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By H. L. Washburn, W. A. McConnell

There is not a coal preparation engineer alive who would equip his newest and most modern preparation plant with all new and untried pieces of equipment. He may install a few such pieces in which he has great confidence, but he will also spend much time assuring himself that everything else in the plant has been subjected to the test of time. He may arrange these units in a unique manner, but in general, they must have proven themselves elsewhere before he will approve them for his plant. A modern coal preparation plant contains only a few items of processing equipment, the remaining items being devices for materials handling. Consequently, pure automation is almost impossible. Although the main aim of automation is conservation of manpower, it generally results in uniformity of product, lower maintenance costs, and the many intangibles that make a better plant.

Jan 8, 1961

By M. J. Scoble, N. Rowlands, L. Piciacchia

Pronounced non-linear behaviour of mine backfill arises from the influence of confining pressure, cementing agent content, curing time, void ratio and water content. Past research into backfill behaviour under stress is reviewed and related to the needs for constitutive laws which can be integrated into numerical modelling for mine design where structures employ backfill support. A method for representing non-linear backfill behaviour is proposed, which is based upon numerical regression treatment of triaxial laboratory data. The non-linear behaviour observed from a program of laboratory triaxial testing of cemented hydraulic backfill is presented. The particular influence of confining stress and curing duration is high- lighted. The paper concludes by considering the alternative means of accounting for such behaviour in mine design.

Jan 1, 1984

G. H. CLEVENGER, Colorado Springs, Colo.-Mr. Crowe's paper will be of great interest to cyanide operators, as it is a distinct new development in cyanidation. After reading the paper it occurred to me that some of us had done practically the same thing some time ago, but without design and unconsciously. I refer particularly to the operation of some of the earlier types of vacuum filter, used in connection with a dry vacuum pump and a receiver, which is somewhat similar equipment to that employed by Mr. Crowe. However, we did not appreciate the good effects we were getting from such of this solution as was precipitated, and it has remained for Mr. Crowe to bring distinctly to our attention the advantages of removing air from cyanide solutions before precipitation. Full credit is therefore due him for this very clever improvement in the cyanide process.

Jan 11, 1918

By P. G. Shewmon, F. R. Winslow

An experimental method is describedfor Ihe determination of the derivative of the surface free energy (y,) with surface orientation using symmetric bicrystals. The method measures the equilibrium root-angle of grain boundary grooves for the same grain boundary on two different surfaces. In contrast to previous methods, the presence of annealing twins is not necessary. Results on silver at 900°C indicate that ??s/?3 is 0.014y, on the (loo), 0.075y, on the (111), and < 0.004?s on the (110). DURING an investigation of the kinetics of grain-boundary grooving on silver&apos; values of the derivative of the surface free energy ?s with respect to orientation were needed. Previous investigations of these so-called torque terms show that, for low-index planes in copper2 and nickel,&apos; a finite derivative exists even near the melting point. These two studies give the only previously published values of the torque on low-index metal surfaces. These investigators measured the equilibrium root angles, both greater than and less than 180 deg, along the lines where a twin boundary intersects a free surface. The technique described here is suitable for materials which do not have annealing twins, and enables the surface for study to be chosen instead of having to work in a direction normal to the twin trace on the surface. The purpose of this paper is to describe this new technique and to report the values found for the (111): (100), and (110) surfaces of silver. To check the technique proposed above, a series of 99.99 pct Ag bicrystals were used. These bicrystals were grown from the melt by a modified Bridge-man technique so that a low-index direction was parallel to the growth direction. Two orthogonal faces were studied on each bicrystal. One of these contained the low index or simple plane normal to

