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By A. G. H. Anderson, Eric R. Jette

A few years ago, while the writers worked on the constitution of ternary and quaternary alloys consisting mainly of iron, chromium and siliconl,2 some information on microstructures and hardness, not incorporated in the published work, alas obtained. It has not been possible to do any further work on the properties of the alloys. The information possessed is hereby presented for the interest it may have in connection with the constitution of the alloys. Microstructures Referring to the iron-chromium-silicon diagram,' the regions that received most attention were those in which the sigma phase appears. It was found that the mode of occurrence of this phase varied much with the condition under which it mas formed, and the mode influenced considerably the hardness of the alloys. In some slowly cooled alloys, well within the alpha + sigma-phase boundary, sigma occurs in pabterns suggesting a eutectic. The structure of such an alloy is shorn in Fig. 1, showing it to be partly coarsely laminated and partly globular mottled. In other annealed and slowly cooled alloys, the lanlinated structure is entirely absent, and sigma appears in an irregular distribution of sharply cornered elongated areas (Figs. 2 and 3). These areas all possess a more or less mottled structure. A carbide phase is also visible in these two photomicrographs; it is represented by bright white arras of various shapes, sometimes apparently enveloping the sigma. Quenched and aged specimens, whose compositions arc: located near the phase boundary between alpha and sigma + alpha regions, have structures not unlike martensite (Figs. 5 and 6). Fig. 4 shows the structurc of alloy No. 35 as quenched from 1100" C.; it is a typical solid solu-

Jan 1, 1938

By Eric R. Jette, A. G. H. Anderson

A few years ago, while the writers worked on the constitution of ternary and quaternary alloys consisting mainly of iron, chromium and siliconl,2 some information on microstructures and hardness, not incorporated in the published work, alas obtained. It has not been possible to do any further work on the properties of the alloys. The information possessed is hereby presented for the interest it may have in connection with the constitution of the alloys. Microstructures Referring to the iron-chromium-silicon diagram,' the regions that received most attention were those in which the sigma phase appears. It was found that the mode of occurrence of this phase varied much with the condition under which it mas formed, and the mode influenced considerably the hardness of the alloys. In some slowly cooled alloys, well within the alpha + sigma-phase boundary, sigma occurs in pabterns suggesting a eutectic. The structure of such an alloy is shorn in Fig. 1, showing it to be partly coarsely laminated and partly globular mottled. In other annealed and slowly cooled alloys, the lanlinated structure is entirely absent, and sigma appears in an irregular distribution of sharply cornered elongated areas (Figs. 2 and 3). These areas all possess a more or less mottled structure. A carbide phase is also visible in these two photomicrographs; it is represented by bright white arras of various shapes, sometimes apparently enveloping the sigma. Quenched and aged specimens, whose compositions arc: located near the phase boundary between alpha and sigma + alpha regions, have structures not unlike martensite (Figs. 5 and 6). Fig. 4 shows the structurc of alloy No. 35 as quenched from 1100" C.; it is a typical solid solu-

Jan 1, 1938

By E. van Walsum

Tunneling methods through rock have, since the successful development of explosives, relied almost solely on blasting. Over the last ten years, rock-tunneling machines (moles) have been developed and some major projects have been carried out successfully with the use of such machines, which rely on the destruction of rock by mechanical means rather than blasting. Various other basically new methods are presently under study, such as the use of laser beams, water jets, etc. For practical purposes, there are presently only two methods commercially available: 1) blasting or 2) tunneling by mole. A contractor would choose at present either one method or the other. Both methods have their advantages and disadvantages (Fig. 1). The thought has occurred that the next practical development in rock- tunneling technology might be a combination of the best features of the mole technique and those of the blasting technique. A preliminary evaluation of this approach indicated that there is definitely a good potential for fruitful developments along these lines. My purpose is to place on record some of the thinking and some of the ideas which were developed along these lines and to point out certain areas where development efforts are required. In trying to find an improved tunneling technique, we looked in particular for the following qualities: 1) safety, 2) continuity, 3) uniformity, 4) automation, and 5) flexibility. TUNNELING BY BLASTING Conventional tunneling by means of blasting proceeds generally in recurring sequences of events: 1) drilling, 2) loading, 3) firing, 4) mucking-out, and supplementary operations (such as scaling and lining). These four operations (drilling, loading, firing, mucking) proceed one after another.

