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By Kenneth A. Moon

An exact statistical treatment of a one-dimensional model is used as a basis for evoluating the reliability of certain simplified expressions for the activity of the solute in interstitial solutions, including one obtained from the exact expression by setting the repulsive interaction equal to infinity. The latter approximation is found to be satisfactory at low and moderate concentration if the repulsive interaction is large, even though not infinite. A similar expression (identical if the co-odination number is two) is derived from the quasichemical expression of Lacher, and is recommended as the best available expression for the excess configurational entropy of interstitial solutions with excluded sites. Some reasonable models are discussed, and the nature of the saturated solutions is determined by inspection. Some of the models reduce to the one -dimensional case. An analysis is given of the excess partial entropy of hydrogen in V-H; Nb-H; and To-H solutions. MOST treatments of the statistical thermodynamics of interstitial solid solutions have followed the classic paper1 of Lacher in making the simplifying assumption that the configurational entropy of the solution is ideal. However, it is becoming increasingly apparent that there are many interstitial solutions with very large so lute-solute repulsions, and for these the assumption of ideal entropy is not valid or useful. It is important to realize that with substitutional solutions large repulsions between the component atoms must lead to phase separation, whereas in interstitial solutions the free energy of the solution is not drastically increased by large solute-solute repulsions until intrinsic saturation is reached at the concentration where further solute would be forced to enter a site in which it would experience the repulsive effect of one or more solute atoms already present. In the limiting case of an infinitely large repulsive interaction, the excess free energy would be attributable entirely to excess entropy, the enthalpy of mixing being zero. AS will be shown below, even if the repulsions are less than infinite, a treatment based on an assumption of infinite repulsions may be very satisfactory up to moderately high concentrations of the interstitial component. Often in solutions where large repulsive interactions exist, there are also small interactions — often attractive—between solute atoms in configurations other than that corresponding to the large repulsion. In such cases the excess free energy will consist of an excess entropy term attributable to the large repulsive interactions, and an enthalpy term corresponding to the other small interactions. Nomenclature to differentiate succinctly between important cases would be a convenience. In this paper the nomenclature shown in Table I will be used. In Table I, and in the preceeding discussion, excess quantities are defined in terms of standard states which are pure solid solvent and pure (possibly hypothetical) solid saturated phase of the structure in question. In practice, it is more convenient to choose the interstitial element as a component, and its conventional standard state. This will add a composition-independent term to the excess entropy and the enthalpy. The earliest paper known to the present author which treats the thermodynamics of athermal interstitial solutions was given by schei12 in 1951, but the statistical derivations in that paper are open to criticism. Speiser and Spretnak were the first to give a correct statistical treatment,3 limited, however, to concentrations sufficiently low that the number of empty sites excluded from occupancy by more than one filled site is negligible. The purpose of the present paper is to extend the statistical treatment to more concentrated solutions, and to examine the magnitude of the errors introduced by assuming that the repulsive interactions are infinite when in fact they must be finite. THE QUASICHEMICAL APPROXIMATION Fortunately, a standard method already exists for taking into account the effect of large interactions upon the entropy of mixing. This is the quasi-chemical method, in which the probability of existence of a given pair of solute atoms in a certain proximate configuration is assumed to be proportional to exp(-w/kT), where w is the energy increase of the solution when the two atoms are moved from isolated locations in the solution to the configuration in question. A quasichemical treatment of interstitial solutions was given in 1937 in a widely neglected paper by Lacher.4 The result comes out

Jan 1, 1963

By J. C. Swartz

Measurements of the effect of precipitation stresses on the solubility of cementite (Fe3C) precipitates in a iron are reported. Solubilities were determined from measurements of the Snoek relaxation due to interstitial carbon after quenching from various equilibrium treatments. Stress-free precipitates were obtained by a spheroidizing treatment of vacuum-melted Fe 0.06 wt pet C. Subsequent equilibration treatments were designed to suppress nucleation of other precipitates. The results for stress-free cementite give a heat of solution of 14.8 i 0.2 keal per mole and an entropy change of 1.1 i 0.2 eu in the temperature range 400" to 715°C. Comparison with previous data indicates that the heat of solution increases about 6 keal per mole as temperature increases from 700" to 1000°C. Data on self-stressed cementite in quench-aged specimens of Fe 0.013 wt pet C indicate 1) an apparent heat of solution of 12.1 i 0.4 keal per mole in the range 280" to 690°C, 2) a strain energy of- 1.1 keal per mole Fe3C accompanying precipitation at 280°C, and 3') a gradual decrease in the strain energy of precipitation with increasing equilibration temperature. In com-parison with 2 and 3 the strain energy calculated for an isotropic model is 1.7 keal per mole Fe3C. The lower values obtained from the experiment indicated substantial stress velaxation by dislocation motion. WHEN a supersaturated solution of carbon in a iron is aged at temperatures in the range 200o to 700oC, the carbon clusters by interstitial diffusion and forms cementite (Fe3C) precipitate particles. Unstressed cementite has a volume per iron atom 9 pet higher than that of a iron;' hence, cementite precipitate particles are usually under pressure from the iron matrix. The pressure would tend to increase the solubility of cementite in iron.' This report describes anelastic measurements of the solubilities of self-stressed and stress-free cementite in a iron. Previous determinations of the cementite solubility are summarized in Table I. The method of cementite formation for each reference was studied to ascertain the state of stress of the cementite. The results judged to be for stress-free and stressed cementite are distinguished in the table. In the next section an estimate of the stress effect is obtained which is clearly too small to account for the large difference between the previous results in parts A and B of the table. THEORETICAL Let AGO be the standard free-energy change of the reaction Fe3C (eem.) = 3Fe (a) + C (in a) [1] in the absence of stresses. Since cementite precipitates appear to be rather pure10 and the carbon is so dilute in the iron,8 the cementite and iron of Eq. [ I] for the stress-free case have essentially unit activities and the activity of carbon equals its atom fraction xoC Then the stress-free equilibrium is expressed by RT In XoC = -?GO 121 To first approximation the change in the chemical potential of carbon due to the precipitation stresses equals the elastic strain energy W accompanying precipitation of a mole of cementite.2 Hence, in the presence of the precipitation stresses the equilibrium is described by RT In x sq = -?G° + W [3] where xsC is the mole fraction of dissolved carbon in the stressed case. An approximate value of W can be obtained from analysis of the inclusion problem in elasticity theory. The inclusion is a small portion of the matrix phase which has suffered a transformation while still imbedded in the matrix. In the absence of the constraint of the matrix the transformation would be equivalent to a uniform dilational strain eT. Both the matrix (a) phase and inclusion (0) phase are assumed to be homogeneous, isotropic materials. When the a and 0 phases have the same elastic moduli, which is approximately true for iron and cementite,11 the total strain energy per mole ß is12 2µVß(eT)2(3 +4 µx)-I [4]

