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By Dorsey Lyon

I. INTRODUCTION THE utilization of hydro-electric power in electro-metallurgical indus¬tries, aside from purely mechanical operations, may he of two kinds. The electric energy may be used to supply the heat necessary for the per¬formance of the chemical reactions of a metallurgical process, or the elec¬trolytic action of a direct current may be employed for extraction of metals, either in a reduction process or a refining process. In discussing this subject, it is well to distinguish between established industries, which are producing metals and alloys at a profit by use of the electric current, and the many processes which are either still in the experimental stage or have not even passed the paper stage of development of a patent. That is, we consider electro-metallurgical industries as commercial operations which are now consuming large blocks of electric energy, while processes which are not in commercial operation are only prospective consumers. Also, owing to the difficulty and risk of any attempt to foresee the effect of the European war upon electro-metallurgical industries, we have felt obliged to disregard the war entirely, and state our opinions regardless of its existence.

Jan 8, 1915

Executive. CHARLES F. RAND, Chairman. JAMES F. KEMP, JOSEPH W. RICHARDS, ALBERT R. LEDOUX, BENJAMIN B. THAYER. Membership. BENJAMIN B. THAYER, Chairman. WALTER R. INGALLS, JOHN H. JANE WAY, JR., JOHN D. IRVING, HERMAN A. PROSSER. Finance. EDWARD L. YOUNG, Chairman. KARL EILERS, JAMES GAYLEY.

Jan 4, 1913

The mountains of Utah contain one of the largest deposits of high grade bituminous coal in the world. According to the United States Geological Survey, there are 13,130 square miles of land known to contain workable coal, and these extensive fields contain 196,000,000,000 tons of coal. More remarkable than the extent of the coal fields is the thickness of the coal beds. Over three-fourths of the output of coal in Utah is recovered from beds ranging from 8 to 17 feet in thickness, as com- pared to one-eighth of the output of the entire country from such beds. In 1917, Utah mined one-third of its coal from seams at least 16 feet thick, compared to one-half of one per cent of the total bituminous output of the country from like seams. Coal at Wales, in Sanpete county, and in the vicinity of Coalville, Utah, was, it is reported, the first discovered by white men in the state. Wales claims the distinction of having produced the first coal mined in Utah. Two men, who had been coal miners in Wales, learned of the coal from an old Indian chief who called it "rock that would burn." In 1857, the town of Wales was founded and coal mined, and in 1858 some coke was manufactured and hauled by ox team to Salt Lake City. South of Wales is Castle Valley, in Wasatch Plateau field. From 50 to 60 miles of the old Spanish Trail from Santa Fe. New Mexico, to Monterey, California, lies in Castle Valley. The coal in this field may or may not have been known at the time the trail was used extensively. The first published reference to this coal, however, was made by a party of the Corps of Topographic Engineers in their journal for October 11, 1853.

Jan 1, 1925

By Roland Blanchard

ABSTRACT RECENT discovery at Mount Isa of copper mineralization in commercial amount at a depth of 1000 ft., coinciding with downward termination of ore at about the same depth within the larger silver-lead-zinc lenses that have been the standby of Mount Isa's production to date, has been cited as an example in support of mineral zoning. A previous paper by the author and Graham Hall1 furnished a detailed description of the geology of the ore at Mount Isa as exposed up to that time, but necessarily dealt mainly with the silver-lead-zinc mineralization. Most of the geologic facts that constitute the first half of the present paper were set forth in the previous one in much greater detail, with full supporting evidence for the facts cited. The large amount of underground development (approximately 20 miles) and the extensive exploration carried out by diamond drilling (100,000 ft.) at Mount Isa, added to extensive microscope work conducted over a period of years, both by the company's staff and by others, had made possible the calculation within fairly close limits of mineralogical composition of the principal mineralized block of ground down to 1000-ft. depth, and had established closely the mineral succession, with reasons for deposition of the various minerals in the patterns now occupied by them. The geologic facts as outlined in the previous paper remain as stated; but because substantial development within the new copper ore body and further exploratory diamond drilling within the new silver-lead-zinc area (Race-course) have taken place since that paper was written, statements and figures relating to those two areas in the present paper supersede those furnished in the previous one. The recent work likewise has established more clearly the paragenetic relationship between the chalcopyrite and galena. Evidence confirming the relationship is furnished in the present paper. The facts of ore occurrence at Mount Isa show [ACCEPTED ZONAL SUCCESSION Silver sulphantimonides Galena Sphalerite Tetrahedrite Arsenical sulphides Chalcopyrite Pyrrhotite MOUNT ISA SUCCESSION Chalcopyrite In the main but Silver sulphantimonides wholly Tetrahedriteably not Galenacontemporaneous Pyrrhotite Sphalerite Arsenical sulphides They show further: (I) that instead of the silver-lead minerals yielding to increased zinc in depth, the zinc yields to increased silverlead; (2) no dovetailing of the silver-lead-zinc sulphides into chalcopyrite takes place; (3) despite the large amount of pyrrhotite deposited in the district (estimated at upward of 100,000,000 tons), its deposition took place under moderately low temperature conditions; (4) no evidence has been found for increase in temperature of deposition, with depth, to deepest exploration in ore (1495 ft.). The anomalous condition at Mount Isa, both as to the unorthodox mineral succession and the largely unorthodox pattern of mineral distribution, is explained in the present paper,