Jan 1, 1970

Although grinding mill liner life has been the subject of extensive studies, evaluation of the effect of liner design a power consumption, a far more significant part of total grinding costs, has been less comprehensive. The factors that effect ball mill energy efficiency are reviewed, and attention is then focused on the mechanism of grinding. The trajectory of the outer row of balls, with different lifting face angles, is derived. Basic recommendations for mill speed and liner configuration are also presented

Jan 1, 1984

By M. G. Driessen

For a number of years the cyclone, familiar to Americans as a dust collector, has been used as a thickener of suspensions at one of the coal-preparation plants of the Netherland State Mines in Limburg. The plant treats nut-size coal at 120 tons an hour in a heavy-medium washer. The diluted medium from the rinsing screens is thickened in cyclones. More recently the cyclone has been adapted to act as a coal cleaner. The principle of the cyclone thickener is the same as that of the cyclones used in industry for catching dust or fine particles suspended in the air or in gases. Generally the latter are more efficient in this respect—the smallest particles that can be caught with reasonable efficiency are considerably smaller than with the cyclone thickeners. The reason is obvious; the ratio of specific gravities between the dust particles in a gas and the gas itself is about 800 times larger than the ratio between, for instance, the specific gravities of shale particles and water. The ratio of the velocities of fall of shale particles (? = 2.5)† in air and in water is as follows: In the range of Stokes: ?air = 93?water In the range of Allen: Wair = 49Wwater In the range of Newton-Rittinger: ?air = 36.6?water The same ratios apply for the velocities in the centrifugal field, from which it follows that it is especially difficult to catch the very fine suspension particles in a liquid. The efficiency of a cyclone thickener depends mainly on the circumferential velocity of the liquid at its innermost radius, because here the centrifugal forces are the highest. However, these velocities cannot easily be calculated, as the flow is three-dimensional, and thus the axial components cannot be neglected .(p. 252, condition 3). We believe that at first a spiral tangential motion along the cyclone wall is created, which causes the inner vortex ascending from the apex of the cyclone (Fig I). At the same time the inner vortex is strengthened by the individual vortices in horizontal planes, and thus a part of the total flow can find another and perhaps quicker way to the outlet. In any case, the exact motion, not only of the fluid but especially of the suspended particles, is so difficult that we have to refer to the experiments to find the exact behavior of this kind of apparatus. Method of Judging PerforMance of Coal Washer Geologists, rather than mechanical en-gineers, would be able to describe the separating or stratifying effect in nature, but even a bather on the shore lying on the soft sand near the sea wonders why all the small sand grains have approximately the same size. A child playing on the border of the river could easily

Jan 1, 1949

By Frank Clemes Smith

In describing a certain class of ores, of ever-increasing importance in the Black Hills, they are variously called " refractory,)' "siliceous," or Potsdam;" the first name serving to distinguish them from the other important class—the free mill-

Jan 1, 1898

By C. G. Bieber, R. F. Decker

The effects of minor constituents on the malleability of nickel alloys are described. These effects are related to the atomic diameter, valence, and position on the Periodic Table. The basic methods for removal or neutralization of deleterious elements are then reviewed. Finally, practical methods for melting nickel alloys are described in detail and related to minor constituent control. L HE first malleable nickel was produced by Fleit-man in about 1870 by the addition of manganese and magnesium to the molten metal to counteract the harmful effects of sulfur. Merica and Waltenbergl explained the mechanism by which these elements accomplished the desired result. They showed that sulfur in concentrations in excess of about 0.005 pct produced films of a brittle low melting eutectic of nickel-nickel sulfide which completely surrounded the grains. When manganese was added to molten nickel it reacted with the sulfur to form manganese sulfide which precipitated as widely scattered globules in the grain boundaries. The further addition of small amounts of magnesium converted the sulfur to a very stable sulfide of magnesium which was relatively insoluble in both the liauid and solid states and therefore occurred as finely divided particles within the grains where it had relatively little detrimental effect upon the malleability of nickel or its alloys. The practice of treating nickel with manganese and magnesium came to be called "deoxidation" and was employed without appreciable modification for the commercial production of wrought nickel and high nickel alloys (in this paper—50 pct or more nickel) until about 1930 even though the results were never entirely satisfactory. At that time a more extensive study was made of the effects of minor constituents on malleability and metallurgical quality. The results, small portions of which have been published,2-4 are presented here with other pertinent data. EFFECTS OF MINOR CONSTITUENTS UPON NICKEL Systematic additions were made of 0.5 pct or less of each of most of the elements of the periodic ta- ble. It was established in this study that some minor constituents other than manganese and magnesium were extremely influential. The malleability, as evaluated by the reduction of area in tension tests, depended roughly on temperature as shown in Fig. 1. Four temperature zones are of interest; the cold malleable zone (up to about 1000° F), the red short zone from roughly 1000° to 1500' F, the hot malleable zone around 2000° F and the incipient melting zone. Most of the malleability problems are associated with the red short zone and the discussion will concern this mainly. The reduction of area in normal tensile tests on high-purity nickel (see curve A of Fig. 1) appeared to have no