Jan 1, 1968

By H. Rumfelt

The author demonstrates an approach for analyzing overcasting requirements for a stripping project. This approach to the problem employs indicated trends in the relationship of the weight of the machine (only electropowered draglines are considered) to its ability to do stripping work. Strip mining in the domestic coal industry is contributing a greater proportion of overall production than at any time in the past. U.S. Bureau of Mines statistics show that the percentage of total production mined in 1958 by stripping methods increased to more than 30 pct, up from 22 pct in 1951. The tendency to favor strip and open pit mining exists in other mining activities, but such trends are not as clearly outlined as in the coal industry. Significantly, the depth of overburden in coal properties considered suitable for stripping is also increasing. A depth of 50 to 60 ft of overburden was once considered to be about the maximum amount that could be handled economically. Today, a depth of 80 to 100 ft is frequently taken into consideration for simple overcasting operations (i.e., excavating overburden and dumping it in the spoil position where it remains indefinitely). Accompanying these changes, there have been continuing studies searching for procedures to appraise deeper stripping problems. Although the only known practicable way to accurately evaluate a proposed stripping venture is to make studies (including cost estimates) step by step, it is nevertheless desirable to have a quick method for making preliminary evaluations of potential strip mining operations. A recently devised digital computer method of providing a preliminary simple overcasting analysis for a stripping prospect relates the indicated trends in the relationship of the weight of the machine to its ability to do stripping work. In addition, this approach employs situations where the geometry of each cut-and-spoil section is assumed to take certain defined relationships for varying overburden depths. Slopes are necessarily considered to be stable, which means such practical factors as the mechanics of soils are neglected for the sake of convenience. Definition of Terms: Photographs A and B show a shovel-type and a dragline-type of simple overcast operation, plus terms used to denote certain parts of a pit. Pits that follow a straight line when projected on a horizontal plane are referred to as straightaway. It has been assumed that all section drawings accompanying this article pertain to straightaway cuts which, in turn, means that areas can be compared by relative volume. The volume of overburden is measured in virgin cubic yards. Material displaced from its virgin state to a spoil area normally occupies a larger volume than when in situ; the difference is termed swell, and it is expressed as a percentage of the original volume. For example, if the original cut volume is denoted V cu yd, and the spoil volume is 1.2 V cu yd, the swell is a positive 20 pct. MAXIMUM USEFULNESS FACTOR (MUF) CONCEPT Men experienced in overburden removal give emphasis to the weight of the machine in relation to its value as an excavator. From the writer's understanding, value has been only loosely defined and discussed generally and vaguely. The concept is considered important, however, since it is based upon the observations of many men. It provides a clue for the approach taken to solve deep stripping problems. In the procedure described below, value has been arbitrarily established as the product of the nominal dipper size of the shovel (or dragline) times a functional dumping reach. MUFs—Shovel: A shovel's capability to handle thick overburden is usually limited by its ability to dispose of the spoil. Thus the dumping reach, as well as its dumping height, is significant. The angle of repose of spoil material must also be considered. Although such slope angles vary among different mines, jobs, and materials, a slope of 1.25 to 1, frequently found in both planning and practice, is used by this author in the illustration of this analytical method. The relationship of the shovel's geometry to a stripping operation is shown in Fig. 1. To gain maximum advantage in constructing spoil piles, the shovel is placed so that its tracks adjacent to the spoil are as close as possible to the rib of the coal deposit. A vertical plane passing through the line

Jan 1, 1961

By F. G. Miller

Earlier studies of the mechanism of flotation showed that coal flotation products are contaminated by composite coal and mineral particles. The mineral matter of these particles has the dual effect of increasing the specific gravity and decreasing the coal surface of the particle available for bubble attachment. The present study showed that these particles are more loosely held in the froth column than the high grade coal particles, especially in the coarser sizes. Consequently, it is possible in the laboratory to produce a secondary concentration of the product by sprinkling the froth product with water to wash these loosely held particles from the froth during formation and recovery. To improve coal flotation, Bethlehem Steel Corp.'s research department has been working on a number of related problems based on both physical and chemical factors. The ideal is of course full understanding of the interrelated effects of both sets of factors. However, detailed studies1 of each physical factor have produced immediately usable results in commercial coal flotation and are providing the basis for our current work on the effect of chemical factors. Since these detailed studies provided the basis for the present investigation of froth sprinkling, their key results are highlighted here. For example, for a highly floatable bituminous coal, particle floatability was shown to be directly related to the percentage of coal surface available for bubble attachment and inversely related to particle mass. The data also underscored that in a given size range the addition of mineral matter to a particle makes flotation more difficult both by adding to the mass of the particle and by decreasing the amount of coal surface available for bubble attachment. Size also affects particle floatability in that as the size of particles of a given specific gravity increases, mass increases and the ratio between coal surface area and mass of the particle decreases. Flotation tests showed that any recovery of the coarsest particles in a coal feed is accompanied by progressively higher recovery of finer and finer particles. Consequently, fine high-specific-gravity particles are recovered with the coarse good coal. As a result, when the entire 14 mesh x 0 size range is processed by froth flotation, the good coarse coal is contaminated with high-specific-gravity fines. It is the small quantities of these fines that must be rejected from the froth product if flotation efficiency is to be increased above its present level. These principles and findings, together with work by Professor V. I. Klassen,' led to the froth sprinkling investigation reported in this paper. Working with Russian coals, Klassen had shown that froth sprinkling washes loosely held refuse particles from the froth and compensates for the water lost in the upper froth layers and increases its stability. As a result, the coal particles are retained in the froth and the loss of coarse coal from the froth is prevented. Decreases in ash of 0.1% to 1.5% were reported by Klassen. Working with a 28 mesh x 0 American coal, the author of the present paper found that single-stage flotation coupled with froth sprinkling produced a product comparable to that obtained by the more expensive method of roughing and cleaning.3 The investigation reported in the present paper expanded study of the effect of froth sprinkling to include each of the standard size fractions of a bituminous coal. The main findings are as follows: (1) For those size fractions between 48 mesh and 150 mesh, froth sprinkling produces a marked reduction in both sulfur and ash. In the case of those sizes coarser than 48 mesh, while this reduction is not as significant, the additional benefit of shorter retention time is still a plus for froth sprinkling. Furthermore, when froth sprinkling is coupled with normal fast flotation, the product purity approaches that obtained by starvation reagent feeding, i.e., gradual feeding of flotation reagent to float the recoverable coal from the pulp slowly in several increments. The specific results for these two size groups are: (a) 14 x 48 Mesh. By using froth sprinkling with fast flotation, product sulfur can be reduced to a level

Jan 1, 1970

By J. L. Walter

Extra-low carbon iron sheet, when deformed and annealed, undergoes exaggerated or abnormal grain growth in the critically deformed regions of the sheet. This exaggerated pmth occurs, for low strains (3 to 6 pct), only in sheet which has a fine dispersion of precipitates in the subsurface region of the sheet and fewer and coarser precipitates in the sheet interior. These particles have been identified as manganese sulfides. Wing the anneal, grains near the surface are gvowth-inhibited by the fine particles but the grains in the interior are free to grow normally. With the additional driving force provided by the strain energy, the interior grains first grow into the small subsurface pains. Eventually, these growing grains grow completely through the sheet. Calculations of limiting grain sizes at various values of strain indicate that a volume fraction of precipitates in excess of 10-' would be required to eliminate exaggerated growth in material strained to 10 pct. OPEN-COIL annealing has made decarburization of sheet steel both efficient and economically practical. Use of such material for porcelain-enameling stock is one of many possible applications of low-carbon iron since carbon in steel is deleterious to porcelain-enameling properties.' However, the extra-low carbon iron presently available presents another problem, that of exaggerated grain growth in regions where the sheet has been deformed as by bending or stretching. In exaggerated grain growth a few grains start to absorb their neighbors and these may become very much larger than the average grains of the sheet. Other names for exaggerated grain growth are coarsening, critical grain growth, secondary recrystallization, abnormal grain growth, or discontinuous grain growth. While this grain growth does not affect the enameling qualities of the low-carbon iron sheet, their presence results in a marked reduction of tensile-yield strength in the region of the sheet containing the large grains. The loss of tensile yield strength may render the material unsuitable for many applications . This report describes the results of a study undertaken to determine the cause of the exaggerated grab growth in extra-1ow carbon iron and, if possi- ble, to prescribe practical procedures for its prevention. GENERAL THEORY The driving force for exaggerated grain growth is the grain boundary free energy. This driving force is proportional to (l/rl + l/r2) where rl and r2 are the mutually perpendicular radii of curvature of the boundary between the growing grain and the grain being consumed. Thus, the greater the difference in size between the growing grain and the matrix grains, the higher the driving force for grain growth. If, however, the matrix grains are free to grow simultaneously, the driving force for exaggerated growth will be diminished. Stability toward growth of the matrix grains may be caused by a) a strong single orientation texture (texture inhibition),' b) a dispersed second phase,3"5 c) the thickness effect,' or d) intergranular segregation.7"9 As exaggerated growth occurs when growth of the matrix grains has been slowed by the stabilizing processes mentioned above, there must be an additional factor acting to promote growth of a few of the grains to the point where they are enough larger than the matrix grains that boundary energy driving forces are sufficient to cause continued growth. For instance, at the annealing temperature, growth-inhibiting inclusions may slowly dissolve and coalesce. Eventually, a grain boundary becomes unlocked and migration occurs at the expense of neighboring grains. Or, an additional driving force may be supplied to some of the grains if the material is strained. Then, since some grains will be strained less than others, the difference in strain energy between adjacent grains may be sufficient to overcome boundary locking and allow growth of the grains with lower strain energies. In the present study, therefore, such factors as the presence or absence of dispersed phases, the nature of the exaggerated growth, and the effect of strain have been considered. EXPERIMENTAL PROCEDURE I) Material and Processing. Three types of low-carbon iron were used in this study; types A and B were commercial grades, each from a different supplier.* The precise details of the processing of

