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By J. L. Kenty, J. P. Hirth

The concept of a critical super saturation, below which the nucleation rate is essentially zero and above which it is essentially infinite, is discussed with reference to vapor-solid nucleation. The necessary and sufficient conditions deduced for observations of this type of behavior are: 1) the nucleation rate must exhibit a sharp dependence on super saturation, 2) the growth rate must be sufficiently large that nuclei become observable in the time period of the experiment, and 3) the number of highly preferred nucleation sites must be small. Experiments reveal that the nucleation of silver on sodium chloride is visually detectable at all experimentally accessible super saturations and does not exhibit critical nucleation behavior. Failure to observe a critical super saturation is attributed to the insensitivity of nucleation rate to supersaturation as a consequence of the particular values of the contact angle and the surface free energy for this system. THE concept of a critical supersaturation, below which the nucleation rate is essentially zero and above which it is essentially infinite, arises naturally in homogeneous nucleation theory. Experimentally this type of behavior has been found by Volmer1 and others for water and other low surface tension liquids, as reviewed by several authors.2'3 The same type of behavior has been predicted and observed for heterogeneous nucleation of solids by Yang et al.4 and others,596 as also recently reviewed.2,7,8 In the work reported here on the heterogeneous nucleation of silver on NaC1, however, no critical super-saturation was found. Similar observations have been made recently for other systems.9-11 These results led to a reexamination of nucleation theory which revealed that there are conditions for which critical behavior is not predicted, either for homogeneous or heterogeneous nucleation. Although heterogeneous nucleation is of primary importance in this paper, some insight into critical behavior for such a case can be gained by considering homogeneous nucleation. Accordingly both types of nucleation theory are reviewed briefly. The requisite conditions for critical supersaturation behavior are then considered. The experimental results for the nucleation of silver on NaCl are presented and interpreted in terms of the theoretical presentation. REVIEW OF NUCLEATION THEORY There are essentially two approaches to nucleation theory, the so-called classical theory involving the concepts of bulk thermodynamics, and the statistical mechanical theory in which nuclei are regarded as macromolecules. The classical theory is based on the work of Volmer and Weber12,13 and Becker and. Doring14 and has been extended by Pound et al.15 The crucial assumption in the classical theory is that the small clusters or nuclei can be characterized by the same thermodynamic properties as those of the stable bulk phase. Thus, the nuclei are assumed to have a surface free energy, y, and a volume free energy of formation (relative to the vapor phase), ,, identical to that of the bulk. For deposition under low super-saturation conditions, the nuclei are large and this assumption is satisfactory. However, in many cases of interest, the nuclei contain only a few atoms and this assumption is highly questionable. The statistical mechanical models originated, for the specific case of a dimer as the critical nucleus, with the work of Frenkel16 and were extended later to larger sizes by Walton,17,18 Hirth19 and, more recently, Ht Zinsmeister. These models describe the nucleus in terms of a partition function, the estimation of which is tractable for clusters of 2 to 10 atoms, but extremely difficult for clusters larger than 10 atoms. Although the classical and statistical mechanical models are expected to apply for the limiting cases of large and small nuclei, both are uncertain for intermediate sizes. In this paper we shall treat only the classical model, recognizing that it is exact only for large nucleus sizes and regarding it as a phenom-enological description for small nucleus sizes. When analyses of experimental data using bulk properties show the nucleus size to be small, the resulting parameters should be regarded as largely empirical parameters describing the relative nucleation potency of the system. Considerable justification for the continued use of classical theory is provided by its general success in predicting nucleation behavior as a function of supersaturation and temperature. We emphasize that the qualitative features of the statistical mechanical models, particularly the critical super-saturation behavior that is central to the present work, are the same as those of the classical model. Of course, potential energy terms and surface partition functions replace the volume and surface energy terms of the latter model. The most recent versions of classical nucleation theory have been extensively reviewed.2,3,7 so that only the results are presented here. For homogeneous nucleation of a condensed phase from the vapor phase, the volume free energy change is ?Gv=vrT = =^ln£ [1] where v is the molecular volume of the condensing species. The supersaturation ratio,

