Search Documents

By James E. Howard

At the request of the Council of the Institute, I have the honor to submit the following remarks upon the Program of Tests under which the current work of the Watertown Arsenal Testing Laboratory is carried on, which comprises, among other items, the tests of steel ingot metal and derivative shapes. The intended scope of the tests may be illustrated by extracts from the descriptive part of the program as submitted by the Laboratory under date of April 17,1907, and subsequently approved by the Chief of Ordnance, U. S. A. Under Item 1, Ingot Metal—Open hearth, acid and basic; Bessemer, acid and basic; crucible; fluid compressed and uncompreesed—descriptive remarks were made as follon-s: "A thorough, fundamental inquiry into the physical properties of steel necessarily begins with the ingot metal. Investigations, having for their object the improvement of steels, should also begin with the ingot. A knowledge of the ingot structure is essential for judging of the subsequent behavior or appearance of the metal. Under ordinary conditions, so little information is obtained from the ingot in individual cases that practically none of importance is acquired. These remarks have particular reference to the state of physical and structural

Jan 1, 1909

By L. A. Willey, William L. Fink

TWO of the aluminum-alloy systems previously studied—the aluminum-titanium and the aluminum-chromium—exhibit a peritectic reaction at the extreme aluminum end of the diagram. Preliminary work indicated that the aluminum-zirconium and certain other aluminum systems were similar in this respect. The present paper, the twentieth of a series from the Aluminum Research Laboratories, reports the results of a recent investigation of equilibrium relations in aluminum-zirconium alloys of high purity, which confirm the preliminary observations. Previous Investigations There has been only one investigation of the aluminum end of the aluminum-zirconium system. Sykesl prepared and studied alloys containing 0 to 70 per cent Zr. The lowering of the freezing point of aluminum by the addition of zirconium was found to be very little, if any (less than 2" C.). He placed the solid solubility of zirconium in aluminum at room temperature between 0.57 and 0.97 per cent. A few other investigators have attempted to determine the composition of the intermetallic compounds occurring in this system. Honigschmid2 obtained the compound ZrAla as a by-product during the preparation of ZrSi2. He made no attempt to prepare other aluminum-zirconium compounds. Weiss and Newmann3 prepared an alloy by heating aluminum with a double fluoride of potassium and zirconium. When this alloy was treated consecutively with caustic soda and hydrochloric acid, there was a residue, which contained approximately 72 per cent Zr and 28 per cent A1 (Zr3AI4). Marden and Rich4 prepared an alloy in the same way, treated it with caustic soda, and obtained a residue of silver-white crystals, which contained 70 per cent Zr and 30 per cent A1 (Zr3A14). Alloys Materials Used.—Electrolytically refined aluminum was employed for thc preparation of all alloys used in this investigation. The chemical

Jan 1, 1939

By William L. Fink, L. A. Willey

TWO of the aluminum-alloy systems previously studied—the aluminum-titanium and the aluminum-chromium—exhibit a peritectic reaction at the extreme aluminum end of the diagram. Preliminary work indicated that the aluminum-zirconium and certain other aluminum systems were similar in this respect. The present paper, the twentieth of a series from the Aluminum Research Laboratories, reports the results of a recent investigation of equilibrium relations in aluminum-zirconium alloys of high purity, which confirm the preliminary observations. Previous Investigations There has been only one investigation of the aluminum end of the aluminum-zirconium system. Sykesl prepared and studied alloys containing 0 to 70 per cent Zr. The lowering of the freezing point of aluminum by the addition of zirconium was found to be very little, if any (less than 2" C.). He placed the solid solubility of zirconium in aluminum at room temperature between 0.57 and 0.97 per cent. A few other investigators have attempted to determine the composition of the intermetallic compounds occurring in this system. Honigschmid2 obtained the compound ZrAla as a by-product during the preparation of ZrSi2. He made no attempt to prepare other aluminum-zirconium compounds. Weiss and Newmann3 prepared an alloy by heating aluminum with a double fluoride of potassium and zirconium. When this alloy was treated consecutively with caustic soda and hydrochloric acid, there was a residue, which contained approximately 72 per cent Zr and 28 per cent A1 (Zr3AI4). Marden and Rich4 prepared an alloy in the same way, treated it with caustic soda, and obtained a residue of silver-white crystals, which contained 70 per cent Zr and 30 per cent A1 (Zr3A14). Alloys Materials Used.—Electrolytically refined aluminum was employed for thc preparation of all alloys used in this investigation. The chemical