Jan 1, 1963

By J. B. Hess, C. S. Barrett

TO reach equilibrium between different phases in cobalt-rich alloys requires prohibitively long annealing cobalt-richalloystimes when temperatures are below about 700°C. The fact that a transformation from face-centered cubic to close-packed hexagonal readily tered takes place at temperatures below this in the cobalt-rich solid solutions is not an indication that thermally activated processes occur at an appreciable rate, for the transformation is well established as martensitic in nature. Wide divergence between heating and cooling experiments and high sensitivity to prior heat treatment make it difficult to judge temperatures of equilibrium between the phases.&apos; One object of the present work was to see if the information object of on the relative stability of phases could be gained by substituting plastic deformation for thermal agitation. Procedures were worked out that led to the determination of a diffusionless type of phase diagram, which represents the temperature of of phase equal stability for phases of the same composition, and the technique was applied to the Co-Ni system. Another object of the work was to see whether or not deformation would generate frequent stacking faults when these were thin lamellae of quentstackingfaultsa phase having higher free energy than the parent phase. The alloys were prepared in 80 to 100 g melts from cobalt (with metallic impurities estimated spectrochemically as follows: Ni, 0.05 pct; Fe, 0.001 pct.; Mg, Si, Cu, Cr, Al, < 0.001 pct) and Mond Car-bony1 nickel (with Fe, 0.05 pct; Si, 0.003 pct; C, 0.61 pct.; Cu, 0.001 pct; Co, Cr not detected, < 0.01 pct). The metals were melted in pure Al2O3 crucibles. An atmosphere of argon, that had been purified by passing over hot magnesium chips, was used for the alloys that, by analysis of the portions of the ingots actually used, were found to contain 15.3, 25.7, and 35.0 pct Ni, and vacuum melting (after degassing) was used for those containing 29.4 and 31.5 pct Ni. After induction melting the alloys were allowed to solidify in the crucible, and slices % in. thick x ½ in. in diam were annealed 12 hr at 1350°C for homogenization. These same specimens were used throughout the series of experiments, with annealing treatments of 4 hr at 900°C in purified hydrogen followed by furnace cooling, alternating with the deformation and X-ray tests discussed below. Results Spontaneous transformation was observed on cooling to room temperature in all alloys containing 29.4 pct Ni or less and by cooling the 31.5 pct alloy to — 195°C but was not observed in the 35 pct alloys after cooling to —195°C. These results are in satisfactory agreement with the cooling experiments of Masimoto.4 From these data it is clear that the temperature of beginning transformation M,,, drops to 20°C with the addition of about 30 pct Ni. The test for spontaneous transformation was metallographic. Specimens were thermally polished by annealing 10 hr in hydrogen at 1350°C, then furnace cooled; if trans- formation had occurred there were relief effects visible on the thermally polished surfaces. These markings were narrow straight lines, usually resolvable at high magnification as clusters of fine lines that resembled slip lines. It was concluded that they resulted from displacements on (111) planes, for the number of directions in individual grains often reached but never exceeded four, and lines could always be found parallel to the thermally etched (111) boundaries of annealing twins. The markings were thus consistent with the idea that the transformation occurs by (111) plane displacements (Shockley partial dislocations moving on (111) planes). This was further confirmed by X-ray tests for stacking disorders. Using an oscillating crystal technique previously employed to detect strain-induced faulting in Cu-Si alloys," streaks indicative of the stacking faults were looked for and found on X-ray films of the spontaneously transformed 25.7 pct Ni alloys, as expected by analogy with Edwards and Lipson&apos;s results on pure cobalt." The streaks were much intensified after rolling at room temperature. Transformation induced by plastic strain was investigated as a function of alloy composition and temperature of deformation. A series of tests was made to determine suitable straining and X-raying techniques. Filing was found inferior to abrasion in converting cubic samples to hexagonal, and abrasion was less effective than peening in producing smooth unspotty Debye rings in the X-ray patterns. Because the diffraction lines were broad, Geiger-counter spectrometer records of filings were less sensitive in revealing small amounts of transformed material than X-ray patterns recorded on films in a small diameter camera. After these exploratory tests the following methods were adopted. Specimens that had been annealed at least 4 hr at 900°C and furnace cooled were mounted in a block of aluminum, brought to temperature, and peened thoroughly with a mullite pestle preheated to the same temperature. The specimens were then quenched to room temperature. In peening, a circular area of % in. diam was given 500 blows. A few control tests showed that an additional 1000 blows did not detectably change the proportions of the phases present. The amount of transformation was judged by X-ray reflection patterns from the peened surface, using the innermost four lines of the cubic and the hexagonal patterns with filtered CoKa radiation,

Jan 1, 1953

By R. J. Fruehan, F. D. Richardson

Electrochemical measurements have been made of the activity of oxygen in copper and its alloys with silver and tin at 1100" and 1200°C. The galvanic cell used was Pt, Ni + NiO/solid ellectrolyte/[O] in metal, cermet, Pt The results do not support any of the equations so far designed for predicting the activities of dilute solutes in ternary solutions from activities in the corresponding binaries. If, however, a quasichemical equation is used with the coordination number set to unity, agreement between observed and calculated activities shows that this empirical relationship can be useful over a fair range of conditions. SEVERAL solution models have been proposed for predicting the activity coefficients of dilute solutes in ternary alloys from a knowledge of the three binary systems involved. Alcock and Richardson1 have shown that a regular model, and a quasichemical model,&apos; in which the dissolved oxygen is coordinated with eight or so metal atoms, can reasonably predict the behavior of both metal and nonmetal solutes when the heats of solution of the solute in the separate solvent metals are similar. But when this is not so, neither model gives useful predictions unless coordination numbers of one or two are assumed. Wada and Saito3 subsequently adopted a similar model to derive the interaction energies for two dilute solutes in a solvent metal. Belton and Tankins4 Rave proposed both regular and quasichemical type models in which the oxygen is bound into molecular species, such as NiO and CuO in mixtures of Cu + Ni + 0. However, their models have only been tested on systems in which the excess free energies of solution of the solute in the two separate metals differ by a few kilocalories. Ope of the reasons why more advanced models have not been proposed is because few complete sets of data exist for ternary systems in which the solute behaves very differently in the two separate metals. For this reason measurements have been made of the activities of oxygen dissolved in Cu + Ag and Cu + Sn. Measurements on both systems were made by means of the electrochemical cell, Pt, Ni + NiO/solid electrolyte/O(in alloy), cermet,Pt [1] The activity of oxygen was calculated from the electromotive force and the standard free energy of formation of NiO, which is accurately known.5 Before investigating the alloys, studies were made of oxygen in copper to test the reliability of the cell and to check the thermodynamics of the system. Of the previous studies those by Sano and Sakao,6 Tom-linson and Young,7 and Tankins et al.8,7 have been made with gas-metal equilibrium techniques; those by Diaz and Richardson,9 Osterwald,10 wilder," Plusch-kell and Engell,12 Rickert and wagner,13 and Fischer and Ackermann14 have been made by electrochemical methods. EXPERIMENTAL The apparatus employed was the same as described previously,9 apart from slight modification. The molten sample of approximately 40 g was held in a high grade alumina crucible 1.2 in. OD and 1.6 in. long. The solid electrolytes were ZrO2 + 7½ wt pct CaO and ZrO2 + 15 wt pct CaO; the tubes 4 in. OD and 6 in. long were supplied by the Zirconia Corp. of America. They were closed (flat) at one end. In one experiment with Cu + O, both electrolytes were used in the cell at the same time. The reference electrodes inside the electrolyte tubes consisted of a mixture of Ni + NiO. They were made by mixing the powdered materials and pressing them manually into the ends of the tubes, with a platinum lead embedded in them. The tubes were then sintered overnight in the electromotive force apparatus at 1100°C. By sintering the powders inside the tubes (instead of using a presintered pellet9) better contacts were obtained between the electrolyte, the powder, and the platinum lead. Troubles arising from polarization9 were thus much reduced. The electromotive force was measured by a Vibron Electrometer with an input impedence of 1017 ohm; the temperature was measured with a Pt:13 pct Rh + Pt thermocouple protected by an alumina sheath. The couple was calibrated against the melting point of copper. The cermet conducting lead of Cr + 28 pct Al2O3, previously found to be satisfactory9 for use with Cu + 0 was also found satisfactory with Cu + Ag + 0 and Cu + Sn + 0. Superficial oxidation was observed, but it did not interfere with the working of the cell. The reaction tube containing the cell was closed at each end with cooled brass heads and suspended in a platinum resistance furnace. The tube was electrically shielded by a Kanthal A-1 ribbon which was wound round it, and the ribbon was protected by a N2 atmosphere between the furnace and the reaction tube. The cell was protected by a stream of high purity argon which was dried and passed through copper gauze at 450°C and titanium chips at 900°C. All the metals used were of spectrographic standard. Procedure. In studies of the system Cu + 0, be-