Jan 1, 1943

By L. D. Mullins, H. B. Bradley

Numerous articles have appeared in the literature citing the application of the potentiometric analyzer to cycling operations. Specific information obtainable by a potentiometric analysis, as noted by various investigators, includes: 1. Pattern sweep efficiency for various injection and production rate programs. 2. Injected fluid breakthrough time at production wells. 3. Optimum production and injection rates. 4. Prediction of injection and/or production well locations. 5. History of advance of the in-jected-produced fluid interface. 6. Ultimate life of the reservoir. 7. Ultimate reservoir production. This note describes a procedure for predicting pressure distribution in a gas-condensate reservoir by using the potentiometric analyzer to obtain potential distribution data on an analog model of the reservoir and then applying Muskat's' equations. The method relates the volumetric weighted average datum pressure to the mean potential in the model.

Jan 1, 1958

By C. Upthegrove

DURING the past year considerable work dealing with physical properties of cartridge brass was done at the University of Michigan in cooperation with the Ordnance Department of the U. S. Army. This paper gives some of the data bearing on the effect of the anneal, previous to the final reduction or rolling, on the physical properties, particularly the hardness. Various phases of the subject of physical properties of cartridge brass have been presented by different investigators. Mathewson and Phillips1 refer to the work of Grard, in 1909, as the first systematic presentation of the relation between temperature-and time of anneal; changing of physical properties and microstructure, and the previous reduction by cold rolling. They discuss the relation between time and temperature of anneal and the previous reduction by cold rolling also; the relation between physical properties and grain size of annealed brass. The degree of deformation previous to the annealing was found to determine the temperature at which recrystallization and corresponding changes in physical properties would take place. Bassett and Davis,2 in establishing the relation between grain size and Brinell hardness; found the hardness for low-temperature annealing to be dependent on the previous degree of reduction, while for anneals above a certain temperature the hardness after the anneal was independent of the degree of reduction. Actual differences in hardness, due to the degree of reduction, disappear only on annealing at 600° C. or above; though the differences for metal subjected to different degrees of reduction and annealed at temperatures between 350° and 600° C. were found to be relatively small. In their determination of the relationship of grain size to Brinell hardness, Bassett

Jan 5, 1922

By John Greenawalt

IN view of the increasing importance of sintering in the beneficiation of iron ores preparatory to their reduction in the blast furnace, the writer believes the time is opportune for an up-to-date, though brief, discussion of the general principles of sintering, as well as a discussion of some of the recent improvements and mechanical developments that have been achieved in this industry, its present trend and future possibilities. Sintering may be defined as the agglomeration of fine mineral particles into a porous mass by incipient fusion caused by heat produced by com-bustion within the mass itself. Its first successful application, in connec-tion with the treatment of lead sulphide ores, was known as blast roasting. In this process the lead ore was given a preliminary roasting in a reverber-atory furnace, then the incandescent mass was placed in a pot with a grate and an updraft was applied. It was soon discovered that much better results were obtained by cooling the ore, moistening it, and placing it upon an incandescent layer of fuel previously placed upon a grate, and then applying the updraft blast of air until the charge was converted into a more or less agglomerated mass. The fuel was sulphur and the process one of desulphurization, which was the principal result desired. The application of downdraft to blast roasting brought about tremen-dous results; the principal one of which was that an air blast of high pressure could be passed through a layer of ore deposited on a grate, or on a grate covered by a layer of coarse porous material, without disturbing the particles of which the layer is composed. The air current is compelled to filter through the pores of the charge, whereas if the same pressure applied to the top surface of the charge with downdraft were applied to the bottom of the charge with updraft, the charge would be completely blown off the grate. Another result of reversing the draft was that a flame could readily be applied to the top surface of the charge for ignit-ing purposes.