Jan 1, 1970

By B. G. Klugh

(New York Meeting, February, 1912). IN a paper before the Institute at Wilkes-Barre, Pa., June 1911,1 Mr. James Gayley discussed the application of this process to iron-bearing materials. The same author2 described the results of operations at the plant at Birdsboro, Pa. The purpose of the present paper is to present further discussion of some technical details involved in the operation of this plant, and of the theoretical and practical relations of this product to blast-furnace practice. Since Oct. 1, 1911, the Birdsboro plant has been in operation at the blast-furnace of the E. & G. Brooke Iron Co. The results have been highly satisfactory, although the material treated, being chiefly the flue-dust currently made by the furnace or taken from the accumulated stock-pile, was excessively high, and yet not uniform, in carbon, so that the desirable control or regularity of the amount of fuel in the mixture treated could not be maintained. Nothing could more forcibly demonstrate the flexibility of the process than the fact that, under these conditions, the sinter produced was, in all cases, of excellent quality. The Dwight & Lloyd process, as such, and its present highly-developed mechanical appliances were described by Mr. Gayley in the paper above mentioned. While the repetition of some particulars will be unavoidable in this paper, it will be confined to features bearing upon the metallurgical principles involved. According to the principle of the process, the finely-divided iron-bearing material to be sintered is intimately mixed with

May 1, 1912

Jan 1, 1970

By Dudley L. Davis, E. C. Peterson

INTRODUCTION THE Darwin District is 30 miles east of Olancha which is 220 miles north from Los Angeles via U. S. Highway No. 6. The ore deposits occur in the Darwin hills that have been elevated above the Darwin Plateau by typical basin and range-type faults. Some of these faults have been active quite recently as shown by the displacement of Quaternary (?) basalt flows and the rejuvenation of erosion in Darwin wash. The ore bodies occur as fissure fillings and replacement of favorable beddings in a thick series of Paleozoic limestones, dolomites, shales and quartzites. Rich oxidized lead-silver ores were discovered in the early seventies. By 1875, Darwin had a population of about 5000, and by 1880 several small mills and smelters had been built. Early exhaustion of surface ores, the isolated location of the district, and fluctuation of metal prices caused intermittent operations until World War II. The district production is estimated at about $3,000,000 prior to 1900 and perhaps $4,000,000 between 1900 and 1945 when Anaconda purchased the major producing mines. For the past two years, daily production has averaged 75 tons of direct shipping and 150 tons of milling-grade ore. At present, 300 tons of mixed oxide and sulphide ore are treated by flotation, the oxidized lead minerals being activated by addition of sodium sulphide after galena and sphalerite have been recovered from the circuit. Extraction averages 85 pct of the lead, 80 pct of the silver, and about 33 pct of the zinc in a bulk concentrate. The mill is designed so that minor changes permit selective flotation of pyritic lead-zinc ores encountered at depth. GENERAL GEOLOGY The oldest rocks in the Darwin hills are a series of Paleozoic limestones, dolomites, shales and quartzites probably Pennsylvanian in age. These rocks have been intruded on the west by the Coso granite batholith and on the east by a granodiorite stock. Numerous sills and dikes grading from orthoclase granite to gabbro are exposed in the underground workings. The sedimentary rocks have been considerably folded and faulted, the most prominent structure being a northwest pitching anticlinal fold, the crest of which lies just west of the ridge line of the Darwin hills. The east limb of this fold has been intruded by the granodiorite stock and east of the stock the sediments show several closely spaced anticlines and synclines. The minor flexures on the west flank of the major fold are structurally important in localizing the ore in the Defiance and Essex mines of the Darwin group. There are three principal systems of faulting and fissuring, most of which are post-intrusive and premineral in age, with minor amounts of postmineral movement. The Darwin tear fault is the largest, most persistent fault in the district. It strikes N 60 to 95°W, dips steeply south and is traceable for about 1o miles. It is a normal

