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By J. N. Hobstetter

It is widely believed that the nucleation of phase transformations in solid metals is accomplished by some type of local atomic fluctuations in the parent phase which arise from spoutaneous difiusion in the metal or alloy system. Under appropriate conditions, these fluctuations are believed to be stable in the sense that the free energy of the entire system is lowered if the fluctuations, or nuclei, grow. Under other conditions they are thought to be unstable in the sense that the free energy is lowered if they redissolve. The criterion for stability is usually taken as the size of the fluctuation. This view has been rationalized by Beckerl in terms of the free energy released by the volume of the nucleus and the free energy associated with the formation of a new surface surrounding the nucleus. The qualitative result of this reasoning is shown in Fig I where the changes in free energy for the surface and volume effects are plotted together with their sum against the radius of the nucleus. There is evidently always a critical size r, beyond which the release of free energy which is proportional to the volume always dominates the increase of free energy which is proportional to the surface area. Borelius2 has also attempted to rationalize the stability criterion for binary alloys, but in terms of the internal concentration of the fluctuations. He has found that, if surface energies are entirely ignored, the fluctuation must still reach a critical concentration if it is to become stable and avoid subsequent dilution. Although the Borelius theory fails to predict many observed nucleation phenomena such as the vanishing of the nucleation rate at the critical temperature, the major premise must certainly be valid. In this paper a reconciliation of the Becker and Borelius views is made by means of a search for nuclei which are at once stable with respect to both size and internal concentration. The increase in free energy per mole accompanying the formation of a nucleus which is just stable, AF., is independent of the path whereby the nucleus is brought into being. It is thus appropriate to seek critical nuclear attributes without reference to the fluctuation mechanism. The rate of nucleation, however, cannot be treated without a detailed understanding of the exact fluctuation process which produces stable nuclei. In this and succeeding papers the purpose will be to find the size, shape and internal concentration of the stable nucleus which is formed with a minimum increase in free energy in a wide variety of systems. The Nature of the Nucleus It is necessary ti have rather detailed knowledge of the nature of a nucleus if AF, is to be computed. Fortunately, enough facts are known or suspected about the nucleus to make possible a detailed analysis. X ray diffraction studies have shown

Jan 1, 1949

By John N. Hobstetter

IT is widely believed that the nucleation of phase transformations in solid metals is accomplished by some type of local atomic fluctuations in the parent phase which arise from spontaneous diffusion in the metal or alloy system. Under appropriate conditions, these fluctuations are believed to be stable in the sense that the free energy of the entire system is lowered if the fluctuations, or nuclei, grow,' Under other conditions they are thought to be unstable in the sense that the free energy is lowered if they redissolve. The criterion for stability is usually taken as the size of the fluctuation. This view has been rationalized by Becker1 in terms of the free energy released by the volume of the nucleus and the free energy associated with the formation of a new surface surrounding the nucleus. The qualitative result of this reasoning is shown in Fig I where the changes in free energy for the surface and volume effects are plotted together with their sum against the radius of the nucleus. There is evidently always a critical size r. beyond which the release of free energy which is proportional to the volume always dominates the increase of free energy which is proportional to the surface area. Borelius2 has also attempted to rationalize the stability criterion for binary alloys, but in terms of the internal concentration of the fluctuations. He has found that, if surface energies are entirely ignored, the fluctuation must still reach a critical concentration if it is to become stable and avoid subsequent dilution. Although the Borelius theory fails to predict many observed nucleation phenomena such as the vanishing of the nucleation rate at the critical temperature, the major premise must certainly be valid. In this paper a reconciliation of the Becker and Borelius views is made by means of a search for nuclei which are at once stable with respect to both size and internal concentration, The increase in free energy per mole accompanying the formation of a nucleus which is just stable, ?fe, is independent of the path whereby the nucleus is brought into being. It is thus appropriate to seek critical nuclear attributes without reference to the fluctuation mechanism. The rate of nucleation, however, cannot be treated without a detailed understanding of the exact fluctuation process which produces stable nuclei. In this and succeeding papers the purpose will be to find the size, shape and internal concentration of the stable nucleus which is formed with a minimum increase in free energy in a wide variety of systems. THE NATURE OF THE NUCLEUS It is necessary to have rather detailed knowledge of the nature of a nucleus if ?Fe is to be computed. Fortunately, enough facts are known or suspected about the nucleus to make possible a detailed analysis. X ray diffraction studies have shown3

