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By A. W. Schlechten

The proposition is advanced that edutcation specifically for exlractive metallurgy is desirable not because the course content is cmique but rather as a means of indoctrinating the student with a backgrocmd that will give him an interest and pride in the profession. Factors that have caused the decline in enrollment in metallurgical engineering courses emphasizing extractive processes are being overcome. There is a need to distinguish between the sciences of metallurgy and the engineering applications to avoid confusion both in and out of the profession. AS a first step in preparing the 1967 EMD Lecture I searched the literature to determine what my predecessors had done hoping thereby to gain some clues for my own performance. The Transactions of the Metallurgical Society show that the first EMD Lec- turer in 1959 was Dr. W. J. Kroll, known chiefly today for his pioneering work on the production of titanium and zirconium, but equally respected by an earlier generation for his contributions to lead refining. He has been followed by a series of well-known and competent metallurgists all possessing specialized knowledge that has served as a basis for their lectures. The EMD Lectures have in general been a review of the development of a certain aspect of the extractive metallurgical industry or a preview of a particular area of science or technology that has applications in extractive metallurgy. The usual format is to describe developments of the past, summarize the present state of knowledge, and make predictions for the future. There has been great variation in the relative amount of time devoted to these three subdivisions, the past, the present, and the future. For example, Professor Gaudin, the 1961 EMD Lecturer, in speaking of Separation Engineering on the Moon, did not have too many examples of past practice and so had to emphasize the future. It is cheering to observe that all of these authorities were optimistic in their predictions. Despite the fact that four of the previous EMD Lecturers have been educators, Professors Gaudin, Pidgeon, Schuhmann, and Kellogg, none of them discussed the subject of education for extractive metallurgists. I might say parenthetically that lecturers in other divisions, such as B. M. Larsen, J. B. Austin, F. D. Richardson, John Chipman, and R. F. Mehl, have commented with concern on the present state of training for extractive metallurgy. What can you say that is new about extractive metallurgy education? Certainly nothing new can be said about the educational process itself. Professional educators do have new approaches to teaching and learn-

Jan 1, 1968

By Maurice E. Peloubet

This discussion of accounting will describe the statements and the information that the accounting system produces, from the point of view of those who use such systems rather than of those who prepare them and who do the detail and technical accounting work. In any well organized mine, quarry, or other enterprise exploiting a mineral deposit, no matter how small, some clerical and accounting work must be done. Miners and other employes must be paid, supplies must be purchased and issued, and various tax and information returns, which even the smallest enterprise must file, have to be prepared. In this chapter it is assumed that the enterprise has employes of this type and that they understand the fundamentals of record keeping and accounting. It would be impossible here to give sufficiently full explanations to enable a man with no previous clerical and accounting training to set up and operate an accounting and cost system for even the simplest extractive operation. Rather, we shall hope first, to tell the investor and the operator, from the chief engineer or president down to a subforeman, what to expect from the accounting statements and records and how to use this information in his daily work; and second, that it will enable the man with some knowledge of accounting or book- keeping, but with little or no experience in any extractive industry, to set up and operate a satisfactory system for a mine or other extractive enterprise. For readers who wish to go further, the bibliography at the end of this chapter contains many references. T he emphasis has, therefore, been placed on the statements to be produced and the purposes for which they are to be used rather than the underlying books and records. These are, with a few exceptions which will be described later, essentially what might be found in any industrial enterprise and would probably, in the extremely small enterprise, consist of handwritten journals, ledgers, analysis books, payroll books, and stores ledgers. In the larger enterprise, various types of mechanical accounting would be introduced in proportion to the complexity of the operation.

Jan 1, 1964

By Fred C., Fred C. Bond

Comminution energy is principally energy of deformation before breakage, which appears as heat. An empirical equation is presented which covers the entire comminution range. The new strain-energy theory considers comminution from the known principles of mechanics and the reduction ratio. Energy requirements according to the different theories are compared.

