Search Documents

By S. G. Epstein

Using the capillary-reservoir technique, electromi-gvation rates of cadmium and indium in liquid bismuth were measured at several temperatures. The electric mobility of cadmium Jrom 305° to 535°C and indium from 310° to 595°C can be expressed as a function of temperature by the equations UIn = 1.52 x 10-3 exp sq caz per v-sec Migraion of both solutes was cathode-divected at a rate rnore than four tiMes tHAt previously found for siluer in liquid bisnmth. The electric mobilities of cadmium and indiulrz in liquid bismuth at 500° C are nearly identical with their respective mobilities in mercury at room temperature. AS part of a systematic study of the variables which are considered to control electromigration in liquid metals, the electromigration rates of cadmium and indium in liquid bismuth have been measured. Mass transport properties of silver in liquid bismuth have been reported previously,&apos; and measurements of tin and antimony in liquid bismuth are forthcoming. Comparisons will be made with literature values for these same solutes in mercury.2&apos;3 This series of solutes was selected to determine the effect of the solute valence on its electromigration. Silver, cadmium, indium, tin, and antimony have nearly equal atomic masses but have chemical valences ranging from +1 to +5. They are all fairly soluble in bismuth above 300°C and all have radioactive isotopes, which are an aid in making analyses. EXPERIMENTAL TECHNIQUE Electromigration of cadmium and indium in liquid bismuth was measured by the modified capillary-reservoir technique previously described.&apos; In this method irradiated cadmium or indium is added to bismuth to form alloys containing about 1 wt pct solute (<2 at. pct solute). Several quartz or Pyrex capillaries: 1 mm ID and 5 cm long, vertically oriented, are simultaneously filled in the reservoir of the liquid alloy. A direct current is passed through two of the capillaries, which contain tungsten electrodes sealed in the upper end. The other capillaries sample the reservoir during the experiment. After a measured time interval the capillaries are removed from the reservoir and rapidly cooled. The glass is then broken away from the solidi- fied alloy, which is then weighed, dissolved in acid, and analyzed for solute content by chemical and radiochem-ical techniques. An electric mobility (velocity per unit field) can be calculated from the amount of solute entering or leaving each capillary by the simplified expression1 in which Ui is the electric mobility of the solute, ?mi the solute weight change, Ci the solute concentration of the reservoir, I the current, p the alloy resistivity, and l the duration of the experiment. This expression is valid as long as the experiment is terminated before a concentration gradient develops across the capillary orifice. Earlier experiments showed that the concentration gradient formed initially at the electrode changes with time and eventually reaches the orifice, due to back-diffusion. This condition produces a solute exchange between capillary and reservoir by diffusion or convection, opposing the electromigration, which results in a lower measured value for the electric mobility. To determine if the concentration gradient had reached the orifice, the capillaries used in some of the experiments were sectioned at 1-cm intervals and the solute content of the alloy from each section was radiochemically determined. A typical concentration profile for an experiment with indium in bismuth is shown in Fig. 1; cadmium in bismuth showed similar behavior. As illustrated in the graph, very little back-diffusion has occurred in the capillary containing the cathode, since the concentration gradient is confined to the upper 1 cm of the capillary. In the capillary containing the anode, however, the concentration gradient is much broader, extending nearly to the orifice, even though the net change in solute concentration is nearlv the same in both capillaries. Since cadmium and indium probably lower the density of bismuth when alloyed, depletion of the solute from the alloy adjacent to the anode would increase the density of the liquid in the uppermost region of the capillary. This would give rise to convective mixing within the capillary, causing the broadened concentration gradient. Conversely, the alloy adjacent to the cathode should have a reduced density as the solute concentration is increased by migration, explaining the "normal" concentration profiles found in these capillaries. This disparity was not found for electromigration of silver in bismuth. Both metals have similar densities at the operating temperatures, and nearly symmetrical concentration profiles were found in the two capillaries of each exueriment. This density effect was also apparently encountered when an attempt was made to measure diffusion coefficients for indium in liquid bismuth by the same technique which was successfully used to measure diffusion of silver in bismuth.&apos; Capillaries 1 mm ID and 2 cm

