chemical, X ray diffraction and other measurements. There are well-known extraction techniques which involve the chemical or electrolytic solution of the less noble matrix (ferrite, marten-site or austenite), thus leaving a residue of the carbide phases. However, the results obtained must be scrutinized carefully1,2 since the carbides may be affected by the chemical or electrolytic action. It is the purpose of the present paper to describe the experiments leading to an electrolytic-extraction technique for quantitatively isolating the carbides from both I and hardened high speed steel. Particular attention is paid to the amount, as well as the composition, of the carbides so that the matrix analysis becomes ascertainable by subtraction from the overall steel composition. Illustrative results are given for the M-2 grade of tungsten-molybdenum steel. Review of the Literature The chemical method of dissolving the matrix selectively with respect to the carbides makes use of dilute non- oxidizing reagents such as hydrochloric or sulphuric acid. Although this simple procedure has led to the determination of the cementite composition,3,4 it achieved only limited success because of the interaction between the acid and the carbide residue. Some of the carbides may not only be destroyed in this way, but the hydrogen released is likely to remove part of their carbon as hydrocarbon gases. The electrolytic technique of isolating carbides has the advantage of rapidly dissolving the specimen (anode) in the presence of less reactive solutions than are practicable with the chemical method. This reduces the possibility of chemical attack on the carbides, and furthermore, the hydrogen evolved during the electrolysis is released at the cathode which is not in close proximity to the carbides. The common electrolytes adopted for this purpose are hydrochloric and sulphuric acids.5-l1 Aqueous solutions of ferrous salts have also been used.12,13 A considerable advance in experimental technique was introduced by Treje and Benedicks14 who developed a double-compartment cell for electrolytic extraction, the anode and cathode chambers being separated by a porous diaphragm. A solution of 15 pct sodium citrate, 2 pct potassium bromide and 1 pct potassium iodide was selected for the anolyte, while the catholyte consisted of a 10 pct solution of copper sulphate, with copper serving as the cathode. This type of cell has a number of desirable characteristics: 1. The anolyte has a pH value close to 7, at least at the beginning of the run. 2. The iron that dissolves from the anode-specimen forms a water-soluble complex ion with the citrate, thereby preventing the precipitation of iron hydroxide (which would contaminate the carbide residue) despite the neutrality of the solution. 3. Copper deposition instead of hydrogen evolution occurs at the cathode, and this avoids an increasing concentration of hy-droxyl ions which (in an otherwise neutral solution) might cause the precipitation of insoluble hydroxides. 4. Contamination of the anode chamber by copper sulphate is inhibited by the porous diaphragm. Houdremont and coworkers15 applied the above method (with the further refinement of excluding oxygen during the electrolysis, washing and drying) to the extraction of carbides from a series of plain carbon steels after various heat treatments. They had quantitative success only with specimens in the annealed condition, and concluded that the size and shape of the carbide particles play an important role in the isolation process, with large spheroids exhibiting the least tendency to decompose during the electrolysis. Up to the present time, the citrate double-cell has not been used to any extent for isolating the carbides of high alloy steels, apparently on the grounds that the complex carbides are more resistant than cementite to attack in the simpler acid electrolytes. In particular, Bain and Grossmann7 and Gulyaev10.10a have employed the hydrochloric acid cell for their investigations of the carbides in high speed steel.* It will be demonstrated here that this type of cell is capable of yielding quantitative results in the case of high speed steel, and actually has certain advantages over the more complicated double cell. However, in order to provide a rigorous test of the quanti-tativeness of electrolytic procedures for the problem at hand, both methods were studied in considerable detail.

Jan 1, 1950

By W. O. Philbrook. K M Goldman, M. M. Helzel

RADIOACTIVE calcium has been used to learn whether calcium can be detected in iron saturated with carbon after it has been melted under CaO- A12O3- SiO2 slags similar to those used in the iron blast furnace. It was hoped that the radioactive tracer technique might make possible a general study of steelmaking reactions in which calcium or calcium oxide are involved. No calcium could be found in the metal under conditions which were favorable for the reduction of calcium, and it has been concluded that the calcium content of the iron was less than 6 x 10 - pct. Some of the problems encountered have been instructive with regard to pitfalls and limitations of tracer methods. Calcium oxide occurs in almost all iron- and steelmaking slags, and it is essential to the success of all commercial basic steelmaking processes. Calcium alloys are sometimes used in the deoxidation of steel and for the innoculation of gray iron. The element calcium is therefore almost as ubiquitous in the steel industry as are carbon and oxygen, but calcium has been thought to be completely immiscible with iron in both the liquid and the solid states.' It does not seem entirely unreasonable to Suppose, however, that some low concentration of calcium might exist in liquid iron under a basic slag with other conditions being favorable, just as silicon and other elements can be introduced into iron by reduction of their oxides from slags under appropriate circumstances. The radioactive tracer technique offered a more sensitive method than chemical analysis of testing this supposition. The reasons for interest in this investigation were strong enough to justify a recognized risk of failure. On the theoretical side, information on the distribution of calcium between liquid iron and a slag and the rate at which the equilibrium distribution is approached would contribute strongly to the general theory of slag-metal interface reactions. Furthermore, any evidence on the presence of calcium in liquid iron might provide a vital clue to the mechanism of the desulphurization of iron by slags. All of the reactions which have been proposed to explain desulphurization postulate that the sulphur ultimately becomes fixed in the slag as calcium sulphide, but the mechanism by which sulphur