Jan 1, 1963

By J. J. Frawley, W. J. Childs

Experiments were carried out to induce grain refinement during solidification by applying vibrational energy (freq 20 kc) to small specimens of bismuth, tin, and bismuth-tin alloys. The results show that if the intensity of the applied sound -field is not great enough to fragment the growing dendrites of a pure metal, no grain refinement is observed and the pain size of the dynamically nucleated specimens is the same as the grain size of a specimen statically supercooled the same amount. Bismuth specimens did not show any grain refinement; whereas, the tin specimens did show grain refinement. This phenomenon is the result of the difference in growth habit between the bismuth and tin dendrites. The bismuth-tin alloys showed grain refinement and, in addition, the segregation pattern was changed. THE solidification process is a change in phase requiring the nucleation of the solid phase from the liquid and the growth of this solid phase at the expense of the liquid phase. Since many physical properties and also the integrity of a casting are dependent on the solidification process, understanding and controlling this process are very important.&apos; A good example in the controlling of a cast structure using heterogeneous nucleation theory is the reduction of grain size in aluminum castings by nucleation catalysis.2 This mechanism of nucleation catalysis has been explained by Turnbull.3 Another technique for grain refinement, which has received much attention but the mechanism has not been fully understood, is to vibrate the solidifying melt. Vibrations can be applied to the melt either by vibrating the mold directly or by introducing a vibrating rod into the melt.4-13 Three mechanisms have been proposed to explain this phenomenon: 1) The mechanical fragmentation of the original dendrites that grew into the melt. These crystals or fragmented dendrites act as new growth sites. 2) The nucleation of new grains in the liquid by the generation of very high pressure pulses caused by cavitation in the liquid. 3) The remelting of the dendrite arms during the solidification process. This mechanism is operative only in alloy systems and would be enhanced by stirring or mechanical vibration. The purpose of this investigation was to determine the mechanism that will increase the number of grains when mechanical energy is introduced into a solidifying melt. APPARATUS The unit used to generate the ultrasonic vibrations was manufactured by the Redford Co., and is similar to the one used in ultrasonic soldering. Fig. 1 is a sketch of the major components used for generating ultrasonic vibrations. The crystal transducer assembly consisted of four lead zirconate ti-tanate piezoelectric crystals in an aluminum holder. An acoustical horn, which was fabricated from stainless steel, was attached to the holder by a set screw. The resonant frequency of this unit was 20,000 cycles per sec. A Pyrex crucible, 4 in. in diam and 4 in. high, was contained in a hole in the top of the horn. The piezoelectric crystals changed volume when excited by an electric signal, thereby generating a sound signal which passed through the horn. The crucible was coupled to the horn by a liquid silicone oil. The purpose of the couplant was to transmit the soundwaves from the horn to the crucible. Without the couplant, much of the sound energy would be lost. The energy transmitted was sufficient at the resonant frequency used, so that acoustical cavitation always occurred in the molten metal. The presence of acoustical cavitation was detected by the characteristic hissing sound emitted from the liquid. EXPERIMENTAL PROCEDURE The influence of ultrasonic vibration on the grain refinement of bismuth, tin, and bismuth-tin alloys was studied. These metals were chosen because of their low melting temperature and the relative ease with which they can be thermally supercooled. The following procedure was used for obtaining large amounts of supercooling. Pure bismuth (99.999+), which was received in bar form, was mechanically broken into pieces small enough to be accommodated in a 50 ml beaker. About 200 to 300 g of bismuth and a few grams of SnCl2 as a flux were placed in the 50 ml beaker and melted by induction heating. The melt was held for 20 min at

Jan 1, 1970

By R. B. Gilmore

It has been the custom of the Railroad Commission of Texas to hold hearings each month with respect to existence and imminence of waste of oil and gas in Texas and its prevention, and to issue orders restricting the production of oil to the reasonable market demands and allocating production to the various fields in Texas. The practice of designating the actual days during the month on which wells are to be shut down was discontinued in the order for November 1942, and orders issued thereafter contain only the number of shut-in and producing days for the month. Orders issued by the Railroad Commission are divided into two main subdivisions, the first a general shutdown order of all oil wells in the various fields in Texas, and second, the exception of certain fields to this general order. Table I shows the producing days for all of the fields in Texas for 1944 under the first of these classifications : The fields that have producing schedules varying from the general order may be divided roughly into three subdivisions, as follows: Table 2 shows the producing days for certain fields that were prorated as a group throughout 1944. Other fields which were occasionally included with this group were also prorated under the general order and by special orders. The producing days for these irregular fields are shown in Table 4. In Table 3 are listed fields that were exempted from any shutdown days during December 1944, the majority retaining this exception throughout 1944. Certain fields included in the general order were added to this group on the first day of the month shown.