Jan 1, 1939

By R. W. Nelson

Methods for determining permeability presented by W. D. Kruger3 in a paper entitled "Determining Areal Permeability Distribution by Calculation" have considerable merit. They can be expected to contribute significantly to analysis of flow in heterogeneous systems. Some rather subtle yet important conditions must be met, however, to assure that the computed permeabilities are correct. The conditions which insure a unique permeability distribution may have been overlooked in the method as proposed and presented in the subject paper. The subtlety of the special requirements may permit good agreement between computed and measured pressures in the reservoir; but the computed permeability may still be in error. The general theory and discussion of the requirements for a unique determination of the permeability distribution are presented elsewhere in more detail.7'8 Accordingly, only major features will be presented here in the notation of Kruger. GENERAL DESCRIPTION OF REQUIREMENTS A brief mention of the route to be followed in showing the special requirements may be helpful. The equation to be solved is a quasilinear, first-order, partial differential equation in the unknown permeability. This equation can be solved through an extension of Lagrange's method by reduction to a system of subsidiary ordinary differential equations. Through consideration of the identity of one of the Lagrange subsidiary differential equations with the stream function, a special interrelationship can be shown. The interrelationship has special significance with respect to the boundary condition. If the boundary function satisfies part of the subsidiary differential equation, no unique solution for the permeability distribution exists. In the physical problem this requirement for uniqueness indicates that the permeability measurements used as a boundary condition can not be along a stream tube. The boundary condition must be along a line, or series of lines, which completely traverse the region and pass through every stream tube.

Jan 1, 1969

By Alexander Knoll, Dwight L. Baker

THIS paper is a report on work undertaken to investigate the results and conclusions of Ravitz and Porter1,2 that galena freed of surface oxidation products and lead carbonate ("clean" galena) is waterrepellent, and that the action of xanthates in flotation is the action of a cleansing agent, enabling oxidized galena particles to expose a pure lead sulphide, water-repellent surface. The apparatus, in construction and use, was essentially that of Ravitz and Porter. The only significant modification introduced by the present authors was the substitution of a three-necked flask for the flotation cell as the "reaction vessel." Our procedure was to place 50 grams of freshly ground, minus 200-mesh galena in the reaction vessel, sweep out all molecular oxygen from the system with oxygen-free nitrogen, and proceed to wash the galena surface free of its oxidation products with repeated small portions of (I) ammonium acetate (500 c.c. of water, 200 grams of ammonium acetate) or (2) ammonium chloride, hydrochloric acid (2 liters containing 200 grams of ammonium chloride and 25 c.c. Of 1.18 sp. gr hydrochloric acid). The galena was next washed with many 100-c.c. portions of oxygen-free, distilled water. The galena was finally considered free of soluble salts when wash water that had been in contact with the mineral for at least 48 hr.* gave negative tests for: (x) lead ion with sulphide; (2) chloride with silver ion; (3) acetate with cuprous chloride, sodium chloride; and (4) ammonium ion with Nessler's reagent. Next 500 c.c. of potassium ethyl xanthate solution, free of dissolved oxygen, was run onto the "clean" galena particles. For this system there were determined: I. The wetting properties of the clean galena particles by shaking the reaction flask and noting the degree of mineral collection at the liquid-air interface. This was, of course, simply a qualitative test, but it proved adequate for our purpose. 2. The removal of xanthate ion from the potassium xanthate solution on being shaken with the "cleansed" mineral. Xanthate concentrations were determined by iodine titration according to the methods of Taylor and Knoll.3 3. The pH of the xanthate solution after having been shaken with the "cleansed" galena. The pH was determined colorimetrically.4 The results of five experiments of the type mentioned above are given in Table x.

