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By Joseph W. Richards

ALTHOUGH bad grammar, the above query is probably, at the present moment, good sense. Why was the Institute started and why does it continue to exist? The small group of men who worked out the original idea felt keenly the necessity of mining engineers and metallurgists getting together in order to discuss their professional problems. That necessity still exists but it does not strike the present generation of engineers so keenly because they have always had the Institute: they do not know what it is to be without it. The Institute is a great graduate school of mining and metallurgy. All of its members who have something to say worth saying are the teachers; all the rest may be learners or critics. No university or technical school can match the experience and information which the authors of its papers possess, no institution of learning has a body of potential listeners so extensive and so vitally interested.

Jan 1, 1921

By S. A. LoPilato, J. T. Smith

SEVERAL techniques have been evaluated for cooling the throat area of rocket-nozzle inserts to prevent erosion or fracture of the inserts during exposure to high operating temperatures and pressures. Self-cooled composites, such as infiltrated tungsten, have shown considerable promise for these applications. These composites can be fabricated by infiltrating the refractory matrix with a lower-melting metal or non-metal which is insoluable in tungsten. During firing, the lower-melting substance undergoes a series of continuous endothermic phase changes which absorb sufficient heat to maintain the nozzle matrix material at or below a safe operating temperature. At present, the state-of-the-art has reached a point where the refractory matrix density and microstruc-ture have been established as the critical parameters to be controlled for optimum self-cooled performance.'" Nondestructive testing has been utilized to ensure that porous tungsten billets were of uniform density and free from cracks or other defects prior to fabrication into rocket nozzle inserts. Ultrasonic-velocity techniques have been employed because of their reliability and reproducibility. The purpose of this note is to present and interpret the test data developed for porous tungsten matrices. For evaluation purposes, tungsten powders with Fisher subsieve sizes of approximately 4 and 18 p have been obtained for study from four commercial sources: the General Electric Co., Wah Chang Corp., Fansteel Metallurgical Corp., and Kennametal, Inc. Porous tungsten matrices were fabricated from the powders by hot pressing in induction-heated graphite die assemblies. Typical billets ranged from 3 in. diam, 2 in, high to 5 in. diam, 5 in. high. The ultrasonic-velocity measurement technique employed was through transmission, pulse echo at a frequency of 1.0 mc using matched barium titanate crystal transducers. The testing equipment included a pulsed ultrasonic generator, an amplifier, a specimen holder, and an oscilloscope, as shown in Fig. 1. The porous tungsten thickness was measured to i 0.0005 in, with precision micrometers while the oscilloscope achieved 0.02 psec time measurement accuracy. The time for a sound wave to pass through the billet, the bulk wave velocity, was calculated to 0.5 pct using Eq. [l]: V-} where V = bulk wave velocity, in. per psec, T = specimen thickness, in., and / = time, psec. To develop inspection standards, the bulk density of a porous tungsten billet was determined by the ASTM water-immersion technique.3 The ultrasonic-velocity measurements were completed at seventeen positions for each billet and averaged to develop a characteristic standard velocity for a particular tungsten powder at several density levels. A plot of ultrasonic velocity vs density is presented in Fig. 2 for six different tungsten powders. This graph has been established as

Jan 1, 1967

By J. W. Galpin, V. L. Minear, W. D. Owsley, F. C. Sturges, B. H. Mott, R. H. Allen, W. W. Weigel, R. E. Moeller

By definition the word "grout" means a thin mortar, or a kind of plaster or cement, and "grouting" means to fill up or finish with grout. The words "cement," "plaster" and "mortar" mean a substance that is used in a soft state which subsequently hardens. Thus, grouting is the filling of void space with a substance that hardens. Construction cements are the most common substances used, either by themselves or in mixtures, but the term grouting is applied quite correctly when other substances such as plastics and certain chemicals are used. Also, the use of the term grouting to cover the filling of voids with materials that do not actually become hard, such as the flotation tailings used in grouting in the southeast Missouri lead district, should be considered correct, as some stiffening does take place and, anyway, it is a better descriptive term than any substitute. Engineers are interested in grouting because some of the materials with which they must work contain voids, and certain conditions can be improved if these voids can be filled with something solid and permanent. Grouting is done to accomplish several purposes: I. To stop the passage of fluids and gases, 2. To cement materials together to make them stronger, and 3. To prevent consolidation of materials by filling void space with something solid as a replacement for the air and water that could be forced out under load. The construction industry uses grouting extensively for all three purposes. Grouting is used to stop water percolation under and around dams. It is used to control water flow in tunnel driving and in shaft sinking. It is used to improve foundation conditions under civil engineering structures by permanently filling void space and thereby reducing settlement, or by cementing broken rock together and increasing its supporting strength. The oil and gas industry does a lot of grouting, primarily to stop the passage of gases and fluids. The search for oil at increasingly greater depths has meant greater investment per well, and the oil industry has spent large sums on development of improved drilling methods. This

