Search Documents

By E. P. JENNINQS

(Cleveland meeting, October, 1912.) LARGE deposits of titaniferous iron-ore occur at Caribou, an old silver-mining camp in Boulder county, Colo., 17 miles west by south of Boulder, and a few miles northwest of the tungsten-mines. Professor Regis Chauvenet 1 published a part analysis of the ore many years ago, but gave no description of the wall-rock. Caribou hill, which contains both the silver-bearing veins and the iron-ore deposits, is a low dome of gabbro surrounded by the Archaean schists and gneisses of the Front range of the Rocky mountains, the peaks of which, a few miles west of Caribou, attain an elevation exceeding 12,000 ft. The gabbro stock is roughly elliptical in outline, with approximate diameters of 1 and 3 miles. The crest of the dome is 10,500 ft. above sea-level, and the town and ore-deposits are 500 ft. lower. Outcrops of the iron-ore occur in the town and extend NW. for 2,000 ft., where they disappear under the swampy meadows of Caribou park. Portions of the deposit are covered by drift, but one continuous outcrop is 900 ft. long and from 200 to 250 ft. wide. A second deposit is 0.25 mile south of the town along the eastern slope of the hill. It is not as well defined as the north bed, but is approximately 1,000 ft. long and from 100 to 200 ft. wide. The easily disintegrated ore does not form prominent outcrops, but the outlines of the deposits are readily traced by the large amount of ore fragments that cover the ground. Trenches and pits sunk on the outcrop expose a roughly banded magnetic iron-ore, with pyroxene as the principal gangue-mineral. The Gabbro. This rock was classified in the field as a gabbro from the presence of pyroxene and striated feldspars, and for convenience the field-name will be retained. 1 Chauvenet, Regis, Biennial Report of State School of Mines, Golden, Colo., p. 16 (1886).

Oct 1, 1912

Jan 1, 1881

By A. R. Rosenfield, G. T. Hahn

The effects of adding 0.025 volume fraction of uniformly dispersed Tho2, particles (particle size -380A) to iron have been examined. The two-phase alloy is shown to have a lower transition temperature and higher cleavage stress than either the base metal or a solid-solution alloy (Fe-3Si). Enhanced cleavage resistance is thought to be a consequence of particles limiting the effective slip distance of dislocations and thus the ability of Pile-ups to act as stress concentrations. Further calculations predict that the highest cleavage strengths are attained with uniform dispersions, where the particle size is kept small (-250A) and the volume fraction is relatively large (-2 to 3 pct). ALTHOUGH a fine dispersion of second-phase particles is known to impart strength to an alloy, the possibility that it might also impart ductility has only recently been explored. Outstanding progress has been made in the production of ductile tungsten alloys containing Tho21,2or (Hf, Zr)C,= but the contribution of the dispersion to ductility has neither been optimized nor fully analyzed. The basis for such an analysis has now been developed1,5 and is discussed briefly below. Experiments on iron are also described that attempt to isolate one of the possible ductilizing mechanisms and test its effectiveness. In analyzing these experiments, it is important to remember that cleavage obeys a stress criterion, and that either a lower ductile-to-brittle transition temperature or a higher cleavage stress is evidence of enhanced resistance to cleavage. DUCTILIZING MECHANISMS Slip Blockage. Cleavage fracture of polycrystals may be initiated at the intersection of a slip band (or twin) and a neighboring grain or a large (-1 to 5 µ) particle. The slip band generates a stress concentration at its head, and either the grain boundary fractures, the particle fractures, or cleavage is initiated in a neighboring grain. Experimental evidence for this viewpoint is found in metallographic studies8-8 and from the observation that cleavage is usually preceded by yielding.8-11 The potency of a slip band as a stress concentrator