Jan 1, 1941

Since production curtailment for other than engineering reasons is gradually disappearing, and more and more wells are now producing at capacity and showing declining production rates, it was considered timely to present a brief review of the development of decline-curve analysis during the past three or four decades. Several of the commoner types of decline curves were discussed in detail and the mathematical relationships between production rate, time, cumulative production and decline percentage for each case were studied. The well-known loss-ratio method was found to be an extremely valuable tool for statistical analysis and extrapolation of various types of curves. A tentative classification of decline curves, based on their loss ratios, was suggested. Some new graphical methods were introduced to facilitate estimation of the future life and the future production of producing properties where curves are plotted on semilogarithmic paper. To facilitate graphical extrapolation of hyperbolic-type decline curves, a series of decline charts was proposed, which will make straight-line extrapolation of both rate-time and rate-cumulative curves possible. Introduction During the period of severe production curtailment, which is now behind us, production-decline curves lost most of their usefulness and popularity in prorated areas because the production rates of all wells, except those in the stripper class, were constant or almost constant. While production-decline curves were thus losing in importance for estimating reserves, an increasing reservoir consciousness and a better understanding of reservoir performance developed among petroleum engineers. This fact, together with intelligent interpretation and use of electric logs, core-analysis data, bottom-hole pressure behavior and physical characteristics of reservoir fluids, eliminated a considerable part of the guesswork in previous volumetric methods and put reserve estimates, based on this method, on a sound scientific basis' At the same time, a number of ingenious substitutes were developed for the regular production-decline curve, which made it possible to obtain an independent check on volumetric estimates in appraisal work, even though the production rates were constant. with the now steadily increasing demand for oil to supply the huge requirements of this global war, proration for reasons of than prevention of underground waste is gradually disappearing. More and more wells are, or will be, producing at capacity or at their optimum rates, as determined by sound engineering practice. With this trend, the character of producing wells seems to regain, more or less, its "individuality," and the old and familiar decline curve appears to have had a comeback as a valuable tool in the hands of the petroleum engineer. It may be timely, therefore, to retrace the development of decline-curve analysis in the past by presenting a brief chronological review of bulletins and papers published during the past three or four decades, which have

Jan 1, 1945

By W. M. Corse

I bring this investigation to your attention to emphasize the needless waste attendent upon the use of tin plate with an unnecessarily heavy tin coating. With our present knowledge, we are unable commercially to produce coatings as light as the lower weights used in this test. If, however, future research should develop means to this end, the resultant product would meet all practical requirements, and a very considerable saving in pig tin would result. DISCUSSION G. H. Clamer.-—The National Canners' Association is studying the action of fruit juices, etc., on solders. Of course these tests will take quite a long time, and we hope by that time the war will be over and there will be no need for conserving tin for war purposes. Germany for a great many years has prohibited the use of more than 37 per cent. of lead in alloys used in contact with food products. The eutectic composition is 37 per cent. of lead and 63 per cent. of tin; alloys containing more than that percentage of lead have some free lead. J. W. Richards,' South Bethlehem, Pa.—A great deal of conservation can result from the packing of dry foods in cartons and in fiber packages instead of using sheet tin. Many of the boxes used for packing things other than food are frequently made of sheet tin because it prints and lithographs well; these could be made of sheet iron coated with copper or some other substitute metal which prints equally well. The Aluminum Bronze Industry W. M. CORSE,† Mansfield, Ohio.—The conservation of tin, in view of the shipping situation, is one of great importance. Several methods of conservation can be employed: 1. Reduction of the amount of tin in an alloy or compound. 2. Substitution of an entirely different metal or compound for tin. 3. A combination of the first and second methods. The second method is the one that I wish to discuss. Metallic aluminum, has been known for a long time, and its use in copper alloys was discovered about 1855 by Lord Percy. The high cost of production of metallic aluminum retarded its commercial development, and it was not until the discovery of the electrochemical processes for its production that it came to be known as a common metal. I have been particularly interested, for the past few years, in working with the alloy known as aluminum bronze, which is usually composed of approximately 90 parts of copper and 10 parts of aluminum, by weight.