Jan 1, 1945

By James F. Howe

EveRy engineer and user of wire rope is desirous of information that will enable him to determine whether the performance of any particular piece of rope is satisfactory, and what conditions can be changed so as to increase the life of a rope. In most cases, it is far from easy to analyze the conditions of service and tell which is the greatest factor in determining the life of wire rope. If we start on a layout for an entirely new rope system, the task of making conditions satisfactory is simplified so far as the engineering details are concerned; but if the plant requiring wire rope is in operation, any change is likely to involve the expenditure of considerable money to replace and change over machinery that must be kept in constant operation, because a large monetary loss will result from a shutdown for even a few days. Often wire rope is kept operating under bad conditions, as the user thinks that it is cheaper and quicker to replace the rope than to make alterations in the hoisting machinery. A typical case is a metal mine operating in what is now almost the center of a large mining city, where it owns a few acres of mineral rights. It was expected that the shaft would go to a depth of 1000 ft. (305 m.), so a moderate-sized rope, about 1 1/4in. (31.7 mm.), was used on a 6-ft. drum with a 7-ft. head-frame sheave and rather short lead from drum to head sheave. This mine has gone deeper each year until it is now 2500 ft. deep and the rope speed has been increased from 1500 ft. per min. to over 3000 ft. The original rope just filled the drum in one layer, now it overwinds three layers. The original ropes were probably 6 X 19 crucible steel and lasted from 12 to 18 mo.; now, the highest grade plow steel is used, yet the average service is only about 6 mo. The cause is not hard to find. If the engineers had known at the outset what would be done with this hoist, the design would have been very different. Conditions at this mine, from a wire-rope standpoint, have gradually become worse and it is difficult to see how rope service on this hoist can be compared with the service of previous years with any fairness to the wire-

Jan 1, 1923

By James F. Howe

EveRy engineer and user of wire rope is desirous of information that will enable him to determine whether the performance of any particular piece of rope is satisfactory, and what conditions can be changed so as to increase the life of a rope. In most cases, it is far from easy to analyze the conditions of service and tell which is the greatest factor in determining the life of wire rope. If we start on a layout for an entirely new rope system, the task of making conditions satisfactory is simplified so far as the engineering details are concerned; but if the plant requiring wire rope is in operation, any change is likely to involve the expenditure of considerable money to replace and change over machinery that must be kept in constant operation, because a large monetary loss will result from a shutdown for even a few days. Often wire rope is kept operating under bad conditions, as the user thinks that it is cheaper and quicker to replace the rope than to make alterations in the hoisting machinery. A typical case is a metal mine operating in what is now almost the center of a large mining city, where it owns a few acres of mineral rights. It was expected that the shaft would go to a depth of 1000 ft. (305 m.), so a moderate-sized rope, about 1 1/4in. (31.7 mm.), was used on a 6-ft. drum with a 7-ft. head-frame sheave and rather short lead from drum to head sheave. This mine has gone deeper each year until it is now 2500 ft. deep and the rope speed has been increased from 1500 ft. per min. to over 3000 ft. The original rope just filled the drum in one layer, now it overwinds three layers. The original ropes were probably 6 X 19 crucible steel and lasted from 12 to 18 mo.; now, the highest grade plow steel is used, yet the average service is only about 6 mo. The cause is not hard to find. If the engineers had known at the outset what would be done with this hoist, the design would have been very different. Conditions at this mine, from a wire-rope standpoint, have gradually become worse and it is difficult to see how rope service on this hoist can be compared with the service of previous years with any fairness to the wire-

Jan 1, 1923

By W. H. Emmons

ALTHOUGH gold is one of the rarer metals, it is widely distributed; it is found on all of the continents and in each of the grand metallogenic provinces of the earth. It is prominent particularly in the shield areas of the earth; these areas have produced a large part of the world&apos;s lode gold and in most of them gold lodes are more important than the lodes of other metals. The Scandinavian shield is the only one that has not produced much gold. Nearly all of the world&apos;s gold has been derived from lodes and from sands and gravels where gold placers formed by the destruction of lodes. The gold derived from magmatic segregations, from pegmatites and from contact metamorphic deposits is quite subordinate to that derived from auriferous lodes. The lodes include all veins and related deposits that are formed by hot waters that move along fissures or other openings and that deposit vein matter in the fissures and by replacement of the country rocks along the fissures. All of the shield areas of the earth are characterized by large areas of granitic rocks including granitic gneisses, granodiorites and other acid intrusives which here are included in the general term "granite." The granites are intruded into schists, ancient lavas and other rocks which here are designated as the "invaded" rocks. The granites are parts of what once were great batholiths: that is, they are the remaining portions of great deep-seated bodies that slope outward, have very irregular roofs and so far as known have no floors but extend downward to great though unknown depths. Some of them are scores or hundreds of miles across and contain islands or "roof pendants" of the invaded rocks at places where the roofs of the batholiths were low-that is, where erosion has not yet completely unroofed the batholiths.