Jan 1, 1968

By R. O. Williams

Analytical representation of the thermodynamics of solutions is highly desirable from the standpoint of accuracy, compactness, and numerical manipulations. In particular, computer calculations are greatly implemented. Mathematical considerations show that previous expressions have one or more serious defects. This investigation shows a Fourier series to be satisfactory but that it is also possible to derive a new series which fits certain additional conditions. Included examples show the value of analytical expressions in giving a simple characterization of each system using some two to five parameters, the elimination of the Gibbs-Duhem integration, and the es timation of the error for the experimental function as well as derived functions. It is further shown that the present characterization provides easy comparison between systems. IN the past, thermodynamic calculations have depended to a considerable extent on tabular and graphical methods. As the volume and precision of such data increase such methods become less satisfactory. Specifically, the selection of the optimum representation and the estimation of errors require statistical methods which in turn require analytical representation. The utilization of such data require further manipulations which are best done analytically for maximum precision. For example, phase equilibria are determined by common tangents to free-energy curves: a graphical determination is normally of low accuracy. As computers are increasingly used analytical representations become almost mandatory. Insufficient mathematical consideration has been given previously to the selection of empirical expressions. Those expressions having some theoretical justification are generally too inflexible and mathematically unattractive. We consider the problem in some detail and show that a Fourier series can be effectively used. Also a new series is defined which has certain advantages. ANALYSIS We wish to consider the analytical representation of the heat of mixing, AH, the excess free energy, ?Gxs, and the excess entropy, ?sXS, as a function of composition, X, for binary solutions relative to the pure components in the same state. When a distinction is not required, we use W to denote any one of the above functions. One may use a Taylor expansion around X = 0 to generate a power series. As the derivatives are un- known we represent the series as W = A + BX + CX2 + DX3 + EX4 + ... [l] where the constants A , B, C , ..- are to be selected to provide some optimum fit. For the extremes of composition W is necessarily zero so it follows that A = 0 [2a] B +C + D + E +••• = 0 [2b] Nonelectrolytes, which we are considering, appear to satisfy the condition that d3W/dx3 = 0 [3] in the terminal regions. This is the basis of the a, ß, and Q functions used by Hultgren et al.&apos; and others. While this condition does not have a strong theoretical basis it does appear desirable that any analytical relation should satisfy this condition. Darken2 and Turk-dogan and Darken3 have shown that many systems exhibit this behavior over an extended range from each terminal region, departure being restricted to a limited intermediate region. Since we have no a priori knowledge as to where this transition occurs we can require that this condition be satisfied only as a limit at the extreme compositions as a general condition. We will show later how more restricted conditions can be included in specific solutions. Darken2 has called this behavior the quadratic formalism; we call our application the limiting quadratic formalism, LQF. This condition applied to the above power series requires that D = 0 [4a] 4-3-2E +5-4-3_F + 6 • 5 . 4G + ••• =0 [4b] The form of the power series normally used, due to Margules,4 is W=X(1-X)(A + BX + CX2 + DX3 + EX4 + •••) [5] where A, B, C, --. are a new set of constants. (Guggenheim5 has given a variation of this expression in a more desirable form. Since, however, it is contained in the above expression it does not require separate consideration.) This form is precisely what results by incorporating the conditions in Eq. [2] into the power series and regrouping the constants. The LQF requires that B =C [6a] and 4.3.2(D-C) +5-4-3(E-D) + ••• =0 [6b] Thus, the correct form of the Margules expression with two adjustable parameters is w =X(1-X)[A + B +X2-2/3x3)] 171 and the EX4 term must be included before three adjustable parameters are permitted.

Jan 1, 1970

By Charles Law McCabe, Lyndon H. Everett, Edna A. Dancy

It has been found that the carbide phase present at equilibrium in the system M-H2-CH4, at about 600°C, is MC for the rare-earth metals Ce and Pr. X-ray diffraction analysis showed that the monocarbides have fcc structures with lattice constants of 5.036 + 0.009Å and 5.131 + 0.001Å for CeC and PrC respectively. Gaseous equilibrium measurements were used to calculate the standard free energy of formation of the monocarbides from the elements. for the formation of (+ 1300) for the formation of PrC. THE rare-earthdicarbides, and their crystal structures, have been known for some years,l but only more recently were the carbides CeC,2,3 Ce2C3 2 and CeCS3 reported. In 1958 to 1959, Spedding et al. published work on the lanthanum-carbon system4 and other rare-earth metal-carbon systems,5 proving the existence of M2C3 and MC2, and measuring the lattice constants. They also demonstrated that tri-rare earth carbides, M3C, exist for the rare-earth metals samarium through ytterbium. However, they concluded that the cerium monocarbide reported by Brewer and Krikorian2 and by Warf,3 and given a fcc structure with a lattice constant of 5.130Å bythe former workers, was, in fact, cerium metal with carbon dissolved in it. They were also unable to find any evidence for the existence of Warf&apos;s CeC3, for which no structural details had been given. Even more recently, Palenik22 reported the existence of only M2C3 and MC2, having been unable to find any evidence for the existence of any other rare-earth carbides. There are no published experimentally derived thermodynamic data for the formation of any of these carbides, although Brewer and Krikorian6 have estimated values of for CeC, Ce2C3 and CeC2. The objective of the present investigation was; to determine experimentally the free energy of formation of any of the reported carbides of cerium and praseodymium, through a study of the rare-earth metal-hydrogen equilibrium. EXPERIMENTAL A methane-hydrogen mixture was circulated, in a closed system over previously prepared cerium or praseodymium hydride, and when equilibrium had been attained, the gas mixture was analyzed by selectively oxidizing the hydrogen and condensing out the water formed. The metal hydrides were used as starting material for convenience because, otherwise, the hydrogen in the gas mixture would immediately dissolve in the metals; in addition, the metals would not react with methane alone at the experimental temperature (around 600°C). The circulating system was based on that used by Browning, DeWitt, and Emmett7 for similar studies on iron carbides. It consisted of a quartz reaction vessel, all-glass circulating pump, analysis tube containing copper oxide that could be heated to 300" C by means of a small furnace, a solid CO2-methanol trap, and a double limb absolute manometer, Fig. 1. A cathetometer, capable of reading to 0.005 cm, was used to measure the difference in height between the two columns of mercury. In its final form, the reaction vessel was enclosed in an outer jacket, containing approximately the same pressure of hydrogen as that within, to reduce errors due to diffusion of hydrogen out through the fused silica of the reaction vessel., The circulating system was supplied with