Jan 1, 1950

By W. N. Carr, J. R. Biard, B. S. Reed

An analysis of the semiconductor injection laser is presented which is based on a phenomenological model using device and material parameters. The intent of the laser threshold analysis is not to predict from theory the actual threshold current density but rather to provide a logical means of interpreting experimental results. The device and material parameters have been selected such that they describe both the threshold conditions and quantum efficiency of the lasev. A technique is proposed whereby the current required to obtain a population inversion is predicted from device 1-V characteristics. Experimental data are presented which support the analysis. THIS investigation is concerned with the characteristics of GaAs lasers fabricated in this laboratory. However, the assumptions used in these calculations should not limit their application to GaAs alone. It is felt that the analysis is sufficiently general to be useful in describing the operation of other semiconductor-laser materials. ANALYSIS heavily doped semiconductors to be considered. The absorption and/or generation of optical radiation may be completely specified in terms of q(E) and the probability functions f,,(E) and f,(E) which define the occupancy of the valence-band and conduction-band levels, respectively. The symbols used in this analysis are listed at the end. Following the approach of all' it can be shown that the effective gain coefficient, g, in the plane of a forward-biased P -N junction is g(E)=-ai@)[1-fv(E)-fc(E)] [1I In particular Eq. [I] holds for the photon energy at which lasing occurs, Ep. Throughout the following discussion Eq. [I] is considered only for the lasing transition E = Ep. For simplicity the functional energy dependence of the various factors is omitted in subsequent equations. Unless otherwise stated the symbols used represent the values at Ep. If the analysis is limited to the P-type side of the laser junction, the function q(l -f,,) is recognized as the band-to-band absorption in the P-type material at thermal equilibrium. Under forward-bias conditions the function f, is determined by the electron quasi Fermi level in P-type material. For sufficiently large forward bias the second term in Eq. [3] will become dominant and net gain will result; i.e., g will become positive. In order to simplify the subsequent analysis several assumptions are in order at this point. a) No conductivity modulation occurs. /„ is independent of f, and therefore go is a constant. b) The P-type material is heavily doped such that the degeneracy of the valence band permits popu-

Jan 1, 1964

By Dunbar D. Scott

The development in the perfection of mine-surveying instruments has been by no means rapid, as it has depended somewhat on the details of construction borrowed from astronomical and geodetic theodolites, largely on the restrictions laid down by mining companies and the prejudices of mine managers themselves, but more than all on the methods used in conducting surveys and the importance attached thereto. Mine-surveying, in some form or other, has been practiced from the very earliest times; but it has never kept pace with the other branches of surveying, or even with the art of mining itself, and cannot be recognized as an exact science until shortly before the beginning of this century. The works of Hero of Alexandria, who lived in the second century B.C., are still extant, and contain descriptions of a rectangular sighting-instrument, which he invented and called a diopter. His improvement upon this simple construction, which possibly he devised for use in the Greek mines for rough leveling-purposes and for laying out any angle, must be considered, says Hübner," as the origin of the highly perfected theodolite of to-day. Whether this instrument came into general use during the first centuries of the Christian era, is not recorded; in fact, no writer undertakes to tell how mine-surveying was conducted until 1556, in which year Agricola expounds the principles of mining and metallurgy in his De Re Metallica, devoting the entire fifth chapter to the practice of mine-surveying (see Fig. 1). In mediæval times those who possessed any knowledge of engineering skill made strenuous effort to keep their art a secret, partly on account of the miners' proverbial conservatism and partly for their own personal aggrandizement, and were, in

Jan 1, 1899

By WM. HUFF WAGNER

Computations and allowances for mine depletion for Federal income tax purposes depend upon the meaning of certain terms in the pertinent provisions of section 114(b) 4 of the Internal Revenue Code. Unfortunately, but one of these terms is defined in the Code. Congress left it to the Commissioner to define the other terms in the Regulations. Even though the Commissioner, through his staff, labored long and earnestly to draft these definitions they have not been satisfactory to the mining industry, because the definitions in the Regulations and the interpretation placed thereon by the Commissioner do not state what the industry believes to be the clear and obvious intent of Congress. Consequently serious and prolonged disputes, unduly delaying the settlement of Federal tax returns involving percentage depletion deductions are continually arising between taxpayers and the Commissioner.