Jan 1, 1962

By Persifor Frazer

General Geology of the Northern Black Hills. The " Black Hills of Dakota," to the northern part of which the following observations apply, occupy a position on either side of the boundary between Wyoming and South Dakota, approximately between 103" 15' and 104" 48' of west longitude and 43 15' to 43" 50' of north latitude. The area is roughly 4160 square miles.* (See Plate I.) As has been pointed out by Profs. H. O. Hofman, I?. R. Carpenter and others, and illustrated by Mr. Newton in the publications of the United States Geological Survey, these hills are made up of a large number of the known formations from the Archean to the Tertiary, which latter constitutes the border of the region. The mining operations are largely confined to the interior of this area, and the centers from which they are conducted (Deadwood, Lead City, Galena, etc.) are situated near the line of junction of the Archean schists and quartzite, supposed to represent the Potsdam Sandstone of the N. Y. series, or the lowest of the Paleozoic measures. The Archean or pre-Paleozoic rocks consist mainly of a mica-schist in which hornblende and garnet are frequently

Jan 1, 1898

Jan 12, 1951

By B. J. Reid, J. N. Greenwood

It has been shown1 that cavities are formed in the grain-boundaries of copper and 70:30 brass (as well as in magnesium) by the application of tensile stresses at elevated temperatures. For a given rate of strain, cavities are formed in brass at a lower temperature than in copper, and they are larger; it was thought that this earlier onset of cavitation in the alloy might be caused by the distortion produced in the metal lattice by the alloying element. If the cavitation is caused by the vacancy-migration mechanism, ' the distortion of the lattice would reduce the energy required for vacancy formation, and thus provide vacancies more readily to assist in the cavitation process. It was decided to study a range of alloys to find out whether increasing amounts of an alloying element would cause any progressive increase in, or modification of, the cavitation in copper. Nickel was chosen for this purpose, since it is soluble in copper throughout the whole range of alloys. A further advantage was its low vapor pressure, which enabled the preparation of the alloys in vacuum and the consequent reduction of their hydrogen content. It has been suggested that cavities may be nucleated by the migration of hydrogen atoms to the less regular atomic spacing at the boundary, and their combination to form molecules. The latter being too large to diffuse back into the lattice, form stable cavities into which vacancies could condense. PREPARATION OF ALLOYS All alloys, ranging from pure OFHC copper to 43.7 at. pct of nickel (carbonyl), were prepared in a vacuum furnace employing high-frequency induction heating. When a charge was melted, vigorous gas evolution occurred initially, after which the pressure was reduced to 10-4 mm Hg, using an oil-diffusion pump. After remaining molten for a further 1/2 to 1 hr to aid degassing, the melt was allowed to solidify in the crucible. In this way contamination by gases evolved from the surface of a separate mold was avoided. The list of alloys prepared is shown in Table I. The percentage of hydrogen present in the OFHC copper was reduced from 0.0054 at. pct to 0.0012 at. pct, as measured by a vacuum-fusion method. The alloys were cold-rolled to 0.03-in.-thick strip, and were homogenized in vacuum for 1 hr at 900°C after every 30 pct reduction. At a thickness of 0.05 in., the strip was held at 450°C for 24 hr under high vacuum (10-5 mm Hg) in an attempt to reduce the hydrogen content still further. Tensile specimens were prepared with a gage length of 1 in., and were finally annealed for 2 hr at 800°C to give an average grain diameter of 0.1 mm. TENSILE DEFORMATION The specimens were deformed in a tensile straining machine operated by a synchronous motor at a constant rate, equivalent to 1.7 pct per hr on a 1-in. gage length. The specimen and grips were contained in a vacuum jacket. A pressure of 10-2 mm Hg was maintained, which was sufficient to prevent surface tarnishing of a specimen held at 650°C for 24 hr. Tests were made between 20. and 650°C and the temperature was controlled to within ±3° over the gage length. The load was measured by the deflection of a cantilever spring. a) Mechanical Properties-The ductility curves shown in Fig. 1 fall into two groups. Figs. 1(a) and (b) for copper and the 5 pct nickel alloy, respectively, show a continuous fall in ductility with a steep fall between 200° and 400°C. Figs. l(c) to (f) show the same sudden loss of ductility between 200° and 400°C. With higher temperatures, however, there is a recovery in ductility values to a maxi-