Jan 1, 1962

By N. A. D. Parlee, I. D. Shah

The solubilities of oxygen in liquid Ag-Au, Ag-Pt, and Ag-Pd alloys have been determined in the range of 940° to 1200°C at 1 atm pressure of oxygen using an improved Sieverts technique. The additions of gold (0 to 57 pct), platinum (0 to 27 pct), and palladium (0 to 22 pct) to liquid silver continuously decrease the solubility of oxygen in liquid silver. Activity coefficients and interaction coefficients of oxygen in these alloys and have been calculated. The interaction coefficientscan be described by the following equations: Approximate second-order interaction coefficients (pM have been calculated. The contribution of the product, pMxNM, to In yo only becomes significant at high alloy concentrations. RECENTLY several investigators1"3 have redeter-mined the solubility of oxygen in liquid silver. In general the recent findings1" for Po, = 1 atm are in good agreement with the equation:4 log %O = 695.4/T + 1.086 [1] It is established1, 2 that the solubility of oxygen follows Sieverts&apos; law reasonably well, at least up to 1 atm partial pressure of oxygen. It should be noted that a very slight deviation from Sieverts&apos; law has been reported by Lupis and Elliott.3 Only recently has the solubility of oxygen in Ag-X binary liquid systems received much attention, and only the Ag-Cu, Ag-Au, Ag-Pt, and Ag-Pd systems have been studied. Par lee, Sacris, and zoellners reported that the solubility of oxygen in liquid silver increases progressively with the small additions of copper (0 to 0.5 pct) up to the point where the copper oxide phase appears. Lupis and ~lliott~ have reported that the solubilities of oxygen in liquid silver decrease progressively with the additions of gold, platinum, and palladium. However, their investigation was limited to 0 to 5 pct of these alloying elements, a range too limited to satisfy the requirements of the research program of this laboratory, where the solubilities of oxygen in the range of 0 to 30 pct were required for the calculation of chemical diffusion coefficients of oxygen in these alloys. The present paper deals only with the solubilities of oxygen in these alloys while another paper will deal with the diffusion of oxygen in these alloys. EXPERIMENTAL METHOD A Sieverts technique was employed which involved an improved design of the reaction tube, Fig. 1, as described briefly in a previous communication.4 Liquid melts (70 to 100 g) were held in Norton Alun-dum crucibles. The induction furnace used had a maximum output of 2.5 kw with very fine control. This induction system had excellent stability and the final equilibrium temperatures measured by calibrated Pt-Pt, 10 pct Rh thermocouples are believed to be within ±2C. These thermocouples were checked against the melting point of pure gold wire, and the results agreed with standard tables (±l°C). Each run involved a careful sequence of operations. The sample was heated to and held at about 900°C in vacuum for 3 to 4 hr with the thermocouple in a retracted position. After melting, the melts were usually exposed to a small amount of oxygen (0.5 to 2.0 cu cm) and then degassed slowly for 1 to 2 min to remove any oxidizable volatile impurities such as carbon and sulfur as CO, CO2, SO2, and SO forth. Argon gas was then allowed to enter the system. The protection tube containing the thermocouple was then

Jan 1, 1969

By Nicholas J. Grant, Hanna Ibach, Bill C. Giessen

The system Ta-Rh was investigated over the entire comnposition range using metallogvaphic and X-ray techniques as well as thermal analysis. Terminal solubility limits, solidus temperatures, and the crystal structures of two new intermediate phases were determined. There are five intermediate phases: o, tetragonal, isostructural with o(Fe-Cr); a1, orthorhomnbic : a2, orthorhombic, isostructural with CozSi; 0 3, a high -temperature phase of unknozun structure; and a TaRh3, cubic, AuCu3 structure. a, aL, a,, and a melt peritectically; and a TaRh, has a maximum melting point. Five peritectic and one eutectic reactions occur. THE Ta-Rh phase diagram has not been fully treated in the literature; however, two inter metallic phases have been described.&apos;-&apos; This study attempts to work out the diagram covering the details of phase boundaries as well as the crystallography of the intermediate phases. EXPERIMENTAL METHODS Starting materials were tantalum powder of 99.8 pct purity, supplied by National Research Corp., Cambridge, Mass., and rhodium powder of 99.9 pct purity, supplied by Bishop Co., Malvern, Pa. Analyses as given by the manufacturers are presented in Table I. In addition to the spectroscopic analysis, an oxygen analysis has been made of the tantalum powder. After preliminary trials, the standard procedure employed in making the alloys was as follows (see Ref. 4 for further details). The powders were weighed, mixed manually, compacted under 16,000 psi, and arc-melted at not more than 500 amp under thoroughly titanium gettered welding-grade argon of 400 mm Hg pressure. The gettering process was repeated after each melt. It had been shown previously5 that under these conditions no oxygen pick-up exceeding 0.001 pct in a hafnium button could be detected. The buttons, ranging from 5 to 10 g in weight, were inverted or, if possible, crushed and remelted three times. Melting presented no difficulty, except for tantalum-rich al- loys, which showed considerable spashing during melting. The average weight loss of 1 wt pct rose to 2.5 wt pct in these cases. Subsequent melting, however, resulted in losses of less than 0.1 wt pct. The melts obtained frequently showed small in-homogeneities, mostly in the tantalum-rich part of the system below 25 at. pct Rh. This was not due to insufficient blending of the elements, but to crystallization taking place from the cooled bottom. This condition was not improved by further re-melting; therefore the following precautions were taken. Cross sections of as-cast buttons were made. For the investigation only buttons were used where these inhomogeneities did not exceed 1 at. pct (estimated from the amounts of haSeS resent). In addition, only the center portions of such buttdns were utilized to minimize errors. Smaller buttons showed smaller concentration gradients and were used as a check. Finally, all alloys were homogenized to eliminate coring (see below). After this, the error in alloy composition due to inhomogeneity was cl at. pct. In order to confirm the concentrations of the alloys and to provide an impurity check, wet-chemical analyses and oxygen-fusion analyses of four key alloys were carried out. The results, together with the concentrations as calculated with the weight balance method, are presented in Table 11. It was found that for three alloys the agreement is very good (< 0.2