Jan 1, 1951

Discussion of the paper of John H. Hall, presented at the New York. Meeting, October, 1913, and printed in Bulletin No. 79, July, 1913, pp. 1247 to 1256. WILLIAM 'R. WEBSTER, Philadelphia, Pa.:-I would like to call ,attention to the fact that the results of the ordinary tension and bend tests do not always give us the information we want even if we figure out the amount of work done. You want a bending test of sufficient width and full thickness. In the case of eyebars, for instance, I have had experience with a 10- by 1-in. eyebar which gave perfectly good results in a full-size test of the finished bar. The 10- by 1.5-in. and 10- by 1.75-in. eyebars from the same heats-of steel were absolutely worthless in full-size tests. The narrow bending tests from all these bars gave good results. Bat after going into the matter fully, we found that if pieces about 3 in. wide and full thickness were used for the. cold bending tests, the heavier material would not stand this test, but failed. That is, in order to check the quality of the rolled bar you should have a wide piece of full thickness for cold bending, as the narrow pieces give misleading results. J. E. JOHNSON, JR., New York, N. Y. :-I would like to ask if there have been any tests made to compare the results of Charpy tests with the true dynamic test similar .to the Wohler test, except that the piece is subjected to a tensile or compressive stress and to alternating stresses in addition, at the same time. This seems to me to approach more nearly than any other test to the conditions of actual service. where the piece is under a fixed initial stress plus a highly variable and often alternating stress. Some tests were made on this plan in England within a year or two. The test piece was Subjected to either a tensile or compressive stress of known amount and simultaneously to alternating stresses in addition. Such a. test as this gives information which we cannot get by a tensile test or even from the tensile strength multiplied by an. elongation. Such tests, however, are exceedingly tedious and require long periods of time in order to obtain valuable results. If material could be subjected to these dynamic tests and the same material to the. Charpy shock test, and if some reasonable qualitative relation could be established between the results of the two tests, then we could assume that the shock test, which is so simple and easy to make, was a measurably accurate test of the dynamic qualities of the material. At present it does not seem

Jan 12, 1913

By L. N. Cosner, C. F. Austin, J. K. Pringle

Shock wave attenuation studies with three igneous rocks are reported: a spessartite elastic to low intensity stress waves, a diorite which is anelastic, and a porous scoria. The level of shock passing through a given thickness of rock has been determined by donor-receptor methods using high speed streak cameras. Test results include shock propagation velocities adjacent to the explosive, the dependence of test results upon test geometry, and the variation in shock wave attenuation in these three common igneous rock fabrics. The utilization of explosives in rock mediums involves a series of interrelated phenomena. These are the detonation process within the explosive, the transfer of energy from the explosion products to the surrounding rock medium in the form of sound or shock waves, and the transmission of the resulting waves through the rock medium to create damage in the rock mass. The subject of this paper is the investigation of the close-in phenomena that occur in the intensely shocked rock immediately adjacent to a detonating explosive charge. The specific aspects studied include propagation velocities, free surface velocities, pulse attenuations and the determination of the equations of state for the test rocks employed. In addition, a series of tests was conducted to indicate the dependence of the test results on the charge diameter utilized. The equations of state for rock materials have been investigated by a number of authors. Lombard, ',' Grine and Fowles,3,4 Zharkov, 5 Hughes and McQueen,6 Chabai,7,8 and Bass9 have published equation of state data on rock materials similar in structure or composition to those investigated in the study. Rinehart10 has prepared a voluminous tabulation of the available equation of state data from these publications and in addition has included data on many other rock and earth materials in his compilation. The reader is referred to the extensive tabulations and bibliography of Rinehart for classical studies involving the equations of state of metals and other solids and liquids. The problems of sympathetic detonation between drill holes in hard rock environments has received the attention of various authors as have the problems of explosive rock coupling close-in stress wave attenuation and explosive diameter effects. 11 to 18 In particular, the don or-receptor geometry of this report is very similar to the geometry of adjacent drill holes in rock. Most published pulse velocity and attenuation work in rock has been devoted to velocities at much lower amplitudes than those associated with close-in explosives phenomena and most attenuation studies involve transmission and attenuation across large spans of material. Excellent work in these areas has been published by the U. S. Bureau of Mines and by many individuals and groups engaged in geophysical research. SELECTION OF TEST MATERIALS A series of rock materials was desired for this test program that would be meaningful industrially, and that would also yield comparative results from a research viewpoint. Based on the availability of a series of related petro-fabrics, for which there is an abundance of physical and shock response data, three igneous rocks were selected as the test series. The applicability of shock wave studies in igneous rocks to industrial problems is readily demonstrated. Hardrock tunneling, quarrying and mining take place in igneous rocks throughout the world. From a research point of view, igneous rocks exhibit a wide variety of grain sizes and considerable diversity in composition, yet the common igneous rocks have a general similarity in their constituent mineral structures and in their grain-to-grain bonding mechanisms. The latter is based on the concept of rock formation through magma cooling and crystallization, though the degree of liquefaction in granitic plutonic masses is indeed a moot question. Three specific types of igneous rock were chosen for study. A coarse-grained granitic textured rock was desired that would serve as a representative of the widely abundant intrusive rocks of the world and