Jan 1, 1919

Jan 1, 1967

By Alexander Knoll, Dwight L. Baker

THIS paper is a report on work undertaken to investigate the results and conclusions of Ravitz and Porter1,2. that galena freed of surface oxidation products and lead carbonate ("clean" galena) is water-repellent, and that the action of xanthates in flotation is the action of a cleansing agent, enabling oxidized galena particles to expose a pure lead sulphide, water-repellent surface. The apparatus, in construction and use, was essentially that of Ravitz and Porter. The only significant modification introduced by the present authors was the substitution of a three-necked flask for the flotation cell as the "reaction vessel." Our procedure was to place 50 grams of freshly ground, minus 200-mesh galena in the reaction vessel, sweep out all molecular oxygen from the system with oxygen-free nitrogen, and proceed to wash the galena surface free of its oxidation products with repeated small portions of (I) ammonium acetate (500 c.c. of water, 200 grams of ammonium acetate) or (2) ammonium chloride, hydrochloric acid (2 liters containing 200 grams of ammonium chloride and 25 c.c. of 1.18 sp. gr. hydro chloric acid). The galena was next washed with many 100-c.c. portions of oxygen-free, distilled water. The galena was finally considered free of soluble salts when wash water that had been in contact with the mineral for at least 48 hr.* gave negative tests for: (I) lead ion with sulphide; (2) chloride with silver ion; (3) acetate with cuprous chloride, sodium chloride; and (4) ammonium ion with Nessler's reagent. Next 500 c.c. of potassium ethyl xanthate solution, free of dissolved oxygen, was run onto the "clean" galena particles. For this system there were determined: I. The wetting properties of the clean galena particles by shaking the reaction flask and noting the degree of mineral collection at the liquid-air interface. This was, of course, simply a qualitative test, but it proved adequate for our purpose. 2. The removal of xanthate ion from the potassium xanthate solution on being shaken with the "cleansed" mineral. Xanthate concentrations were determined by iodine titration according to the methods of Taylor and Knoll.3 3. The pH of the xanthate solution after having been shaken with the "cleansed" galena. The pH was determined colorimetrically.4 The results of five experiments of the type mentioned above are given in Table I.

Jan 1, 1941

By Blamey Stevens

(Butte Meeting, August, 1913.) THE following paper aims to make a full explanation of the phenomena of rock jointing. It may be unnecessary to give any general description of what are termed joints in rocks, but. Professor Geikie's clear and faithful generalizations are so illuminating that no excuse need be given for introducing the following and other quotations into this paper: "Almost all rocks are traversed-by vertical or highly inclined divisional planes termed joints. These have been regarded as clue in some way to contraction during consolidation (fissures of retreat) ; and this is no doubt their origin in innumerable cases. But, on the other hand, their frequent regularity and persistence across materials of very varying texture suggest rather the effects of internal pressure-and-movement within the crust."1 General Explanation.-In this paper I show that the phenomenon of jointing may to a large extent be accounted for by the pressure of the water contained in the pores of the rock. To understand this, each constituent grain of. the porous material may be considered to be separately compressed by the 'water which submerges it. As all the grains are held together by cohesion, the whole mass is contracted by this pressure. In an indefinitely extended mass, however, there must be a limit to the possible contraction without rupture, because the material is restrained from. moving freely by other material around its boundaries. The mass of rock thus becomes broken up. This phenomenon is known as " shrinkage " jointing. The terra "shrinkage" is an apt one, if it be understood that the shrinkage of the rock is often brought about by change of stress. Stresses.-The compressive component of water stress on the individual grains is evidently the same as that of the water with which it is in contact. This is so, both. before and after the jointing is formed. Before the jointing is formed there is, however, a tensile stress in one or more directions which keeps the material from contracting.