Jan 1, 1964

By Joseph G. Franzone, Alan K. Kuhn, Jerry J. Oliver

INTRODUCTION Tailings produced by many uranium milling operations consist of fine sands with some silt and slimes. When fine sandy materials are placed by hydraulic methods behind an impermeable dam, they are deposited in a loose state and some portion remains saturated. These saturated, loose fine sands are highly susceptible to liquefaction, the phenomenon in which a monotonic or cyclic disturbance causes excess pore water pressure and, concurrently, a total loss of strength in the sand. Once liquefied, the fine sand flows, causing collapse of supported structures. The potential for such a liquefaction failure was identified and successfully treated at Sohio Western Mining Company&apos;s L-Bar Uranium Operations near Seboyeta, New Mexico. The Sohio tailings dam is an earthfill starter dam with tailings raises constructed upstream of the starter dam crest. Beginning with the start of mill operations in 1976, tailings were deposited hydraulically in the impoundment behind the starter dam. As the tailings level approached the crest of the starter dam, beached tailings were excavated and placed in lifts by a dozer to form two raises above the crest of the starter dam. As the impoundment has gradually filled with tailings, the decant water pond level has risen. Correspondingly, the water level in the tailings dam, upstream of the chimney drain, has also risen. By August 1980, the phreatic surface was above the crest of the starter dam and stability analyses indicated that the tailings dam did not have the safety factor of 1.0, under static loading with liquefaction, implicit in the 1980 New Mexico State Engineer&apos;s requirements. The problem related directly to the high phreatic surface in the loose sandy tailings behind a dam structure that was not capable of resisting failure which might develop in liquefied tailings. Two methods of stability enhancement were considered for the Sohio dam. One method was reinforcement of the dam using a clay buttress placed against the downstream slope. The other method was installation of horizontal drains through the starter dam to drain decant water and lower the phreatic surface. Either method would increase the stability of the dam. However, the comparative analysis of the methods indicated that horizontal drainage offered significant advantages in cost and could provide a more direct remedy of the source of the problem, the saturated section of tailings. In addition, a drainage system would be more amenable to modification and more quickly installed than a buttress. On the other hand, a clay buttress could be more directly controlled, would involve routine earthwork, and has successful precedent. Therefore, the buttress approach would involve less risk. After weighing the advantages of both methods and the costs versus risks, the horizontal drainage approach was selected. Consequently, a horizontal pipe drain system was recommended and designed (D’Appolonia, 1981a). This paper describes the design and installation of the drainage system and its initial performance. PIPE DRAIN SYSTEM DESIGN Design Criteria and Parameters To increase the stability of the dam to acceptable levels, the drainage system had to lower the phreatic surface behind the dam to the level calculated to give a minimum safety factor of 1.0 under conditions of liquefaction. In addition, the system needed to be essentially self-operating, easy to maintain, and economical. To accomplish these objectives, the following design criteria were established: 1. The pipe drains must lower the phreatic surface at least 4.3 m (14 ft.) at the midpoint along the dam (the deepest section) and by proportionately smaller amounts toward the abutments to satisfy safety factor requirements.

Jan 1, 1982

By Robert G. Johnson, Richard J. Prosen

THE present work was done in connection with a program for investigating metal-to-ceramic braze techniques using the well-known reactivity of titanium with certain ceramic oxides. The investigation extended over the range of 0 to 30 pct Ti. The indium was obtained from the Indium Corp. of America and was specified to be 99.97 pct pure. The titanium was supplied by Metals Disintegrating Co. and was stated to be 99.5 pct pure. Each 2 to 4 g quantity of the alloy compositions studied was prepared using a mixture of 300 mesh powders pressed into pellet form. The pellets were heated in thin-walled molybdenum crucibles using a resistance-wound furnace in a vacuum less than 10-4 mm of Hg. Little reaction occurred between the molten alloy and the crucibles at the temperatures and short time intervals used. Only slight spectroscopic traces of molybdenum were found in the melt after a typical period of heating. The points shown on the phase diagram of Fig. 1 represent thermal arrest measurements. The phase boundaries shown are consistent with the thermal arrest and X-ray data obtained. The temperatures were determined using a Pt-Pt 10 pct Rh thermocouple with the junction spot-welded to a short molybdenum rod. The rod was almost completely immersed in the liquid metal, so that good thermal contact with the melt was achieved. The small mass of the crucible and its contents made it possible to obtain many heating and cooling curves in a few minutes time, an advantage which helped to minimize the effects of indium evaporation at the higher temperatures. A Brown strip chart recorder was used to display the thermal arrest curves. To check the technique, the melting point of 99.999 pure Al was measured and found to be within 1 of 660.2c, the accepted melting point. The upper limit of temperature with this technique was about 900°C beyond which the evaporation rate of indium became great enough to alter appreciably the alloy composition during the runs. A peritectic transition was found at 796°+ 5°C from 1.5 to 30 wt pct Ti. It was not found at 0.5 or 1.0 pct. A small super-cooling effect was observed. The melting-point transition to the B + L phase was found up to 20 pct Ti but not at 25 pct. Within the 1 deg accuracy of the measurement, the transition temperature was that of pure indium, 156°C. The liquidus line to the left of the 1.5 titanium point was located only approximately. The two crossed circle points at 1.0 and 0.5 pct Ti place a lower limit on the liquidus line and were determined by observing visually the cessation of vibrations in the melt caused by the damping effect as B-phase crystals were formed during cooling. The B-phase boundary was found at 23.8 pct Ti by X-ray analyses of small single crystals of the B phase isolated from 2 pct Ti melts. The compound was found to be Jetragonal with lattice dimensions of c = 3.052A and a = 10.094W. From the unit cell dimensions and the measured density of 6.42 i 0.05 g per cc, the compound was determined to be In4Ti3 which has 23.8 pct Ti. The calculated density of 6.44 g per cc is obtained assuming 2 mol