Jan 1, 1967

By D. L. Albright, G. A. Colligan

An investigation has been conducted to determine the nature of the crystallographic substructure of nickel and a 1.0 wt pct Ag-Ni alloy which had been undercooled 105°C prior to solidification. A rotating back-reflection X-ray technique and modified Weissmann diffractometer were used to orient single-crystal sections from these poly-crystalline ingots and to determine the substruc-tural features of these single crystals, The sub-grain size in the pure nickel ingot is 0.5 mm diam while the silver-doped nickel subgrain size is only 0.1 mm diam. The misorientation between adjacent subgrains is approximately 1 deg of arc in both ingots, and the spread of orientation of sub-grains about the mean orientation of the crystal is 5 deg of arc in both ingots. The addition of silver results in a stable impurity substructure which is preserved during isothermal solidification and subsequent cooling to room temperature. In the absence of silver the initial impurity substructure is destroyed by dislocation interactions which produce a secondary substructure which grows to a size five times larger than the initial substructure. THE process of undercooling a metal entails cooling of the molten sample below the equilibrium freezing point without the occurrence of solidification, i.e., by exercising proper constraint over the experimental variables contributing to nucleation in the melt. The current work of walker1 and Colligan Metal reports undercooling large continuous samples of nickel by imposing appropriate restrictions upon the parameters of solidification. The silver-nickel equilibrium diagram3 reveals the presence of a monotectic reaction at 1435°C. At this temperature the maximum solid solubility of silver in nickel is approximately 3 wt pct, but this solubility decreases with decreasing temperature and the solute is rejected as a silver-rich liquid phase at temperatures below 1435°C. Thus, the 1.0 wt pct solute should be held in solution during undercooling and solidification and subsequently precipitate as a silver-rich liquid phase at grain and subgrain boundaries following solidification during cooling below 1435. This assumes no solute segregation sufficient to cause the monotectic reaction. One would expect this second phase to inhibit grain and subgrain growth by retarding dislocation motion after solidification is complete. The effectiveness of silver addition in growth retardation of high-angle grain boundaries has been demonstrated by Colligan and suprenantS4 The principal [l00] dendrite growth directions in a 2 wt pct Ag-Ni alloy undercooled 53 all radiated from the nucleation site. A similar pure nickel ingot undercooled 59°C exhibited a random orientation of [l00] dendrite directions with respect to the nucleation site. Since undoped nickel ingots do not retain any evidence of the casting or solidification texture and silver-doped ingots do retain this texture, it is reasonable to assume that considerable grain growth has taken place in the pure nickel. These particular experiments were performed in order to reveal the differences, if any, in the features of the crystallographic substructure of undoped undercooled nickel and silver-doped undercooled nickel. 1) EXPERIMENTAL PROCEDURE Data are reported on selected specimens from two massive (approximately 260 g) undercooled ingots of nickel. One ingot consisted of electrolytic nickel and the other of this same material with 1.0 wt pct addition of high-purity silver. Powder patterns were taken of both the as-received and as-solidified materials; in all cases the reflections recorded were attributable to the individual elements nickel and/or silver. Fig. 1 is a. schematic diagram of the apparatus employed for the undercooling experiments. The equipment consists in part of a fused silica crucible for containing the charge. A fused silica tube encloses the system, which is covered by a brass cap to permit partial sealing of the inert atmosphere. This cap contains a hole through which a Pt-Pt 13 pct Rh thermocouple is inserted for temperature measurement. The charge is inductively heated under a purified argon atmosphere.

Jan 1, 1963

By H. M. Strong

Nickel and carbon form a metastable nickel-nickel carbide eutectic system which was ohsen)able by freezing latent-heat arvests at pressures 210 khars. The eutectic freezing temperature Is pressure had a slope of -0.9°Cper kbar. At 50 khars, the nickel-nickel carbide eutectic was at 1297° * 5°C and 0.34 mole fraction Ni3C. The composition of the eutectic increased at an initial rate of 0.004 mol fraction per kbar. The carbon content of the a phase also increased with pressure. Seveval illustrations of nickel carbide microstruc-tures are given and data on the lattice expansion of nickel in terms of carbon content are included. IRON, cobalt, and nickel form a variety of carbides with compositions varying between MeC and MC. Of the three, the carbides of iron are most easily recovered. The nickel carbides are so unstable at temperatures above 900°C that their occurrence in Ni-C alloys is unusual. Under sufficient pressure, however, the temperature range for the stability of the ferrous metal carbides is likely to be increased, or their decomposition suppressed (e.g., see Hilliard' on FesC), providing an opportunity to study the unstable carbides more closely. This was found to be true for nickel carbide which, under pressure, formed a eutectic with nickel. This paper describes the conditions of formation of nickel-nickel carbide eutectic compositions and their subsequent recovery. Despite the comparative instability of the nickel carbides, something is already known about them through various chemical reactions at temperatures not exceeding a few hundred degrees, and from their recovery by the very rapid quenching of molten Ni-C alloys from temperatures of about 1450°C or above. At least four carbides of nickel have been reported: A discussion of the state of knowledge about Ni3C is given by ansen.' The studies of Morrogh and williams7 who obtained Widmanstatten nickel carbide structures and of sidorenko8 who first obtained nickel carbide eutectic structures are also of interest. Sidorenko used short heating times for molten nickel in a graphite crucible followed by very rapid quenching to obtain the eutectic structures. Long heating times produced only the nickel-graphite eutectic probably due to the presence of graphite crystals in the melt which nucleated graphite crystallization. According to the early work summarized by anssen,' nickel carbide may form at temperatures far above the melting point and may be recovered by very rapid quenching. More recently, Giardini and Tydings, working on diamond synthesis, found evidence for "free nickel carbide'' in high-pressure reactions carried to temperatures far in excess of the limit for diamond growth, followed by rapid thermal quench. They stated that nickel carbide was not found in association with diamond growth. In the present work, observations were made on the melting and solidification temperatures of Ni-C alloys as a function of composition, temperature, and pressure. The nickel-nickel carbide eutectic was found at pressures above 10 kbar and its variation with pressure followed up to 60 kbar. Nickel-nickel carbide microstructures were recovered by quenching under pressure from temperatures of about 1400°C and higher. The formation of nickel carbide structures under ordinary diamond-growing conditions was usually observed but the role of carbide formation as an intermediate step in diamond growth needs more study. EXPERIMENTAL METHODS The melting and solidification temperatures of various nickel-graphite compositions were observed by latent-heat arrests in the sample holder illustrated in Fig. 1. The samples were composed of mixtures of carbonyl nickel powder and National Carbon Co.'s SP-1 graphite packed to densities of about 6.4 g per cu cm. They were contained within

Jan 1, 1965

By B. W. Gandrud

WET-PROCESS coal-washing tables as we know them today have been in use in this country for approximately 25 years. The literature records only a few table installations worthy of note prior to adoption of the present-day differential-motion table. According to Phillip,1 six Campbell bumping tables were being operated by the St. Bernard Coal Co., Earlington, Ky., in 1893. As late as 1923, according to Richardson, 2 such tables were in operation in the Rosedale washery of the Cambria Steel Co., at Johnstown, Pa. Bumping tables probably were not used to any considerable extent except in the plant at Earlington, and at two or three plants in Pennsylvania, but they may be considered as. forerunners of the present-day coal-washing table. The transition from bumping tables to the type of tables now in use signalized a revolutionary change in table design. The advantages of the new design over the old were so outstanding as to make its adoption inevitable. BUMPING TABLES Bumping tables, as the name implies, utilized a bumping action for conveying the refuse and discharging it over the refuse end. The tables were hung from rods attached to overhead supporting beams. A shaft and cam arrangement at one end of the table served as the actuating mechanism and imparted to the table an endwise, back-and-forth, swinging motion. A bumping block was fixed in the proper position at the shaft end, so that the table would strike against it at the end of each backward swing. The hanger rods or stirrups were so adjusted as to give the table a slight uphill slope toward the refuse end; that is, the end next to the driving mechanism. The feed box was near the upper end of the table and designed to spread the mixture of coal and water over the width of the table. Wash water was added a short distance below the feed box. With the table in motion and coal mixed kith water being fed to it through the feed box, a certain amount of stratification took place, depositing heavy refuse at the bottom of the bed in contact with the surface of the table. Constant bumping and a certain amount