Jan 1, 1948

By Louis H. Berkelhamer

"INTRODUCTION ""Free silica"" includes all free forms of silicon dioxide, such as quartz, chalcedony, tridymite, cristbbalite, opal, diatomaceous earth, and lechatelierite. The term, has been used rather loosely however, as synonymous with quartz, as quartz is the most abundant form of free silica. ""Combined silica,"" on the other hand, has been reserved to denote silica combined with other elements as silicates.Improvements in methods for the determination of free silica, and quartz in particular, have been the subject of considerable interest during the past decade, owing mainly to the accented and increased knowledge concerning quartz as a causative factor in silicosis. Analysis for quartz, however, is of importance in many other fields, including the determination of quartz in ceramic raw materials, such as feldspar and clay; the evaluation of a beneficiation procedure by the ore dresser, such as in the concentration of iron ore; control studies of a manufactured product, such as silica brick; and routine analysis of rock, mineral, and ore samples by chemists and petrographers."

Jul 1, 1944

By T. A. Boyden

The Free World uranium market is now characterized by production nearly twice that of consumption result- ing in a rapid build-up of uranium inventories. Low- cost production from high-grade deposits in Australia and Western Canada will gradually add another 10 to 15 million pounds U308 annually into Free World production throughout the 1980's. This latter material cannot be absorbed in further inventory build-up and can only displace higher cost production. The result is a restructuring of the Free World producer industry. United States and Eastern Canadian producers have the higher cost production which gradually will be displaced from the market during this decade. As United States production declines, United States utilities must increase their reliance on foreign supplies in order to meet their needs. This paper reviews the elements that will cause the restructuring of the Free World producer industry and the expected response of the United States utility industry to that developing situation.

Jan 1, 1982

By J. F. Cuderman

In situ experiments at the Department of Energy's Nevada Test Site (NTS) have extended the technology of propellant-based fracturing to include liquid- filled, uncased boreholes. Previous work had developed the technology for liquid-free, uncased wellbores. Test results show that fracturing behavior is considerably more complex in liquid- filled boreholes than in the liquid-free case. Compared to liquid-free boreholes, liquid-filled boreholes have faster pressure risetimes and lower peak pressures, large hydraulic-type fractures propagating several meters beyond the end of the test zone, numerous oscillations in the pressure history, and variable types of fracturing within a single test region. Multiple fracturing is initiated in the wellbore of a fluid-filled borehole when the proper propellant mixture is used but, unlike fluid-free wellbores where up to eight fractures propagate, only one to three hydraulic- and/or shear-type fractures propagate. Hydrodynamic effects involving liquid compression during borehole pressurization appear to be responsible for the differing phenomena observed in fluid- filled boreholes.