Jan 1, 1962

By N. A. Gokcen

The construction and operation of a simple and accurate vacuum-fusion apparatus are described in detail. Absolute accuracy of the oxygen analysis has been determined by the reduction of oxides weighed to 20.01 mg. The Bureau of Standards steel samples have been analyzed repeatedly, and their inadequacy for the acceptable range of oxygen is presented. The limits of interference of manganese, aluminum, and titanium, and the effects of tin and water-cooling of the furnace tube have been investigated in detail. ANALYSIS by the vacuum-fusion method consists of melting a sample in a degassed graphite crucible under high vacuum and extracting oxygen as carbon monoxide, and nitrogen and hydrogen as gaseous elements. The resulting gas mixture is analyzed for its constituents, from which oxygen, nitrogen, and frequently hydrogen may be determined within 1/2 hr or less. The history and summary of methods1-4 and extensive reviews of literature&apos;.&apos; for the determination of gases in metals have been published in detail. The foundation of the modern vacuum-fusion method of analysis was laid by Jordan and Eckman,11 and Oberhoffer and his associates.1, 10 Diergarten,11, 12 Meyer,13 Thanheiser et al.,14, 15 Ericson and Benedicks,16 Ziegler,17, 18 Sloman,16-23 Thompson et al.,24 and later many others contributed to the improvement, accuracy, and limitations of the method. In some investigations, however, the limitations of the procedure and the errors involved in the analysis require further critical examination and evaluation. In many apparatuses, lunnecessarily complicated and cumbersome features and elaborate precautionary measures do not have conclusive advantages. The purpose of this invest:igation was, therefore, a) to construct a very simple and accurate apparatus, b) to determine the absolute accuracy of results, c) to establish the limits of interference of manganese. aluminum, and titanium, d) to reexamine critically the reduction and recovery of oxygen from oxide powders of various sizes, and e) to evaluate critically the eight steels of the Bureau of Standards."&apos; Apparatus The apparatus used in this investigation is shown in Fig. 1. It has been used for over three years, during which several modifications were made. A brief description of the apparatus is as follows. The transparent silica or Vycor tube, E, is joined to the Pyrex head, B, by mean of a face to face ground joint sealed with mercury. A similarly sealed ball and socket joint would also have been satisfactory. A standard tapered ground joint, successfully used by some investigators, was tried, but in the absence of grease or vacuum cement it was very difficult to disassemble the joint. The graphite crucible, G, 15/16 or l 1/8 in. OD, 2 1/2 or 3 in. high, 1/10 in. wall, shown enlarged in Fig. 3a, is made from the rods containing less than 0.08 pet ash. Two baffles, overlapping sufficiently to prevent spattering, are inserted in two opposite slots cut on a band saw. Two small holes in the baffles permit the temperature measurement of the melt. A second type of crucible, Fig. 2, G, shown enlarged in Fig. 3b, is also satisfactory, though not as convenient as the crucible shown in Fig. 3a. Somewhat similar but more elaborate crucibles with baffles were first tried by Ericson and Benedicks,&apos;" but were abandoned in favor of a crucible with a stopper and a peripheral graphite powder filter. Various versions of their crucible with a stopper have later been used by other analysts, 10-27, 27-30 The crucible is packed directly in E, Figs. 1 and 2, with —35 + 48 graphite powder for shielding and insulation. A minimum layer of 7 mm of powder is necessary for keeping E cool and minimizing the blank. The first use of graphite powder was made by Sloman,10-23 Who found that —200 mesh was the most satisfactory. The author tried various size powders from +20 to —100 mesh and found that a) particles of 28 mesh or larger were not sufficiently insulating and were heated by the induction current, b) the powder finer than 60 mesh packed too much and did not readily permit the escape of gases even when the crucible was heated very slowly; hence, the powder was occasionally blown out of the side in the crucible and in the mercury pump. The optimum size powder is, therefore, 35 to 48 mesh size or 0.4 mm in average diameter. The furnace is designed to eliminate excessive amounts of