Jan 1, 1950

By C. G. Dunn, F. W. Daniels, M. J. Bolton

IN recent investigations1. a data on relative grain boundary energies in silicon iron have been obtained. The present investigation is a continuation of this work along similar lines for the purpose of obtaining additional information on boundary energies. One aim has been to extend the data for a (110) series, which was formerly studied,' to small differences in orientation, since a recent theory3,4 based on a dislocation model of grain boundaries predicts a E. ? (A-ln ? )* form of energy curve for small differences in orientation. Another aim has been to provide data for a (100) series—all grains having (100) planes parallel with the surface of sheet speci-mens—and to compare the results with the predicted form of energy curve. Finally, information on the nature of approach to equilibrium conditions was to be obtained through observations on the movements of grain boundaries. Recently published papers2,3,5 have treated the mathematical problem of expressing equilibrium conditions for grain boundaries for the general case when boundary energy depends upon boundary orientation. The equilibrium equations, which relate equilibrium angles and grain boundary -free energies, contain additional terms that express the variation of energy with boundary rotation. It has been necessary in the present investigation, however, to neglect these additional terms since no data for their evaluation were available. Dropping the additional terms leads to the following approximate equations which were used: E12/sin ?3 = E18/sin?2 =E28/sin?1 or those of the form: E28 + E13 cos ?3 + E12 cos ?2 = 0 Experimental Procedure Except for sample F1, all specimens were made from two lots of silicon iron called C and L respectively. The compositions of these are listed in table I. In the preparation of 12 three-grain specimens for the present investigation, a controlled grain growth technique, which has been described previously,' was used. After preparation, the specimens were notched at the boundaries to shorten them as a means of providing more rapid approach to equilibrium in the anneals. Initial grain boundary angles were determined from micrographs taken at X500. Seven anneals, totaling about two days at 1300°C and two to four days at 1400°C, were run in an atmosphere of pure dry argon as described in a previous paper.' Boundary changes generally could be followed without metallographic surface preparation, because thermal etching occurred during the anneals. These observations indicated angle changes of as much as 35" in some instances, with the major changes occurring during the first anneal. Annealing was discontinued when the angles reached stationary values. Fig. 1 gives a schematic diagram for purposes of defining crystallographic and boundary directions for three grains with common plane parallel with the sheet. Differences in orientations (expressed by A) are the angles between [00l] directions. They can be calculated with the aid of the ?'s. The grain boundary angles can be calculated from the w'S. Results Results are given in table 11. Types of crystal-lographic planes refer to those parallel with the sheet. Orientations are given in terms of [00l] direc-tions as shown in fig. 1. Except for grain 3 of specimen H6, which was unintentionally tilted 7" out of a (100) plane, all grains generally were within 1" or 2" of the plane specified. The directions of boundaries were measured generally to within 1" on both upper and lower surfaces, and the average direc- tions were determined for use in calculating the grain boundary angles. Variations in grain boundary directions refer to deviations from average directions. Boundaries near the junction point for all specimens generally were very close to perpendicu-

Jan 1, 1951

By C. C. Templeton, S. S. Rushing

Methods previously developed for the study of air-liquid displacements in microscopic capillaries (inner diameters of 3 to 40 microns) have been used to investigate oil-water displacements in capillaries initially filled with water. Displacement calculations assuming perfect displacement and no capillary pressure hysteresis yielded oil effective viscosities smaller than the macroscopic viscosities. For a given liquid pair, the oil effective viscosity decreased both with decreasing capillary size and with increasing oil-water viscosity ratio. This behavior can be explained by the existence of an annular water film (20 A to 260 A thick) on the capillary wall. When the capillary was first filled with oil, the ratio of the oil effective viscosity to the normal oil vircosity was highest for the first water displacement and decreased with subsequent displacements. Sometimes the oil effective viscosity ratio during the initial water displacement was greater than unity. INTRODUCTION In a previous paper1 a technique was described for studying air-liquid and liquid-liquid displacements in very small capillaries of uniform diameter, in the hope that such microscopic data would further the understanding of the nature of multiphase fluid flow through porous media. That paper contained comprehensive data for air-liquid displacements in Pyrex capillaries, with a few data for oil-water displacements in capillaries initially filled with water. The purpose of this paper is to present more complete results for oil-water displacements in capillaries initially filled with water, and to describe for the first time such observations in capillaries initially filled with oil. In this way the effect of the wetting history of the system upon the displacement process may be studied. METHODS The basic techniques employed were described in the previous paper.1 The measuring procedure and the working equations will be briefly summarized here and a few modilications will be pointed out. For the present study, temperature control within 0.l °C was obtained by placing the microscope and its immediate accessories in a thermostated air bath made of a steel frame covered with plexiglas. The water and oils used in this work were the same as in the previous paper,1 with the addition of "Medium Mineral Oil, U.S.P. supplied by the Harshaw Scientific Co. When the first liquid was introduced into the horizontal capillary, the air-liquid static capillary pressure Poc was measured along the observable length of the capillary. From the relation Poc = 4y cos 0/d, the capillary diameter d could be calculated from Poc if the "microscopic" air-liquid boundary tension, To = y cos On, was taken as equal to its known "macroscopic" value. This calculation involves assuming that cos 6 = 1 and that capillary size or the resulting high interfa-cial curvature has no effect on surface tension, or y cos 6, as was verified by our work, and also by that of Cohan and Meyers on air-liquid-solid systems. For several capillaries these calculated diameter values were compared with values measured visually with a filar micrometer eyepiece. For a given capillary the average values for the two methods agreed within 1 or 2 per cent, but the visual values were less reproducible than the calculated values. Further the calculated values were much less subject to personal bias and took into account any slight ellipticity that might be present. Hence diameters calculated from air-liquid Poc data were used throughout this paper. The second liquid was introduced in such a way that a single spherical interface separated the two liquids. Displacements were always made with a constant pressure, Pt, between the ends of the capillary. The times (t) at which the interface passed certain