Jan 7, 1913

By William L. Fink, H. R. Freche

The constitution of the aluminum-cobalt alloys has been the subject of relatively few investigations. Brunckl analyzed the residue which remained after treating the 17 per cent cobalt alloy with dilute hydrochloric acid. The results of the analyses indicated the existence of a compound Co3Al13. Guillet2 published a liquidus for the aluminum-cobalt system which contained two maxima corresponding to CoA16 and CoAl2 and two eutectic points at 30 and 74 per cent Co. The most extensive investigation of the system was carried out by Gwyer13 whose results are summarized in Fig. 1. It will be noted that at the aluminum end there is a suppressed eutectic at 644' C. By extrapolation of the duration of the eutectic arrest to zero, the composition of the compound was placed at Co3Al13. Another thermal arrest was noted at 550" C., which Gwyer attributed to a peritectic reaction. The present investigation of the aluminum end of the aluminum-cobalt system is the eleventh of a series dealing with the constitution of aluminum-rich alloys prepared from electrolytically refined a1uminum.l Preparation of Alloys.—The alloys used in this work were all prepared from electrolytically refined aluminum, the analysis of which is shown in Table 1. In preparing some of the alloys, metallic cobalt (98 to 99 per cent) was used either directly or in the form of an intermediate alloy, the composition of which is given in Table 1. In order to obtain alloys of higher purity, cobalt was introduced into some of the alloys by means of chemically pure cobaltous chloride which was readily reduced by the aluminum. A small electric furnace with nickel-chromium heating elements was used in the preparation of the alloys. Chemical Analysis.—An analysis sample from each melt was chill-cast in the form of a plate 3/16 in. thick. In all cases the casting temperature was well above the liquidus. Cobalt was determined electrolytically in all alloys containing more than 0.05 per cent cobalt and by the nitroso-

Jan 1, 1932

By R. P. Killmeyer, B. S. Gottfried, J. T. Wizzard

The US Department of Energy's Coal Preparation Branch has developed a computer program to calculate the performance characteristics of coal washing devices. This program uses specific gravity analyses of the clean coal and refuse streams as input, and generates dependent and independent performance criteria for the washer. Partition curves are internally represented in a functional form by a Weibull function. Comparisons are made between performance criteria calculated by hand and the performance criteria calculated by the program for 120 different dense medium cyclone tests. Results show that the computer program gives results in close agreement with hand-calculated values while greatly reducing the amount of time involved in performing the analyses.

Jan 1, 1984

By AIME AIME

THE following compilation of State bureaus and officials that deal with mineral resources is compiled in part from a new "Check List of State Agencies and Officials Concerned with the Management of Natural Re- sources," compiled for the National Resources Committee, Washington, D. C., by Clifford J. Hynning. Alabama-Geological Survey of Alabama, University. Walter B. Jones, State Geologist. Chief Mine Inspector: W. B. Hill- house, 614 Lincoln Life Bldg., Birmingham.