Jan 1, 1949

CARACAS PETROLEUM Established February 24, 1957 Meets second Tuesday monthly W F Shelton, Chairman Homer N Mead, First Vice-Chairman Jose G Paez, Second Vice-Chairman T A Moore, Treasurer E A Moore, Secretary Cia Shell de Venezuela Apartado 809 Caracas. Venezuela

Jan 1, 1958

By Samuel G. Lasky

What the evidence prevails upon the mind to believe, depends upon the mind as well as upon the evidence. M. L. IN a recent discussion of the mineral resource position of the United States, published in the September 1946 issue of MINING AND METALLURGY, I expressed my conviction that ore deposits of major magnitude remain to be found in this country and that they can be found without undue cost or risk. I stated with equally strong conviction, however, that if the search for such deposits is to be notably successful there must be, among other things, a reorientation of philosophy and mental habits on the part of many who would be connected with the search. I would now like to enlarge upon that statement. For such a purpose, we may consider that the search for concealed deposits involves four steps: (I) the selection of areas for further study; (2) the geologic study of those areas in order to verify their general favorableness and in order to choose specific patches worthy of being tested; (3) the decision whether exploration of the patches chosen should actually be undertaken; and (4) the exploration itself. The first two steps and the last rest upon the judgment and skill of geologists. The third step-the decision whether exploration should be undertaken-rests upon management. In my opinion, the philosophies or principles that have guided these steps in the past are now inadequate. PHILOSOPHY OF APPRAISAL If concealed deposits are to be looked for, how are the places of their possible concealment to be recognized? Every known mineralized area still in the prospect stage has already been repeatedly examined and condemned. As for those deposits concealed under later rocks, there may be not even the clue of a near-by outcrop for engineer or geologist to consider. How then, are we to know where to look? Geologic Probability In the early days of our mining industry, ore deposits were found mainly by "following the ore." Later, as such opportunities decreased, and as geologic concepts became accepted, deposits were found more and more through use of the notion of geologic probability. Many instances can be cited wherein a courageous operator ignored the implications of the unsuccessful efforts of predecessors and, solely by "following the ore," converted a discredited prospect into a good mine. Similar experience doubtless will occur in the future, but "following the ore" will no longer in itself find new deposits in the amount needed. Nor can enough new ore be expected from further use of the notion of geologic probability, for, as mentioned above, our known prospects `have already been ex-