Jan 1, 1986

By H. H. Kellogg

Equations representing the standard free energy of formation as a function of temperature, for thirty metallic chlorides, are presented and plotted on a free-energy vs. temperature diagram. The use of these data for calculations on reduction of metallic chlorides, refining of metals with chlorine, and chlorination of metallic oxides and sulphides is illustrated. CHLORINE metallurgy' has attracted metallur- gists for more than a century because the unusual properties of the metallic chlorides—low melting point, high volatility, and ease of formation from the oxides—make possible many useful extractive processes. Interest in chlorine processes is undergoing a renaissance due to present availability of chlorine at relatively low prices, and to recent advances in technology. During the present century there have accumulated a considerable number of reliable values of the thermodynamic constants for the metals and their chlorides. These data permit the calculation of free-energy equations for many metallurgically important reactions. Consideration of free-energy values makes possible certain predictions of the direction and extent of a given reaction, as well as the effect of temperature, pressure, and composition upon the result. Reaction rate, although not predictable from free-energy data, is usually sufficiently great at elevated temperatures that diffusion of the reactants and products to and from the zone of reaction determines the actual rate. Thus, if the free-energy indication is favorable, the chances are good that a high temperature metallurgical reaction will proceed at a reasonable rate, if adequate provision for rapid diffusion has been made. This paper presents standard free-energy equations for a number of metallic chlorides, based on data which are scattered throughout the literature. The equations are presented in a form that simplifies their use, and typical examples are given of the application of free-energy data to metallurgical processes. Free Energy of Reaction The free-energy change (AG) of a reaction is the true measure of the "driving force" of the reaction under a given set of conditions, and this is related to the standard free-energy change (AGO) of the reaction as follows: For the reaction: bB + cC = dD + eE ?G = ?G°+RTln ADd. AEA / ABb. ACc where A, = activity of constituent (i) T = absolute temperature, OK R = gas constant The criterion of a spontaneous reaction from left to right, at constant temperature and pressure, is a negative value for the free-energy change (?G). The standard free energy of the reaction is equal to the free energy of the reaction when all the reactants and products are at unit activity, since under these conditions the second term on the right-hand side of eq 1 is equal to zero. The concept of activity is treated fully in many textbooks on chemical thermodynamics1 and in a recent article by Chipman.2 Briefly, the activity (A,) of a constituent (i) is a measure of the reactivity of this constituent relative to its reactivity in some arbitrary standard state. For liquids and solids the standard state most often used is the pure liquid or solid constituent. Thus the activity of a pure liquid or solid in a metallurgical reaction is equal to unity. Gases under moderate pressure and at elevated temperatures behave very nearly as 'idea1 gases,' and the standard state is chosen as the gas at 1 atm pressure. The activity of an ideal gas is therefore equal to its partial pressure, and this relation is sufficiently exact for real gases in most metallurgical reactions. For a liquid or solid solution there is in general no simple way to express the activity of a constituent as a function of its concentration, and activity must be determined by experiment. A few solutions follow a so-called 'ideal' behavior, and if the pure constituent is chosen as the standard state, the activity of a constituent in an ideal solution becomes equal to its mol fraction. When a reaction reaches a state of thermodynamic equilibrium at constant temperature and pressure, AG becomes equal to zero and eq 1 reduces to: [ADd . AEe ?G°=RTln Abb ¦ Ac c equilibrium [2] The brackets surrounding the activity term are used to emphasize that each of the activities is an activity under equilibrium conditions—not just any arbitrarily assigned value. The bracketed term is the equilibrium constant (K) of the reaction. Eq 2 makes possible the calculation of equilibrium activities for a given reaction, if AGO is known at the desired temperature. The standard free-energy equations presented in this paper were calculated from the fundamental thermodynamic values of enthalpy of formation at 298°K (AH°,), standard entropy at 298°K (So298), heat capacity as a function of temperature (Cp), and enthalpies of transition, fusion, vaporization, and sublimation for the various constituents. Where possible the data reported in the recent "Selected Values of Chemical Thermodynamic Properties," published by the Bureau of Standards," were used. A large number of data came from the publications

Jan 1, 1951

By R. A. Wood, R. I. Jaffee, H. R. Ogden, D. N. Williams

Dispersion-containing titanium-copper alloys were prepared having mean free paths varying from 1.0 to 9.7 P. Tensile studies at room temperature and at 1000°F showed that little or no strengthening occurred when the mean free path exceeded 3 p. However, at lower values of mean free path appreczable strengthening was observed. A considerable amount of strengthening also resulted from copper in solid solution. DURING the past several years, an increasing amount of study has been devoted to dispersion hardening, an alloying process in which increased strength is obtained through the addition of a ran-

Jan 1, 1961

By A. F. Daily

Free World consumption of diamonds of all types closely follows the fluctuations of the business cycles in the large industrialized countries, particularly the U.S. Sustained purchasing by this country for stockpiling purposes has been a major factor in Free World demand for crushing bort and industrial diamonds, and it has been for this reason that investments in larger plants have been made by all major diamond mining companies during the past few years. For the purposes of this study, the diamonds produced in the Congo and elsewhere in the Free World are divided into three types:

Jan 5, 1961

By S. Peng, Vaughan R. Voller

"Free boundary problems are a common occurrence in materials processing operations. An important example is the filling of material into molds. This paper looks at filling problems associated with polymer processing, in particular Resin Transfer Molding (RTM) and Compression Molding. A general, single governing equation is developed which on numerical solution provides predictions for the position of the polymer front in the mold during filling. Both fixed and deforming finite element solutions are developed. Application to polymer filling test problems reveal that the fixed and deforming grid scheme are accurate and compare closely with each other.IntroductionProblems arising from the analysis of material processing operations often involve the tracking of a moving boundary, on which a balance conditions needs to be met, or the locating of a free surface that defines the solution domain. Material processing examples of so called ""free and moving boundary problems"" include; the tracking of solidification/melting fronts[l], the tracking of the metal/gas interface during the filling of a mold[2] and location and shape of a skull (freeze line) in a melting furnace[3].Computational solution of free and moving boundary problems usually fit into one of two classes, viz.1. Fixed grid scheme: In which the spatial domain is covered by a fixed grid (mesh) of node points and the solution uses an auxiliary variable (e.g. a local liquid fraction) to track the moving boundary or locate the free surface.2. Deforming grid scheme: In which the grid in the spatial domain is continuously deformed (or adapted in a steady state problem) such that a specified set of grid points lie on the moving boundary or the free surface.Details on the basic underlying features in these two classes of solution can be found in the excellent monograph by Crank [4]."

Jan 1, 1994

By Roe-Hoan Yoon, lsmail Yildirim, Jinhong Zhang

Inorganic fillers and pigments such as kaolin, diatomaceous earth silica, and talc were treated with various surfactants, and the changes in their surface properties monitored. When they were treated with a cationic surfactant, they became hydrophobic and the overall surface free energies were decreased substantially. The decrease in surface free energy was mostly due to the decrease in the acid-base component (ysab) of the surface free energy, indicating that hydrophobizing an inorganic pigment entails a reduction in ysab. It was found that the surface characterization technique employed in the present work was useful for studying the effects of using various other surfactants for surface treatment.

Jan 1, 2003

By F. D. Osgood, H. M. Cooper, A. C. Fieldner

The analyses in the tables are arranged geographically with respect to county and towns, and are grouped as follows: l The proximate analysis--moisture, volatile matter, fixed car bon, and ash; 2 The ultimate analysis-carbon, hydrogen, nitrogen, oxygen, sulphur, and ash; 3 The calorific value of heat of combustion; 4 The softening temperature of ash, when such determinations were made. Ultimate analyses are given in three conditions-namely, (1) as received, (2) moisture free, and (3) moisture and ash free Proximate analyses and heating values are given generally in one condition -namely, as received, some are in two conditions, as received and moisture free.

Jan 1, 1928

By R. P. Walters, M. J. Lynch, D. R. Flinn

The Bureau of Mines evaluated tthhee feasibility of substituting platinum- coated metals for bulk platinum shapes as a means for conserving platinum . Platinum coatings were prepared using four different methods of electrodeposition , then tested and evaluated . In order for platinum coatings to be useful in process environments , they must be thick , adherent , stress - free , and pore - free . The Bureau evaluated direct - current , current reversal , cathode shielding , and pulsed- current plating techniques for producing a pore-free platinum electrodeposit from a molten cyanide bath . Aqueous corrosion tests of Fe - 10Cr substrates coated with approximately 25 μm of platinum showed that pulse plating yielded the most corrosion- resistant and , hence , the most pore -free coatings . The morphology of coating cross sections was in all cases columnar . The average grain size of pulse -plated deposits was independent of thickness , while all other plating techniques produced grains that increased in size as the coatings became thicker . It is believed that the constant grain size in the pulse - plated deposits resulted from better mass transport during the electrodeposition .