Jan 1, 1957

By J. Lindbo, B. Vigeholm

IN transmission electron microscopy, specimen thicknesses quoted are frequently based upon either traditionally familiar values or a few evaluations representing the whole material. Taking aluminum in 100 kv TEM as an example, average and maximum values are widely accepted as being 2000 to 2500 and 6000 to 7OOOÅ, respectively. It is the purpose of this note to revise these figures and to point out the importance of evaluating individual specimens carefully. All evaluations have been based upon slip trace widths and lattice orientations as determined from diffraction patterns. In many cases where two or more slip systems have been operating the geometrical method described by Crocker and Bevis1 has been applied as a check. The foils were usually oriented to within 2 deg from the exact Bragg angle. Kikuchi patterns were used as indications of correct orientations but not applied in the evaluations. The tilt of the foil surface relative to the beam normal may with certain geometrical relations between the tilt axis and the operating slip plane lead to substantial errors.2'3 Where these geometries were inevitable the samples were omitted in the investigations. Various measures were taken in order to overcome ambiguities, e.g., comparison with neighboring grains, tilts, evaluations based upon two or three slip systems,' and comparison with extinction contour evaluations where s = 0 conditions were obtained. Errors caused by misinterpretation of the slip traces on a micrograph are easily avoided by considering the bright-dark sequence on opposite surfaces and by taking into account the tapering of the foil usually leading to a distinguishable divergence of the pair of traces. In the investigations described here the interpretation was further facilitated as the slip trace formation was observed on the microscope screen and sketches taken down. In a few observations slipping was so violent that the distinction of pairs was considered dubious and consequently given up. To assess average values, thickness evaluations carried out in two independent investigations were analyzed: I) 99.998 pct A1 extruded, cold-drawn, and recrys-tallized to grain sizes between 35 and 500 um were deformed in tension at room temperature. In order to determine the dislocation densities as a function of strain,4 specimens prepared by spark machining and electropolishing in a PTFE holder were analyzed in the electron microscope at 100 kv. Thicknesses were evaluated for 569 selected areas. Histogram I in Fig. 1 shows the results, the average thickness being 4900Å. II) Electropolished specimens prepared from 99.9999 pct A1 with magnesium contents from 0.005 to 0.5 pct rolled to foil and annealed were subjected to fission fragment irradiationa2 For volumetric dose and defect concentration determinations thickness evaluations were performed on 123 areas. Histogram II in Fig. 1 shows the thicknesses of these areas averaging 4250Å. Whereas in investigation I no selection related to thickness has been made, some thin as well as thick areas have been omitted from I1 for experimental reasons. This and the application of two different microscopes although of the same type may account for the difference in average thickness. Assuming a mean error of 10 pct for a single evaluation, the error of the average should be negligible. In order to investigate the maximum transmissible foil thickness in aluminum, specimens were prepared from single crystals with (111) and (110) orientations parallel to the beam, and from polycrystalline material. Maximum values of thickness that could be measured were given by the stopping of the dislocations. The visibility often extended far beyond the end of the slip trace, but with no means of knowing the

Jan 1, 1970

By G. L. F. Powell

TURNBULL and Cech1 reported undercooling small droplets (approximately 50 mp in diam) of a large number of metals by approximately 0.18 TE (TEoK = the equilibrium freezing point). This was considered to be the undercooling for homogeneous nucleation in

Jan 1, 1968

By P. M. Kelly, E. P. Butler

The stability of a 70/30 Mn-Cu alloy aged to peak damping has been investigated using electron microscopy, X-ray diffraction, and torsional pendulum measurements. Storage at room temperature or at 100" C causes a reduction in damping capacity. This is shown to be due to the formation of subdomains which "lock" the main domain structure and so hinder their movement. After storage the damping capacity can be restored by a retransformation treatment, which generates structures identical to those found in newly aged specimens. Plastic deformation by rolling also causes a decrease in damping capacity. In this case the damping capacity can only be restored by retransformation if the amount of deformation is less than about 5 pct. THE general metallography and structure of these high damping capacity alloys has been discussed in Part I of this work.1 Part II deals with some of the variables that affect the damping capacity. In particular, the stability of the damping capacity of a 70/30 alloy aged for 2 hr at 425° C and quenched has been investigated. The temperature sensitivity of the damping capacity of a 70/30 alloy aged for 2 hr at 450° C has been reported by Birchon.2 The damping capacity begins to decrease with increasing temperature, and is very low above the M, temperature of 125°C. The cubic — tetragonal transformation is completely reversible and there is no apparent thermal hysteresis associated with the change in damping capacity. Another important effect was first reported by Dean and his coworkers.3 They noticed a decrease in the damping capacity with time for specimens of a quenched tetragonal alloy. More recently workers at the Admiralty Materials Laboratory 4 have studied the stability of an aged 70/30 alloy. They found that the damping capacity decreased to half its original value after about 1000 hr at room temperature. EXPERIMENTAL The techniques used for electron microscopy and X-ray diffraction have been described in Part I. The damping capacity was measured by means of a torsional pendulum, using rectangular specimens, 3 by 0.3 mm with a 6 cm gage length. The specific damping capacity, S.D.C., was calculated as a percent amplitude decay in free vibrations over 10 cycles, starting at an amplitude which corresponded to a 700 psi surface shear stress. Because of the stress dependence of the damping,' the values obtained were about a third those reported for a 5000 psi surface shear stress.' RESULTS a) Effect of Aging Temperature. The effect of aging temperature on the damping capacity is shown in Fig. 1. The damping capacity reaches a peak of 12 pct after aging at 400° to 425°C) then begins to decrease as the volume fraction of a Mn increases. At higher aging temperatures the structure becomes cubic again with a low damping capacity. b) Stability of the Aged Structure. The damping capacity of the aged alloy decreases with time at room temperature. This process could be accelerated by storing at 100°C, when about 100 hr were required for the damping to fall to half its original value. The results of room temperature and 100°C storage, for times up to 1000 hr, are shown in Fig. 2. The damping capacity starts to decrease after about 24 hr at 18° C and 1 to 2 hr at 100°C. It was found, however, that the damping could be almost completely restored by retransformation. The specimens were held at a temperature above the M, for a short time, 250° C for 5 min, and then quenched. The values of damping capacity for specimens that were aged, stored, and then retransformed are shown by the full points in Fig. 2. X-ray measurements of the c/a ratio and hardness readings on the specimens did