Jan 1, 1947

Jan 1, 1967

By Howard Martens, Pol Duwez

XPERIMENTS were performed on a Cr-Fc alloy Econtaining 44.7 pet Cr in order to determine the heat evolved during the transformation of the a solid solution into the s phase, and the change in volume accompanying the transformation. Since previous measurements on the rate of formation of a from s indicated that the reaction was quite fast as soon as the equilibrium temperature of 820°C was exceeded by some 50°, standard thermal analysis experiments were performed on heating specimens of s at the rate of approximately 40°C per sec. A definite thermal arrest was observed at 870"C, Fig. 1. This result indicates that the reverse seaction of into a is exothermic. From the heating curve of Fig. 1, taking 15°C per sec as the heating rate in the neighborhood of the transformation, 2.4 sec as the time for transformation, and assuming that the specific heat of the alloy at 850°C is an average between iron and chromium, namely 9.5 cal per mol per "C, the latent heat of transformation is approximately 342 cal per mol. The order of magnitude of this latent heat was also obtained by comparing the heating curve of Fig. 1 with a similar curve obtained with pure iron under identical experimental conditions. It was found that the length of the thermal arrest for s was about 1.8 times as long as that for iron. Since the latent heat of the a to 7 iron transformation is 203 cal per mol1, 2 the latent heat of it to a would be 365 cal per mol, which is in relatively good agreement with the value determined from the heating curve. For the determination of volume change, thermal expansion curves were recorded using a specimen containing 44.7 pet Cr and completely transformed to cr by previous treatment. The curves were recorded at a rate of heating of about 4°C per min and at approximately 840°C a sharr, increase in length of about 0.08 pet took place. Fig. 2. It is therefore established that the specific volume of a near the transformation temperature is about 0.24 pet smaller than that of a, and consequently, when the s phase forms in an a matrix, it would tend to shrink away from the matrix. Since the s phase is known to be extremely brittle, these results offer an explanation for the microscopic cracks often observed in the a phase under the microscope. The results of this study are in qualitative agreement with previously published data on stainless steel 19-9DLa and on a Cr-Fe alloy containing 45 pet Cr.' The increase in density due to the transformation from n to s given in ref. 4 is 0.90 pet. These measurements, however, were made at room temperature. whereas the presently reported 0.24 pet is the change at the temperature at which the transformation takes place during heating. In the graph of Fig. 2, the percentage change in length that would be observed at room temperature is given by the length X, which is about 0.27 pet. This would correspond to 0.81 pet in volume change. Acknowledgment This work was done at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. DA-04-495-ORD-18 with the Army Ordnance Corps, Washington, D. C. The authors wish to thank this agency for permission to publish the results of this investigation. References I H. Klinkhardt: Measurements of True Specific Heats at High Temperatures. Annalen der Physik (1927) 84, pp. 167-200. - H. Esser and W. Runghardt: Influence of the Method, of Dctcrmination on the Measured Heat Content of Iron. Archtvo ffur Dct Eisenhiittenwesen 11934) 8, pp. 37-38. J. J. Gilman, P. K. Koh, and 0. Zmeskal. Delta Ferrite Formation and its influence on the Formation of Sigma in a Wrought Heat Resisting Steel. Trans. ASM 1 1949) 11, pp. 1371-1388. 1 J. M. Thomas: Discussion of ref. 3. Trans. ASM (1949) 41, pp. 3 390-1392.

Jan 1, 1957

In any earth-moving operation, more profit may be earned or lost by equipment scheduling than by any other single facet of the project. Many now-defunct earth movers would have survived the cost-profit squeeze had they followed an efficient, cost saving, equipment scheduling program. The ideal program would have every item of the equipment fleet working all of the time. In practice this ideal situation is not possible. Several basic methods of equipment scheduling, with an infinite number of minor variations, are used. The first approach is the use of a "minimum equipment fleet," of which all items or equipment are scheduled each working shift.