Jan 1, 1947

By L. D. Jaffe, R. K. Pitler

IT would clearly be advantageous to produce molten titanium, suitable for alloying and casting, directly from the relatively inexpensive tetra-chloride, without using a metallic reducing agent. Accordingly, a preliminary investigation has been made of the production of titanium by hydrogen reduction of the tetrachloride in an electric arc furnace. For the reaction: TiCl4(g) + 2H2(g) ? Ti(s) + 4HCl(g), Lockhart and his colleagues' have calculated equilibrium constants at 800" to 1500°K, based on tables of Brewer.' Extrapolating these data on the assumption that the heat of reaction varies linearly with temperature, and using Brewer's value for the heat of fusion, there is obtained for the reaction: TiCl4(g) + 2H2(g) ? Ti(l) + 4HCl(g) an equilibrium constant at 2100°K (100" above the melting point) Kp = (PHCl)4/pTlcl4 (Ph2)2 = 0.167 atm. If this is correct, starting with hydrogen saturated with TiC14 at 25°C, where the vapor pressure of the latter3 is 12.6 mm, and maintaining the overall pressure at 1 atm, 99 1/4 pct of the TiC14 would be reduced to Ti at equilibrium. An arc furnace designed for the melting of titanium and lined with water-cooled copper was used for the preliminary experimental check. Its inside diameter was 2 7/16 in. and height 6 in. The water-cooled electrode was tipped with 3/4 in. diam tung-sten. In the one run carried out, the furnace was charged with a starting batch of 293.35 g of scrap titanium,' analyzing 99.24 pct Ti. After the system was twice pumped out and flushed with argon to remove air, the arc was struck in argon and kept at 400 amp dc, electrode negative, for 1 min to melt the starting batch. Commercial tank hydrogen, dried by passing over silica gel and bubbled through technical grade TiC14 at room temperature, was then admitted to the furnace. The inlet tube directed this gas downward toward the arc and melt; the gas outlet was at the top of the furnace. The quantity of gas passed through was not measured accurately but is estimated to be about 50 liters per min at a few mm of mercury above atmospheric pressure. The arc was held in the H2-TiC14 mixture at 400 amp with little difficulty. After 10 min the arc burned through the copper lining above the melt, admitting water and ending the run. (This had happened frequently in straight melting runs under argon, and is not thought due to the atmosphere used.) In the furnace were found an ingot, several small pieces, and a little metallic powder, evidently formed when water entered the hot furnace. Some titanium also clung to the electrode. The portions were weighed and separately analyzed for titanium. Their total weight was 321.76 g of 94.82 pct overall purity. Much of the impurity consisted of tungsten broken off when the titanium was removed from the electrode. No detailed impurity analysis was made because the starting materials were impure and flooding the furnace introduced further contamination. Thus, the metal recovered contained 305.08 g Ti, as compared to 291.12 g in the starting batch. Titanium could not have been carried over from previous melting runs in the furnace, as the interior was sandblasted and the electrode ground clean before the run. Evidently at least 13.96 g of Ti were produced from TiCl4. Since this would require complete reduction of 430 liters of TiCl, gas at 12.6 mm of Hg, the efficiency of the process must have been rather high. Experimental work is continuing. No reason is seen why the process could not be scaled up to the size of a 30-ton steel-melting arc furnace. In a large unit there would be a large molten pool from which liquid metal could be withdrawn for alloying and casting. The problems of electrodes and power supply are similar to those arising in arc furnaces for melting titanium. Unreacted TiC14 and the HC1 in the exhaust gases could be recovered; unreacted H2 could be dried and re-used. The melt would be saturated with hydrogen, whose solubility in liquid titanium is unknown. Small amounts of hydrogen seem to have little effect on the properties of titanium.5 If the amount introduced was so large as to impair properties or cause casting difficulties, it could be reduced by holding the melt under an inert gas or by pumping on it, prior to casting. Acknowledgment The authors would like to thank I. Preble and M. Goldman for their valuable aid in the experimental work and the thermodynamic calculations, respectively. References 1R. J. Lockhart, J. J. Ward, M. J. Hussey, and J. W. Clegg: In unpublished report, "U. S. Air Force Project Rand. Titanium and Titanium Base Alloys." Battelle Memorial Institute (1949) 37-44. 2 L. Brewer et al: Chemistry and Metallurgy of Miscellaneous Materials—Thermodynamics. Ed. by L. L. Quill. pp 13-39, 60-192. (1950). McGraw-Hill Book Co. 3 K. Arii: Scientific Reports. Tohoku Imp. Univ. (1933) 22, 182. 4 R. S. Dean, J. R. Long, F. S. Wartman, and E. L. Anderson: Transactions AIME (1946) 166, 369-381; Metals Technology (Feb. 1946) TP 1961E. * R. I. Jaffee and I. E. Campbell: Transactions AIME (1949) 185, 646-654; Journal of Metals (Sept. 1949) TP 26813.

Jan 1, 1951

By C. R. Hayward

THE CHAIRMAN (ALBERT SAUVEUR, Boston, Mass.).-I am sure we are indebted to Prof: Hayward for his addition to our knowledge of the influence of sulphur on steel. As he has said in this paper, sulphur has had many defenders in recent years. It seems to me, however, that, while it may be old school to believe in the detrimental action of sulphur, it is not yet old school to believe in segregation; that while it may be that 0.1 per cent. of sulphur has no very great effect on the physical properties of steel, a ladle analysis of 0.1 per cent. of sulphur may readily result in 0.2 or 0.3 per cent. sulphur being present in the segregated portion of the ingot, and that, it seems to me, might be a rather serious matter. J. S. UNGER, Pittsburgh, Pa.-Prof. Hayward has presented the results of an investigation along a line to which I have devoted considerable time and attention, and I am particularly pleased to note that his results are in accord with my own and further tend to prove the fact that the old, established prejudice against sulphur is based more on belief than actual facts. I have felt for years that tooo much stress was placed on the harmful influence of certain elements in steel such as sulphur, phosphorus, copper, etc., but it has only been within recent years that efforts have been made to, establish the truth. Practically all the investigations made to date have proven that these elements within reasonable limits are harmless and, in fact, that for certain purposes the addition of these elements is beneficial. In referring to copper, J. E. Stead, Vice-President of the British Iron and Steel Institute, said at their last meeting: "Even today one comes across steel specifications in which copper is barred, which can only be regarded as ail indication of ignorance, if not stupidity, of those who prescribe the composition of steel, for it has been long ago proved that copper in steel, instead of being an evil, is quite harmless, and is sometimes distinctly beneficial." Sulphur owes its evil name to the early days of the manufacture of steel. Chemical analyses were crude, and failure due to either poor raw materials or metallurgical treatment were many. Sulphur being a comparatively easy element to determine with reasonable accuracy, particular attention was called to the amount of sulphur, and the failure was attributed to it, without giving any consideration to other causes. A pre-