Jan 1, 1969

By J. Chipman, H. Towers, M. Paris

A simple radioactive tracer technique is used to measure the diffusion coefficient of calcium ion in molten slags. In a slag of 40 pct Ca0-40 pct Si0,-20 pct Al203, Dc " at 1450°C is 1.3x10-6 cm' sec-'. THE application of the principles of thermodynamics to steel and iron making problems has proved so fruitful that the kinetic approach has tended to be neglected. It seems probable that in some reactions the rate-determining step is the dif-fusivity of the reactants or of the products. But knowledge of the diffusion coefficients of the constituents of liquid slag and metal is singularly lacking. The present work was undertaken as a first step toward supplying such data for slags. Furthermore, any additional information on the physical properties of liquid slags might be expected to help in elucidating their structure. It is essentially a preliminary investigation, the course of which was determined more by the necessity of establishing a method than by the immediate intrinsic interest of the results. For example, the selection of calcium ion to be studied was dictated by the suitability of the isotope Ca45 in that it is a simple emitter with a long half-life. Of the other ions commonly encountered in slags, the isotopes of iron and manganese have relatively complex radiations as well as the normal disadvantage of requiring control of the oxygen potential of the atmosphere; Mg27 and Al29 have half-lives measured only in minutes; Si3' has a simple decay process but its half-life of 2.8 hr is too short for preliminary studies; the only useful oxygen isotope is the stable O18; and there remain only sulphur and phosphorus both of which have suitable isotopes but were rejected as being of less fundamental interest than calcium. Similarly a lime-alumina- silica slag was used in preference to calcium silicate primarily because of its low melting point and its capacity to form a glass on fairly rapid cooling. Literature Review Very few studies of diffusion in liquid silicate systems have been reported. In order to determine the origin of diopside inclusions in felspathic rocks, Bowen1 investigated the diffusion between diopside and various mixtures of albite and anorthite. Platinum crucibles were used with diopside, the heavier of the two liquids, forming the lower half of the cell and diffusion taking place against gravity. Change in concentration along the diffusion path was found by measuring the refractive index of the quenched glass. Nearly thirty years later McCallum and Barrett2 used essentially the same method to determine the diffusion coefficient of lime in lime-alumina-silica slags. In this case the interest was to find the rate-determining step in the process of slag attack on refractory materials. In an investigation of the kinetics of the sulphur reaction, Derge, Philbrook, and Goldman8 determined the diffusion coefficient of sulphur in a typical blast furnace slag by the simple procedure of melting a slag containing 2 pct S over an identical slag sulphur-free. They make no claim to a high degree of accuracy but suggest that D, is of the order of 10-6 cm2 sec-l. Other high temperature liquid diffusion studies have been concerned with metals. Holbrook, Furnas, and Joseph4 determined the diffusion coefficients of silicon, phosphorus, sulphur, manganese, and carbon in liquid iron by immersing a small carbon crucible containing pure iron-carbon alloy in a large vessel containing iron with a high concentration of the particular element. Their results were confirmed by Paschke and Hauttmann5 using a similar method. Diffusion coefficients in silicates in the glassy state have been studied by Johnson, Bristow, and Blau6 Both Na24 and Ca45 were used as tracers but only the

Jan 1, 1954

By S. Chander, D. W. Fuerstenau

The inherently sluggish nature of the reactions involving sulfide minerals, particularly molybdenite, in aqueous solutions under ambient flotation conditions make their investigation complicated and difficult. Since the physicochemical nature of sulfides is known to be controlled by electrochemical reactions, a number of attempts have been made in the past to study sulfide mineral-collector interactions through rest potential and electrode polarization measurements. The purpose of the present investigation was to study the interaction of potassium diethyldithiophosphate (KDTP) with molybdenite. In the present investigation of the interaction of KDTP at the molydenite surface, molybdenite electrode rest potential measurements and electrode polarization behavior were experimentally determined under various solution conditions. The standard reduction potential for the equilibrium between dithiophosphate ions (DTP-) and bis(diethoxythiophosphoryl)disulfide (DTP) [(DTP). + 2e :i7-± 2DTP- (1)] can be evaluated from the electrode rest potential measurements on a platinum electrode in deoxygenated KDTP solutions saturated with freshly prepared (DTP)2. Experimental A platinum wire was used as the electrode for potential measurements. Prior to each measurement the elec-