Jan 1, 1949

By W. M. Corse

AT THE TURN of the century the nonferrous alloy industry was awakening to the value of scientific metallurgy, and brass foundries and rolling mills began to establish their own research laboratories for scientific research and control. As the industry grew and its scope broadened it became apparent that an organization was needed that would stand in the same relation to the nonferrous industry as the American Foundrymen's Association did to the iron foundry business. The brass founders' group of the foundrymen's association discussed the matter and it was finally decided to appoint a com- mittee to draw up a constitution for a new organization to be known as the American Brass Founders' Association. Charles J. Caley was chairman and Dr. Richard Moldenke secretary of this committee. The object of the organization as defined by the constitution was the study of the technological development of alloying and founding non- ferrous metals, and furthering the advance of nonferrous metallurgy and the standardization of materials and operations in cooperation with the Bureau of Standards and engineering societies.

Jan 1, 1932

By AIME AIME

The following acts of the Directors are reported for the information of members:¬ At a meeting held November 3, 1905, Messrs. Henri Le Chatelier, of Paris, France, and Andrew Carnegie, of New York, N. Y., having been nominated by a large number of members, and recommended by unanimous vote of the Council, were unanimously elected Honorary Members, in recognition of their distinguished services to the arts and professions represented by the Institute. At a meeting held February 7, 1,906, Dr. James Douglas, of New York, N. Y., having been" nominated by a large number of leading members, and recommended by unammous vote of the Council, was unanimously elected an Honorary Member, in recognition of his distinguished services to the practice and the literature of mining and metallurgy, his zealous and loyal devotion to this Institute, his fraternal generosity towards professional colleagues, and his effective advocacy, by public utterance and private example, of the free communication of technical knowledge and experience. At the same meeting, By-Law IV., which now authorizes the Secretary to appoint an '1 Assistant Editor," was amended by substituting the words, " Assistant with the title of Editor." At the same meeting, the resignation of Mr. Theodore Dwight, as Assistant Secretary and Assistant Treasurer of the Institute, was presented and accepted, and the Secretary was instructed to express to Mr. Dwight the thanks of the Board for his loyal and efficient services, and its regret that he could not continue in that position. . [SECRETARY'S NOTE.-Mr. Dwight's resignation, dictated solely by the demands of private business, covers only his immediate management of this office. He is still a Director and Councilor, and a representative of the Institute in matters connected with the new Carnegie Building, etc.-R. W. R.] At the same meeting, the Secretary and the Treasurer reported respectively their appointment of Mr. Henry WT. B. Howard as Assistant Secretary and Assistant Treasurer, to fill

Mar 1, 1906

By H. S. Geismer

INTRODUCTION. THERE are three general methods available for obtaining commercial brown iron-ore : hand-screening; washing; and washing and concentrating. Hand-screening has produced a large tonnage of ore in the past, but is rapidly falling into disuse, except as a preliminary step, largely because modern furnace-practice requires all foreign material to be separated from ores before they are delivered to the furnace, and hand-screened ores can rarely be made to fulfill that requirement. Another argument against hand-screening is, that the waste-pile often contains as much ore as the screen recovers. The operation known as hand-screening consists of throwing the ore-bearing material against a stationary inclined screen of 0.5- to 0.75-in. mesh, similar in construction to the screens employed in sand-pits. The recently-prospected brown-ore deposits of Cuba seem to offer possibilities for hand-screening not possessed by the average American deposit, since these ores are not associated with worthless clays. Washing, and washing and concentrating, may be discussed together, since concentrating is never practical on brown iron-ore, except to treat ores that have already been washed. (Strictly speaking, washing might be classed as concentrating, but it is never so designated by brown-ore men.) The various steps of removing ore-bearing material and converting it into ore suitable for blast-furnace use, may be grouped under five heads: loading for transportation ; transporting ; feeding into the washer; washing; and concentrating. These five subjects will be considered in consecutive order. Each of these successive steps may be accomplished in a number of different ways, the choice depending entirely upon the character of the ore-bearing material to be treated.