Jan 1, 1959

By R. A. Wolfe, H. W. Paxton

Self-diffilsion coefficients for cr51 and Fe55 in 12 pct Cr-Fe and 17 pct Cr-Fe for Fe55 in chromium, and for Cr51 in vanadium have been measured. The results are compared with other values for the Fe-Cr system, and with the various theories of diffusion in hcc metals. Some empirical correlations are discussed between Do and Q in hcc systems, or, expressed differently, the constancy of ?G*/T solidus for seveval bcc metals and alloys is noted. It appears very probable that a vacancy mechanism is operative in bcc metals, hut this cannot he stated with certainty. THE great bulk of work on diffusion in metals, both experimental and theoretical, was for many years concentrated on those with close-packed and, in particular, fcc lattices.1,2 There appears to be little doubt that the mechanism of diffusion in these solids is vacancy migration, leading to mass transfer and in substitutional solid solutions to a Kirken-dall effect.3,4 For bcc metals, the picture is much less clear. The Kirkendall effect certainly occurs in several alloys.5-10 However, attempts to understand the factors contributing to the pre-exponential in the usual expression for the diffusion coefficient D =D, exp {-Q/RT) by extension of ideas useful in close-packed lattices have not always been successful. Zener,11 Leclaire,12 and Pound, Paxton, and Bitlerl3 have suggested that various forms of ring diffusion may be important in some bcc metals. For close-packed metals, Do is usually about 1 sq cm per sec and Q - 35Tm kcal per mole (Tm = melting temperature in OK). The theory of Pound et al. suggests for ring diffusion that Do may be about 10-4 and Q, although difficult to calculate with any precision, would be significantly less than 35 T,. The experimental results on self and solute diffusion in ? uranium14,15 and ß zirconium,10 and for solutes in 0 titanium,17 and possibly for self-diffu- sion in chromium below about 0.75 T,," gave some credence to this theory. However, not all bcc materials display low values of DO and Q, and the exceptions were not predicted by any theory. Furthermore, it has recently become apparent that, in bcc materials, log D is not always linear with T-l if a sufficiently wide range of temperature is studied.16,18 This variation may be such that Q may increase18,19 or decrease20 with increasing temperature. The present work was undertaken in an attempt to provide further diffusion data on bcc metals, and to try to understand the factors which contribute to differences in behavior between the various elements. For part of this work, the Fe-Cr system was chosen since it is of considerable technological importance, and data on 12 pct Cr and 17 pct Cr alloys appeared well worthwhile to supplement that existing for the remainder of the stern.18,22 The diffusion of Fe55 in chromium was studied as an example of a more or less "normal" tracer element in a possibly abnormal host lattice. Finally, no data were available for vanadium, the neighbor of chromium in the periodic table, because of lack of a suitable isotope so cr55 was used as a tracer in a few preliminary experiments. For convenience, we shall refer to elements whose Do and Q are low compared to those predicted by Zener&apos;s theory as "anomalous". PROCEDURE This investigation determined self-diffusion rates by means of radioactive tracers and the integral-activity method first utilized by Gruzin.23 In this method a thin layer of radioisotope of the diffusing element is plated or coated onto a planar surface of the diffusion sample, which is then given an isothermal-diffusion annealing treatment. The determination of an activity-penetration curve involves measuring the residual activity of the specimen after each successive layer or section has been removed parallel to the original planar surface. The method used here is essentially the same as that used by Gondolf18 and Kunitake.21 Two radioactive tracers, cr51 and Fe55, were used in this investigation. Diffusion coefficients were determined for the diffusion of one or both of these tracers in four different materials, viz., Fe-12 wt pct Cr alloy, Fe-17 wt pct Cr alloy, chromium, and vanadium. The diffusion samples had nominal dimensions of 1.5 cm diameter and 0.5 cm thickness. The grain size was several millimeters for the Fe-Cr alloys and at least 1 mm for the chromium and vanadium samples. Accurately planar surfaces

Jan 1, 1964

By N. J. Grant, A. W. Mullendore

Three aluminum alloys of 0.94, 1.92, and 5.10 pct Mg, prepared from very high purity metals, were tested at 500°, 700°, and 900°F in creep rupture. The degree of strengthening through solid-solu-tion alloying and the effects on the deformation characteristics and fracture were examined. The ductility of the alloys as a function of stress and temperature was closely followed. STUDIES of the creep process in pure metals in recent years have done much to expand the understanding of the fundamental deformation and recovery processes that contribute to overall creep behavior. In order that this knowledge may be applied to commercial alloys, it is necessary to know the principles governing the effect of alloying on the mechanisms of creep. A limited amount of work has been performed in this field, but few investigators have attempted to follow the changes in particular creep mechanisms with alloying. Recently, studies of the effects of solid-solution alloying on the plastic properties of aluminum have been conducted by Dorn, Pietrokowsky, and Tietz,1 Sherby, Anderson, and Dorn,2 and Sherby and Dorn.3 This paper presents the results of an investigation of the effect of solid-solution alloying of high purity aluminum with magnesium on the creep-rupture properties, and correlates these observations with changes in the creep mechanisms. This work is thus an extension of the creep-rupture observations of Servi and Grant4,5 and the deformation studies of Chang and Grant.6,7 Experimental Procedure Three alloys of aluminum containing approximately 1, 2, and 5 pct Mg were tested. These alloying additions are all within the solid-solubility limit at the testing temperatures.&apos; The analysis of the materials is presented in Table I. The tests fall into two categories: l—creep-rup-ture tests at 500°, 700°, and 900°F, and 2—structure study tests performed primarily at 700°F. Speci-mens of 0.160 in. diameter with milled flats for metallographic observations" &apos; were utilized for the structure studies. All specimens were annealed in one step to give the desired grain size for the tests. Table II presents the annealing data and final grain sizes. The specimens were polished electrolytically before testing with Jacquet solution (2/3 acetic anhydride, 1/3 perchloric acid) at 25" to 30°C, and 15 to 20 v. Creep-rupture testing was performed under constant load with the apparatus previously described." Results and Discussion Creep-Rupture Properties: The log-log plots of creep-rupture data are presented in Figs. 1 and 2. For these very pure single-phase alloys, the minimum creep rate and the rupture life both exhibit straight-line dependence on stress in this method of plotting as they have for commercial alloys0,10 and for pure aluminum." Curve breaks, based on the use of straight-line segments, at 500°F have been found by metallographic study to correspond to a transition from low to high temperature behavior and so represent zones of equicohesion. Specimens on the high creep-rate side of the break showed normal granular deformation processes whereas those on the low creep-rate side showed rapidly increasing grain-boundary sliding and migration with extensive evidence of intercrystalline cracking at 500°F. Two micrographs of the 0.94 pct Mg alloy, Fig. 3, show the increased participation of the grain boundary in the deformation process at 500°F with decreasing stress. In Fig. 3a is shown the structure of a specimen which exhibits little deformation along the grain boundaries and failed transgranularly; in Fig. 3b is shown the increased deformation along the grain boundaries at a lower stress for a specimen which showed appreciable intercrystalline cracking. The severity of intercrystalline cracking increased with increasing magnesium content at 500°F. Intercrystalline cracking disappeared in most of the specimens at 700°F and persisted only in the 5 pct Mg alloy at high creep rates. At 900°F all of the specimens deformed with extensive grain-boundary participation, including extensive grain-boundary migration. None of the alloys at 900°F showed intercrystalline cracking.