Jan 1, 1968

By H. R. Fife

AN extended study of dustproofing Freeport-seam coal has empha-sized several fundamental features in the successful treating of bituminous coals. The extent of the exposed surface area and its absorption proper-ties for the dust-retaining film were found to be the most critical factors affecting the efficiency of fly-dust prevention. From recently published screen data and specific surface-area measure-ments on United Kingdom coals, an approximation of the surface exposed by mine-run coal and by 1-in. slack was made. The total surface area exposed by an average ton of this mine-run coal was estimated at 3768 sq. yd., while a ton of 1-in. slack represents a total surface area of 8779 sq. yd. with no additions for porosity. It is important in coal treating to consider that in mine-run coal the fraction above 1/4 in. in size represents 79.5 per cent of the total weight, but only 4 per cent of the total surface, while the fraction below 150 mesh contains 47 per cent of the total surface and only 1.2 per cent of the total weight. Also, one should appreciate that, in a 1-in. slack, the domestic stoker fraction (1 in. to 8 mesh) contains 76.3 per cent of the weight and 8.2 per cent of the surface, while the fraction below 150 mesh represents 3.3 per cent by weight and 54.8 per cent by sur-face area. Wax extraction data on 1-in. to 0 slack from mine-run treated Free-port-seam coal showed that the coating was distributed uniformly as a function of exposed surface; hence, nonuniformly on a weight basis. This distribution of the coating on mine-run coal therefore limits the extent of treating that is desirable on bituminous coal at this point in the preparation. The treatment of Freeport mine-run coal before it reached the tipple gave a 70 to 80 per cent reduction of fly-dust in the tipple, a satisfactory treated commercial slack coal, and an indicated change in the trend of tipple degradation. The premium-treated domestic sizes required a supplemental treatment for complete dustproofness.

Jan 1, 1937

By AIME AIME

THE organization of the Board of Directors was effected Tuesday afternoon in ' executive session. Messrs. Bassett,. Buehler, Cates, Daveler, Eavenson, Eilers, Elliott, Evans, Guess, Lovejoy, Moulton, Rickard, Tally, Turner,, Wraith and Wright being pres¬ent. Messrs. Tally, Bassett, Rickard, Mathews and Cates were chosen to form the Executive Committe with Mr. Tally as Chairman, and Messrs. Krumb, Guess and Moulton for the Finance Committee with Mr. Krumb as chairman. Karl Eilers was reelected as Treasurer and H. Foster Bain as Secretary, after which the Directors adjourned for the usual dinner reported elsewhere. At the open session of the Board, at which in addition Messrs. Allen and McAuliffe were present, the work of organization was continued with appointments to committees as listed herewith. Various actions of the Executive and Finance Committees were confirmed, the budget for 1931 formally approved, the meeting dates for the year adopted, 34 new Members and Associates, 13 Junior Members and 31 Student Associates admitted by election and transfer and 29 resignations accepted.

Jan 1, 1931

By H. W. Highriter

THE method developed and used in this laboratory for the production of metallic uranium of such purity that it is ductile and can be cold-worked to fine wire or thin sheet by rolling has already been described1. It consists, briefly, in the electrolysis of potassium uranous fluoride (KUF5) in a molten bath composed of equal parts of sodium and calcium chlorides. The bath is contained in a graphite crucible, electrically heated to about 775° C., the crucible serving as the anode for electrolysis. The uranium deposits in finely divided form mixed with salts upon a molybdenum cathode suspended axially in the crucible. Upon com-pletion of the electrolysis the cathode is removed and cooled, the deposit broken and leached to remove salts. The metal powder is washed with water and dilute acetic acid and dried in vacuo to reduce oxidation. Suitable amounts are then pressed into pellets and heated in vacuo by high-frequency induction, using a thoria crucible. The uranium melts and flows away from the pellet, leaving a shell, which is largely oxide. In general, this method produced a satisfactory metal, although at times the uranium was not ductile. The investigations recorded here were made to find the cause of this embrittlement. It was known that the metal generally contained carbon, derived from disintegration of the graphite crucible in which electrolysis is conducted, in amounts dependent upon the thoroughness of washing the metal powder. Accordingly, analyses of several samples, both ductile and brittle, were made by combustion and absorption of C02 in Ascarite, using air instead of oxygen to reduce the temperature and rate of oxida-tion. Several of these metals were made with special precautions to reduce carbon content. The results show no relationship between ductility and carbon content in the range investigated (Table 1).