Jan 1, 1932

By M. W. Fabjanczyk, E. G. Alexander

INTRODUCTION The purpose of this paper is to summarise development of design processes used in the 1100 oreoody as a result of experience encountered. Design methods have been developed as a result of the history of ground behaviour, free-standing qualities of cemented back fill and mass blasting techniques. This paper contains an historical review of design methods previously described by Matthews ( 1972 ) , Hornsby and Sullivan (1977 and 19781, Kirkby, Blair and Hutton (19781, and Stewart (1980). The reasoning behind design philosphy changes are discussed and placed into context with methods now adopted. The 1100 orebody is Mount Isa&apos;s main producer of copper ore (5 million tonnes per year ) . Proven reserves are 120 million tonnes at 3.2% Cu. Location of the 1100 orebody in relation to overall mine geometry was well described by Dayton (1976). Geology The orebody is located in a series of massive brecciated shale lenses, in either a siliceous or dolomitic matrix, surrounded and separated by a uniform shale sequence. The whole formation is truncated at depth by a faulted contact with a greenschist facies metamorphic sequence below (Figure 1 and Figure 2) Mathias and Clark (1976). The breccia is known locally as silica dolomite and contains nearly all the economic mineralisation. Interfingering of shale and breccia often results in irregular boundaries to the silica dolomite and the ore limits. Geometry The geometry of the orebodies is shown by Figures 1, 2 and 3. Figure 3 also shows the location of the copper orebodies in relation to the lead orebodies. Structure Although the orebody is contained within the massive breccia (u.c.s. 150-250 MPa), it is cut by shear zones sub-parallel to the regional bedding (north-south striking, dipping approximately 60o to the west), and diagonally by major transverse faults (Figure A). These major faults have continuity in excess of 300 metres, with varying amounts of displacement up to 200 metres, and are zones of potential movement.

Jan 1, 1981

By G. S. Ansell

RCENTLY, in investigating the high-temperature creep properties of an aluminum, SAP-type alloy, MD 2100, fabricated by Professor F. V. Lenel of Rensselaer Polytechnic Institute, Ansell and Weertman1 found unusually low creep rates. These creep rates are 4 or 5 orders of magnitude lower than is predicted by the slowest creep mechanism based upon dispersion-hardened alloy theory. They ascribed these results to a lack of both normal active dislocation sources and a continuous three-dimensional dislocation network. If one couples these results with the following factors of production and microstructure: 1) The compacted and sintered aluminum powder compact is hot-extruded, with an extrusion ratio of 25:1.2 2) The alyminum oxide particles are approximately 140A units thick, and have a spacing varying from 0.05 to 1.5 1. 3 3) The alloy has plate-shaped grains with minor axes of about 5 X 10 -3 mm and major axes several orders of magnitude greater than this.&apos;

Jan 1, 1960

By T. M. Olson, B. G. Lewis

The adsorption of selenite on bentonite, kaolinite, and an iron--coated illite was studied to determine the importance of several soil variables on selenite removal from uranium mill tailings pond seepage. Adsorption capacities of the clays of selenite varied by orders of magnitude and decreased in the following order: illite > kaolinite > bentonite. Maximum adsorption of selenite on the clays was observed between pH 2.5 and the clay&apos;s zero-point-of-charge. Substantially less selenite was adsorbed on these clays in actual mill tailings solutions than in model systems. Virtually all selenite was removed from the tailings at pH 7. The principal removal mechanism at this pH is suggested to be the adsorption of selenite on freshly precipitated metal hydroxides. It is concluded that selenite can be removed from tailings seepage in soil or in clay liners in the presence of kaolinitic clays and iron oxides. Selenite would also tend to be removed from tailings seepage in calcareous strata.

