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By P. R. Sperry

A METHOD was recently devised to indicate two or more successive stages of the migration of grain boundaries in aluminum, and to record the direction of the migration. This technique was used for the study of the various types of boundary migration occurring in high purity aluminum.' The method employs alternate annealing and electrolytic etching treatments, repeated as many times as desired. All successive sets of grain boun- dary positions revealed by the various etches appear superimposed on each other. The last etch is designed to leave an oxide film on the surface which is optically anisotropic. The orientation of the oxide film at each point is determined by the orientation of the underlying aluminum grain. When viewed with polarized light using crossed nicols and a Biot-Klein quartz plate, grains with differing orientations appear in different colors, as described by Hone and Pearson.' The last boundary positions are revealed by these color differences. The first step of the process is to obtain a desired starting grain size by annealing, for example, if high

Jan 1, 1951

By H. A. Schwartz, A. F. Gorton, H. R. Payne

In a previous paper1 we published what we believed to be a correct stable equilibrium diagram for an iron-carbon alloy containing + 1.20 per cent. silicon. The purpose of the present paper is to record the results of studies concerning the effect of silicon on the location of the eutectoid points of both systems, including also certain incidental observations of general interest. We prepared white cast irons containing roughly 21/2 per cent. carbon, 0.05 per cent. manganese, and 0.03 per cent. each of phosphorus and sulfur, but of accurately known silicon contents which varied from 0.40 to 3.32 per cent. These were completely graphitized, and both A1 points determined, as in our previous work, the specimens being converted from the stable to the metastable condition and vice versa by appropriate heat treatments. Each stable alloy was heated to a few degrees above Arl for 3 to 7 hr., quenched and analyzed for total and graphitic carbon, the difference being the "combined" or, better, agraphitic2 carbon content of the saturated solid solution just above the eutectoid transformation. One specimen was lost through accident, and the 0.40-per cent. silicon material gave an anomalous result ascribed to difficulty in maintaining the stable system in the presence of but little silicon.

Jan 1, 1923

By H. R. Payne, A. F. Gorton, H. A. Schwartz

In a previous paper1 we published what we believed to be a correct stable equilibrium diagram for an iron-carbon alloy containing + 1.20 per cent. silicon. The purpose of the present paper is to record the results of studies concerning the effect of silicon on the location of the eutectoid points of both systems, including also certain incidental observations of general interest. We prepared white cast irons containing roughly 21/2 per cent. carbon, 0.05 per cent. manganese, and 0.03 per cent. each of phosphorus and sulfur, but of accurately known silicon contents which varied from 0.40 to 3.32 per cent. These were completely graphitized, and both A1 points determined, as in our previous work, the specimens being converted from the stable to the metastable condition and vice versa by appropriate heat treatments. Each stable alloy was heated to a few degrees above Arl for 3 to 7 hr., quenched and analyzed for total and graphitic carbon, the difference being the "combined" or, better, agraphitic2 carbon content of the saturated solid solution just above the eutectoid transformation. One specimen was lost through accident, and the 0.40-per cent. silicon material gave an anomalous result ascribed to difficulty in maintaining the stable system in the presence of but little silicon.

Jan 1, 1923

By S. Edward Drummond, Charles D. Haynes, Stephen H. Stow

This paper is a preliminary report on the occurrence and distribution of economically interesting heavy minerals (kyanite, sillimanite, staurolite, zircon, monazite, ilmenite, leucoxene, rutile) in sands from the sea floor surface of the offshore area, Alabama-Mississippi. Weight percent of heavies derived from the +60 portion of 97 samples is contoured in [Fig. 1]. Five hundred grains from 42 of the heavy mineral separates were identified and sized microscopically; the data were converted to weight percent for each mineral species and are summarized in [Table 1]. Heavy Mineral Distribution In the Gulf, there is a general westward decrease [(Fig. 1)] in maximum abundance of heavies from 2.4% north of Sand Island at the mouth of Mobile Bay to slightly over 1.0% south of Petit Bois Island and a corresponding decrease in the Mississippi Sound from 1.4%, north of Dauphin Island to slightly over 0.25% north of Horn Island. Average concentrations of heavies for different areas are found in Table 1. There is westerly longshore transport in this area; the interaction of the longshore current with discharge from Mobile Bay and disruptions of the current by Sand Island, possibly aided by a shoaling effect, appear to be the cause of the preferential deposition and concentration of heavies (2.4%) north of Sand Island in 10 to 14 ft of water.