Jan 1, 1959

By Arthur F. Johnson

THE principal costs of making a pound of aluminum are for 9 kw-hr of electricity and for 1.9 Ib of the oxide (A1203) called alumina. A pound of alumina is made by digesting 2 or 3 lb of bauxite in hot caustic solutions, settling and filtering out the oxides of silicon, iron, and titanium and precipitating and calcining the A1203 as a pure, white powder. The cost of foreign bauxite delivered at an alumina plant in the U.S. may equal or exceed the cost of its chemical treatment to make alumina. Some of the principal factors affecting costs in the utilization of foreign bauxites are: transportation from mine to market, mineralogical and physical composition of the bauxite, thickness of the bauxite beds and their clay and forest overburden, amen- ability of the bauxite to beneficiation and to caustic extraction of the alumina, and lastly size of bauxite deposits and rate of mining employed.

Jan 6, 1954

By H. J. French

AT THE request of a committee of the Engineering Division,1 National Research Council, a study of the properties of boiler plate at various temperatures up to about 900° F. (482° C.) has been instigated. The following is a report of preliminary tests made on two grades of ½ -in. plate and includes a description of the apparatus used in the determination of the proportional limit. Detailed reference to the many published investigations in connection with the properties of steel at various temperatures will be omitted from this report. Suffice to state that results obtained for variation in tensile strength elongation, and reduction in area with temperature are in substantial agreement with the effects now generally considered to be correct. Comparison of proportional limit values with results obtained by other investigators will be found in the conclusions.

Jan 2, 1920

Jan 1, 1954

By José G. Aguilera

With the imperfect knowledge that me have of the geology .of the country in general, and of the numerous mining districts in particular, it is impossible to present an accurate idea of the geographical and geological distribution of the mineral deposits of the Mexican Republic. But, notwithstanding this, it is elear that the deposits are concentrated in limited regions of the country, and that certain deposits are so closely associated as to indicate, beyond doubt, a genetic relationship. The mineral deposits are numerous, and the most of them are found in the western part of the country in a zone following a SE.-NW. direction from Oaxaca to Sonora. In the eastern

Jan 1, 1902

By K. P. Wang

Under the Communist regime marked industrial progress has been achieved on the China mainland. Within a decade, the country has been transformed from an economy primarily agricultural to one bristling with industrial possibilities. The industrial capacity of Communist China is beginning to approach that of Japan and will probably surpass it by 1962, the last year of the Second Five-Year Plan. The slogan already is Beat the United Kingdom by 1972, a goal which most observers feel will be achieved ahead of schedule. During the early years of the industrialization program in Communist China, emphasis has been placed on basic goods; hence additional time will be needed to make large quantities of the more complicated products. However, regardless of the current stage of industrial development, it is apparent that the necessary forward momentum has been created. The many capital construction projects being brought into production and the additional projects being initiated confirm this observation. The accuracy of Communist China's industrial statistics can be questioned, but their order of magnitude is clear. To properly evaluate the industrial capability of the country, differentiation must be made between the absolute quantities that reflect overall strength and the per capita quantities that reflect living standards. While Communist China is well on the road to becoming a world power, its living standards will remain below European levels for many years to come.