Jan 1, 1955

By G. L. Simard, D. J. Salley, J. Chupak

DITHIOPHOSPHATES and xanthates are the principal collectors for sulphide minerals, and consequently any knowledge of mineral-collector systems of this type is of value. In the present investigation an attempt was made to obtain information on the interaction of a typical dithiophosphate with galena. In carrying out this study, radioiso-topes, so much discussed in the past few years,&apos;, &apos; were extensively employed. By using radioactive dithiophosphate synthesized from radioactive phosphorus, a rapid and sensitive analytical procedure G. L. SIMARD is in the Research Division, Stamford Research Labs., American Cyanamid Co., Stamford, Conn.; J. CHUPAK, formerly in the Research Division, Stamford Research Labs., is now at Camp Detrick, Frederick, Md.; and D. J. SALLEY is in the Research Division, Stamford Research Labs. AlME New York Meeting, Feb. 1950. TP 2815 B. Discussion (2 copies) may be sent to Transactions AlME before April 30, 1950. Manuscript received Oct. 17, 1949. was at hand. This permitted determination of such important quantities as the rate of uptake of dithiophosphate by the mineral, the amount existing at equilibrium on the mineral surface and in the solution, and the desorption of the agent from the surface. Such measurements were possible even on single crystals of galena. In addition the exchange of dithiophosphate between the solution and the sorbed phase was examined, a matter which could be accomplished only by the use of isotopes. It is desired to point out at this time that throughout this paper the term "sorption" has been employed to designate the uptake of agent by mineral, without implication as to the nature of the process by which the uptake was accomplished. Experimental Materials: Galena: The galena was from the Tri-State district. For studies on ground mineral four preparations were used during the course of the investigation. These were prepared from selected large crystals by wet grinding in order to reduce surface oxidation. Alcohol was chosen as a convenient medium for this purpose. The ground mineral was then fractionated by sedimentation in alcohol, dried by evacuation, and stored in a nitrogen-filled desiccator. Data on the preparations are tabulated in table I. The size analysis indicated that the areas of the preparations were of comparable magnitude, even though the absolute values may be somewhat incorrect. Dithiophosphates: Nonradioactive dithiophbsphate (di-isopropyl or di-secondary butyl) was obtained by purification of a commercial product. An aqueous acid solution of the agent was extracted with petroleum ether, the ether layer dried, and the dithiophosphate precipitated as ammonium salt with anhydrous ammonia. Several repetitions of this process resulted in a nearly colorless, flaky product of good purity. (General formula (RO,)PSSNH,). Radioactive dithiophosphate was synthesized by heating radioactive elementary red phosphorus* • For early experiments (1943 to 1944), the elementary red phosphorus was obtained from the cyclotron group at the Crocker Radiation Laboratory of the University of California. Berkeley, through the courtesy of Dr. Joseph W. Hamilton. For more recent work (1946 to 1949). the elementary radioactive Phosphorus has been supplied by the Oak Ridge National Labarotories on allocation from the U. S. Atomic Energy Commission. with sulphur at 270" to 300°C to produce radioactive P,S,. The latter was then treated with the desired purified alcohol (isopropyl or secondary butyl) at 60" to 80°C to form the dithiophosphoric acid derivative. Purification was effected in the same manner as for the nonradioactive material. The effectiveness of the purification method was established by the isotopic dilution method." The same technique was used to show that only negligible decomposition of neutral or of carbonate solutions of the dithiophosphate took place over a period of a day; this was true whether or not galena was suspended in the solutions. Procedures: Radioactivity: The activity of a solution was obtained by counting with a small glass-jacketed, silvered Geiger counter, using a conventional scaling circuit.&apos; Crystals and other solids were counted under a bell-shaped, mica-window counter tube. Sufficient counts were made so that the probable error of counting was of the order of +I-3 pct. The specific activity in terms of counts per minute