Jan 1, 1935

By Thomas M. Drown

IN a communication to this Institute at the Baltimore meeting, February, 1879,* on the "Determination of Silicon in Pig Iron and Steel," the method recommended was the treatment of the metal with nitric acid until action had ceased, and then evaporating with sulphuric acid until the nitric acid was nearly or quite driven off After filtration of the siliceous and carbonaceous residue, and washing with hot water and hydrochloric acid, a silica was obtained, on ignition, which was quite pure. Since this paper was read before the Institute, we have had large experience with the method, and * Transactions, vol. vii, p. 346.

Jan 1, 1880

By Richard Borg

The partial molal free energy of Cd in each of the four intermediate phases, Cd3 Cu, Cd8 Cu5, Cd3Cu4, and CdCu2 is determined using the Knudsen vapor pressure technique. Measurements are made also within the two-phase regions, and thus the variation in FCd is now known across the entire phase diagram. The absolute values are all less the 2.0 kcal and increase regularly with increasing Cd concentration. The small absolute value of the free energy precludes the possibility of obtaining highly accurate values; nevertheless, the results are compatible with those previously reported for the liquid phase. Additional results are reported concerning the lattice parameters of the 6, E, and b phases. THE elements Cu and Cd combine to form four intermediate phases which are designated* and E and which include respectively the following inter metallic compounds: CdCu2, Cd3Cu4, Cd3 Cu5, and Cd3 Cu. The extent of each phase with respect to temperature and composition is shown in Fig. 1 which is the equilibrium diagram drawn according to Hansen.1 All four phases are brittle, and most probably are true intermetallic compounds. Only the crystal structure of the 6 phase has been thoroughly investigated.2,3 The structure is cubic and isotypic with y brass. The structure of Cd3 Cu has not been previously reported, It is hexagonal with a = 8.11 and c = 8.76 0.02Å and the structure is presently being determined.* The compounds Cd3 Cu4 and CdCu, have been each previously the subject of a single investigation. Cd3Cu, is presumed to be cubic4 with the space group Fd3m, whereas CdCu2 is hexagonal2 with the C14-type structure. Cu2 Cd is found by X-ray analysis to be hexagonat with lattice parameters a = 5.00A and c = 16.17Å. The material appears to be pure Cu2Cd as all reflections could be indexed on the basis of the single hexagonal structure. These values disagree with those of Kripyakevich and coworkers5 who report a = 4.96Å and c = 7.98Å. Their investi-

Jan 1, 1962

By Morgan Walker, C. D. Watson, Reid W. Bond, D. L. Trax

Common practice in the Mid-Continent until recently was to prolong the natural flow of oil wells as long as possible by agitation, and then swab for a short period until the well was put on the pump. Comparatively recently the gas-lift has superseded the swabbing and agitating period and in some cases encroached on the natural flowing life, particularly where it was evident that the potential oil capacity of the well was greater than the gas supply, or lifting medium. The majority of wells are finished with either 6¼, 65/8 or 8¼-in. casing and connected to a separator through a flow line which is usually 65/8 in. The flow line is generally designed to eliminate sharp turns and has reduced the gas-oil ratio and therefore increased the efficiency in a good many instances. Until recently all wells were allowed to flow without restriction against the possible trap pressure until it was deemed advisable to put them on gas-lift. This resulted in a fairly efficient flow during the early life of the well if the well was rather large but was usually inefficient in small wells and in the later flowing life of large wells, on account of the large area in the casing and therefore excessive slippage. Recently, considerable effort has been made to increase the efficiency of small flowing wells by running tubing to eliminate as much slippage as possible. With large wells there is a considerable trend toward back-pressuring, or beaning to find out whether it is possible to reduce the gas-oil ratios and increase the flowing life. The greater number of fields that have been back-pressured have been produced in that manner through necessity, either to restrict production for proration purposes or, in fields producing by hydraulic pressure, to reduce water encroaching. The recent Cromwell sand development in Little River is an example where both back-pressuring by means of high-pressure traps and beans and flowing through tubing were used to conserve gas, reduce the high gas-oil ratio and prolong the flowing life. It