Jan 1, 1984

By E. A. Beck

For a number of years many attempts have been made to use thermit in order to do away with piping in ingots. Some of these attempts were successful, while others did not give the expected results. Nearly every plant had its own method of using the thermit, and no special care was taken to study the results or to find the causes for lack of success. Formerly the principle of the process was to decrease the piping by introducing a can filled with thermit, attached to an iron rod, into the head of the ingot directly after it had been poured. In this case the thermit reaction took place in the upper part of the ingot, and it was thought that through the heat produced the head would keep liquid longer and piping thus be reduced. In other words, the aim was to keep the head of the ingot open by making use of the heat of the thermit reaction, which would thereby give the gases in the steel sufficient time to escape. This result can be attained by the application of a large enough quantity of thermit, but it would not be economical in general practice, and could only he used for high-grade material. Many steel-makers abroad and in this country have had this experience. The Th. Goldschmidt A. G., Germany, has, therefore, made a special study of this question with the cooperation of a well-known steel company, and has worked out a new method for the application of thermit for this purpose. The results obtained have been most satisfactory and reliable, and this process is now used in Germany on a large scale in many prominent steel-works. The thermit is applied in cans, as in former years, but the principle of the process is entirely different. The object of using the thermit is not to heat the steel and keep it liquid,

Jan 1, 1914

By J. H. Johnson, H. J. Schock

The cases of no auxiliary ventilation and ventilation with tubing were mathematically modeled, using a turbulent dispersion model. The Scooptram® used to load is modeled as a variable-speed, variable-strength source of pollutants moving in and out of the dead-ended drift. Model predictions are compared to experimental measurements. A parametric analysis was performed to determine If a relationship existed between C02 and NO levels. It was concluded from this analysis that when modeling a load-haul-dump cycle, it is necessary to use a model that can predict changes in source strength as well as source location. Carbon dioxide was used as a tracer to calibrate the model since, knowing the fuel flow rate, it is possible to calculate C02 production. The model was then verified after this calibration process using additional experimental results. With the calibrated model, it is possible to predict pollutant concentrations at any location in the heading using an engine map and the previously calculated flow field.

Jan 1, 1984

By J. Farkas

A techno-economic assessment for the recovery of several elements from seawater is presented. Gold recovery has been used as an illustration for the economic evaluation of several processes. Current technology does not present any economically viable alternative to recover gold from seawater because its concentration is several magnitudes too low. However, with the increasingly larger availability of concentrated seawater, mainly from desalination and other processes, coupled with advances in technology, especially genetically modified specific microorganisms, may make the recovery of gold and other desired elements from seawater a reality in the near future.

Jan 1, 1984

By G. A. Vissac

IN the presentation which follows, washability curves, such as are commonly used in making studies preliminary to the cleaning of any coal or to the concentration of any mineral, have been reduced in each instance to a single straight line; thus all the most important characteristics of the coal or mineral are represented in a form more advantageous than that in which such data usually are shown. To obtain consistent results, float-and-sink data must be based on a single definite narrow size range, which may be designated "a coal unit." It will be shown that such units, each embodying a different size range, can be grouped to form what may be termed "a composite coal." A three-dimensional presentation will emerge, which will closely identify the coal, illustrate its characteristics in a new manner and explain many obscure facts. FLOAT-AND-SINK TESTS For the preliminary study of any cleaning or concentration problem, or in the control of any operation, float-and-sink tests must be made. The results of these tests are grouped in tabular form and then illustrated in various systems of curves; but if such a graphic representation is to have the utmost practical value, it must offer at least the following advantages: (I) It must be easier to read than the tabular results, and (2) it must be easy to plot, check and interpolate. The first requirement will be attained by reducing the number of curves to a minimum, and the second by some system of representation that will use only straight lines. Of the many washing curves now in use, only the "recovery curve," often known as the "composite curve "-a somewhat misleading term-will be considered. Any point on the recovery curve will show what percentage of weight of clean coal can be recovered when the mineral is washed at a certain specific gravity. As an example, the tests listed below Fig. I are illustrated in the drawing by a curve obtained by plotting (I) as abscissas the ash content of the coal recovered and (2) as ordinates the corresponding percentage of refuse discarded; but, in general practice, instead of writing down that weight, it is customary to set down its complement, which is the corresponding weight of coal recovered. From this curve can be deduced the information necessary for the solution of most practical problems. NEW FORM OF GRAPHIC PRESENTATION The resemblance of the recovery curve in Fig. I, or, for that matter, the recovery curve obtained in common practice, to a power curve is apparent. The general equation of such a curve is y = axn where n is negative. Taking logarithms: log y = a + n log x. Using a logarithmic scale, the equation of the recovery curve will be Y = A + bX. On this logarithmic basis, the recovery graph will be a straight line, using the same variables as in Fig. I ; namely, the ash con-