Jan 1, 1975

By C. N. Reid

Slip-line studies on deformed chromium single cvystals showed the usual bcc behavior. At room temperatuve, cross slip was prevalent—slip was not confined to a given plane, but the slip direction was (111). At -10O0K, slip occuvred on (110) planes, twins on(112) planes, and cleavage on (1001 planes. A single-crystal tensile specimen with an axis close to [011] showed a pronounced yield drop and high strain rate sensitivity which zclere used to derive relevant parame tevs in a dislocation dynamics treatment. Transmission electron microscope studies confirmed the existence of (110) slip planes and showed ecidence of loops punched out by precipitates and of grown-in dislocations promoting tangling. OF recent years experimental studies have been made of the deformation characteristics of single-crystal molybdenum and tungsten, but very little has been published on the behavior of single-crystal chromium. During a study of the mechanical properties of chromium, single-crystal studies were made which have already been partially described.&apos; However, additional information was generated which was not directly relevant to the main theme of Ref. 1, and, therefore, was not reported. In view of the need for complete documentation of deformation modes, the experimental observations made on the deformation of single-crystal chromium are summarized here, together with an electron-microscope study of the associated dislocation structures. It was found that, in terms of the deformation modes, chromium is a conventional bcc metal, showing a very pronounced yield-point phenomenon. Further, it was found that the flow strength of these crystals is very sensitive to the strain rate. Finally, the crystals were observed to contain many unidentified precipitates, which often were associated with prismatic dislocation loops. EXPERIMENTAL METHODS Single crystals were grown from rods of wrought chromium by the method of zone annealing. Rods of "1/4in.-diam were supported vertically in an argon atmosphere while an induction coil was moved up the rod at 1 in. per hr. The power was adjusted to just below that required for melting, and the process produced single crystals in about 30 pct of the rods used. The orientations of the crystals, in general, lay near [011] and are summarized in Fig. 1. Before this treatment, the wrought material contained 35 pprn C, 68 ppm O, and 12 ppm N.* An analyzed single crystal *Usual metallic impurities found in iodide chromium are: Al, 5 ppm; Ca, A ppm; Cu, 2 ppm; Fe, 75 ppm; Yg, 0.5 ppm; Yn, < 3 ppm; Mo, < 3 ppm; Ni, 4 ppm; Si, < 20 ppm; Ti, < 1 ppm; V, 4 ppm; Zr, < 3 ppm. contained 10 pprn C, 79 ppm O, and 50 pprn N. Tension and compression specimens were shaped from the crystals by mechanical grinding, followed by the electrolytic removal of about 0.010 in. from the surface in a perchloric/acetic acid bath. All specimens had a gage length of 0.75 in., and tension specimens had a diameter of 0.100 in., while that of the compression samples was 0.200 in. Mechanical tests were carried out at a rate of 1.3 pct per min, and temperatures below 0°C were attained by means of a nitrogen cryostat similar to that of Wessel.2 EXPERIMENTAL RESULTS Modes of Deformation. In addition to the tensile properties of these crystals, which are described in Ref. 1, deformation markings on the surface were studied. Crystals A and F, Fig. 1, were deformed in tension at 300°K to 10 and 16 pct strain, respectively. The surfaces contained visible slip lines, about 1 C( apart, composed of both straight and wavy segments. They did not define a single plane, and so determination of the slip plane was not possible. However, the slip direction was deduced by comparing the axial orientations of the crystals before and after deformation. Fig. 2 is representative, and shows that the axis ro-

Jan 1, 1968

By P. T. Bail, J. E. Bobek

In reservoirs containing soft shales interbedded with oil-producing sands, it is possible to have water movement from the shales into the sands during reservoir depletion. This paper presents the results of scaled flow-model tests performed to investigate the efficiency of oil displacement by this vertical influx of water into oil-producing sands. In these model tests, the effects of rate of influx and rock wettability were considered. Oil recoveries by shale-wafer influx and by water flooding were cornpared after 0.4 hydrocarbon volume of water entered the producing sand. This comparison was made for water-wet and oil-wet systems. In water-wet sand, shale-water influx produces slightly less oil than conventional water flooding; in oil-wet sand, shale-water influx produces about one-half as much oil as conventional water flooding. In another type of comparison, it was found that shale-water influx followed by water flooding recovers less oil than water flooding alone. This is true for both water-wet and oil-wet sands. A comparison of tests run at different rates of shale-water influx shows that oil recovery is insensitive to rate in water-wet sand; in oil-wet sand, oil recovery decreases with decreasing rate of influx. INTRODUCTION Localized subsidence of the earth&apos;s surface has accompanied the depletion of some oil reservoirs, particularly in California,1, 2 along the Texas Gulf Coast,3 4 and in the Bolivar Coastal fields of Venezuela. Subsidence occurs when fluid withdrawals reduce the pressure in the reservoir. The reasons for subsidence accompanying a reduction in reservoir pressure are not known with certainty.10° However, there is considerable evidence that compaction of soft shale beds adjacent to producing oil sands can be a major cause of this subsi-dence.3, 6, 10-12 When the shales compact, a limited amount of water moves from the shales into the producing sands. A schematic illustration of this oil-producing mechanism is shown in Fig. 1. As the pressure in the sand declines due to oil production, a predominantly vertical pressure gradient develops at the sand-shale boundary. This causes water to move from the shale into the sand as indicated by the solid arrows. This paper reports the results of scaled flow-model tests to investigate the efficiency of oil displacement by the vertical influx of shale water into producing sands. The model tests were not performed with the aim of duplicating the recovery behavior of any specific reservoir. The primary purpose of the tests was to obtain a better understanding of oil displacement by shale-water influx. A knowledge of the oil- and water-production characteristics of even a simplified reservoir system should be of value to engineers estimating the performance of reservoirs where shale-water influx is occurring in conjunction with other production mechanisms. The following limitations and assumptions apply to the model work. 1. The sand of the prototype reservoir is homogeneous and horizontal. 2. The shale-water influx is uniformly distributed along the top and bottom of the sand member being studied. 3. No effects of edge-water drive or dissolved-gas drive that might accompany shale-water influx are considered. PROTOTYPE RESERVOIRS Scaled-model tests were performed to study oil displacement from three prototype reservoir sections. The reservoir sections modeled consist of single sand layers out of a sequence of -sand and -shale layers, as illustrated in Fig. 1. Each prototype represents a homogeneous, high-permeability, unconsolidated sand layer. In the field, the prototype is oriented in such a manner that one end is at the radius of drainage of a producing well and the other end is pointed toward the producing well (Fig. 2). The sand and fluid properties and the dimensions of the three prototypes are given in Table 1. The capillary pressure relationships for the three prototypes are presented in Figs. 3, 4 and 5. The oil-water per-