Jan 1, 1930

By K. R. Evans

The deformation mechanisms occurring in polycrys-talline, commercially pure titanium and a Ti-8 pct A1 alloy have been investigated and compared to earlier results by Levine on high-purity titanium single crystals and by Conrad on commercially pure titanium. In accord with Levine, two consecutive deformation mechanisms are observed to exist below 500°K with the transition temperature between mechanisms, Tc, strongly dependent upon interstitial composition. T, is found to be 210°. 375° -430°, and 450°K for alloys A large number of investigations have been conducted to determine the rate-controlling mechanisms of plastic deformation occurring in fcc and bcc metals. Very few investigations of a similar nature have been conducted for hexagonal metals. In fact, until very recently, magnesium is the only hexagonal metal which has been systematically investigated for determination of the rate-controlling deformation mechanisms.1"3 From these investigations, it was concluded that basal slip below 420°K occurs by the intersection of forest dislocations,1'3 while for prismatic slip the Peierls mechanism is rate-controlling at low temperatures with interstitial compositions of 0.024, 0.42, 0.61, and 1.13 at. pct expressed in terns of oxygen equivalents. The low-temperature mechanism is found to be an impurity obstacle mechanism in contrast to Levine's earlier conclusion of the Peierls barrier. Measurement of the activation parameters for deformation and estimation of the force-distance profile of the obstacles show their retarding force to be effective over longer distances from the obstacle as the interstitial composition increases. and thermally activated cross slip at higher temperatures. 2 The potential technological importance of titanium alloys has prompted recent studies of the deformation and fracture characteristics of titanium and its alloys. 4-8 Levine' systematically investigated the low-temperature deformation behavior of high purity titanium single crystals oriented for either basal or prismatic slip. It was concluded that the Peierls mechanism was rate-controlling at temperatures below 210°K, while above this temperature an undefined mechanism was rate-controlling. Conrad 7,8 concluded from an analysis of the composition dependence of the critical shear stress at 0°K and measurement of the activation parameters that the low-temperature deformation of titanium is controlled by an impurity

Jan 1, 1969

By H. P. Allen

THE Achotla mill of the Cia. Minera de Pe[n]oles is of special interest in that it is one of the few still employing the chloridization process. The ore milled comes from the Suriana mine and consists of both oxide and sulphide, from neither of which can the gold or silver be extracted by a simple cyanide treatment. The mill was built in 1927, after several years of study in the development of the process1, and operated from December of that year until October 1930. Operations were resumed in February 1935, and have been continuous since, treating approximately 5000 tons per month, while the mine is getting up to full tonnage of 6500 tons per month. Transportation Of Supplies The property is in Guerrero, Mexico, some 175 km. by airline southwest of Mexico City. The mill site is at Temisco (Fig. I), 8 km. from the Balsas River and 4.8 km. by aerial tram from the mine. At Temisco are the general office, shops, warehouses and laboratory serving both mine and mill. Here sufficient water is available either from a small creek running through the property or from the Balsas River, also convenient and ample storage space for the tailings. With the exception of the mine timber and a few native building materials which may be obtained locally, all supplies for both mine and mill are brought down the Balsas River from Balsas, the terminal of a Mexican National Railway line out of Mexico City. The method of transportation on the river is interesting. Rapids with very fast water are numerous, prohibiting the use of mechanically propelled boats. Those used resemble large, flat-bottomed rowboats some 22 ft. long by 8 ft. wide (Fig. 2). They are manned by two oarsmen sitting in the bow, each handling one large oar, and usually another man in the stern who, with his oar, assists in steering the boat, especially when the rapids are run. From 3 to 7 tons of freight are carried on each boat, depending upon the stage of the water, which governs also the time

Jan 1, 1937

The term metamorphism as commonly used means any change in a rock in either form or composition, from whatever cause. By metasomatism, according to Lindgren, is meant a metamorphism that involves a change in the chemical composition of a rock by the addition or subtraction of substance. Certain types of metamorphism are due to the action of mineralizing solutions, and are closely connected with ore deposition; they form, therefore, valuable guides in the exploration for ore- deposits. Other types of metamorphism are due to regional processes, and are not connected with ore deposition. By dynamo-regional metamorphism is meant a primary alteration of rocks over large areas under conditions of pressure, flowage, and heat. This process produces schists and gneisses from either sediments or igneous rocks. It is thought that there is little migration of minerals or of elements in dynamo-regional metamorphism, and that the changes are due chiefly to recrystallization and rearrangement of original minerals in bands with their major axes oriented normal to the direction of greatest pressure. Under these conditions limestones are commonly altered to marble, and sandstones to quartzite, basic igneous rocks to greenstone or serpentine, while rocks of normal or acid com- position commonly yield the usual types of schist or gneiss. Dynamo-regional metamorphism, extending over large areas, has no connection with mineralizing processes, and is, therefore, no guide to ore deposits; while this process has certain features, such as characteristic mineral associations, in common with contact metamorphism, the results of the two processes may usually be distinguished without difficulty.