Jan 4, 1917

The Role of the Drilling Contractor BY FERRIS E. SAINSBURY Ron Haxby, Occidental Minerals What is the best method for drilling a 12-in. diam hole to a depth of 1200 ft and maintaining the deflection within 25ft from vertical? Ferris Sainsbury: In order to drill a 12-111. hole down to 1200 ft, In most places you would have to employ a rotary tricone bit With a down-the-hole hammer, I expect by that depth significant Inflows of water would be experienced Even with foams, we would not be able to get the water out of a hole of that diameter So the down-the-hole tricone method of drilling would be best. To keep it straight, we would probably employ the largest square drill stem compatible with the diameter of the hole. Ron Haxby: Is it common in drilling contracts to put in a vertical hole clause? Ferris Sainsbury: You can put in the vertical hole clause Ron Haxby: Does it cost more? Ferris Sainsbury: Normally, if the hole deviates, the driller can correct it with deflection wedges and will charge it back to you at cost, plus 10% or somewhere along that range Any drill hole has a tendency to go perpendicular to the dip, and there are times when stabilization systems are not successful in preventing the hole from turning into the dip of the formation. The only solution, in this situation, is to go in with an oriented wedge and kick the hole back out.

Jan 1, 1979

Jan 1, 1900

By Albert G. Anderson

I'm sure many of you have wondered what the term "Cross Flow Filtration" means. I shall explain it so that you more clearly understand it, and I hope you will be able to make it a useful tool for you in the future. In the simplest form of cross flow filtration contaminated fluid. or feed stream, is fed at a high velocity down the center of a porous tube, clear fluid weeps through the porous wall of the tube while the suspended solids concentrate in and are swept away by the feed stream. (See figure A). The high velocity flow of the feed stream tends to keep the inside of the tube free from a build up of contamination. By utilizing this cross flow approach to filtration, we have been able to concentrate such things as paint pigments, titanium dioxide, iron oxide, precipitated metals such as uranium yellowcake or silver, cadmium, some metal hydroxides, as well as gelatinous particles such as yeast cells. You will recognize that cross flow filtration lends itself to a recirculation loop system due to the necessity of maintaining a high velocity on the inside of the tube. This means that we generally have a storage tank from which we are recirculating, and the solids will concentrate in the storage tank. (See figure B). The storage tank design becomes an integral part of the total system and is very important to the total function of the system. The cross flow filter system requires only low pressure, and will work with centrifugal pumps, diaphram pumps or in some cases no pump at all. As an example, if we wanted to filter a 10 GPM (37.8 liters/min.) stream that contained 1% of submicronic particulate, we would flow the 10 GPM (37.8 liters/min.) into the storage tank and recirculate through the filter at a flow of anywhere from 30 GPM to 100 GPM (113.6 to 378.5 liters/min.) depending upon the filterability of the particles from the liquid. As the contaminated fluid recirculates, the solids will build up in the storage tank and loop until they reach a level, which is dependent upon the design of the tank. Then the settling rate in the tank becomes equal to the amount of the solids being fed to the tank, and as a result you reach an equilibrium in the amount of solids being presented to the inside of the porous tubing. We have in effect created a dynamic settling tank or thickener. A flow of 10 GPM (37.8 liters/min.) of clear filtrate comes off for either recycle or disposal with periodic removal of thick mud from the bottom of the tank. The thick mud can be either processed through a centrifuge, a rotary drum filter. a flat bed pressure type filter, or other means. Often the small volume of filtrate from the mud de-watering stream can be recycled back into the recirculation tank so that any fines in the feedback are again concentrated, thus closing the loop on the continuous process 100% removal system. Cross flow filtration will not do efficient molecular separation. We work primarily with discrete solids but we do separate them totally from the liquid carrier fluid. I know some of you will raise your eyebrows when I say that we remove 100% of the particulate, but in measurement tests, we have measured the filtrate cleanliness with instruments that record as low as .05 ppm and the instruments read zero, so that it is less than .05 ppm.