Jan 10, 1967

Jan 1, 1968

By K. C. Mills, E. T. Turkdogan

A number of investigators1 6 have noted the presence of a liquid miscibility gap in the Fe-Sn binary system. However, the first attempt to measure the

Jan 1, 1964

By E. J. Lintner

CLAY mining in the 'United States is by no means a small industry for approximately ten million tons of shale and clay are recovered yearly. The bulk of this tonnage enters into the manufacture of paving, building and refractory brick, draintile, pots, sewer pipe, stoneware, and wall and floor tile. This group of manufactures is commonly known as the heavy clay products industry. The winning of the raw materials for this industry constitutes merely a step in the manufacturing process because the manufacturer usually owns and operates his own source of supply. The mining of kaolin and the whiteware and chinaware claps, however, is usually a separate industry.

Jan 1, 1936

LIST OF THE MEETINGS OF THE INSTITUTE AND THEIR LOCALITIES FROM ITS ORGANIZATION TO OCTOBER, 1904 Transactions Number Place Date Vol Page 1 Wilkes-Barre, Pa May, ?71 1 3 2 Bethlehem, Pa August, ?71 1 10 3 Troy, N Y November, ?71 1 13 4 Philadelphia, Pa February, ?72 1 17 5 New York, N Y May, ?72 1 20 6 Pittsburg, Pa October, ?72 1 25 7 Boston, Mass February, ?73 1 28 8 Philadelphia, Pa May, ?73 2 3 9 Easton, Pa October, ?73 2 7 10 New York, N Y February, ?74 211 11 St Louis, Mo May, ?74 3 3 12 Hazleton, Pa October, ?74 3 8 13 New Haven, Conn February, ?75 3 15 14 Dover, N J May, ?75 4 3 15 Cleveland, 0 October, ?75 4 9 16 Washington, D C February, ?76 4 18 17 Philadelphia, Pat June, ?76, 5 3 18 Philadelphia, Pa October, ?76 5 9 19 New York, N Y February, ?77 5 27 20 Wilkes-Barre, Pa May, ?77 6 3 21 Amenia, N Y October, ?77 6 10 22 Philadelphia, Pa. May, ?78 6 18 23 Chattanooga, Tenn May ?78 7 3 24 Lake George, N.Y. Oct. ?78 7 25 Baltimore, Md. Feb. ?79 7 26 Pittsburgh Pa, May ?79 8

Jan 1, 1923

LIST OF THE MEETINGS OF THE INSTITUTE AND THEIR LOCALITIES FROM ITS ORGANIZATION TO OCTOBER, 1904 Transactions Number Place Date Vol Page 1 Wilkes-Barre, Pa May, ?71 1 3 2 Bethlehem, Pa August, ?71 1 10 3 Troy, N Y November, ?71 1 13 4 Philadelphia, Pa February, ?72 1 17 5 New York, N Y May, ?72 1 20 6 Pittsburg, Pa October, ?72 1 25 7 Boston, Mass February, ?73 1 28 8 Philadelphia, Pa May, ?73 2 3 9 Easton, Pa October, ?73 2 7 10 New York, N Y February, ?74 211 11 St Louis, Mo May, ?74 3 3 12 Hazleton, Pa October, ?74 3 8 13 New Haven, Conn February, ?75 3 15 14 Dover, N J May, ?75 4 3 15 Cleveland, 0 October, ?75 4 9 16 Washington, D C February, ?76 4 18 17 Philadelphia, Pat June, ?76, 5 3 18 Philadelphia, Pa October, ?76 5 9 19 New York, N Y February, ?77 5 27 20 Wilkes-Barre, Pa May, ?77 6 3 21 Amenia, N Y October, ?77 6 10 22 Philadelphia, Pa. May, ?78 6 18 23 Chattanooga, Tenn May ?78 7 3 24 Lake George, N.Y. Oct. ?78 7 25 Baltimore, Md. Feb. ?79 7 26 Pittsburgh Pa, May ?79 8 28 Montreal, Canada Sept, ?79 8