Jan 1, 1977

By R. C. Davis, R. F. Berry, G. W. White, B. T. O’Connell, L. A. Stacha

P,, and v, may now be solved for by trial and error between Eqs. 2 and 3, by assuming time approaching zero and equating PI, to P12. Observe that the pressure under the slug, P12 of Eq. 3, does not remain equal to the P1, at the valve in Eq. 2 as the slug proceeds up the hole. To plot the profile of pressure vs depth, it is necessary to express P12 in terms of P11. To do so, the extent to which the original submergence length S changes with respect to time must be analyzed. At the end of time t after injection, the actual value of L in Fig. 3 is The fall-back v,(t) is now distributed in the gas and exerts pressure on the bottom. This, in addition to the weight of the gas, amounts to the difference in pressures from point to point. With the average pressure profile calculable, a true numerical value for the average pressure in the tubing may be obtained. The value of v, must be obtained experimentally, and since v,, S and D are known, the basic Eq. 1 may be solved for the amount produced. Knowing P, and the actual volume of tubing occupied by gas (vat), it is possible to calculate the volume of gas at standard conditions which is present in the

By G. E. Agar

The energy required for dry grinding of phosphate rock in ball and roller mills has been analyzed by the method suggested by Charles and others. The findings are not wholly in agreement with Charles' predictions; but, nevertheless, the method of analysis is shown to be sound. Some of the deviation is probably attributable to the characteristics of a dry grinding system. Many laboratory and pilot plant scale experiments have been made to determine the energy requirements for size reduction. This topic was recently reviewed by Agar and Brown' and it was apparent that very little if any data exists in the literature which permits one to apply the Charles 2-Holmes3 analysis to industrial size systems. More recently, the idea has been put forward that the postulate of comminution by impact used by Charles and others was not sufficient to explain size-reduction throughout the grinding operation. The opportunity exists in the grinding operations of International Minerals and Chemical Corp. (IMC) to analyze the energy-size relationship for dry grinding phosphate rock in both ball and roller mills. This situation arises because the mills are used for custom grinding and make products from 50% to 85% minus 200 mesh. BACKGROUND A correlation of particle size in a comminuted material with the energy expended in size reduction was proposed by charles2 to be of the form

Jan 1, 1965

By C. L. Dake

Chemistry of Iron Solution IRON is much more soluble in the ferrous than in the ferric form. Where, as in the case of the ferrous silicates and the sulphides, the iron is already in the ferrous form, it may go at once into solution and be removed, upon the breaking down of the parent rock. If in the ferric form, it must first be reduced; usually by the decay of organic matter, the demand of the decaying carbonaceous matter for oxygen being so great that the latter is abstracted from the ferric compounds and the iron is thereby reduced and rendered' soluble. The iron may go into solution as the sulphate, or in the presence of excess CO2 as ferrous carbonate. It is probably soluble as salts of the organic acids.1 Recent work indicates that these are important in the formation of bog ores.2 There is considerable variety of opinion concerning the behavior of these organic compounds.3 The secretions about the roots of plants and trees also cause the solution and removal of iron and a consequent bleaching of the soil.4 While the matter is not yet well understood, we can probably say definitely that the so-called organic acids are a group of colloids which possess slightly acid properties, and the salts of which are partly soluble