Jan 1, 1939

A dinner was given to Ambrose Swasey by the United Engineering Society, at the Engineers' Club, on November 14. Those present -included -twenty-one presidents and past presidents of the Founder Societies. Charles F. Rand, President of United Engineering Society, presided. President Robert S. Woodward, of the Carnegie Institution of Washington, and Dr. Robert W. Hunt, of Chicago, made addresses to which Mr. Swasey responded. Dr. Michael I. Pupin, Chairman of Engineering Foundation, made the closing address. The evening was marked by the high character of the addresses, inspiration for grave duties lying before the engineering profession, and by the spirit of good fellowship. Among the seventy-two persons present were the following members of the Institute: E. E. Bartlett, William N. Best, J. Parke, Channing, C. R. Corning, F. C. Cottrell, J. V. Davies, J. V. N. Dorr, H. S. Drinker, Karl Eilers, H. M. Howe, A. C. Humphreys, Robert W. Hunt, Wm.. B. Jackson, D. S. Jacobus, J. H. Janeway, J. E. Johnson, Jr., John Johnston, George F. Kunz, Edwin Ludlow, Philip N. Moore, Fred'k. H. Newell; Wm. H. Nichols, H. Hobart Porter, Charles F. Rand, R. M. Raymond, .Jesse M. Smith, E. Gybbon Spilsbury, Bradley Stoughton, . Joseph Struthers, Benj. B. Thayer, Wm. H. Wiley, S. T. Wellman.

Jan 1, 1919

GENTLEMEN Submitted herewith are the report of the Treasurer for the year 1938 and reports for the same year of the following standing committees: Admissions, Membership, Papers and Publications, Mining and Metal¬lurgy (Magazine), Library, Speakers for Local Sections and Student Societies, and Student Relations. To these reports members are referred for further details. Membership.-The end of the year 1938 saw Institute membership at an all-time peak: 12,474, made up of 2898 Student Associates and 9576 members of other classifications. The next highest level had been reached at the end of 1921 when corresponding figures were: total, 10,329; student members, 1450; all other classifications, 8879. The net gain for the year was 1495, of which 751 were Student Associates and 744 in the other categories. Two factors contribute to the growth of membership: (1) the enrolment of new members; and (2) the retention of members already on the roll as reflected in a relatively small number of resignations and suspensions for nonpayment of dues. For the first, much credit goes properly to the general Membership Committee that functioned for a second year under the chairmanship of Clyde E. Williams. With the cooperation of Institute members in general, to whom Mr. Williams expresses appreciation in his report, the Committee has been successful in acquainting eligible nonmembers with the purposes, activities and advantages of the Institute. The result has been the receipt during the year of 1162 applications, exclusive of Student Associates. This compares with 1212 during 1937 and 1266 during 1936. However, in considering this modest decline, account must be taken of the somewhat less prosperous conditions prevailing in the mineral industries and, consequently, among engineers engaged ?in those industries.

Jan 1, 1939

COMPARED with the equipment used in most industrial processes, the open-hearth furnace has a relatively short life. The most important quality of an open-hearth refractory, therefore, is its rate of failure. This discussion of the physics and chemistry of the individual refractory materials will keep upper- most the question "Why, how, and where does it fail?" CAUSES OF FAILURE The principal causes of failure of open-hearth refractories are, in their order of importance: 1.Reaction with iron oxides. 2. Reaction with slag. 3. Flow and failure under load. 4. Melting. 5. Spalling. 6. Mechanical breakage. Reaction with Iron Oxides and Slag. Reaction with iron oxides and slag is by far the most important cause of failure. Liquid iron oxide comes near to being the "universal solvent" sought for by the alchemists. Among the materials commonly used in the open-hearth furnace, magnesia has the greatest resistance to this liquid and fireclay the least. The relations of iron and oxygen at high temperatures are illustrated in Fig 14-18. The liquid iron oxide that forms wherever iron is in contact with air or combustion gases cannot be given a definite formula. The percentage of oxygen at steelmaking temperatures may range from 21 to 28 (iron 79 to 72), depending upon the temperature and the oxygen pressure and also upon whether or not the liquid is in equilibrium with metallic iron. Oxide mixtures exist not only in the solid and liquid phases but also in the vapor phase, for metallic iron and its oxides have