Aug 1, 1911

By E. H. Bunce

CONTINUED progress in zinc metallurgy has been shown during 1933 by the adoption of new methods as well as the modernization of old processes and equipment, and by the initiation of new fields of activity for future advancement. The use of suspension roasting continued to grow as its advantages and adaptability became increasingly, apparent. The process developed by the National Smelting Co., Ltd., several years ago, of completely roasting on large sintering machines with utilization of the gas for acid manufacture has worked so successfully that an additional machine was installed during the year. At both the Swansea and the Avonmouth Works all of the ore for smelting is now roasted on the large sintering machines, thereby completely eliminating the old hearth-roasting furnaces. Work continued on obtaining partial purification of zinc ores from lead and cadmium by close control of conditions on the sintering machine, and in a few instances by chlorine additions to the ore before sintering. Ores so treated were either partially roasted or com-

Jan 1, 1934

LIST OF MEMBERS, ASSOCIATES AND JUNIOR ASSOCIATES ALPHABETICALLY ARRANGED ||Abad, Leopoldo F, College of Min, Univ of California Berkeley, Cal '23 ||Abarquez, Ramon F, Met, Bureau of Seience Manila, P I '24 ||Abbey, Robert Graham, Student, Case School of Applied Science Cleveland, Ohio '21 Abbort, A N , Mines Supt , Mazapil Copper Co , Ltd Concepcion del Oro, Zacatecas, Mexieo '23 Abbott, Clarence E , Gen'l Supt , Iron Mines Div , Tenn Coal, Iron & R R Co , 1405 Minnesota Ave , Bessemer, Ala '04 Abbott, Louis Benjamin, Chief Engr, Consolidation Coal Co, Elkhorn Div Jenkins, Ky '15 Abbott, Robert R , Met Engr , Peerless Motor Car Co Cleveland, Ohio '12 ||Abbott, Wells Osborn, Ray Consolidated Copper Co Hayden, Ariz '23 Abeel, George H, Jr, Cons Min Engr 4812 W 17th St, Los Angeles, Cal '18 Abel, Albert E, Asst to Pres, Valley Mould & Iron Corpn Sharpsville, Pa '19 Abeloff, Miran S Address Wanted '21 Abernathy, G E, Kansas State Teachers College Pittsburg, Kans '20 Abey, Hiroshi, Min & Met Engr. Takata & Co, 2 Yeirakucho, Niehome, Kolimachi-ku, Tokyo, Japan '17 ||Aborn, Robert H 24 Groveland St, Auburndale, Mass '19 Abouchar, Sylvain Sley, Min Engr & Geol , Care of S H Sekaly, 13 Rue El Nimr, Cario, Egypt '17 Abraham, Arthur W 1828 N Alexandria Ave, Los Angeles, Cal '20 Abrahams, A. I 115 East 82nd St. New York, N Y '14 ||Abrahamson, C. Walter, Min Engr, Brule Min Co Stambaugh, Mich '21 Abrams, Charles Jackson Columbia Bldg, Spokane, Wash '21 Abrams, David H, Min Engr, S E Dickey & Co, 809-11 Johnstown Trust Bldg, Johnstown, Pa '20 Acker, E 01C, Met 128 East Washington Lane, Germantown, Philadelphia, Pa '86 Acker, William L, Diamond Drill Contractor Mears Bldg, Scranton, Pa '18 Ackerman, Ernest R, Pres Lawrenee Portland Cement Co Plainfield, Union Co, N J '15 Adachi, Jinzoo 11 Shiba Park, Shiba-Ku, Tokyo, Japan '88 Adachi, Yuich, Meeh Engr, Anzan Steel Works, Anzan, South Manchuria, China, (Via Dairen) '21

Jan 1, 1923

By William B. Plank

AGAIN the records show an unprecedented enrollment of students in the mineral technology schools of the United States and Canada. In the current year, 1938-'39, 9619 students were resident in the 53 schools of the United States arid 1014 in the six schools of Canada. These data are from my fifth study of the mineral technology schools of the United States and Canada. the last previous study having been made for the year 1936-'37. The undertaking as previously was made under the auspices of the Mineral Industry Education Division of the A. I. M. E. The data or, the various schools were collected in the same way as for former studies.