Jan 7, 1915

THE Woman's Auxiliary now has its own publica-tion, a monthly news letter that is mailed direct to all its members. It is a lively and readable sheet. Any member of the Auxiliary failing to receive it should communicate with Mrs. J. E. Johnson, Jr., 49 Church Lane, Scarsdale, N. Y., and get on the mailing list. The detailed reports of the meetings will hereafter ap-pear in the News Letter rather than in MINING AND METALLURGY. The regular Board meeting held on March 3, with Mrs. Barron presiding, was well attended and the re-ports of the committees, and from local sections, showed a keen interest in the work. of the organization. Steps are being taken to endow a "Mary Young Westervelt Scholarship," libraries are being built up in mining towns, and interesting reunions .are being held by the members in the various local sections. The Auxiliary is filling an important place and doing it well. Women of the families of Institute members not already affili-ated with it would find it pleasant to get in touch.

Jan 4, 1927

BEFORE me is a colored mining-claim map of the productive portion of the Robinson Mining district-sometimes called the Ruth-Kimberly area-that lies a few miles west of Ely, Nevada. It covers an area of 20 sq mi and at the end of 1954 had produced just under 2,000,000 tons of copper and about 2,000,000 oz of gold as a by-product. The three principal colors on the map and the meaning of each are: Red -Property of the Nevada Mines Division of Kennecott Copper Corporation, formerly known as the Nevada Consolidated Copper Company. Yellow -Property of the Consolidated Coppermines Corporation. Green --Consolidated Coppermines property under lease to Nevada Mines. The striking feature of the map is the crazy-quilt intermingling of the colors and the tendency of property lines to intersect ore bodies. For example, the westerly one-fourth of Nevada Mines' Copper Flat pit, source of most of the ore,up to date, is in Coppermines property. Nearly half of Nevada Mines' Veteran pit is on leased claims; and Nevada's new Deep Ruth shaft is on a right of way on ground originally owned by Coppermines. On the other hand, the original Ruth underground mine and the new Kimbley pit are on Nevada Mines property; and the Morris and Brooks opencut mines, the most important of Cop-

Jan 1, 1957

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Jan 1, 1942

The following very cordial letter, addressed to the President of the American Institute of Mining Engineers by the President of the graduates of the School of Mines of Saint-Etienne, will he deeply appreciated by all American engineers and will perhaps be of use to engineers going "Over There." Members are requested to communicate the substance of this letter to friends or acquaintances in France: Dear Mr. President: Now that the American armies are crossing the ocean to come to our side in the defence of the liberty of the world, and the intellectual elite of your great country is very ably cooperating with us in this supreme struggle, we ardently desire to give them a whole-hearted reception upon their arrival on the shores of France. The representatives of your illustrious association will be more especially welcome among their French colleagues, and both at Saint-Etienne and at Pans, we desire that their sojourn he rendered comfortable and congenial in every way possible. We therefore put ourselves unreservedly at their disposal. At Paris especially those of our colleagues

Jan 7, 1918

The Commissioner of Education has issued a call for a public conference on business training for engineers and engineering training for students of business. This conference, national in scope and character fully representative of all interests, will be held in Washington, D. C. on June 23 and 24. Educational institutions, commercial organizations, and educational and engineering societies will be given an opportunity to state their views. Engineers, educators and business men will be invited to discuss the following major topics: Business Training for the Engineer; Engineering Training for Commercial Enterprises; Significance of the. War Experience for Engineering Education; Training of the Engineer for Foreign Projects. This conference has been called on behalf of the Conference Committee on Commercial Engineering. This Committee is composed of administrative professors in engineering and commerce from several of the large educational institutions and representatives from the American Institute of Mining and Metallurgical Engineers, Society for the Promotion of Engineering Education, The American Society of Civil Engineers, American Institute of Electrical Engineers, American Society .of Mechanical Engineers, and a committee f fifteen on Educational Preparation for Foreign Service.