Jan 8, 1960

By P. Chaudhari, Michael B. Bever

The heat of solution at infinite dilution of selenium in bismuth, the heat of mixing of selenium and bismuth, and the limit of solubility of selenium in bis~rzuth have been determined at 573, 623; and 663°K by metal solution calorimetry. The heat of forrrzation of the compound Bi2Se at these temperatures has been determined from the heat effects associated with the precipitation of the compound from a saturated solution oj selenium and bismuth. The published information on the thermodynamic properties of the system Bi-Se is limited. The heat of solution at infinite dilution of selenium in bismuth at 623°K has been measured.' The heat of formation at 273 K1 and room temperature2 and the heat capacity at 80 K3 of the compound Bi2Se3 have been reported. An estimate of the heat of formation of the compound BiSe at room temperature has been published.2 Information on the phase relations in the system Bi-Se is available.' In the investigation reported here the following quantities have been determined at 573", 623", and 663°K: 1) the heat of solution at infinite dilution of selenium in bismuth, 2) the heat of mixing of selenium and bismuth in bismuth-rich solutions, 3) the limit of solubility of selenium in bismuth, and 4) the heat of formation of the compound BizSe. These quantities were determined by the addition of selenium to bismuth-rich solutions in a metal solution calorimeter. The determination of the heat of formation at the tem- perature of the calorimeter bath involved the precipitation of the compound from a saturated solution in the calorimeter. 5,6 This method differs from that commonly used which requires the addition of the compound and of a mechanical mixture of its components and yields the heat of formation at the temperature from which the additions are made (273 K EXPERIMENTAL PROCEDURE AND CALCULATIONS The solution calorimeter has been described in detail.' Pure bismuth (99.999+ pct) was used as the bath at the start of a run. The calorimeter was calibrated with small amounts of bismuth added from 273°K; the differences of the heat contents of bismuth at 273°K and the temperatures of the baths are listed in Table I. After the calibration, additions of hexagonal selenium (99.999+ pct) were made. Loss of selenium by evaporation was negligible. No unusual experimental difficulties were encountered.9 The differences in the heat contents10 of selenium at 273°K and the temperature of the bath, listed in Table I, were subtracted from the measured heat effects to give the "adjusted heat effects". The methods by which the heat of solution at infinite dilution, the