Jan 1, 1942

By A. D. Hill, R. S. Schechter, M. P. Walsh, I. H. Silberberg, M. J. Humenick

There are many uranium deposits which are too deep, too poor in quality or too small in extent to be economically strip mined. It now appears that this uranium can be mined using in situ leaching processes. A number of field tests have been, are being or will be conducted to demonstrate the feasibility of In site leaching. Preliminary results are encouraging, but a major question concerns the restoration of the mine site, which is generally contained within an aquifer. It is necessary to ensure that the quality of the water is not adversely affected by the mining operation. One component of the lixiviant is necessarily a cation and, during the course of mining, the ion exchange sites of the minerals in the mine zone become saturated with this cation. Ammonium is the cation now commonly used. Clearly, any restoration procedure or question involving the rate of cation migration with the groundwater all necessarily involve the process of ion exchange coupled with flow in porous media. The equations describing this process are presented in this paper and numerical solutions obtained. Preliminary results showing the effect of isotherm shape, cation exchange capacity, flow and dispersion are presented. These results demonstrate that in many situations cation migration in ground water will be slow.

Jan 1, 1979

By Vsevolod Krivobok

IT is generally recognized that "low temperatures" have a definite effect on the properties of metals and alloys. Furthermore, it is also generally understood that the effect is decidedly adverse. The possibility that the same low-temperature treatment might be employed for the purpose of improving certain properties of the .alloys has received less attention until recently, and the experimental and theoretical knowledge consequently is meager. The effect of low temperatures may be studied in two ways: by studying such properties as tensile strength, hardness, impact resistance, etc., at low temperature, and by studying the properties of alloys at room temperature after these alloys have been subjected to a low-temperature treatment. Even in the latter case, certain properties will differ materially from the same properties obtained on identical material but without cold treatment. In other words, subjecting alloys to cold treatment results in an irreversible change in mechanical properties. Changes of this character are usually indications of the appearance of a new phase or phases, and would be likely to occur in alloys which, either by virtue of their composition or by heat treatment, are retained at room temperature in a metastable condition. Consequently, studies of the effect of low temperatures logically should be conducted from the physicochemical point of view, since the results of such studies not only would furnish metallurgists with interesting theoretical data but would clearly indicate the classes of alloys that would hold promise of improvement, and, possibly, of new applications. As the present investigation deals with chromium and chromium-nickel alloys of iron of the stainless variety, it has been thought desirable to present the data concerning low-temperature properties of these alloys, available from the most recent and most comprehensive work of H: S. Russell.&apos; A summary, of these data is given in Table 1. The data are confined to a limited number of alloys of the type dealt with in the present

Jan 1, 1931

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 &apos;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 Victor V. Damiano

THOMPSON1 proposed a very convenient nomenclature in which an imaginary regular tetrahedron was used to facilitate the analysis of dislocation interactions in fcc materials. The faces of the tetrahedron were constructed parallel to four different sets of (111) planes, and the six edges of the tetrahedron then represented the six 1/2 [110] Burgers vectors. The lines which joined the midpoint of a tetrahedron face with the ends of one of its edges represented the Burgers vectors of the partial dislocations into which the six 1/2 [I101 Burgers vectors dissociate. Using Frank&apos;s2 notation, all of the dislocations and their partial dislocations were identified and numerous possible interactions were postulated. The case of hexagonal crystals is unfortunately more complex, but it appears convenient to introduce a system similar to that of Thompson1 to describe the various slip planes and Burgers vectors encountered in cph structures. The system proposed has limited application but serves to identify the following slip systems {0001} <l20>, {1010} <1120>,

Jan 1, 1963