Jan 6, 1919

SINCE dad first took us to the ocean we have always seen a plump elderly gentleman who, with supine composure, floats over the crests spouting whale-like to the wonderment of small boys. Floating requires certain physical and mental characteristics that it takes many years to acquire. These are, in order of importance, confidence, beef, and complete relaxation. Possibly a rough parallel can be drawn between the mining industry and the dignified paunchy gentleman riding the billows. Mellowing in a downtown club he reminisces over his rough-and-tumble youth; when frontiers were being pushed to continental limits and the great mines were discovered on a first come first serve basis. Those were the days of the empire builders. They created the methods, made their own laws, and gambled their very lives on the outcome. For these efforts and sacrifices they shared in the great wealth which was made. There were no comparisons between the small and big operators because they all started small and those with the most financial know-how slowly merged into the big companies of the present.

Jan 12, 1951

Equilibrium in Lead Smelting. By S FREDERICK RAVITZ AND KENNETH E FISHER (Tech Pub 681, also Trans , vol 121 2300 words) Four liquids are ordinarily produced in lead smelting, namely, bullion, speiss, matte and slag To determine whether these exist together in equilibrium, the distribution of gold and silver among them was measured To crucibles containing similar mixtures of all four products, varying amounts of silver were added, and the crucibles were heated together under the same conditions for 3 hr, during which the charges melted and separated into four layers After cooling, these layers were assayed for silver, and the distribution coefficients, 1 e , the ratios of the concentration of silver in any particular layer to that in the bullion, were calculated In each experiment, each distribution coefficient was found to be constant, regardless of the amount of silver used Similar results were obtained using gold instead of silver The constancy of the distribution coefficients indicates that the bullion, speiss, matte, and slag exist together in equilibrium

Jan 1, 1937

By W. N. Best

THIS paper is not intended as a scientific discussion of the combustion of oil but is written from, the standpoint of an operator who has the experience and qualifications necessary to guide others in producing the most economic results in the use of liquid fuels. Oil, in this paper, usually, means petroleum or its products but incidental reference is made to other liquid and gaseous fuels, so that the term may be considered, as referring to all liquid and gaseous hydrocarbons in comparison with solid fuels, as coal and. wood. However, only a few of the principal factors in the use of oil as a fuel can be given. The present, and prospective, high price of coal is causing users of fuel to renew inquiry as to the merits of other forms of fuel for industrial purposes. Crude oil (petroleum) is proving to be one of the world's most valuable mineral resources. The recent discovery that oil underlies a considerable area of the United States, Mexico, and other parts of the world to a greater extent than was formerly believed and the large production of some of the wells in these areas shows the probable quantity of fuel oil that may now be available. Through the energy of Lord Cowdrey, who was one of the pioneers of the oil industry in Mexico, oil has been discovered in England; some prominent geologists believe that it may be found yet, in quantity, in Great Britain. For years, oil has been known to be of great value in the manufacture of metals. It has proved incomparable in forge shops, steel foundries, heat-treating furnace s, and wherever accuracy of temperatures is essential, or where a maximum output is desired as well as quality of metal. In some types of equipment, the output produced with oil as fuel is double that obtained with coal and, at a reduction of 50 per cent, in the cost of the fuel. For example, in drop-forging plants, the metal is always waiting for the man when oil is used as fuel, whereas with coal, the man must wait for the metal to become sufficiently heated.