Jan 1, 1970

By P. A. Laxen, H. R. Spedden, A. M. Gaudin

WHEN a mineral particle is fractured, bonds between the atoms are broken. The unsatisfied forces that appear at the newly formed surface1 are considered to be responsible for the adsorption of ions at the mineral surface. A knowledge of the mechanism and extent of ion sorption from solution onto a mineral surface is of interest in the development of the theory of flotation.2,3 Study of the adsorption of sodium from an aqueous solution on quartz offers a simple approach to this complicated problem. The availability of a radioisotope as a tracer element meant that accurate data could be obtained.4,5 Three main factors which appeared likely to affect the adsorption of sodium are: 1-concentration of sodium in the solution, 2-concentration of other cations in the solution, and 3-anions present in the solution. Hydrogen and hydroxyl ions are always present in an aqueous solution. By controlling the pH, the concentration of these two ions was kept constant. The variation in the amount of sodium adsorbed with variation in sodium concentration was then determined under conditions standardized in regard to hydrogen ion. The effect of concentration of hydrogen ions and of other cations was also measured. A few experiments were made to get a preliminary idea on the effect of anions. The active isotope of sodium was available as sodium nitrate. Standard sodium nitrate solutions were used throughout these experiments except when the effects of other anions were studied. It was found that sodium adsorption increased with sodium-ion concentration, but less rapidly than in proportion to it. Increasing hydrogen-ion concentration, or conversely decreasing hydroxylion, brings about a comparatively slight decrease in sodium-ion adsorption. Increasing the concentration of cations other than hydrogen or sodium decreases somewhat the adsorption of sodium ion. It would appear as if the kind of anion is a secondary factor in guiding the amount of sodium ion that is adsorbed. Materials and Methods Quartz The quartz was prepared as in previous work in the Robert H. Richards Mineral Engineering Laboratory4 except for the refinement of using de-ionized distilled water for the final washing of the sized quartz, prior to drying5 To minimize the laborious preparation of quartz, experiments were made to determine whether the sodium-covered quartz could be washed free of sodium and re-used. The experiments were successful as indicated by lack of Na&apos; activity on the repurified material and by its characteristic sodium adsorption. Table I gives the spectrographic analyses of the quartz used. The quartz ranged from 16 to 40 microns in size, averaging about 23 microns (microscope measurement), and had a surface of 1850 sq cm per g (lot I), 2210 (lot II) and 2000 (lot III) as determined by the Bloecher method.6 Radioactive Sodium Method of Beta Counting for Adsorbed Sodium: Na22, the radioisotope of sodium, possesses convenient properties.7 It has a half-life of 3 years, thus requiring no allowance for decay during an experiment. On decay it emits a 0.575 mev ß radiation and a 1.30 mev ? radiation. The decay scheme is illustrated in the following equation: [Y Nam S. - &apos;Net 3 years] The ß radiation is sufficiently strong to penetrate an end-window type of Geiger-Mueller counting tube. This, in turn, makes it possible to use external counting, a great advantage in technique. Furthermore, it permits the assaying of solids arranged in infinite thickness, while assaying evaporated liquors on standardized planchets. The equipment used was standard and similar to that employed by Chang8 The original active material was 1 ml of solution containing 1 millicurie of Na22 as nitrate. This active solution was diluted to 1000 ml. Five milliliters of this diluted active solution was found to give a quartz sample a sufficiently high activity for accurate evaluation of the sodium partition in the adsorption measurements. Also, 1 ml of final solution gave a sufficiently high count for precision on the liquor analyses. The sodium concentration of the diluted active solution was 1.2 mg per liter, so that 6 mg of sodium for 60 ml of test solution and 12 g of quartz was the minimum amount used. The active solution was stored in a Saftepak bottle. Procedure for Adsorption Tests: The method consisted of agitating 12 g of quartz with 60 ml of solution of known sodium concentration for enough time to establish equilibrium between the solution and the quartz surface. The quartz was separated as completely as possible from the solution by filtering and centrifuging. The activity on the quartz and in the equilibrium solution was measured and the partition of the sodium was calculated from the resulting data. The detailed procedure for the adsorption test is set forth in a thesis by Laxen5 In brief, it included the following steps: 1-Ascertainment of linearity between concentration of Na22 and activity measured. 2-Evaluation of factor to translate activity on solid of infinite thickness in terms of activity on an evaporated active film of minute thickness, on the various shelves of the counter shield. 3-Taking precautions to avoid evaporation of water during centrifuging.

Jan 1, 1952

By A. Totani, S. Nakajima, H. Okazaki

The phase diagram for the SnTe-SnSe system has been studied in the temperature range from 300° to 900°C by differential thermal and quenching techniques. The X-ray measurements were made on quenched specimens. High-temperature diffraction was also made to study the phase transition in SnSe. The system is proved to be of a eutectic type in which no intermetallic compound exists. The eutectic point is at the composition SnTeo.55 Seo.45. the eutectic temperature being 755°C. Solid solubility limits are SnTeo.6Seo.r and SnT eo. 3s Seo.6s at the eutectic temperature, and change almost linearly to SnTeo.aaSeo.lz and SnTeo.18 Seo.az as temperature decreases to 300°C. It was shown that the SnSe phase has a phase transition of the second order at about 540°C and that the transition temperature decreases with increase of the SnTe content. THERMOELECTRIC properties of tin telluride (SnTe) and tin selenide (SnSe) have been studied extensively in recent years. The variation of physical properties with composition could be of interest if these compounds form an appreciable crystalline solution. The purpose of present investigation is to confirm the formation of crystalline solution or intermetallic compound, if any, and to establish the phase diagram for this system. The crystal structure of SnTe is NaCl type with a cubic unit cell1 (a = 6.313A). The crystal of SnSe having an orthorh2mbic unit cellz (a = 11.496, b = 4.1510, and c = 4.4437A) is isomorphous with tin sulfide (SnS) which has a distorted sodium chloride structure. It has been known that SnSe has a phase at at 540°C; the transition has been assumed to be of the second order. As far as we know, only two studies on the SnTe-SnSe pseudobinary system have been reported. The conclusion obtained in these papers is that, in the composition regions near SnTe and SnSe, the system forms a crystalline solution of the SnTe structure and the SnSe structure, respectively, and that, in the intermediate region, both phases coexist. However, neither the variation of the solid solubility vs the temperature nor the liquidus and solidus were investigated. Hence present writers have attempted to determine the phase diagram of the system by differential thermal analysis (D.T.A.) and X-ray diffraction. EXPERIMENTAL Sample Preparation. Starting materials, SnTe and SnSe, were prepared by the direct fusion of commercially available high-purity (99.999 pct) elements. Stoichiometric amounts of each couple Sn-Te or Sn-Se were weighed into a clear fused silica ampule. After evacuation to a pressure below 10-3 mm Hg, the am- pule was sealed, and annealed at 900°C for 5 hr. The melt was quenched in water. X-ray analysis confirmed the formation of a single phase of SnTe or SnSe. The other samples, SnTel-,Sex were synthesized from these SnTe and SnSe by mixing them in the required ratio, followed by annealing at 900°C and quenching. These samples were used directly for D.T.A. For X-ray measurements, samples were annealed at 700°, 600°, or 500°C for 100 hr or at 300°C for 150 hr, and then quenched in water. It was found that the lattice constants of the SnTe phase annealed for 150 hr at temperatures above 500°C did not differ from those annealed for 100 hr at the same temperatures. However the X-ray phase analysis showed that at 300°C the annealing for 150 hr was necessary to attain a true equilibrium state. D.T.A. The solid-liquid equilibrium temperature was determined from D.T.A. measurements. The sample was sealed in an evacuated silica tube and molybdenum powders sealed in an another tube were used as a reference material. The sample and the reference tube were placed in a nickel block and were heated from room temperature to 900°C at a rate of 3°C per min and then cooled down at the same rate to 600°C. Thermocouples for these measurements were Pt-Pt. Rh (10 pct) and the error of temperature measurements was within + l0C. D.T.A. curves were obtained on a two-pen recorder and an automatic controller (PID type) was used for the program of heating and cooling. When temperature reaches the solidus from the low-temperature side, there appears an endothermic peak. The solidus temperature was determined by extrapolation of the straight portion of the starting flank of this peak to the base line. In a similar way, the liquidus temperature was determined from an exothermic peak on D.T.A. cooling curve. In the case of supercooling, if any, its degree can be estimated from the magnitude of the abrupt temperature rise. X-Ray . X-ray powder patterns were taken by a diffractometer using CuK, radiation. Since the SnSe crystal is cleaved easily, the powders become flaky when SnSe-rich samples are ground in an agate