Jan 1, 1965

By W. Petruk

The behaviour of galena, chalcopyrite and tetrahedrite during floration of a fine-grained base metal ore from New Brunswick was investigated by image analysis study of the mill concentrates and tailings. The minerals were analyzed to determine the grades and recoveries as related to free and unliberated mineral grains and their size distributions. The results show that only 37 wt % of the galena was liberated but 88 wt % of the free galena was recovered, indicating good mill performance for the lead. The lead recovery was 65 wt %, with the main loss due to unliberated galena. Most of the unliberated galena lost to mill tailings is so fine-grained that galena liberation and Pb recovery would not improve significantly by re-grinding. Chalcopyrite liberation was 56 wt % but only 75 wt % of the free chalcopyrite was recovered. Copper recovery was 45 wt %, with the chalco-pyrite loss in the mill tailings being both as large free grains, and as small and large unliberated grains. It was calculated that copper recoveries could be improved about 8 to 10 wt % by changing the concentrator operations and by regrinding. Concentrator operations hive already been modified and copper recoveries have improved about 5 wt %. About 29 wt % of the silver was lost to tailings mainly as both free and unliberated, large and very small, Silver-bearing tetrahedrite grains. It was calculated that about 25 wt % of the silver in the tailings might be recovered by improved milling conditions and by regrinding.

Jan 1, 1981

By Pat McCarran

WHEN this Government was founded, the framers of the Constitution wrote into that instrument a provision that Congress should "coin money and fix the value thereof;" and the Constitution prohibits making anything but "gold and silver" lawful money. So silver is written into our basic law. Shortly after President Washington took office in 1789 the Congress passed the first Mint Act, setting up the U. S. Mint. In that Act, signed by President Washington on April 2, 1792, the weight of the American dollar was fixed, and it was provided how much silver should be contained in a silver dollar and how much gold should be contained in a gold dollar. It was decided that 371 1/4 grains of pure silver was to be the standard dollar of America. That standard with respect to the pure silver content of the dollar has never changed.

Jan 1, 1947

By Kunihisa Katsuyama, Yuji Ogata, Yuji Wada

The one free surface blasting of a concrete block was simulated by Discontinuous Deformation Analysis(DDA) method. Comparing the simulated results with the concrete block blasting experiment, the crack growth and the free surface displacement which were simulated by DDA were observed with a high speed camera.

Jan 1, 1996

By L. S. Darken

It has been known for sometime that in an ionic lattice, such as that of Ag,S or FeO, the migration velocity of the anion may differ markedly from that of the cation, the cation being usually the more mobile. It has been shown, for example, that during the formation of silver sulphide tarnish on silver, the tarnish layer grows principally by the motion of silver cations through an essentially stationary silver sulphide lattice. Similarly, the growth of wüstite scale on iron proceeds principally by motion of iron ions, this being accomplished with the aid of vacant iron lattice sites into which the iron may readily move. Likewise investigations of solid solutions of various salts show that there is usually considerable difference in the mobility of the different cations. Measurements of the mobility of various metals in liquid mercury indicate that the various metals move at different rates relative to the mercury. In view of the foregoing it seems reasonable to suppose that when any single phase solution is acted upon by a field, the atoms of different elements respond in different ways; in particular, that the force arising from a particular concentration gradient in a binary alloy would cause the atoms of one component to move with a drift velocity which is in general different from that of the atoms of the other component. The recent experiments of Smigelskas and Kirkendall' support this viewpoint, since they found, in essence, that during diffusion in alpha brass zinc moves appreciably faster than copper. This was evidenced by the relative motion of inert molybdenum wires. Such a phenomenon is incompatible with the place interchange theory of diffdsion proposed by several authors, most recently by Bir-chenall and Mehl.2 This theory has, however, also been questioned3v4 for other reasons, principally because of the high energy required for direct atomic interchange. The rather large difference between self-diffusivity, as determined by tracer technique, and mutual diffusivity, as determined with the aid of another element at low concentration, might also be interpreted as favoring the above idea; however. Birchenall and Mehl have pointed out that there is another possible interpretation of this difference; this is discussed later. A rather interesting and pertinent observation was made by Schwartz, who noticed that tungsten lamp filaments, heated by direct current, commonly fail by necking down in the region at the temperature gradient near the positive end, with a concomitant swelling at the corresponding position near the negative end. He introduces considerable auxiliary evidence to show that this phenomenon is occasioned by the motion of tungsten cations which migrate in the high temperature region from the positive end toward the negative end. The mechanism of this migration is not clearly understood. If, however, this experimental evidence be accepted, we are forced to conclude that alloying elements in the tungsten may migrate by the same or a Similar mechanism, whatever it may be, at a greater Or lesser rate, thus giving rise