Jan 1, 1932

By H. D. Wilde

DURING 1934 conditions in the production division of the petroleum industry were reasonably satisfactory but nevertheless a decided feeling of insecurity existed largely because of the uncertainty of controlling production to consumptive demand. Over-production, especially in the East Texas field, threatened a general collapse of crude prices but in spite of this, posted prices were high. Stimulated by the prevailing posted prices, wildcatting activities were wide-spread. Although a number of small discoveries were made, particularly in the Gulf Coast belt and Oklahoma, no fields of major importance, unless it was the Fitts pool in Southern Oklahoma, were brought in. Meanwhile, the Petroleum Division of the A.I.M.E. continued its activities. It sponsored the collection of production and geological data on both foreign and domestic fields. The data on all but a few producing districts in the world were published in the "Petroleum Development and Technology" volume of the "Transactions" and comprise one of the most complete tabula¬tions of this sort ever published. Work of this kind is being continued.

Jan 1, 1935

By Francois E. Heuze

INTRODUCTION Rock slope stability typically is governed by the geological discontinuities. This stability can be improved by drainage, unloading, adjustment in slope orientation, adjustment in slope angle, and also by reinforcement such as bolts or tendons. This paper addresses the modeling of bolt reinforcement in rock slopes. Most geological discontinuities such as joints have rough surfaces; they dilate during shear displacement. Their shear strength is characterized by two envelopes (Fig. 1); the peak envelope is distinct from the residual envelope when the joints can dilate. If the dilation is restrained transversely, such as with bolts, the normal stress will increase and the joint strength also will increase. It has been demonstrated that this increase may be considerable (Obert et al., 1976). The new normal stress at peak strength is a com- posite function of the properties of the rock mass and of the steel (Heuze, 1979). Hence, the dilation and its resultant effects on joint shear strength must be included in the analysis and design of the reinforcement. We present a model which can be used to perform such an analysis. Early studies of rock reinforcement in mining and civil applications (Lang, 1957 - Panek, 1962 - Osen and Parsons, 1966 - Lang, 19721, did not consider the specific effects of bolts on joint shear strength. In 1973, Heuze and Goodman reported direct shear tests on rough sandstone joints with bolts perpendicular to the joint plane (Fig. 2). The peak shear strength of such joints was greatly in excess of the shear strength of the unbolted joints. The excess

Jan 1, 1983

By AIME AIME

HE State of Utah has an area of 84,990 sq. mi., and like other inland states in the West its population, although steadily increasing, is relatively small. The fact that it is a state possessing vast mineral resources is attested by a careful study of statistics which have been compiled by Federal and State investigators. Some idea of the extent of these resources and the degree of development of a particular state or region may be gained by such a study, but in the case of Utah statistics and other available information fail to portray completely the true extent and value of its existing metallic and non-metallic resources. The State is probably more widely known for its production of metallic ores which has placed it in an eminent position among the metal mining states of the Nation.