Jan 1, 1968

By R. B. Burt, James A. Barr, I. S. Tillotson

THE pumping of solids in water suspension is an important part of many metallurgical and mining operations. In most cases, it is still in the rule of thumb category for which no universal formula has been developed, and much research is needed. Because of the limited and incomplete data available, this article may be classed as an experience paper, which is presented with the hope that some contribution will be made toward the development of the so-called universal formula. This formula, if and when developed, may be evolved from several factors, many of which are not now available for general application. The designing engineer is interested in obtaining accurate forecasts on: 1-the minimum velocities needed to prevent choke-ups in the pipeline, which in turn dictates pipe sizes, 2-power required for pumping, 3-pump selection. The basic factors for a given problem will include: 1-weight per unit of time of solids to be handled, 2-specific gravity of solids, for calculation of volume, friction and power, 3-screen analysis of solids with the colloidal acting, i.e., the slime fraction, a very important factor, 4-shape of particle or some means of determining a friction constant, 5-effects of percentage of solids, 6-development of a viscosity factor to be used in the overall calculations, 7-calculation of the lower limits of pipeline velocities permissible, 8-calculation of total head, pump horsepower, and 9-setting up of pump specifications. In certain limited cases horsepower and total heads and minimum velocities may be computed and a suitable pump selected from basic data, but in many cases, as in mining of Florida pebble, phosphate, experience rather than a hydraulic formula still should be used as a basis of selection. Pumping Florida Pebble Matrix Pumping at the Noralyn mine of International Minerals and Chemical Corp. will be used as an example. Other areas will vary as to the characteristics of the matrix, especially the slime content. A typical screen analysis of this matrix is: +14 mesh, pebble size,* 2.1 pct; -14 +35 mesh, 11.4 pct; -35 +150 mesh, 60.5 pct; -150 mesh, 25.0; total, 100 pct; moisture in bank, 20.0 pct; weight per cu ft in bank, 120 lb. The -150 mesh fraction may increase to as much as 35 pct in adjacent areas. When thoroughly elutriated, the matrix has a relatively slow settling rate, which is an important factor in permitting lower pipeline velocities without choke-ups. Exact data is not available to evaluate settling rates. For a factor of 100 a suspension of clean building sand in water is suggested. When pumping long distances, a quick settling matrix allows the coarser solids to settle out along the bottom of the pipeline, causing drag, turbulence, and increased friction. With a slow settling matrix as at Noralyn, turbulence acts to keep the solids in suspension at a lower friction head, regardless of the pumping distance. When the pebble, content of the matrix, i.e., the +14 mesh fraction, is in excess of 10 pct of the total solids, trouble may be expected from settling out even in normal pumping distances. To prevent choke-ups and maintain tonnage, an additional pump must be added in the long runs, where one pump would otherwise be satisfactory. A typical pulp handled is: total volume, 7800 gpm; water, 4500; solids pumped per hr, 4200 lb; sp gr pulp, 1.4; percent solids in pulp, 46.; pipe size, 16-in. ID; pulp velocity, 12.85 fps; probable critical velocity, 10 fps, as below this minimum -velocity choke-ups would be numerous. In calculating friction heads the Armco handbook is used where a roughness factor based on 15-year-old pipe is set up. Because the pipe used in pumping matrix is, smooth and- polished because of the scouring, action of the phosphate and its silica content, the head losses in the Armco table for water are practically the same as in pumping the Noralyn matrix through smooth pipe, plus the fact that conditions vary widely over short periods, making accurate determinations difficult to obtain. New pumps and pump, changes are being tested continuously and a wealth of data built up. This has resulted in a substantial improvement and lower relative costs in pumping matrix. The Florida phosphate industry is constantly seeking to offset higher wage and material costs with improved technique. Until a few years ago a 12-in. discharge pump was commonly used, with heads as low as 80 ft. Sizes have gradually increased and heads more than doubled. For example, the following pump was placed under test at the Noralyn mine: make, Georgia Iron Works; size, suction 16 in., discharge 14 in.; impeller, 39-in. diam; motor, 600 hp, slip ring; full load speed, 514 rpm. The results were increased head, higher capacity than the older design, with fewer pumps in the line from mine to washer.

Jan 1, 1952

By R. E. Collom

VARIOUS chapters already written in the history of development of the North Dome of Kettleman Hills are monotonously identical in the one underlying theme of conservation of oil and gas. Discovered on Oct. 4, 1928, by Milham Exploration Co. with its wildcat Elliot No. 1, the field has been subjected to practically every modern form of produc-tion restraint in the name of conservation. The record thus far developed shows that conservation was had for a time, at a price; and that unitiza-tion must he blessed by single ownership or 100 per cent participation to be effective. In fact, incomplete unitization places a heavy handicap upon its participants in the competitive development that follows.

Jan 1, 1937

NEW MEMBER, The following list comprises the names of those persons who became members during the period Mar. 10 to Apr. 10, 1915: Members ADAMS, Louis WINFIELD, Supt., Rolling Mills, Lehigh Plant, Bethlehem Steel Co., So. Bethlehem, Pa.. ALLEN, ARTHUR WATTS, Mine Mgr Rodeo, San Juan, Argentina., BALL, EDWIN MARCOTTEL, Mine Supt., Ishkooda. Mines, Care Tenn. Coal, Iron & R. R. Co., H.F.D. 1, Birmingham, Ala. BOLN, CHARLES A., Oil salesman 135 S. 2d St., Philadelphia., Pa. BOYD, DAVID F., Naval Officer Navy Department, Washington, D. C. CAPERTON, GEORGE HENRY Charleston, W. Va. COGGESHALL, GEORGE W., Chem. Engr., Institute of Industrial Research, Washington D C

Jan 5, 1915

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'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 ' and resembles an itinerant oscillator model of the liquid state.'" 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's equation:' where D is the diffusivity. sq cm sec-'. 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' 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