Jan 1, 1949

By L. S. Darken

It has been known for sometime that in an ionic lattice, such as that of Ag,S or FeO, the migration velocity of the anion may differ markedly from that of the cation, the cation being usually the more mobile. It has been shown, for example, that during the formation of silver sulphide tarnish on silver, the tarnish layer grows principally by the motion of silver cations through an essentially stationary silver sulphide lattice. Similarly, the growth of wüstite scale on iron proceeds principally by motion of iron ions, this being accomplished with the aid of vacant iron lattice sites into which the iron may readily move. Likewise investigations of solid solutions of various salts show that there is usually considerable difference in the mobility of the different cations. Measurements of the mobility of various metals in liquid mercury indicate that the various metals move at different rates relative to the mercury. In view of the foregoing it seems reasonable to suppose that when any single phase solution is acted upon by a field, the atoms of different elements respond in different ways; in particular, that the force arising from a particular concentration gradient in a binary alloy would cause the atoms of one component to move with a drift velocity which is in general different from that of the atoms of the other component. The recent experiments of Smigelskas and Kirkendall' support this viewpoint, since they found, in essence, that during diffusion in alpha brass zinc moves appreciably faster than copper. This was evidenced by the relative motion of inert molybdenum wires. Such a phenomenon is incompatible with the place interchange theory of diffdsion proposed by several authors, most recently by Bir-chenall and Mehl.2 This theory has, however, also been questioned3v4 for other reasons, principally because of the high energy required for direct atomic interchange. The rather large difference between self-diffusivity, as determined by tracer technique, and mutual diffusivity, as determined with the aid of another element at low concentration, might also be interpreted as favoring the above idea; however. Birchenall and Mehl have pointed out that there is another possible interpretation of this difference; this is discussed later. A rather interesting and pertinent observation was made by Schwartz, who noticed that tungsten lamp filaments, heated by direct current, commonly fail by necking down in the region at the temperature gradient near the positive end, with a concomitant swelling at the corresponding position near the negative end. He introduces considerable auxiliary evidence to show that this phenomenon is occasioned by the motion of tungsten cations which migrate in the high temperature region from the positive end toward the negative end. The mechanism of this migration is not clearly understood. If, however, this experimental evidence be accepted, we are forced to conclude that alloying elements in the tungsten may migrate by the same or a Similar mechanism, whatever it may be, at a greater Or lesser rate, thus giving rise

Jan 1, 1949

By John Griffen

HYDRAULIC classification as explained by Rittinger and others was largely restricted to conditions wherein the free-falling velocities of the particles were conceived as governing the separations effected (see chapter 9). The laws governing classification under free-falling conditions have been summarized by Chapman and Mott as follows:

Jan 1, 1943

By Stephenson IM

Research to develop the use of L.D.slag as an aggregate in road construc-tion is described. The chemistry and mineralogy of L.D. slags are shown to be generally similar to S. Yorkshire arc furnace slags, which have been success-fully used for road construction for many years, although both free lime and iron contents were found to be higher. Physical and mechanical properties are good but the slags' high density will result in lower "covering capacity"."Weathering" in stock piles is shown to significantly reduce free lime levels fairly rapidly although around 50 per cent of the mean "fresh free lime" content is still present even after two years treatment.

Jan 1, 1979

By Terry I. Mudder

Metal complexed cyanides in wastewaters form as a result of interactions of free cyanide with metals present in the wastewater and exhibit varying degrees of stability, toxicity, and treatability. Thiocyanate, a pollutant commonly found in cyanide bearing wastewaters, is formed through the interaction of free cyanide with sulfur containing species (i. e. pyrrhotite) both present in the wastewater. In certain industrial processes, such as the beneficiation of gold and silver, cyanide is an essential reagent. Since free cyanide, complexed cyanides, and thiocyanate are potentially toxic to humans and aquatic organisms, these compounds must be removed from wastewaters prior to their discharge into surface or ground waters serving as potential potable water sources, marine or fresh water habitats

Jan 1, 1984