Jan 1, 1939

By H. B. Bell, P. C. Lidster

A study has been made of the use of ThO2-Y2O3 solid electrolytes to determine activity of chromium in Fe-Cr and Ni-Cr alloys in the temperature range 1300° to 1700°K. This method has been shown to give results which agree with the best vapor pressure measurements. SEVERAL investigations1"5 have been made of chromium activities in Fe-Cr alloys. Most of these have been made by vapor pressure measurements using knudsen cell techniques while one has been made using gas equilibration with H2/H2O gas mixtures. In the present investigation electromotive force measurements have been made on this system using a thoria yttria solid electrolyte. This system was -chosen to establish the technique of measurement at low oxygen potentials, before extending it to Fe-Ni-Cr alloys. The cell used was Pt Cr • Cr2O3 ilThO2 • Y2O3 llalloy • Cr2O3 IPt Since the oxygen pressure of the chromium-chromic oxide mixture lay in the range 10"19 to 1027 atm in the temperature range investigated, thoria yttria electrolytes were used. It was soon found during the investigation that considerable care was required to prepare satisfactory electrolytes and a study was made to find the best method of preparing pellets of TI1O2-Y2O3 solid solution of as near theoretical density as possible. Various compositions in the range 2 to 15 mole pct Y2O3 were studied but the experimental measurements were made with electrolytes containing 4 to 5 pct Y2O3. The method of preparation finally adopted was to use thorium oxalate and yttria as raw materials. The thorium oxalate was decomposed at 900°C for 6 hr to give a reactive powder. This powder was then mixed with the appropriate amount of yttria and ground in an agate mortar for about 4 hr. The powder was moistened with absolute alcohol as a lubricant and pressed in a metal die at a pressure of 7 tons per sq in. The pellets were then heated at 1100°C for 24 hr followed by 24 hr at 1250°C. After this firing cycle the material was reground and repelleted and again fired at 1100° and 1250°C followed by heating for 7 days at 1600°C. It was found in later experiments that a further firing of 4 hr at 2000°C improved the density further and gave pellets of only 2 pct porosity. After firing, the pellets were polished on emery paper and finally with the 2 µ diamond paste. The polishing was followed by a final firing of 24 hr at 1500°C. Investigation showed that this final treatment minimized reaction between the electrolytes and chromium oxide. It was believed that this was because of a lowering of the surface energy of the electrolyte surface. Two types of investigation were carried out to check that the pellets were satisfactory oxygen ion elec-

Jan 1, 1970

By AIME AIME

THOUGH the Annual Meeting of the Institute-officially numbered 158 on the records was delayed a bit at the start by low steam pressure on the locomotives bringing members to New York, the crowd that finally arrived more than lived up to expectations, and the technical program had few difficulties because of absent authors or lack of competent discussers. The transportation difficulties were occasioned by the fact that Monday, Feb. 15, was the third coldest day in the 72 year history of the New York Weather Bureau, the official temperature being 8 below zero. The New York Central's premier train, the 20th Century, due at 9:30 a.m., arrived about 6:30 p.m., and the Commodore, another crack train from Chicago, was about equally late.

Jan 1, 1943

Frank Clemes Smith, Deadwood, 8. D. (communication to the Secretary): The reading of Mr. Chance's interesting paper suggests a few ideas relative to his discussion of certain Black Hills gold-ores. Mr. Chance refers to his examination, in 1897, of " the (Carboniferous) limestone plateau-country which encircles the central area of the Black Hills," and says that " it had been generally assumed that the mineralization of this formation was confined to the northern area;" further, that he "found, however, a general mineralization, extending in zones or belts throughout the region," and that the ores, being more or less specially

Jan 1, 1900

Since I have had the pleasure of watching the development of this process very closely, I feel that I ought to say a few words on the subject, although I cannot add much to what Mr. Roe has already said. I wish, however, to bear witness to the hard work, persistence and skill which have been exercised during the past two years, and which have so well deserved the success attained. Those of us who remember the history of the past efforts in this line, such as the rotary puddlers, in which also some of us had a part, can easily appreciate the problems involved, and may well be skeptical as to the outcome. Such, at least, was my frame of mind when the process first came under my notice. Now, after having seen every heat, but three, of the many made, it really seems to me that a process and plant for the mechanical puddling of iron has at last been developed which is practical, economical and successful. Of course I do not mean by this that either the process or the machines are developed to their highest point, technically or economically, but that, in my opinion, these goals are in plain view, and that the difficulties which remain are such as will be overcome by developing the skill of the operator through practice ;