Jan 1, 1938

By Robert Mehl

A STUDY of the structures arising from the decomposition of the a solid solutions in the Cu-Zn and the Cu-Al systems is of peculiar interest in the study of the mechanism of precipitation from solid solutions. It is possible in these alloys, by varying the composition within the ß field, to precipitate from the same basic lattice phases having different lattice structures. It has been rather generally assumed heretofore that the type of structure originating from the decomposition of a solid solution-the Widmanstätten structure-is determined by the lattice structure of the parent solid solution alone. In the first paper of this series1 evidence was advanced which threw doubt upon this hypothesis; but definite proof of the correctness or incorrectness of the hypothesis should be forthcoming from a study of these alloys, for if the structures originating, for example, from the precipitation of the a phase from ß and of the -y phase from the ß in the Cu-Zn system should be shown to be crystallographically different, the hypothesis would necessarily be held as definitely disproved. Furthermore, the newer proposal enunciated in the first paper of this series-that the origin of the Widmanstätten structure lies in a cooperation between the lattice of the parent solid solution and that of the precipitate-which at present seems the only alternative hypothesis, would in such an event be given added weight. The work here reported shows that the Widmanstätten structures originating in the precipitation of the a phase from the a and in the precipitation of the -y phase from the ß in the Cu-Zn system are indeed crystallographically different; and incidentally presents some new descriptive information on the Widmanstätten structure from a more general point of view.

Jan 1, 1931

By C. A. Fisher

THE Salt Creek Oil Field of Wyoming occupies a unique position among the major oil fields of this country. Many years before the beginning of actual production in this area, in 1911, it had attracted country-wide attention as a district holding oil possi¬bilities. Even foreign capital, mainly French and Belgian, had sought out this district as having oil values and spent many thousands of dollars 'in an effort to acquire property rights' in this field which was very largely located on the public domain. Owing to inadequate laws governing the acquisition of oil lands on the Federal domain and a careless practice having grown up among oil land locators of that time, a complicated title situation quickly developed in Salt Creek. This condition of uncertain titles together with the isolation of the field from industrial centers were doubtless the two most potent factors in retarding its early development. After actual production began in 1911 governmental regulations, suits between the government, and the locator, disputed ownerships between locators and claim and counterclaim continued to retard the field's development. It is believed that the title situation in the Salt Creek Field, where potential values of such magnitudes were involved, was responsible more than any other factor for the ultimate passage of the government leasing act in 1920 affecting all oil lands on the Federal domain.