Jan 1, 1925

Air-sand Process of Cleaning Coal Discussion of paper by THOMAS FRASER and H. F. YANCEY, presented at the New York Meeting, 1926, and issued, as Pamphlet No. 1561-F, with MINING AND METALLURGY, February, 1926. T. DEVENNY, Edgarton, W. Va.-How near the size of the sand can the coal to be treated be brought? Do you use an 8-mesh coal on that cleaner? J. J. RUTLEDGE, Baltimore, Md.-From the little I have seen of the apparatus in operation, I should say 8-mesh. In my experience in metalmine concentration work, trying to separate different minerals on one jig, sometimes I have succeeded and sometimes not. This apparatus has appealed to me; something of this kind should be useful with the silicates and carbonates of zinc. I think this apparatus has possibilities in metal mining. Recently in our coal field a screen has been introduced for cleaning coal; it is giving excellent service. When I asked the inventor why he did not take it to the metal mines, he said there was a good and sufficient reason, in a patent way. There may be reasons why it would not be applicable for metal mining; but the simplicity of it appeals to me and I cannot see why it could not be so used. T. FRASER (written discussion).-We feel that 8-mesh would be about -the minimum size of coal practicable to treat by the air-sand process. This would depend partly upon the friability of the coal. The more nearly the lower size limits of the coal- approaches the size of the sand, the more .time will be required in screening the sand out of the cleaned coal, which would mean a little more chance of breakage. In regard to the treatment of ores; this would necessitate the use of some heavier mediums than ordinary silica sand, or some other means of making the separation at a higher specific gravity than is required for coal. We are now working on a method of obtaining this effect for the preparation of anthracite coal without resorting to the use of heavier and more expensive material than common sand.

Jan 1, 1927

By E. T. Cox

The peninsula of Florida is remarkable for the uniform character and simplicity of its geological structure. Major Henry Whiting, of the U. S. Army, was one of the first to give an account of the physical features and rocks of Florida, in an article published in 1839, in the American Journal of Science (vol. xxxv., p. 47). He says: " The rocks found in situ are all calcareous, though siliceous boulders are occasionally seen, and nodules of hornstone are here and there mingled with the limestone, which elicit sparks and are sometimes used by the Indians for flints."

Jan 1, 1896

By G. Sachs, S. I. Liu

Introduction In a previous investigation on the effects of repeated strains of large magnitude on the aluminum alloy 24 ST, it was found that the reduction in ductility by straining in tension was partially restored by a subsequent compression.&apos; As illustrated by the dashed line in Fig I,$ the ductility (e~) retained after prestraining in tension by a certain amount (el) and measured in a subsequent tension test is represented by a straight line sloping down under 4s°. If a compression of the same magnitude as the first tension is inserted (€2 = — €1) between prestraining and final testing in tension, such a "balanced" tension-compression cycle yields a ductility considerably higher than that present after prestraining in tension only. The results of these tests can be correlated with those of an investigation on the effects of prestraining in compression.~ As also shown in Fig I, the ductility in subsequent tensile tests decreased with com- pression, at a rate considerably slower than that after prestraining in tension. The above discussed testing conditions can be considered as special cases of a general straining cycle, consisting of first, straining in tension by an amount el, subsequently straining in compression by an amount e2, and finally determining the retained &apos;ductility, e,, in a tensile test. Prestraining in tension is then represented by el > o and e2 = o. Prestraining in compression is given by e~ = o and e~ < o. Balanced cyclic straining is defined by the condition el > o and cz = — 61. In order to obtain further information on the effects of straining cycles consisting of tension and subsequent compression, further tests were made, varying both the tension strain, el, and the compression strain, e2, within extreme limits; el varied between 0.06 and 0.28 and e2 between — 0.008 and —0.h approximately. Apparently, such tests have not been previously performed. They revealed phenomena which have not been recognized to date, The results of the investigation are herewith reported, without attempting to correlate them with internal processes within the metal structure. However, in order to assist in an analysis of this type, the results have been represented in various manners. In addition, further test data on the effects of prestraining by compression were provided by using specimens of various contours (notched specimens) in the sub-

Jan 1, 1949

By Andy B. Wallace

Veins in the Pyramid district of northwestern Nevada occur along steep fractures in Oligocene and Miocene quartz latite tuffs. The vein mineralization is zoned from a central enargite-pyrite zone outward through a complex polymetallic pyrite-tetrahedrite-sphalerite-galena-chalcopyrite-bornite-chalcocite zone, and finally to an outer zone of pyrite and galena. Wall rock alteration includes advanced argillic and sericitic envelopes along veins superimposed on district-wide propylitization. The ore distribution and alteration patterns were probably produced by an increase in pH, a decrease in sulfur fugacity, along with cooling of the migrating hydrothermal fluid.

Jan 1, 1981

By R. T. DeHoff

A theoretical development is presented which reformulates Fick&apos;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&apos;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.&apos; 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.&apos; 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