Jan 1, 1969

By THEODORE DWIGHT

Members of the Institute have already received a special pamphlet descriptive of the United Engineering Society building, and wilt doubtless be interested in the progress that has been made up to date-February 24th-in erecting this home for the engineering profession. The old buildings on lots Nos. 25 to 33 W. 39th St., New York, were,&apos; removed many months ago, but final contracts for the new, building were not let until the summer of 1905. The size of the building is 115 ft. on 39th Street, and 88 ft. in, depth; the height from, the sidewalk to the top of the parapet is 220 feet. The cubic contents of the building from the. bottom of the basement floor, to the top of the roof, including the pent houses, is 2,290,000 cubic feet. The number of light&apos;s, in the building will be between 4,000 and 4,500. The air supply for Auditorium and Lecture. Halls will amount to nearly 10.0,000 cu. ft, per minute, and the exhaust. to 90,000 cu. ft. per minute. In excavating for cellar and foundations, the average depth where good rock was. found was 37 ft.-it varied, however,: from 27 to 65 ft., due to an old water-course having run through the center of the lot; this condition, and the presence of soft rock, which rapidly disintegrated when exposed to air and water, made the foundation-work very difficult. As two of the column-footings of the building have to sustain a weight of 3,000,000 11) each, the most substantial foundations are necessary; 13,000 cu. yd. of earth were excavated for the foundation and basement; and 1,600 cu. yd. of concrete were necessary, to build up the footings. In the completed building there will be about 3,500,000 bricks. Owing to the number of auditoriums, and their location, and the placing of the library on the top floor; where allowance will have to be made for the enormous weight of 300,000 books, the structural steel work has been unusually complicated in this building. For instance, over the auditorium there are two 60-ton plate-girders, made up

Mar 1, 1906

By Charles R. Keyes

A COMPLETE transformation has taken place in the boras industry during the year 1908. A most remarkable factor in this radical change in method of producing the crude borates has been its removal from the realm of industrial chemistry to the field of mining. With the development of extensive deposits of borate-minerals interstratified in thick sequences of Tertiary clays and sands, their winning becomes a strictly mining-enterprise, of the same kind and of the same certainty as the digging of coal or iron-ore. The major supply of the world&apos;s production of commercial borax now comes from the United States. While formerly all of the boric salts of commerce were laboriously extracted from the waters of saline lakes of the arid regions, or from the bottom-salts of desiccated ponds, it later was largely slowly leached from ancient desert shales and clays. During these periods the borax industry was a very hazardous and expensive vocation.

Oct 1, 1909

By J. E. Johnson

Discussion of the paper of Bradley Stoughton, presented at the Cleveland meeting, October, 1912, and printed in Bulletin No. 71, November, 1912, pp. 1245 to 1275. J. E. JOHNSON, JR., Ashland, Wis. :-Is it true that titanium reduces the chill in chilling iron? If so, as I think Mr. Stoughton has stated elsewhere, then I do not see how titanium is beneficial in car-wheel mixtures. One of the most difficult things to do is to get a proper chill and a proper degree of toughness, and the goodness of an iron of the given composition for charcoal-iron purposes is denoted by the chill which it will take as compared with its composition. If titanium reduces that chill, then it does not seem to me as good for car-wheels as its absence would be, and I should like to have it explained what effect titanium has on the chill of a given iron. MR. STOUGHTON : It is true that titanium reduces the chill of iron quite noticeably, yet, at the same time, if I am correctly informed, 90 per cent. of all chilled-iron rolls are made to-day with the titanium treatment, and a great many car-wheels, but one has to make changes in the silicon added and also, if I am correctly informed, in the manganese. The advantage of titanium is that when the proper changes are made, so that we get the same depth of chill with the titanium as we otherwise would without, the chill is much harder than before, and also the body of the roll or wheel is tougher and somewhat stronger, especially under shock. JAMES F. KEMP, New York, N. Y.:-This subject is obviously one of great importance to the iron industry, in that if we call find a method of using titaniferous ores, we will prolong the life of our iron reserves. Fifteen or more years ago, primarily from the study of the ores in the Adirondacks, I be-

Dec 1, 1912

By J. PARKCEH CHANNING

Discussion of the paper of Lewis T. Wright, presented at the New Haven meeting, February, 1909 (Trans., xl., 492 to 495). J. PARKE CHANNING, New York, N. Y. (communication to the Secretary*):-Mr. Wright, in his introductory paragraph, says: " It is commonly believed by metallurgists that in copper-smelting, the copper in the slags, which is irreducible by continued smelting, is retained in the form of &apos;prills&apos; of matte." On a recent visit to Greenwood, B. C., I was discussing with J. E. McAllister, the general manager of the British Columbia Copper Co., and the former metallurgist of the Tennessee Copper Co., this very question; and he held strongly to the idea that the copper in slag was in two forms-one portion contained in occluded matte and the other as an oxide. He believed that this same rule would apply to the silver in the slag. From my experience I am strongly inclined to agree with Mr. McAllister; and it appears quite reasonable that in furnaces treating oxidized copper-ores, and to a less degree in furnaces treating sulphide ores, there is always bound to be present a certain amount of copper oxide and silver oxide, which will behave like any base and get into the slag as such. We all know that in Arizona, in the early days, when it was customary to produce black copper, because the ores were nearly all oxidized or carbonates, and sulphur was scarce, the slags as a rule carried 2.5 per cent. of copper and seldom ran less than 1.5 per cent. of copper. The economic point was determined by the extra coke necessary to produce the reducing action. In connection with the extra saving in copper, Arthur L. Walker, now professor of metallurgy at Columbia University, and formerly general manager of the Old Dominion Copper Mining Co., at Globe, told me that with coke at $60 per ton it never paid him to make slags containing less than 2.5 per cent. of copper. *Received Oct. 8, 1909.