Jan 1, 1903

By Samuel Daniels

THE Al-Cu-Ni-Mg alloy is much benefited by heat treatment and, in such con¬dition, is preferable to the Al-Cu-Fe-Mg alloy either as cast or as heat-treated, when both are reheated to temperatures of from 400° to 600° F. and compared, cold, with respect to strength and to hardness. The main differences between the alloys do not arise until the reheating temperature exceeds 400° F., above which they gradually soften. This softening is characterized metallographically by the appearance of intragranular precipitate. The Al-Cu-Ni-Mg alloy is weakest and least hard after being reheated at 600° F., the AI-Cu-Fe-Mg alloy at about 700° F. The former starts to reharden at 700° F., the latter at 800° F. There is a tendency for both alloys to lose strength and hardness with prolongation of time at the reheating temperatures of 500° and of 700° F. The Al-Cu-Ni-Mg alloy is considerably stronger and harder than the Al-Cu-Fe-Mg alloy when both are heat-treated and reheated for long periods of time at 500° and 700° F. Although the latter can be made harder initially than the AI-Cu-Ni-Mg alloy by suitable quenching and aging, heat treatment, in general, favors the retention of this initial (strength and) hardness after reheating to a much greater degree in the Al-Cu-Ni-Mg alloy. The percentage of elongation of the two materials in any condition is very small. CERTAIN aluminum alloys have been used for pistons and other parts operating at temperatures up to 650° F. because of their lightness, high thermal conductivity and specific heat, fair strength and hardness at elevated temperatures, excellent machineability, and moderate resistance o corrosion. In the piston, the inertia forces and the bearing loading and with this the vibration are decreased. The piston head functions at a lower temperature (about 200° F. below one of cast iron), so that, because of the lessened tendency toward carbonization and detonation, higher compression ratios may be used. On the other hand, the aluminum alloys do not have the wearing and bearing qualities of cast iron; also they have a large coefficient of expansion, allowance for which must be made in the design.

Jan 2, 1926

By Milton E. Wadsworth, Edward M. Eyring

BETTER understanding of solid surfaces and their associated adsorption products is of both academic and practical value. The study of detergents and their behavior in cleaning surfaces is fundamentally related to the nature of the products adsorbed and their ability to compete for certain surfaces. Similarly in flotation, the nature of the adsorbate before and after adsorption is basic to clear understanding of the process. The recently developed pellet technique1,2 employing infrared spectroscopy provides a powerful tool for the study of solid surfaces. Absorption bands, which are infrared-active, may be observed for adsorbed products. Also any changes in the surface substrate that occur as a result of adsorption may be detected by means of differential spectra. In applying the pellet technique to solids of large surface area, French and his coworkers3 have surveyed the adsorption of organic flocculants on clay minerals, oleic acid on fluorite, and ammonia on cracking catalysts. Recent work on application of differential infrared spectroscopy to the study of solid surfaces' has demonstrated that the difference between a sample and a reference can be obtained with double-beam instrumentation. In this way displacement of surface products, adsorption of new products, and differences in the substrate, if any, may be detected. Experimental Procedure: Potassium iodide pellets were used in this study, prepared from recrystallized analytical reagent grade KI. Grinding was carried out in a Fisher mechanical agate mortar. Two-gram plates containing the solid under study were pressed in a special evacuated die constructed in the laboratory at the University of Utah." Concentration depended on the solid in question. Zinc sulfide and willemite are sufficiently transpar- ent in the infrared region for concentrations as high as 20 mg of mineral in 2g of KI to be used. Zinc oxide is even more transparent, permitting concentrations as high as 60 mg in a 2-g plate. For non-differential operation, however, much lower concentrations (2 to 10mg/2g KI) had to be used. Spectra were obtained on a Per kin-Elmer 21 double-beam recording infrared spectrophotometer. A sodium chloride prism was used giving a spectral range of approximately 2 to 15 v wave length. For differential runs a resolution of 1000 was used and the scanning speed was controlled commensurate with instrument response. The response was checked continuously and each spectrum was repeated several times. For nondifferential runs a resolution of 927 was used. Zinc oxide used was analytical grade oxide fume. The zinc sulfide was precipitated from solution with analytical grade zinc sulfate and sodium sulfide. The precipitate was washed and centrifuged several times and dried. Before use the precipitate was washed in dilute HCl and then treated with saturated NH4Cl to remove any bulk oxides and sulfates. X-ray patterns of the precipitate were comparable to that of the natural mineral sphalerite. The precipitate was much more satisfactory than finely ground natural ZnS because of its very large surface