Jan 1, 1925

By P. H. Wendland

Calculations are presented for the design of a silicon photodiode in which the incident light beam makes multiple passes between the detector surfaces. Total internal reflection is used for this "light-trapping" effect. By this means, the optical path length can be extended to several millimeters, while the electrode separation remains less than 102 cm, as required for nanosecond response time. Data are presented for a Schottky barrier photodiode constructed on a multiply reflecting silicon base wafer. It is shown that the long-wavelength response is considerably extended in such structures without a corresponding sacrifice in high-speed response. The development of efficient and powerful lasers at 1.06 p has stimulated interest in detectors which operate at this wavelength. In typical silicon photodiodes, for detecting 1.06 p radiation, the requirements for high speed and high sensitivity are mutually exclusive. Since the absorption coefficient is only 25 cm-', a lo-'-cm path length is required to absorb 92 pct of the incident 1.06 p radiation. If the electrode separation is greater than 10 cm, however, the carrier transit time will be greater than 1 nsec. This problem can be solved by allowing the incident light beam to make multiple passes between the electrodes. The optical path length can then be extended to several millimeters, as required for complete absorption, while the electrode separation remains less than 10' cm, as required for nanosecond response time. In a typical photodiode geometry, one ohmic contact and one rectifying contact are formed on the two opposite surfaces of a base wafer, and the wafer thickness determines the electrode separation. The objective of the multiple reflection design is to allow all 1.06 p radiation to enter the detector front surface and to form the back detector surface so that no 1.06 radiation can exit. Total internal reflection at the back detector surface is well-suited for light trapping of 1.06 p radiation because the relatively large dielectric constant of silicon leads to a critical angle of 16.5 deg for total internal reflection. LIGHT TRAPPING It is well-known that, as light passes from one medium such as air into another medium such as glass or silicon, the angle of refraction is always less than the angle of incidence. In the limiting case, where the incident rays approach an angle of 90 deg with the normal, the refracted rays approach a fixed angle +, beyond which no refraction is possible: this is called the critical angle. It follows from Snell's law that where = critical angle, n - index of refraction of air, n' - index of refraction of the medium. Applying the principle of reversibility of light rays, all internal angles of incidence greater than +, will produce total internal reflection and "light trapping". The index of refraction of silicon at 1.06 p is 3.5,' and the critical angle is thus 16.5 deg. Fig. 1 shows these relationships for silicon. This very small critical angle in silicon is significant because all incident angles between 16.5 and 90 deg will produce total internal reflection and "light trapping". This effect can be implemented with a "prismlike" geometry, so that incident light can be introduced into the sample without loss and "trapped". PHOTOSIGNALS A precise knowledge of the absorption coefficient at 1.06 in silicon is of critical importance to the design of fast and efficient silicon photodiodes for 1.06 radiation. Dash and newman2 show a value of 25 cm-l, and our measurements have corroborated this value. Assuming that the collection of photoinduced minority carriers is perfect, the quantum efficiency of a photodiode is dependent only on the absorption coefficient. It then follows from Lambert's law that where QE is the quantum efficiency in pct, a is the absorption coefficient, d is the optical path length, and the reflectivity at the surface is assumed to be completely suppressed by an optical interference layer. Fig. 2 gives the maximum quantum efficiency for 1.06p radiation of a silicon photodiode with optical path length d, using Eq. [2]. The ultimate response time of a fully depleted photodiode to an incident light pulse can be considered to be the arrival times of all photoinduced carriers at the contacts, i.e., the minority carriers at the junction interface and the majority carriers at the oppo-

Jan 1, 1968

By D. L. Gardner, H. L. Barr

The following report covers the history of the development of the mine, present equipment, methods and costs of mining and milling. In addition, a description of the ore deposit is given with emphasis on the origin of the fractures, mode and types of ore occurrence, and mechanics of granite emplacement. An endeavor has been made to present a complete and accurate statement of the San Mauricio mine, the highest grade gold mine in the Philippine Islands. Credit is gratefully acknowledged to the mine staff for descriptions and details regarding their particular field of work. All analyses were made by Mr. T. A. DeVore, head chemist, San Mauricio Mining Co. Messrs. Edward Wisser, J. E. Fyfe, A. F. Skerl and W. B. Meek, geologists, have contributed geologic information and ideas, for which thanks are extended. The Executive Committee of Marsman and Co., Inc., Managers of the Company, has kindly given permission for publication. Mr. J. B. Stapler, Division Manager, Marsman and Co., has had the courtesy to read the manuscript and to give critical and helpful suggestions. Location of Area and Scope of Work San Mauricio Mining Co. controls a group of 113 claims that lie immediately north of the town of José Pafiganiban (formerly Mambulao), Camarines Norte, Luzon, P. I. (Fig. 1). Exploration work commenced in the spring of 1934; active development began in the fall of that year and has continued to the present date. Mill construction was begun Ocl,. 15, 1935, and production started March 10, 1936. Total production to June 1, 1939, is P10,499,105.15 ($5,249,552.57).