Feb 1, 1911

By W. L. Mamme, G. Y. Chin

The problem of selection of the active slip systems for a crystal undergoing an arbitrary strain was analyzed by Taylor and by Bishop and Hill in terms of a minimum (internal) and a maximum (external) work criterion, respectively. These two criteria have now been generalized to include crystallographic slip on several sets of slip systems, twinning mixed with slip, and slip by (noncrystallographic) pencil glide. The generalized treatment also takes into account the possibility of a Bauschinger effect and of unequal hardening among the shear systems, which were considered in the Bishop and Hill work. Optimization techniques of linear and nonlinear programming are shown to be applicable for the numerical calculation of the minimum or maximum work. In the case of crystallographic shear, the constraint functions are linear and hence the optimal work is obtained as the saddle value of the lagrangian function Wi(y) e minimum and W,(u) + (a) for the maximum, where Wi is the (internal) work, We is the (external) work, Y is the crystallographic shear strain, u is the applied stress, and and are constraints. It is shown that the Lagrangians are functionally the same and the saddle value of one problem is identical to the saddle value of the other, proving that the two analyses are completely equivalent. In the case of pencil glide, although the constraint functions are nonlinear and neither convex nor concave, the equivalence of the optimal values to the saddle value of the Lagrangian (which is again identical for both problems) is still valid. WHEN a crystal deforms plastically by crystallographic shear, five independent shears are generally required to accommodate five independent strain components specifying the deformation. Assuming slip as the only shear mechanism, Taylor1 in 1938 analyzed the deformation in terms of a minimum work criterion. He hypothesized that of all combinations of five slip systems which are capable of accommodating the deformation, the active combination is that one for which the internal work C is a minimum, where 1 TI is the critical resolved shear stress for slip on the 1-th slip system and is the corresponding simple shear. By further assuming equal 72 for all equivalent slip systems and no Bauschinger effect, Taylor re- duced the minimum work problem to one of minimum and applied the analysis to the case of axisym- Metric flow by {111}(110) slip in fcc crystals. However, he did not consider the question of whether the resolved shear stress has in fact attained the critical value for slip on the newly found active systems without exceeding it on the inactive systems. In 1951 Bishop and ill&apos; put forth the maximum work analysis in which slip is again assumed as the only deformation mechanism. In this analysis, the work o1 done in a given strain ij by a stress ujj not violating the yield condition is maximized. In addition, the analysis takes into account the possibility that the critical resolved shear stress for slip may not be equal among the slip systems and that the slip behavior may exhibit the Bauschinger effect. As with Taylor, a single set of slip systems—{111)(110) — was analyzed numerically. It thus appears that the Bishop and Hill treatment is on a more sound physical basis than the Taylor treatment. However, Bishop and Hill showed that where there is equal hardening among all slip systems and when there is no Bauschinger effect, Eq. [11 ] of Ref. 2, as assumed by Taylor, the results of their maximum work analysis are the same as those of Taylor&apos;s minimum work analysis. Hence at least under those conditions there is an implication that the Taylor analysis does lead to a critical resolved shear stress for slip on the predicted active systems without violating the yield condition on the inactive systems. Recently, the Taylor analysis was applied for numerical solutions of the axisymmetric flow problem, for slip on {110}(111), {112}(111). {123)(111) systems as well as a mixture of all three sets of svstems."1 Computational techniques based on the optimization theories of linear and nonlinear programming4 were employed in these solutions. The same techniques were employed in the solutions of an axisymmetric flow problem of deformation by slip on (111) (110) systems and twinning on (111)(112) systems5 which had been considered theoretically from a modified Taylor approach. The utilization of these techniques has led to the realization that the solutions of Taylor&apos;s minimum work problem imply the solutions of Bishop and Hill&apos;s maximum work problem. The two problems turn out to be dual problems in the well known sense of mathematical programming. It is thus the purpose of this paper to first generalize the minimum and maximum work analyses to include crystallographic slip on several sets of slip systems, twinning mixed with slip, and slip by (non-crystallographic) pencil glide, as well as the possibility of a Bauschinger effect and of unequal hardening

Jan 1, 1970

By M. L. Rudee, R. A. Huggins

Samples of iron containing nitrogen or carbon have been given treatments similar to those used in cold-work peak (CWP) measurements and examined by transmission electron microscopy. It was observed that the unusual and nonreproducible behavior of the carbon CWP can be explained by a strong tendency for carbon to form grain boundary precipitates at temperatures below those used for CWP measurements. These precipitates dissolved at the temperatures used in the CWP measurements. There was no evidence for nitrogen precipitation at grain boundaries. There was no indication of precipitation along dislocations in either carburized or nitrided samples given treatments similar to those of CWP measurements. Although it is possible that subelectron-microscopic clustering had occurred, this observation supports the theories of the CWP that are based on continuous atmospheres rather than on individual precipitates. In an earlier paper,&apos; the present authors developed a new distribution function to predict the occupation of sites for interstitial impurity atoms around a dislocation. When this distribution was applied to the case of carbon and nitrogen in iron, it predicted that, if the temperature dependence of the concentration of solute atoms in the matrix was controlled by the presence of equilibrium carbide or nitride precipitates, the tendency for nitrogen to segregate to dislocations would be greater than that for carbon even though their binding energies to dislocations are identical. The cold-work internal-friction peak (CWP) is considered by most authors to be produced by the interaction of interstitial impurities with dislocations. Many investigators have studied the CWP in iron containing carbon and nitrogen and have observed a significant difference between its behavior in the two cases. In this paper a series of experiments will be reported that were initiated to determine whether the application of the new distribution function would explain the observed differences between the carbon and nitrogen CWP. Although it was found that the distribution function, pev se, did not explain the differences, the differences became clear, and some insight into the mechanism of the CWP was realized. Before reporting the present experiments, the literature pertaining to the differences between the carbon and nitrogen CWP in iron and the various mechanisms proposed for the CWP will be reviewed. LITERATURE REVIEW Snoek2 first observed the CWP in iron specimens containing nitrogen, but also reported a weak and unreliable peak in carburized samples. Later, Ke3 established that the CWP height was proportional to the degree of deformation. The presence of nitrogen alone would produce a peak of the same size as found in a sample containing both nitrogen and carbon, and KG concluded that the CWP was caused by nitrogen. In a discussion of G&apos;s paper it was reported that Dijkstra had investigated the CWP in samples that contained only carbon. He found it to be much smaller than the nitrogen peak and "unstable". KG et al.4 charged specimens of iron with both carbon and nitrogen. They observed that the carbon CWP was much smaller than that observed in nitrided samples, but that aging at 300°C caused the carbon peak to increase. A similar treatment produced no change in a nitrogen peak. Annealing at higher temperatures caused the height of the CWP in both the nitrogen and carbon samples to decrease. This behavior was also observed by Kamber et al. 5 who found that the activation energy for the annealing of the CWP was identical with the activation energy for the self-diffusion of iron. They concluded that the annihilation of dislocations by climb caused the reduction in the CWP height. Kamber et al. studied the "unstable" carbon peak in detail. They measured both the Snoek and CWP during various aging treatments. In carburized samples, aging at 100°C caused the Snoek peak to disappear, although the CWP peak remained small. However, a subsequent treatment for 5 hr at 240°C caused the CWP to reach a maximum. They proposed that an additional location for the carbon, other than whatever site produced the CWP, is present. In nitrided samples the CWP was completely developed as soon as a measurement was made; additional sites are not present. No explanation of either the additional site or the difference in the behavior of carbon and nitrogen was offered. petarra5 performed a systematic study of the effect of composition on the CWP. Using three kinds of "pure" iron, he showed that there was a residual CWP when the carbon and nitrogen concentrations had been reduced to less than that detectable by Snoek-peak measurements. He observed the same general annealing behavior and composition dependence as previous investigators, with the following exceptions. On first measuring the carbon CWP, it was found to be identical with the residual peak, and essentially independent of the carbon content. If the CWP was measured a second time in the same sample, it increased in size, but was still only about one-fourth the size of a CWP in a sample of the same iron nitrided to the same composition. On the other hand, a series of annealing experiments showed that the nitrogen CWP was not al-