Jan 1, 1957

G. M. TAYLOR,* Colorado Springs, Co1o.-I do not think the plan outlined in this paper would work at Cripple Creek. Most of our men have had a pretty good education. The Cripple Creek district is a lessee district-I do not think there is one mine operating in Cripple Creek to-day that does not have the leasing system. We have as many men leasing on our property as we have mining and every plan who is working for wages is looking for n lease-everyman has mined for him- self, he has been his on7n boss on n lease, either on our own property or

Jan 1, 1919

By John M. Lovejoy

CURRENT production of petroleum on such a vast scale presents many interesting problems- the solutions of which are important not only to those directly interested in the business, but to the nation as a whole. The industry is relatively young. Until the discovers of the Lucas gusher at Spindletop in 1901 petroleum production had not exceeded 60,000,000 bbl. per year compared with 1,100,000,000 bbl. in 1936. In 36 years then, the modern oil business, production, transportation, refining, and marketing has developed. I will first present a brief history. of oil production as a background for consideration of the present situation.

Jan 1, 1937

By JOHN D. SUMMER

THE Premium Price Plan for copper, lead, and represent, the approach of the Office of Price Administration to the urgent of wartime problem of securing increased output of nonferrous metals. Some of the problems encountered in too operation of the Plan and the considerations which led to it?s adopt it will here he reviewed. The Plan provides for extra payment by the Metals Reserve Co., to mine operators who exceed established quotas of production. Producers are thus directly, compensated for the higher costs of working ores that are not commercial at the ceiling price, although the metal obtained from these ores is directed into regular channels of distribution at the established prices for copper, lead, and zinc. Higher-cost metal is thus available to fabricators and to the government agencies at the regular ceiling price and the dual objective of increased production and table pries is achieved.

Jan 1, 1943

By Philip S. Mathews

THE tremendous stimulus given to the mining industry by the gold and silver policy of the present administration has found the capital market for mines ill prepared to afford practical means of financing. Particularly has this been true of the host of abandoned high-cost producers and prospects which increased gold and silver prices have made potentially profitable. In a comparatively short time, experience has demonstrated abundantly that valuable properties have frequently failed to secure capital, while questionable properties have drawn to themselves and their promoters more of the public moneys than their prospects justify. Singularly enough the fault is usually attributable to faulty financing. Discussion and study of this problem are vital to the industry.

Jan 1, 1936

By R. T. DeHoff

A theoretical development is presented which reformulates Fick's first law for diffusion in the solid state. The diffusion flux of component i in a multi-component system, Ji, is related to its local concentration, ci, and local jump frequency, ri : where a is a geometric factor and d is the jump distance. The product, ciri , is defined as the local concentration of atomic jumps for component i. The analog to Fick's second law is also derived. A solution to this equation is presented, which permits the experimental determination of the variation of atom jump frequency with composition in multicomponent systems. HISTORICALLY, the description of diffusion in the solid state has been presumed to be best approached as an application of more general diffusion laws, known as the phenomenological equations. These equations relate the flux, Ji, of the various components, expressed in atoms, grams, or volume, to the driving force involved, expressed as either a compositional or chemical potential gradient, sumption that the flux is simply proportional to the driving force is the foundation of this approach. The phenomenological equations take the form: where the concentration gradients are assumed to be the driving force, and: if the chemical potential gradient is taken as the driving force. The coefficients Dij in Eq. [1.] are the "diffusion coefficients"; the elements of the corresponding matrix in Eq. [2], the Mij, are called the "mobilities". Eqs. [I] and [2] may be considered to be definitions of these phenomenological coefficients. A formidable body of literature has been generated about these equations; this literature dates back to their original formulation for the simplest case of binary diffusion in a fluid, by Adolf Fick, in 1855.' This description has been shown to be self-consistent. However, the "constants of proportionality", the Dij or ,Mij, are not constant: they vary with composition in all but the simplest systems. Even in the case of tracer diffusion, wherein it can be shown that the diffusion coefficient is constant, the mobility, which is considered in irreversible thermodynamics to be the more physically meaningful quantity, varies with the concentration of the tracer involved.' In more complex systems, it is necessary to evaluate the entire matrix of phenomenological coefficients, as a function of composition, in order to describe diffusion locally. Further, in order to determine this matrix experimentally, it is necessary to produce diffusion couples that have different sequences of compositions; the matrix may be evaluated only at points where these "composition paths" cross.* Finally, and perhaps most

Jan 1, 1969