Jan 1, 1941

By D. L. Gardner, H. L. Barr

The following report covers the history of the development of the mine, present equipment, methods and costs of mining and milling. In addition, a description of the ore deposit is given with emphasis on the origin of the fractures, mode and types of ore occurrence, and mechanics of granite emplacement. An endeavor has been made to present a complete and accurate statement of the San Mauricio mine, the highest grade gold mine in the Philippine Islands. Credit is gratefully acknowledged to the mine staff for descriptions and details regarding their particular field of work. All analyses were made by Mr. T. A. DeVore, head chemist, San Mauricio Mining Co. Messrs. Edward Wisser, J. E. Fyfe, A. F. Skerl and W. B. Meek, geologists, have contributed geologic information and ideas, for which thanks are extended. The Executive Committee of Marsman and Co., Inc., Managers of the Company, has kindly given permission for publication. Mr. J. B. Stapler, Division Manager, Marsman and Co., has had the courtesy to read the manuscript and to give critical and helpful suggestions. Location of Area and Scope of Work San Mauricio Mining Co. controls a group of 113 claims that lie immediately north of the town of José Pafiganiban (formerly Mambulao), Camarines Norte, Luzon, P. I. (Fig. 1). Exploration work commenced in the spring of 1934; active development began in the fall of that year and has continued to the present date. Mill construction was begun Ocl,. 15, 1935, and production started March 10, 1936. Total production to June 1, 1939, is P10,499,105.15 ($5,249,552.57).

Jan 1, 1941

By M. H. Caron

BASIC U. S. Patent 1,487,145 on ammonia leaching of nickel ores was issued to the author on March 18, 1924. Equivalent patents in other countries were obtained later. The Dutch Syndicate Brikcarbo became interested in the process in 1935; and a couple of years later the late Dr. H. Foster Bain sent samples of Surigao laterite iron ore to Delft and witnessed tests made there on this material for the Philippines Commonwealth. As a result, the author was asked in April 1940 by Dr. Bain to go to the Philippines to erect and take charge of a pilot plant for the process. The World War prevented carrying out this proposal. The Dorr Co. also became interested in the process at about the same period. The investigations by the Freeport Sulphur Co. on the process as applied to the Cuban nickeliferous laterites, which resulted in the Nicaro enterprise, and the results of this operation have been well described elsewhere.1,²,³,4,5 This Nicaro plant was, in operation for almost two years, and during this period produced about 10 pct of the world nickel production from laterites containing 1.35 pct nickel. This plant and its operation were war measures and, in view of this, activities were suspended in April 1947. The results obtained fully demonstrated the technical feasibility of the process and its economical aspects on a commercial scale. In this respect, it should be understood that it is probable that improvements may be made by further development, and that there are possibilities for advantageous application of the process to garnierite and similar ores with higher values in nickel than the laterite iron ores at Nicaro. While the articles cited above have given a certain amount of information, no general article containing all the important process data has been pub- lished. Since the process is of more than local interest, a fuller knowledge of the fundamental and practical factors of the method may be welcome to those interested in this new field of metals technology. The author, accordingly, takes pleasure in submitting this article to the AIME as it represents in a condensed form the results of many years of research. The brief outlines of the fundamental and other factors and the explanation of observed phenomena are presented with as little discussion of details as possible, consistent with clarity. It is a special satisfaction to the author to make some contribution of his own in return for the benefits of the many valuable publications issued by the Institute during his thirty years of membership. Ores Adapted for Ammonia Leaching: All nickel and cobalt ores which originate from weathering of peridotites or similar basic rocks having sufficient values are suitable for treatment by the ammonia leaching process after a preliminary reduction under proper conditions. The formation of these deposits was probably as follows: In the course of time the basic rocks were attacked by atmospheric agencies; MgO and SiO2 were gradually leached out, and secondary nickel minerals formed, such as garnierite, a hydrated silicate of nickel and magnesia. These secondary products are, however, not stable. They decompose in a further stage of weathering and ultimately only a relatively small residue of insoluble oxides remains, known as laterite iron ore with a small nickel content and very little cobalt. Under these mantles of laterite, richer nickel values may be found, usually indicated by the occurrence of garnierite. The more the ore is disintegrated by nature, the higher the iron content and the better the nickel extractions that may be expected therefrom. Table I shows extractions that may be expected from different types of ores, assuming treatment of -200 mesh products and that all precautions have been taken for obtaining maximum extractions. As for the distribution of the various nickel minerals and compounds that may be present, great variations may occur from locality to locality as well as vertically in a deposit. From such "run of