Jan 1, 1967

By H. E. Cline, J. L. Walter

Grain boundary sliding and migration were studied in pure aluminum bicrystal and polycrystal samples with two-dimensional grain structure. Scratches, 50 P apart, were used for measurement of sliding and migration distanceso. Samples were deformed at constant rate at 315C and events recorded continuously on wrotion picture film. Electron micrograPhs of boundary-scratch intersections were obtained. Yield and flow stress values were measured. The sequence of sliding and migration events for a three-grain junction is described in detail. Sliding depended only on the resolved shear stress imparted to the boundary. Sliding was accowmodated by formation of shear zones in grains opposite triple points and adjacent to curved boundaries. These shear zones provided the driving force for grain boundary migration. Migration caused rumpling of the boundaries, decreasing the sliding rate. Sliding and migration generally began at the same time, occurred simultaneously and ended at the same time. In the bicrystal, sliding and migration rates were proportional. Initial sliding rules of 5 X joe cm per sec. were measured for the polycrystal and bicrystal samples. These sliding rates agree wilh the internal friction experirnents of K;. The observations seem consistent with a viscous boundary sliding nzechanism. GRAIN boundary sliding is the translation of one grain relative to its neighbor by a shear motion along their common boundary. Sliding is thought to be an important mode of deformation at elevated temperatures and at low strain rates such as prevail in creep,&apos; and perhaps in the area of superplastic behavior.2"4 Although much work has been done to investigate grain boundary sliding, the effort has not led to the identification of a mehanism. KG showed that grain boundaries in aluminum exhibit a viscous nature under very small displacements of internal friction measrements. Various dislocation mechanisms have been proposed but are without conclusive experimental support. Attempts to relate sliding to 6&apos;s viscous boundaries have been unsuccessful in that measured rates of sliding are always several orders of magnitude lower than KG&apos;S results would predict.= In bi crystals7and polycrystalsR of aluminum tested under constant load, the grain boundary sliding was found to be proportional to the total creep elongation which indicated that sliding might be controlled by deformation of the grains. Shear zones were observed to extend beyond grain boundaries at triple points to accommodate the sliding.8 Surface observations brought forth the opinion that sliding and migration occurred alternately, in sequence.&apos; Measurements of sliding at the surface have been criticized because they might not be representative of the interior of the sample. Generally speaking, it seemed that much of the previous work and knowledge was based on observations made at relatively low magnification and examination of samples after deformation had been accomplished. Thus, it was the purpose of the present study to continuously record, at high magnification, the events occurring during the deformation of pure aluminum. Samples with two-dimensional grain structures were used to simplify interpretation of the results. The sliding and migration of small areas of many samples were continuously recorded by time-lapse motion pictures. Replicas of the surface were used to provide high-resolution electron micrographs. These observations, coupled with tmsile strength data, provide sufficient information to arrive at an understanding of the phenomenon. EXPERIMENTAL PROCEDURE An ingot of 99.999 pct A1 was rolled to sheet, 0.127-cm thick. Tensile specimens, with a gage length of 0.85 cm, were machined from the sheet. Bicrystal tensile specimens, of the same dimensions, were spark cut from a large bicrystal ingot. The grain boundary was oriented at 45 deg to the tensile axis. The surfaces of the tensile samples were ground flat on fine metallographic paper and were then electropolished in a solution of 75 parts absolute alcohol and 25 parts of perchloric acid. The solution was cooled in an ice-water bath. Using a weighted sewing needle suspended from a small pivot on a precision milling machine, a grid of fine scratches, 50 p apart, was scribed on one surface of the sample. The polycrystalline samples were then annealed in hydrogen for 15 min at 350" to 400°C to produce a two-dimensional grain structure of about 0.2-cm average grain diameter which would not undergo further growth at the test temperature, 315OC. Examination of both surfaces of the samples showed that the grain boundaries were perpendicular to the surface of the polycrystal and bicrystal samples. A hot-stage tensile machine was constructed for use with an optical microscope as shown in Fig. 1. The specimen is shown mounted in the grips. The grips ride in V-ways so that the sample can be mounted without damage. The rear grip is free to slide so that when the sample expands during heating it is not put under a compressive stress. When the grips and samples are at temperature, the rear grip is locked in place by two set-screws. The other grip is connected to a synchronous drive motor which, through a worm gear and a fine-threaded rod, deforms the

Jan 1, 1969

By J. E. Ryan

TRONA, Calif., is a miniature urban community of some 3500 people, located on the northwest shore of dry Searles Lake in the extreme northwest corner of San Bernardino County, approximately 186 miles north and east of Los Angeles. Since it is situated on the Mojave Desert, a typically desert climate prevails with wide variations in temperature between day and night, extreme daytime summer heat, and cool to cold winters. Rainfall averages somewhat less than 4 in. per year, and dust storms are common. The rate of evaporation, .however, is great, amounting to 6 to 9 ft of water per year. The extremely low humidity makes the summer heat of 110°F tolerable with only a mild, temporary discomfort. Nature of Deposit During the periods when Searles Basin was flooded, the waters that passed through Indian Wells Valley spread out to form a broad, shallow lake providing, in effect, a settling basin for suspended sediment. The drainage into the deeper and more isolated Searles Basin thus was clarified to a great degree before concentration began. Today, the elevation of the dry surface of Searles Lake is 1618 ft, and the salt deposit measures 5x7 miles. At the eastern and northeastern margins of the main playa zone and just at the foot of the alluvial slope of sand and coarser wash from the Slate Range mountains, a rim of crusted salts rises a few feet above the level of the flat. The deposit is a saline efflorescence composed of salts that were presumably brought up with rising ground waters to be deposited at the surface by solar evaporation. This deposit consists chiefly of trona, and it is after this Trona Reef that the town Trona was named. Strip mining operations have been conducted in the past at infrequent intervals for the recovery of crude trona salts. The main focal point of interest in Searles Lake from a commercial standpoint is the main salt body located almost centrally in the basin. The exposed portion of this porous saline deposit covers approximately 12 sq miles and averages 71 ft deep. Its interstitial voids, which constitute 50 pct of the total volume, are permeated with a brine, which is in equilibrium with the soluble salt deposits. The brine is the raw material for the operations of the American Potash and Chemical Corp. plant at Trona, shown in Fig. 1. The soluble salt deposits are of interest for their potential values in future technologic development. The brine, which is stratified according to slight differences in density, stands usually within 6 in. of the surface of this exposed, firm, salt body. The surface is usually dry and will support the weight of heavy mobile units and drilling equipment. Occasionally, however, surface waters from the higher watersheds encroach upon the main salt body during infrequent periods of precipitation on the surrounding mountains. This water dissolves surface salt, becomes a dilute brine, and has been observed to stand as high as 18 in. above the salt surface when undisturbed. Windstorms will shift the water back and forth across the lake surface. The exposed salt body is surrounded by additional submerged areas of commercial soluble salt deposits covering some 20 sq miles, hidden from view by marginal playa mud. These vary in depth up to as much as 30 ft. Thus, the outline of exposed and submerged salt deposits of commercial value is estimated to cover a total area of 32 sq miles, which is roughly circular but slightly elongated from northwest to southeast. It has been estimated that each square mile contains about 100 million tons% f alkali salts. The results of drill borings in the past 15 years have brought to light the interesting fact that the main salt body lies superimposed on an impervious mud deposit from 10 to 15 ft thick containing relatively little soluble salt. Under this deposit lies a second soluble salt body 35 ft deep. The lower salt body is interspersed with numerous insoluble mud lenses and its composition is considerably different from that of the primary, or main salt deposit. Recent drill borings have not penetrated beyond 300 ft. They have, however, revealed that underlying the lower salt body, the mud sediments carry deposited minerals of trona, nahcolite, mirabilite and much less soluble carbonates or sulphates of calcium and/ or magnesium. This structure is shown in Fig. 2. Current Lake Survey Program Several hundred holes have been drilled in the deposit. However, to carry out a thorough and carefully correlated study of the composition of the soluble salts and other minerals in the dry lake basin, a drilling program was inaugurated recently and is now nearing completion. In this survey, pattern drill holes are sunk at regular lh-mile intervals to a depth of approximately 150 ft. Drilling equipment consists of a No. 51 C. P.