Jan 1, 1923

LIST OF THE MEETINGS OF THE INSTITUTE AND THEIR LOCALITIES FROM ITS ORGANIZATION Transactions Number Place Date Vol Page 1 Wilkes-Barre, Pa May, ?71 1 3 2 Bethlehem, Pa August, ?71 1 10 3 Troy, N Y November, ?71 1 13 4 Philadelphia, Pa February, ?72 1 17 5 New York, N Y May, ?72 1 20 6 Pittsburg, Pa October, ?72 1 25 7 Boston, Mass February, ?73 1 28 8 Philadelphia, Pa May, ?73 2 3 9 Easton, Pa October, ?73 2 7 10 New York, N Y February, ?74 211 11 St Louis, Mo May, ?74 3 3 12 Hazleton, Pa October, ?74 3 8 13 New Haven, Conn February, ?75 3 15 14 Dover, N J May, ?75 4 3 15 Cleveland, 0 October, ?75 4 9 16 Washington, D C February, ?76 4 18 17 Philadelphia, Pat June, ?76, 5 3 18 Philadelphia, Pa October, ?76 5 9 19 New York, N Y February, ?77 5 27 20 Wilkes-Barre, Pa May, ?77 6 3 21 Amenia, N Y October, ?77 6 10 22 Philadelphia, Pa. May, ?78 6 18 23 Chattanooga, Tenn May ?78 7 3 24 Lake George, N.Y. Oct. ?78 7 25 Baltimore, Md. Feb. ?79 7 26 Pittsburgh Pa, May ?79 8 28 Montreal, Canada Sept, ?79 8 29 New York, N.Y. Feb, ?80 9

Jan 1, 1923

Ferrous and Nonferrous Physical Metallurgy Established as a Division April 26, 1918 T A Read, Chairman O T Marzke, Past Chairman J H Jackson, Senior Vice-Chairman David Swan, Vice-Chairman D C Johnston, Secretary-Treasurer AIME, 29 West 39th Street New York 18, New York

Jan 1, 1960

By J. B. Clark

In multiphase ternary diffusion studies, plots of the variation bf the composition on the isotherm constitutes one of the most effective methods of presenting experimental results, especially if such plots are made in a manner which relates the composition path on the isotherm with the diffusion layer structure in the couple. Unfortunately, if different conventions for plotting are used serious misinterpretations occur readily, causing apparent disagreement between investigators who actually share the same viewpoint. A common convention for mapping these diffusion paths is needed at this time because with the increasing use of the electron-probe X-ray microanalyzer, a much greater number of ternary diffusion studies can be expected in the near future. In an effort to prevent unnecessary confusion in the future litera- ture, a convention for these plots is proposed, as outlined below. A hypothetical example of the use of these conventions is given in Fig. 1 where the path of composition through the diffusion structure of the 100 pct A/50 pct B, 50 pct C couple is plotted on the appropriate isotherm of the ABC system. The lower case letters relate the region in the diffusion layer structure to the appropriate composition on the ternary isotherm. 1) The diffusion path is plotted on the isothermal section corresponding to the diffusion temperature of the couple. 2) The terminal compositions of the plotted diffusion path are the initial compositions of the couple halves—provided infinite boundary conditions are maintained. If, in either couple half, infinite conditions are not maintained, then the path terminates at the composition of the exterior surface of the couple. If, at this surface, the composition varies with time or if the plotted path is time dependent, then the diffusion time should be noted beside the plotted path. 3) A solid line crossing a single phase field (e.g., line a-b in Fig. 1) denotes an existing layer of that phase in the diffused couple. 4) A dashed line crossing a two-phase field parallel to the tie lines (e.g., line g-h) represents an interface between the two phases with interfacial compositions designated by the ends of the tie-line. The line represents no spatial extent. 5) A solid line crossing a two-phase field so as to cut tie lines (e.g., line b-c or line j-k) represents a locally equilibrated columnar two-phase layer. The solid line should cut those tie lines which correspond to the lateral interfacial equilibria along the columnar