Jan 8, 1920

By William Y. Holland, Roger M. Cook

In view of the increasingly widespread deterioration of concrete structures as the result of the interaction of the alkalies sodium and potassium released by hydration of portland cement and susceptible rocks and minerals in aggregates, it is believed that a paper summarizing the geographic distribution of these aggregates will be of interest to producers and users of concrete, concrete products, and concrete-making materials. THIS paper reviews the problem of alkali-aggre-gate reaction in concrete and describes the geologic and geographic occurrence and distribution of alkali-reactive sand and gravel in western United States. It includes no discussion of crushed stone or synthetic aggregates. Most deposits of sand and gravel are accumulations of particles of rocks and minerals from a variety of sources, and it is not unusual for at least one or two varieties of the rocks to contain some form of reactive material. Examination by petro-graphic methods of many sands and gravels, as well as manufactured aggregates, has shown that a comparatively high proportion of the deposits does contain, in greater or lesser degree, rocks and minerals known to be deleteriously reactive with the alkalies of cement. Fortunately the amount of reactive materials is commonly less than that necessary to cause deleterious effects in concrete. As investigation of unsound concrete structures progresses, it becomes evident that the alkali-aggre-gate reaction is even more widespread than supposed, Figs. 1 and 2. Even though some parts of the country appear at present to be immune, further investigations will probably show that the effects of alkali-aggregate reaction can be seen in many structures in these areas, although only on a small scale in most of them. Many concrete structures will, of course, have lived their useful life before disintegration from this cause is serious, and in others the alkali-aggregate reaction may never become significant even though the microscopic evidence of reaction is present. The alkali-aggregate reaction first was reported to be a cause of deterioration of concrete in 1940 when Stanton1 described expansion of concrete pavements in California. Similar expansion and deterioration of concrete was recognized during succeeding years in concrete structures located in many parts of the country, but particularly in the western states. A number of concrete laboratories2 became interested in the problem. It was soon determined that only certain combinations of aggregate and cement caused the alkali-aggregate reaction to take place, and moreover that the reaction progresses only in the presence of water. Further research proved that cements containing more than 0.60 pct total alkalies (pct Na,O + 0.658 x pct K2O), when used with aggregates containing appreciable amounts of reactive ingredients, caused the reaction to take place, usually with subsequent deterioration of the concrete. During the last few years this limitation has been adhered to in both government and private construction as the maximum allowable alkali content of cement to be used with aggregates of known alkali reactivity. Because of this limitation, it appears that deleterious reaction either has been reduced or eliminated in many recently built structures in which it probably would otherwise have occurred. Recent tests have shown that the degree of expansion obtained with any particular cement-aggre-gate combination depends not only on the alkali content of the cement but also upon the relation of this alkali content to the amount and degree of reactivity of reactive constituents in the aggregate.' In laboratory mortar bars, opal and cements with alkali content of as low as 0.2 pct (as equivalent of Na2O) have produced deleterious expansion as the result of alkali-aggregate reaction. These experiments demonstrate that aggregates containing even 0.1 pct of opal are deleteriously reactive. It was soon determined that alkali-silica gels were formed by the interaction of the alkalies of the cement and the reactive aggregate, Figs. 3 and 4. Osmotic or swelling pressures produced by the continued hydration of these gels cause expansion of the concrete with resulting cracking, warping, and dislocation. Evidence of the alkali-aggregate reaction can be seen by a petrographic study of the deteriorated concrete. Among the first structures studied by this method was Parker Dam on the Colorado River, California-Arizona. In the concrete from this dam pebbles of rhyolite, andesite, siliceous limestone, and chalcedonic chert were found to be reactive.

Jan 1, 1954

By Claude H. P. Lupis, John F. Elliott

IN the recent past, extensive use has been made of the interaction coefficient in treating the thermody-namic behavior of components in solutions at dilute concentrations. The development of this concept by wagner1 and chipman2,3 is sufficiently well-known so that its elucidation here is not necessary. The present discussion is focused on the relationship between E and e. The usual forms of the coefficients are:

Jan 1, 1965

By E. J. Ripling

A NY mechanism proposed to explain hydrogen embrittlement in titanium and its alloys must, of course, be consistent with the experimental data that characterize this embrittlement. Unfortunately, however, the mechanical behavior of hydrogen-bearing titanium, at least a-ß titanium, has not been unequivocally defined. Lenning, Craighead, and Jaffee have clearly shown that hydrogen cmbrittles a-titanium by elevating its transition temperature, probably as the result of the formation of titanium hydrides. Therefore, in these alloys, hydrogen acts like at least one other interstitial contaminant, namely, nitrogen.&apos; On the other hand, ß-titanium has been shown by these same investigators to tolerate very large amounts of hydrogen without suffering severe mechanical damage.2 Mixing these two phases, however, to form the most important class of commercial alloys, the a-ß alloys, again results in severe hydrogen embrittlement, although the mechanism by which the embrittlement is produced is not of the same type as that which causes brittleness in a alloys. Ductility damage due to hydrogen increases as the strain rate is reduced in a-ß alloys, while embrittlement in a alloys increases as the strain rate is increased, since the latter is a transition temperature behavior. Steel, like the a-ß alloys, becomes more hydrogen sensitive at slow strain rates, suggesting that the mechanism producing the embrittlement in these two metals is similar. Brown and Baldwin&apos; described the hydrogen-produced ductility depression in steel as a function of testing temperature and strain rate by defining the slope of the two surfaces that produced the depression in a three dimensional chart, Fig. 1. One of these surfaces was given by the equations (de/de)4 > 0 (de/dT) < 0 [1] while the other was defined by the pair of equations Surfaces of the type given by Eq. 1 are suggested in two ways. One is an embrittlement mechanism wherein the diffusion rate of hydrogen is competitive with the rate at which the material is being deformed, as suggested by the planar pressure theory of Zapffe and his co-workers.&apos; The other is the diffusion controlled extension of Orowan&apos;s theory on delayed fracture in glass by Petch and Stables.&apos;&apos; Surfaces of the type given by Eq. 2 are also compatible with a mechanism of pressure build up in voids, according to de Kazinczy,&apos; since the solubility of hydrogen in the metal increases with testing temperature so that as the temperature is raised, the pressure in the voids is reduced. Kotfila and Erbin recently presented some data on the dependence of ductility on testing temperature and strain rate for the a-ß 3 pet Mn complex alloy at four different hydrogen levels.H Although data were presented for only three testing temperatures at three different strain rates, their results indicated that surfaces of the types defined in Eqs. 1 and 2 are produced in the alloy when the hydrogen level is sufficiently high—200 and 300 ppm—Fig. 2. Jaffee and his co-workers presented data on a number of different a-ß alloys which indicated the existence of surfaces of the type described by Eq. 2, but the ductility recovery at low temperatures as given by Eq. 1 was not found." In an attempt to aid in crystallizing this description of the ductility dependence of hydrogen-bearing a-ß alloys, tests were conducted by the author on a-ß titanium 140A with three different hydrogen contents. The tensile properties of two as-received rods and one vacuum annealed rod* were obtained over a range of testing temperatures and strain rates as shown in Figs. 3 and 4. Hydrogen analyses were made by the Battelle Memorial Institute on four pieces of the rod whose properties are shown as solid circles in Fig. 4. The hydrogen content of these pieces, taken at widely spaced intervals within the rod, were 280, 270, 289, and 270 ppm, indicating that the hydrogen content within a single as-received rod was quite uniform. One of the broken test pieces whose properties are shown in Fig. 3 as solid circles was also analyzed, and found to have a hydrogen content of 310 ppm. The analyses obtained on two of the vacuum annealed specimens were 92 and 170 ppm.

Jan 1, 1957

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 R. W. Heckel, J. H. Smith, H. W. Paxton

The habit plane of proeutectoid cementute precipitated from austenite was studied using a two-trace surface (analysis coupled with a direct X-ray back-reflection determination of the orientatzon of the parent Matrix. The results were the same as those obtained by earlier workers1 - 2 who used Indirect methods to determine the orientation of the matrix. The data indicate that a range or habit planes in the parent phase is operative which is not in agreement with accepted existing theories. In 1933, Mehl, Barrett. and smith1 obtained a non-unique result in a study of the Widmanstätten habit plane of proeutectoid cementite. Their data are shown in Fig. 1. These results were verified by Greninger and Troiano,2 although they did not pre-sent any data. Both of these investigations relied upon indirect methods of determination of the matrix lattice orientation. Theoretical considerations of Widmanstatten precipitates have usually proved or assumed an orientation relationship between matrix and precipitate; the habit plane expressed relative to the matrix is generally unique, although it may be irrational.3 Opinion is divided as to the factors influencing the choice of habit plane. Mehl4 felt that a nucleus which was plate shaped to minimize strain energy and surface energy during its formation could maintain this shape by the point effect of diffusion; the

Jan 1, 1961