Jan 1, 1952

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&apos; 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 &apos;idea1 gases,&apos; 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 &apos;ideal&apos; 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 J. B. Cheatham, J. W. McEver

A laboratory investigation of the behavior of casing subjected to salt loading indicates that it is not economically feasible to design casing for the most severe situations of nonuniform loading. When the annulus is completely filled with cement, casing is subjected to a nearly uniform loading approximately equal to the overburden pressure, and, although the modes of failure may be different, the design of casing to withstand uniform salt pressure can be computed on the same basis as the design of casing to withstand fluid pressure. Failure of casing by nonuniform loading in inadequately cemented washed-out salt sections should be considered a cementing problem rather than a casing design problem. INTRODUCTION Casing failures in salt zones have created an interest in understanding the behavior of casing subjected to salt loading. The designer must know the magnitudes and types of loading to be expected from salt flow and he must be able to calculate the reaction of the casing to these loads. In the laboratory study reported in this paper, short-time experimental measurements of the load required to force steel cylinders into rock salt are used as a basis for computing the salt loading on casing. These results must be considered to be qualitative only since rock salt behaves differently under down-hole and atmospheric conditions and also may vary in strength at different locations. The beneficial effects of (1) cement around casing, (2) a liner cemented inside of casing, and (3) fluid pressure inside of casing in resisting casing failure are considered. ROCK SALT BEHAVIOR UNDER STRESS The effects of such factors as overburden loading, internal fluid pressure, and temperature on the flow of salt around cavities have been studied extensively at The U. of Texas. Brown, et al.1 have concluded that an opening in rock salt can reach a stable equilibrium if the formation stress is less than 3,000 psi and the temperature is less than 300°F. At higher temperatures and pressures an opening in salt can close completely. These results indicate that calculations based upon elastic and plastic equilibrium for an open hole in salt should be applied only at depths less than 3,000 ft. In most oil wells the tem- perature will be less than 300F in the salt sections, therefore no appreciable temperature effects are anticipated. Serata and Gloyna2 have reported an investigation of the structural stability of salt. .They assume that the major principal stress is due to the overburden. Other stresses can be superimposed if additional lateral pressures are known to be acting in a particular region. In the present analysis an isotropic state of stress is assumed to exist in the salt before the hole is drilled, since salt regions are generally at rest. This assumption is partially verified from formation breakdown pressure data taken during squeeze-cementing operations in salt. Experimental measurements of the elastic properties of rock salt indicate a value of 150,000 psi for Young&apos;s modulus and a value of approximately 0.5 for Poisson&apos;s ratio. A value of % for Poison&apos;s ratio with finite Young&apos;s modulus would indicate that the material was incompressible. Values ranging from 2,300 to 5,000 psi have been reporteda for the unconfined compressive strength of salt. These variations may be due to differences in the properties of the salt from different locations or at least partially to differences in testing techniques. Salt is very ductile, even under relatively low confining pressures. For example, in triaxial tests reported by Handin3 strains in excess of 20 to 30 per cent were obtained without fracture. When casing is cemented in a hole through a salt section, the casing must withstand a load from the formation if plastic flow of the salt is prevented. To determine the forces which salt can impose on casing, circular steel rods were forced into Hockley rocksalt with the longitudinal axis of the rods parallel to the surface of the salt. The force required to embed rods 0.2 to I in. in diameter and 1/2 to 1 in. long to a depth equal to the radius of the rods was found to be F/DL =28,700 psi (± 3,700 psi) , .... (1) where D is the diameter, and L is the length of the rod. CASING STRESSES Since an open borehole through salt at depths greater than 3,000 ft will tend to close, cemented casing which prevents closure of the hole will be subjected to a pressure approximately equal to the horizontal formation stress after a sufficiently long time. As a first approximation the horizontal stress can be assumed to be equal to the overburden pressure. This is in agreement with the suggestion by Texter4 that an adequate cement job can prevent plastic flow of salt and result in a pressure on the casing approximately equal to the overburden pressure. He also advocated drilling with fully saturated salt mud

Jan 1, 1965

By J. M. Oblak, W. A. Owczarski

A cellular appearing recrystallization product formed by annealing a cold-worked nickel-base super-alloy at 1800°F has been studied by electron nzicroscopy. Prior to deformation, an equilibrium micro-structure of fcc matrix y and cuboidal ,,&apos;, Ni (Al, Ti), precipitates of CuzAu structure had been established by an age at 1825°F. The strain-free recrystallization cells consist of very large rodular y&apos; particles in a y matrix. They precipitate is oriented and coherent both before and after recrystallization. The results showed that y&apos; coarsening accompanies recrystallization at 1800°F. However, it does so as a secondary effect and does not necessarily take place at lower temperatures. The structural similarity of this reaction to cellular precipitation in other systems indicates that lattice strain may also play a significant role during some cellular precipitation reactions. THERE have been numerous microstructural investigations of recrystallization in single-phase materials but two-phase systems have received much less attention. The second phase can either remain inert or be altered along with the matrix during recrystallization. If the second phase is an oxidelm3 or a relatively inert pre~ipitate,~, recrystallization is retarded when the interparticle spacing is less than 1 p. Prior to the onset of recrystallization, these materials show a well-polygonized substructure with the subgrain size limited by the interparticle spacing. Since recrystallization by the motion of preexisting grain boundaries6 is not observed, retardation has been related to particle pinning of the subboundaries. This pinning prevents coalescence&apos; or growth8 of subgrains to a critical size (formation of a high-angle boundary) necessary to initiate recrystallization. In a material such as a nickel-base superalloy both y matrix and y&apos; precipitate are altered by the recrystallization reaction. Haessner et al.&apos; studied the recrystallization of a cold-rolled Ni-Cr-A1 alloy by electron microscopy. The material was initially cold-rolled in the supersaturated condition. upon annealing at 750°C, immediate precipitation of 7&apos;occurred. Presence of this 7&apos; greatly retarded the onset of recrystallization which eventually took place by the development of randomly oriented, strain-free grains. The original •/ was dissolved at the recrystallization interface and reprecipitated as oriented, coherent par-tiles in the new grain. Recrystallization caused a refinement of .)&apos; particle size. Recently ~hillips&apos;&apos; investigated recrystallization of Ni-12.7 at. pct Al. Reduction by cold rolling presumably elongated the p&apos; precipitate into lamellae that remained coherent with the matrix. After recrystallization at 600" to 750°C, there was no unusual change in y&apos; particle size al- though there was a tendency toward clustering along the prior rolling direction at 750°C. Above 750°C, the recrystallized grains were generally free of precipitate. Studies in the somewhat analogous Cu-3.23 wt pct CO" and Cu-2 wt pct&apos;2 systems demonstrated that the coherent cobalt-rich fcc precipitate in these alloys obstructed softening, initiation, and completion of recrystallization. The precipitates were deformed into lam~llae during rolling and those of diameter less than 250A remained coherent. Recrystallization took place by the growth of new grains into the recovered or poly-gonized material. In the first study," both matrix and precipitate reoriented in the same manner upon passage of the recrystallization interface. There was no change in particle size or morphology. Tanner and ~ervi,~ on the other hand, observed that motion of the recrystallization fronts was strongly hindered by the pinning action of coherent precipitates in the deformed material. Particles in contact with a pinned boundary coarsened and coalesced leaving a denuded zone in the unrecrystallized region. When the number of pinning points was sufficiently reduced by coalescence, the boundary swept past these particles and through the denuded zone. The authors1&apos; considered this as a variation of discontinuous precipitation with both chemical driving force and deformation strain energy contributing to recrystallization. Preliminary observations by the present authors had revealed that recrystallization in Udimet 700, a nickel-base superalloy, occurred in an entirely different manner. Optical metallography showed that the recrystallized product formed as cellular colonies containing coarse y&apos; particles elongated in the direction of cell growth. In this investigation the structural features of this reaction were investigated by transmission electron microscopy. EXPERIMENTAL PROCEDURE As-received I$-in. rounds of Udimet 700* were (wtpct) 18.4 15.2 4.95 4.42 3.43 0.06 0.031 0.14 Bal. solution-annealed for 4 hr at 2150" and then fast air-cooled. An initial y-~&apos; structure was established by a 4-hr age at 1825°F followed by a fast air,cool. Essentially the equilibrium volume fraction of ?&apos; at 1825°F is precipitated within 4 hr. Microstructural examination showed no measurable increase in the amount of precipitate after longer aging times. Deformation consisted of swaging to 52 pct RA with 6 pct reduction per pass at room temperature. To reduce the precipitation potential to a negligible amount, recrystallization anneals were conducted at 1800"~ (982"~). Microstructures were investigated by optical and transmission electron microscopy. To prepare foils for electron microscopy, the material was first sliced into 30-mil slabs parallel to the swaging direction. Discs were dimpled and electrolytically cut from

Jan 1, 1969