Jan 1, 1951

By Bahrein Petroleum Company

In Comodoro Rivadavia, well 8. 132, drilled in zone No. 2, has discovered between 5205 and 5297 ft., the dcepest pool yct found in this field. The oil production in Bahrein for the year 1939 totaled 7,588,554 bbl., a decline of 709,444 bbl. from the 1939 production of 8,297,998 bbl. The production for the first seven months of 1939 remained fairly constant, the daily average by months during this period ranging between 20,000 and 22,000 bbl. per day. The daily average rose in August to the year's high of 23,800 bbl. per day, then dropped gradually to the year's low of 18,787 bbl. per day for November. The daily average for the year was 20,791 bbl. At the end of 1939 there were 59 wells producing and 8 wells drilling.

Jan 1, 1940

By Bahrein Petroleum Company

In Comodoro Rivadavia, well 8. 132, drilled in zone No. 2, has discovered between 5205 and 5297 ft., the dcepest pool yct found in this field. The oil production in Bahrein for the year 1939 totaled 7,588,554 bbl., a decline of 709,444 bbl. from the 1939 production of 8,297,998 bbl. The production for the first seven months of 1939 remained fairly constant, the daily average by months during this period ranging between 20,000 and 22,000 bbl. per day. The daily average rose in August to the year's high of 23,800 bbl. per day, then dropped gradually to the year's low of 18,787 bbl. per day for November. The daily average for the year was 20,791 bbl. At the end of 1939 there were 59 wells producing and 8 wells drilling.

Jan 1, 1940

Recognizing the fact that the problems of the committee named by the Board to prepare the "official ticket" for officers and Directors of the Institute are various and difficult; and desiring to assist this committee by setting forth some of the principles that should guide the committee and some of the qualifications that should be required of candidates, the following instructions are formulated and the Secretary is directed to publish them in MINING AND METALLURGY concurrently with the publication of the names of each newly appointed Nominating Committee and to send a copy to each member of the Committee. Each year the Nominating Committee is to select "official" candidates for eight places, as follows:, (1) President and Director (2) Vice-President and Director (3) Vice-President and Director (4) Director (5) Director (6) Director (7) Director (8) Director

Jan 1, 1939

By R. E. Cech

Metallographic observations on hydrogen-reduced nickel oxide crystals suggest that nucleation of nickel occurs at structural singularities in the oxide. The fully reduced structure contains micron-diameter, worm-like voids occupying 40 to 50 pct of the volume. The crystallographic orientation relationships between nickel oxide and nickel resulting from oxide reduction are recorded and discussed. THE process of reduction of oxide to metal is one of considerable complexity involving a chemical reduction reaction, mass transport of reducing agent to the point of reaction and of reaction product away from it, and finally a transformation whereby metal atoms released from the oxide rearrange to form a stable reduced phase. In addition, nucleation of the reduced phase affects the overall reaction kinetics. Thus far only the thermodynamic aspect of reduction has received the attention warranted by the importance of

Jan 1, 1960

By AIME AIME

Adjustable Pyrometer-Stand. By L. W. BAHNEY, xxxvii, 33. Agency of Manganese in the Superficial Alteration and Secondary Enrichment of Gold-Deposits in the United States. By WILLIAM H. EMMONS, xlvi, 767. Application of Descriptive Geometry to Mining-Problems. By JOSEPH W. ROE, xxxix, 173. ARNOLD, C. EVERARD. The Giroux Shaft at Kimberly, Nev., xlii, 461. BAHNEY, L. W. An Adjustable Pyrometer-Stand, xxxvii, 33. BALL, SYDNEY H., and SHALER, MILLARD K. Mining-Conditions in the Belgian Congo, xxxix, 253. BEALS, ROGER L., and TWEEDY, GEORGE A. Cyanide-Plant and Practice at the Minas del Tajo, Rosario, Sinaloa, Mexico, xxxviii, 123.

Dec 1, 1910

By K. Osseo-Asare

The thermodynamics of solid-aqueous solution equilibria up to 200°C In the systems Me-NH3 H2 0 (Me=Cu, Ni, Co) are summarized with predominance area diagrams generated with the DIAGRAM computer program. The implications of the diagrams to ammonia hydrometallurgy are discussed.

Jan 1, 1981

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