By J. F. Butler

Boron nitride, BN, has been identified in boron low-carbon steels by means of light microscopy, electron microscopy and diffraction, and chemical analysis. This boron nitride is responsible for strain aging suppression in these steels through the removal of nitrogen from solution; however, small oxidizing potentials which result in deboronization In the austenitic temperature range also result in boron nitride decomposition and the subsequent occurrence of nitrogen strain aging. THE addition of boron to low-carbon steels is an effective means of eliminating the detrimental effects of strain aging;&apos;,&apos; however, the mechanism by which boron suppresses strain aging has not been established. In studying the effect of heat treatment on the strain aging of boron low-carbon steels, Butler3 found that no detectable nitrogen was present in the ferrite solid solution after various heat treatments even though the total nitrogen analyses of the steels were 0.003 pct N. Apparently the function of boron in suppressing strain aging is the removal of nitrogen from solution to form a relatively stable second phase. A clue to the identity of this phase was found by Speight4 who extracted from an aluminum-killed boron steel an acid insoluble residue which contained boron and nitrogen in proportions corresponding to the compound, BN. Shyne and Morgan5 found that the addition of nitrogen to a hardenable boron steel lowered its hardenability in a manner which suggest-d the presence of nucleating particles (presumably BN) even at high austenitizing temperatures. Although this indirect evidence for the presence of boron nitride in boron steels has been found, the compound was not identified metallographically as a separate phase in these steels. Because boron has an affinity for oxygen comparable to that of silicon,5 boron steels must be thoroughly killed with aluminum in order to prevent the reaction of boron with oxygen.7 The affinity of boron for oxygen also is demonstrated through the ease of deboronization of a boron steel in an oxidizing atmosphere. Digges, Irish, and Carwile8 found that a mixture of wet natural gas and air caused both deboronixation and decarburization of a boron steel at 1900°F. The boron content rose at the surface of the steel due to the formation of boron oxide. Shyne and Morgan9 encountered deboronization at much lower oxygen potentials; loss of boron occurred in steels treated at 1750o F under argon purified to 0.0014 pct 0, even though decarburization did not occur. Boron oxide, B2O3, is much more stable than the nitride, BN, as is indicated by the standard free energies of formation at 980oC: -235 kcal per mol of B2O3 (liquid) and -28 kcal per mol of BN (crystal). It is evident that the oxygen potential must be kept low in the presence of BN in order to prevent its decomposition and the subsequent formation of B2O3&apos; The purpose of the work described in this paper was to identify the nitride phase responsible for the removal of nitrogen from solution and to study its stability under oxidizing conditions. IDENTIFICATION OF BN In order to identify the phase containing boron and nitrogen, several alloys high in boron and nitrogen were made up in a small vacuum furnace. In alloys 3 and 4, Table I, electrolytic iron was used as a charge material. Boron additions were made in the form of 18 pct B ferro-boron after the iron was molten. In the case of alloy 3, the charge was solidified at this point; for alloy 4, nitrogen at 1 atm pressure was admitted over the melt before it was

Jan 1, 1962

By R. J. Reynik

A semiempirial small flunctation theory of diff- sion in liquids is presented, which employs a fluctuation energy assumed quadratic for a small atomic or molecular displacement and Einstein&apos;s random-iralh model. The resulting diffusion equation is given by In these equations. D is the diffusivity, is the average liquid shite coordination number (at interatomic distance d. cm. T is the absolute temperature, xu. em, is (the diffusive displacement. K, is the quadratic fluctuation energy force constant, and rg, cm, are the radii oj diffusing atoms A and B, respectively. The quantities Xn and K are calculated from the computer-filled values of the slope and intercept. respectively. The radius of self-diffusing atom or radii and of diffusing atoms A and B are eta United and compared with values reported in the literature.. The predicted linear variation of diffusivity with. It tempera lure htm been observed in approximately thirty-iire metallic liquid systems, and in over seventy-fiee other liquid systems, including the organic .alcohols, liquified inert gases, and the molten salts, ALTHOUGH the average density within a macroscopic volume element of liquid is constant for fixed total number of atoms. pressure. and temperature, there exist microscopic: density fluctuations within the respective volume element. As such the microscopic volume available to an atom and its Z first nearest neighbors at any instant of time fluctuates above and below the average volume available to these atoms. If one assumes that liquid state atoms vibrate as in a solid. and further postulates that the mean position of any atom in the liquid state is not stationary. but shifts during every .vibration a distance 0 5 j 5 xo. then every atom in the liquid state continuously undergoes diffusive displacements which vary in the range 0 5 j 5 ro. Mathematically. for a binary liquid system consisting of atcrms A and B. the maximum diffusive displacement. .YO, is defined by the equation: where d is the average liquid state interatomic distance at specified liquid state coordination number Z. and v~ \ and vg are the effective radii of diffusing atoms A and B: respectively. For self-diffusion. r^ equals rg , and Eq. [I.] reduces to: It is interesting to note that Eq. [l] or [2] can be used to compute the radii of the diffusing atoms, provided one had an experimental evaluation of xo. As such. the computed radii could be compared with metallic or crystallographic ionic radii to ascerlain the electronic character of the diffusing atoms. Thus it is proposed that in the liquid state the n~otion of an atom relative to its original equilibrium position of oscillation represents the thermal vibration of any atom and its Z first nearest neighbors. while the small and variable displacements. 0 5 1 5 xc,. of the centers of oscillation represent the complex diffusive motions of the atoms at constant temperature and pressure. This is consistent with data obtained from slow neutron scattering by liquids1 &apos; and resembles an itinerant oscillator model of the liquid state.&apos;" It is further postulated that the atomic displacements characterizing the liquid state diffusion process are essentially a random-walk process. As such. it nlay be described by Einstein&apos;s equation:&apos; where D is the diffusivity. sq cm sec-&apos;. j2 is the mean square value of the diffusive displacement. and i> is the frequency of density fluctuations giving rise to diffusion. FORMULATION OF DIFFUSION EQUATION The effective spherical volume occupied by an atom, as a consequence of a microscopic density fluctuation which enlarges the volume available to any atom, exceeds its average liquid state atomic volume by an amount: where AV is the enlarged spherical volume, v is the radius of the diffusing atom. and j is the elementary displacement distance from the original center of oscillation of the vibrating atom to a new center of oscillation position. For small atomic displacements. where c is a constant whose value depends upon the assumed geometry of the enlarged volume. For a spherical increase in volume, c equals 4nr2. Following the treatment of Furthl&apos; and ~walin." assuming the enlarged volu~nes AL7 for the diffusing atoms are distributed in a continuunl. the probability of finding a fluctuation in the size range 0 5 j 5 xo defined by Where c includes the geometric constant cl and Eij) is the fluctuation energy causing the volume change. But the proposed model assumes all the Z first nearest-neighbor atoms are centers of oscillation. and hence the probability that any of these atoms is adjacent to a fluctuation of magnitude 05j5xo is unity. Thus:

Jan 1, 1970