Jan 1, 1951

COMPARED with the equipment used in most industrial processes, the open-hearth furnace has a relatively short life. The most important quality of an open-hearth refractory, therefore, is its rate of failure. This discussion of the physics and chemistry of the individual refractory materials will keep uppermost the question "Why, how, and where does it fail?" CAUSES OF FAILURE The principal causes of failure of open-hearth refractories are, in their order of importance : 1. Reaction with iron oxides. 2. Reaction with slag. 3. Flow and failure under load. 4. Melting. 5. Spalling. 6. Mechanical breakage. Reaction with Iron Oxides and Slag. Reaction with iron oxides and slag is by far the most important cause of failure. Liquid iron oxide comes near to being the "universal solvent" sought for by the alchemists. Among the materials commonly used in the open-hearth furnace, magnesia has the greatest resistance to this liquid and fireclay the least. The relations of iron and oxygen at high temperatures are illustrated in Fig 14-18. The liquid iron oxide that forms wherever iron is in contact with air or combustion gases cannot be given a definite formula. The percentage of oxygen at steelmaking temperatures may range from 21 to 28 (iron 79 to 72), depending upon the temperature and the oxygen pressure and also upon whether or not the liquid is in equilibrium with metallic iron. Oxide mixtures exist not only in the solid and liquid phases but also in the vapor phase, for metallic iron and its oxides have

Jan 1, 1964

By A. D. LeClaire

This paper claims to provide a description of diffusion processes in solids which is said to be a reformulation of Fick's Laws and therefore, presumably, is supposed to be as general as those laws. In fact, it appears to provide no more than an atomic model of a rather restricted type leading even to results in conflict with experiment. The restriction lies in the assumption, carried throughout the paper, that even in a chemical gradient the jump frequency i of an atom of species i is a function only of the composition on the plane from which it jumps, i.e., ?i = ?i(cl, c2 ...). This means that atom jumps in opposite directions from a site would occur with equal probability. There would then be no tendency for atoms to migrate preferentially in one direction along the gradient, so the model is incapable of accommodating the well established phenomenon of atom drift in a chemical gradient.10-" A more general model that does not suffer this difficulty was discussed in a paper13 I wrote in 1958, and the results therein already contain as a special case those given by Dr. DeHoff. The simplest sufficiently general assumption is to suppose that ?i is a function ?i(a1 a2,...; wl, w2, ..-) of the concentration aj and ? ?j at the site from which and to which, respectively, a jump is made. Any such function can always be expressed as a function of the sum and difference of its arguments. Thus d is the jump distance and g a geometrical constant. Obviously this is zero, i.e., no drift, if ??ri/??j = 0. X is written in this form, revealing two components of the total drift, because it can be shown that only the second component, depending on ??'i/???(?j -aj), actually contributes to the net diffusion flux Ji. This component can be shown,13 by a straightforward ther-modynamic transcription, to be responsible for the so called "thermodynamic factor" in the Darken approximation for a chemical diffusion coefficient is the activity coefficient of i. Because the jump rate ?i in DeHoff's approximation has no dependence on the concentration gradient it does not seem possible to derive the Darken equation from his Eq. [6] without the further rather arbitrary assumption that ?i = const ri. It is to be noted too that the author's derivation of Eq. [12] is only valid when ?i is in fact a function only of the cj at the plane from which the atom jumps—for only then is ci?i a unique function of position and therefore of A. Author's Reply R. T. DeHoff I am indebted to Dr. LeClaire for his penetrating discussion of my paper, "A Reformulation of Fick's First Law". I concede that it does appear initially that the relationship presented in my paper could be derived from the detail atomic model of random walk and atom drift presented in Dr. LeClaire's approach. However, there are some important differences in concept and viewpoint which deserve further amplification. Dr. LeClaire's description is penetrating, detailed, and fundamental. His approach describes an extremely complex phenomenon, the displacement of atoms in a multicomponent gradient, at a sophisticated level. For precisely these reasons, his analysis has not proved to be useful for experimental studies that have practical objectives. For example, in order to obtain the information required to complete the analysis of the jump frequency distribution in a ternary system, the following series of experiments would, I believe, be required: 1) chemical (gradient) experiments, covering the composition range;

Jan 1, 1970