Jan 1, 1963

By Howard N. Eavenson

TWO months ago, just after the coal code hearing in Washington, one of our leading liberal weeklies printed a study of the coal industry made by an economist in the Administration, and on the outside cover bad it featured as "Coal-A Dying Industry." There are, of course, different opinions as to the accuracy of this characterization and I want to present some of the facts about the outlook for the bituminous industry for a short time ahead. In view of what has happened in the industry within the recent past it would be futile to attempt to make any prophecy about what is likely to occur in the future. We all know that a prophet is not without honor save in his own country, but it is likely that anyone undertaking this role about this industry would soon find himself in no man's land. One can, with some slight degree of safety perhaps, outline present conditions and tendencies and draw some inferences as to what the future may hold.

Jan 1, 1933

By J. J. Rutledge

I. DESCRIPTION OF THE CLINTON ORES AND ASSOCIATED POCKS. THE Clinton rocks in Stone Valley comprise (1) thick layers of deep-red shale, (2) layers of reddish-gray shale interspersed with beds of sandstone and thin beds of extremely fossiliferous limestone, and (3) yellowish-gray shales alternating with thin layers of olive-colored shales. These layers of shale are all very thin and are at no point massive.1 A bed of gray-white sandstone varying in thickness from 12 to 30 ft. occurs in the tipper portions of the Clinton shales. This is called the ore sandstone, a name given to it by Rogers and adopted also by the Second Pennsylvania Geological Survey. It is the surest guide to the presence of the iron-ore bed, which lies below its lower edges at distances varying from 10 to 20 ft. This ore sandstone, in the valley, lies generally at very low inclinations, but often is locally subjected to considerable changes in dip. At its outcrop this ore sandstone weathers very easily and yields a rather sparse crop of stone, Composed of dirty, iron-stained boulders. Upon the roads these boulders are quite well rounded, and bear fragments of crinoid stems and other fossil forms. The ore sandstone exhibits at many points evidences of former movements in this very great thickness of the shales, and as it is the only stratum in this series competent to transmit and record stresses due to structural movements, its evidence is of considerable importance in determining the occurrence of movements in times past.

Nov 1, 1908

By AIME AIME

MOTHER example of the broad field that is covered by the mining industry is the recent erection by the Phelps Dodge Corp. of a modern hospital building at Douglas, Ariz., and an identical one at the rejuvenated mining town of Morenci. Managers of even small mining properties are often called upon to build schools, houses, stores, maybe a jail, and provide sanitary arrangements, possibly the while acting as mayor of the town. Those who direct larger properties may have to build hospitals, as in the present instance, construct sewage disposal plants, and sometimes even build and manage railroads. A mining camp achieves its reputation among mining men not entirely by the grade or amount of its ore, or the skill of the operating staff in mining and milling it at a profit-the operation soon acquires a reputation as either a desirable or an undesirable place to live, regardless of its remoteness from what is euphemistically termed civilization. Such a community is indeed fortunate if it can boast of a good hospital.

Jan 1, 1940

By F. D. Wright, H. D. Fara

The solution to the plastic and elastic stresses around a circular shaft in a hydrostatic stress field that has appeared in two editions of a widely used book on rock mechanics1 is in error. Although this is a relatively minor matter, the correct solution was not found by a literature survey, so it appears worthwhile to present it. For a homogeneous, isotropic, rigid plastic-elastic body in plane strain which obeys Tresca's yield criterion the following equations must be satisfied:'," In the plastic zone,

Jan 1, 1963

By Bieniawski, Z. T.

The importance of understanding the phenomena associated with rock fracture has long been fully appreciated in rock mechanics. This is clearly apparent from the special attention paid to rock fracture in the comprehensive papers published within the past four years. These papers present a picture of how the knowledge of brittle fracture of rock was gradually enriched and also show that what was often taken for granted three or four years ago is no longer considered as valid today.

Jan 1, 1972