Jan 1, 1980

By AIME AIME

QUALITY and size do not ordinarily go hand in hand, but there is good evidence that both these attributes reached a new peak at the Annual Meeting of the Institute in New York just concluded. Certainly, the total attendance of 2500 was far above any yet attained, as might be expected with the recent rapid growth of Institute member- ship. General comment indicates that the quality of the papers also was notable, though not measurable by so definite a yardstick as attendance. During the meeting 49 technical sessions were held, at which more than 250 formal papers were presented. In addition, there were some thirty special meetings of committees, Divisions, and other Institute groups. In reporting the Annual Meeting eleven years ago the statement was made that "unless the Engineering Societies should build for themselves a new building it is probable that no meeting can be larger," and "the fifth floor, where a buffet lunch is served each day, has reached its full capacity and it seems quite evident that any future development of Institute meetings must be along the lines of quality, not size." Unfortunately the angel to succeed Andrew Carnegie, who financed the building of the present home of the Institute 35 years ago, has not yet ' appeared. Even if some one would merely build another elevator or two in the present building it would help. Fortunately, the modern auditorium of the American Radiator & Standard

Jan 1, 1940

By S. A. Falconer

Much attention and publicity has been given, during recent years, to grinding, classification, flotation, and thickening. The various technical papers, and symposiums held to discuss these important phases of milling, have contributed to a better under- standing of the fundamental principles and operating variables involved. Another important part of milling- to the flotation operator-is a treatment step to which frequently too little attention is given-" conditioning," or the treatment the ground mineral pulp receives before it enters the flotation machines. Conditioning" is a hackneyed and frequently misused term, commonly employed to describe the pretreatment of surfaces of minerals in ore pulps or mill pr6ducts prior to froth flotation. In general, such pretreatment is for the purpose of changing the flotation characteristics of these mineral surfaces to enable them to respond in some desired predetermined manner when subjected to flotation. Taggartl states that the function of conditioning is "either to insure selective collector coating of one mineral species while another species is not; or to take such steps as will compensate for departure there from."

Jan 1, 1949

By C. R. Kuzell

IN COMPARISON with recent years 1932 has yielded much less tangible evidence of progress in copper reduction and refining. The industry has been extremely quiet, especially in the United States. Design and construction has been throttled by lack of new capital expenditures. The excess producing capacity of the whole industry and the extremely gloomy outlook for the future have made it unwise to tie up more capital except under special conditions. The plants built during the previous year have, however, been placed in operation. Older plants have been abandoned, temporarily shut down, placed on part time operating basis, or continue to operate at a low percentage of normal capacity. In the United States the Phelps Dodge Corporation at Douglas, Ariz., has completed the remodeling of the former Calumet & Arizona smelter. A new roaster and Cottrell plant chimney was completed this year. Though operations have been limited the new equipment has been found to justify all expectations. The reverberatory plant addition consists of two furnaces 26 by 107 ft. inside dimensions, with a high arch, and modern steel binding of excellent design. Natural gas fuel gives good results. One of these furnaces will treat 1000 tons of solid charge per day with a fuel consumption of approximately 3,000,000 B.t.u. per ton. The larger converters have not only yielded the expected lower costs, but have simplified operations in the converter department. One of the noticeable results is the greater cleanliness in the environment and the absence

Jan 1, 1933

By Paul M. Tyler

ROUGHLY one-half the value of mineral products at mines or quarries must be spent for wages. In view of the steady increase in hourly wages that continued for several decades prior to the onslaught of the recent depression, it is perhaps surprising to discover that labor's share of the gross proceeds of the mining and quarrying industries of the United States declined to 46.8 per cent in 1929, compared with 52.2 per cent in 1919 and 53.2 per cent in 1909. The actual percentages vary in different branches of the industry and in different localities but the downward trend is unmistakable. For the period 1909 to 1919 it was quite marked in every industry and from 1919 to 1929 it was apparent in all but six: namely, gold and silver lode mining, placer gold mining, crude gypsum production, marble quarrying, asbestos production, and fluorspar Tninino mining

Jan 1, 1933

Established as a Division February 16, 1948 H Rush Spedden, Chairman Neil Plummer, Associate Chairman Stephen E Erickson, First Regional Vice-Chairman D A Dahlstrom, Second Regional Vice-Chairman Win T Marston, Secretary-Treasurer Dorr-Oliver, Inc 77 Havermeyer Lane Stamford, Connecticut

Jan 1, 1960

By J. C. M. Li

The steady state shape of a shrinking cylindrical grain boundary of miform boundary energy is shown to be circular. This is based on the principle of either the minimum rate of entropy production or the minimum thermokinetic potential. The circular shape corresponds also to a state of minimum (not maximum) velocity. The steady state shape of a grain boundary moving between two inclined surfaces is a circular cylindrical arc whose position and curvature will be afjected by the nature of the surfaces. The minimum thermokinetic potential is the only valid criterion in this case. THE preceding paper1 reports an interesting experiment in which it is shown that a grain boundary moving between two inclined surfaces assumes a circular cylindrical arc whose axis nearly coincides with the line of intersection of the two surfaces. The driving force is well defined since it is the energy of the grain boundary itself. The velocity of the grain boundary is found not to vary linearly with the driving force. Several interesting questions arise: 1) What principle determines the shape of a moving grain boundary? 2) What is the effect of the inclined surfaces? 3) How do we understand the nonlinear velocity-driving force relationship? It is attempted in this paper to discuss the first two questions based on irreversible thermodynamics and in a following paper to discuss the third question based on dislocation theory. STEADY STATE SHAPE OF A SHRINKING LOOP (A CYLINDRICAL GRAIN BOUNDARY) In irreversible thermodynamics, there are two criteria for the steady state. One is the minimum rate of entropy production2 which is based on the symmetry of phenomenological coefficients and is applicable to linear force-flux relations with constant coefficients. The other is the minimum thermokinetic potential3 which is based on the integrability of a certain Pfaffian differential equation and is applicable to nonlinear systems with variable coefficients. In the case of a shrinking grain boundary loop (a two dimensional version of a cylindrical grain), the flux of atoms across the grain boundary can be taken as the local boundary velocity v measured perpendicular to the boundary (the number of atoms transferred per unit area per second is equal to the product of atom density and the velocity of the boundary). The local thermodynamic driving force can be taken as y/p with y being the grain boundary energy (invariant with respect to the orientation and curvature of the grain boundary) and p being the radius of curvature. Such driving force can be understood by considering the loop as an elastic string with tension y. As shown in Fig. 1, across a length ds along the loop, the direction of y changes by an angle d@ which is ds/p. Because of this change of direction, the tension exerts a force perpendicular to the curve equal to yd@. The force per unit length is then y/p. According to the experimental observation, the velocity v is a power function of y/p, where M is the velocity at unit driving force and 'n is a constant. The rate of entropy production per ds along the loop is vyds/pT, where T is the temperature. For a given length L of the loop, the total rate of entropy production is The thermokinetic ptentia13 has only a differential definition and its existence depends on the integrability of this definition. In this case, Eq. [3] happens to be a total differential and the thermokinetic potential can be defined as which turns out to be the same as the rate of entropy production, Eq. [2], except for a constant factor n + 1. Strictly speaking, since the flux-force relation is not linear, the rate of entropy production may not be a minimum at the steady state. However, because of the proportionality between Eqs. [2] and 141, the state of minimum thermokinetic potential happens to be the same as that of minimum rate of entropy production. The steady state shape thus can be obtained by minimizing either integral [2] or [4] for a given L.

Jan 1, 1970

By H. Foster Bain

I. INTRODUCTION. By H. FOSTER BAIN.+ THE recently aroused public interest in the conservation of our natural resources has peculiar importance to mining-men, since they deal with resources which are stored products. Within certain limits, the fertility of a worn-out soil may be restored, deforested areas can be replanted, one year's wasted water-supply is followed by another; but coal and ores, once taken out, cannot be mined again, and should therefore be conserved with especial care. This means, however, not that mining should be restricted, but that it should be done most economically and with the minimum of waste.

Nov 1, 1908