Jan 1, 1951

By J. Chupak, D. J. Salley, G. L. Simard

DITHIOPHOSPHATES and xanthates are the principal collectors for sulphide minerals, and consequently any knowledge of mineral-collector systems of this type is of value. In the present investigation an attempt was made to obtain information on the interaction of a typical dithiophosphate with galena. In carrying out this study, radioiso-topes, so much discussed in the past few years,&apos;, &apos; were extensively employed. By using radioactive dithiophosphate synthesized from radioactive phosphorus, a rapid and sensitive analytical procedure G. L. SIMARD is in the Research Division, Stamford Research Labs., American Cyanamid Co., Stamford, Conn.; J. CHUPAK, formerly in the Research Division, Stamford Research Labs., is now at Camp Detrick, Frederick, Md.; and D. J. SALLEY is in the Research Division, Stamford Research Labs. AlME New York Meeting, Feb. 1950. TP 2815 B. Discussion (2 copies) may be sent to Transactions AlME before April 30, 1950. Manuscript received Oct. 17, 1949. was at hand. This permitted determination of such important quantities as the rate of uptake of dithiophosphate by the mineral, the amount existing at equilibrium on the mineral surface and in the solution, and the desorption of the agent from the surface. Such measurements were possible even on single crystals of galena. In addition the exchange of dithiophosphate between the solution and the sorbed phase was examined, a matter which could be accomplished only by the use of isotopes. It is desired to point out at this time that throughout this paper the term "sorption" has been employed to designate the uptake of agent by mineral, without implication as to the nature of the process by which the uptake was accomplished. Experimental Materials: Galena: The galena was from the Tri-State district. For studies on ground mineral four preparations were used during the course of the investigation. These were prepared from selected large crystals by wet grinding in order to reduce surface oxidation. Alcohol was chosen as a convenient medium for this purpose. The ground mineral was then fractionated by sedimentation in alcohol, dried by evacuation, and stored in a nitrogen-filled desiccator. Data on the preparations are tabulated in table I. The size analysis indicated that the areas of the preparations were of comparable magnitude, even though the absolute values may be somewhat incorrect. Dithiophosphates: Nonradioactive dithiophbsphate (di-isopropyl or di-secondary butyl) was obtained by purification of a commercial product. An aqueous acid solution of the agent was extracted with petroleum ether, the ether layer dried, and the dithiophosphate precipitated as ammonium salt with anhydrous ammonia. Several repetitions of this process resulted in a nearly colorless, flaky product of good purity. (General formula (RO,)PSSNH,). Radioactive dithiophosphate was synthesized by heating radioactive elementary red phosphorus* • For early experiments (1943 to 1944), the elementary red phosphorus was obtained from the cyclotron group at the Crocker Radiation Laboratory of the University of California. Berkeley, through the courtesy of Dr. Joseph W. Hamilton. For more recent work (1946 to 1949). the elementary radioactive Phosphorus has been supplied by the Oak Ridge National Labarotories on allocation from the U. S. Atomic Energy Commission. with sulphur at 270" to 300°C to produce radioactive P,S,. The latter was then treated with the desired purified alcohol (isopropyl or secondary butyl) at 60" to 80°C to form the dithiophosphoric acid derivative. Purification was effected in the same manner as for the nonradioactive material. The effectiveness of the purification method was established by the isotopic dilution method." The same technique was used to show that only negligible decomposition of neutral or of carbonate solutions of the dithiophosphate took place over a period of a day; this was true whether or not galena was suspended in the solutions. Procedures: Radioactivity: The activity of a solution was obtained by counting with a small glass-jacketed, silvered Geiger counter, using a conventional scaling circuit.&apos; Crystals and other solids were counted under a bell-shaped, mica-window counter tube. Sufficient counts were made so that the probable error of counting was of the order of +I-3 pct. The specific activity in terms of counts per minute

Jan 1, 1951

By N. A. Gokcen, J. Chipman

A revised treatment of the authors&apos; published data eliminates the complex relation previously proposed between concentration of silicon and activity coefficient of oxygen in liquid iron. Revised values of the thermodynamic properties of the liquid solution are presented. IN a recent experimental study of the reaction SiO2 (s) = Si+ 2O; Kf, = [% Si] [% O]² [1] the authors&apos; found a substantially constant equilibrium product in liquid iron at 1600°C of 2.8x10-5 They also reported extensive data on the reactions: SiO2 (s) + 2H2 (8) = Si- + 2H2O (g); K&apos;2= [% Si] (H2O/H2 [2] and H, (g) + 0 = H2O (g); K&apos;3 =( H2 O [31 (H2) [%O] From the results on reaction 3 and earlier data of Dastur² on this same reaction in the absence of silicon, they determined the activity coefficient of oxygen, f0, on the basis of the definition K3 = (H2O)/ (H2)f0 [% 0] where K, is the equilibrium constant and f0, is taken as unity in the pure Fe-0 system. Similarly values of fsi were deduced from results on reaction 2. In a more recent study" of analogous reactions in the system Fe-A1-0, it was found impossible to reconcile the results on reaction 3 with Dastur&apos;s data; accordingly the latter were ignored and the equilibrium results were extrapolated to find a value of K, at zero concentration of aluminum. This procedure failed to locate the cause of the discrepancy but it did yield reasonable values of activity coefficients. It also avoided introduction of the complex empirical relation between the oxygen activity coefficient and the concentration of the added element. The same type of discrepancy exists for system Fe-Si-0.&apos; In the earlier paper an attempt was made to fit both sets of data by a single curved line (Fig. 6 of ref. l), the form of which is contrary to the theoretical requirement of a finite slope at infinite dilution. In the light of experience on the Fe-A1-0 system the discrepancy must be recognized as one which can be resolved only by more refined measurements. Accordingly Figs. 6 and 10 are retracted. It is pointed out also that until the discrepancy is resolved Figs. 7, 8, and 11 are subject to some uncertainty. Qualitatively the following conclusions still appear valid: 1—The activity coefficient of oxygen is reduced by addition of silicon. 2—In dilute solutions the activity coefficient of silicon increases with its concentration. 3—With respect to equilibrium in reaction 1, the above effects are approximately compensating. The discussion of K&apos;1 in the previous paper requires no revision. It was pointed out that the constancy of the product [% Si] [% 0]² ndicated a compensating effect of the activity coefficients of silicon and oxygen. Therefore, as a very good approximation, K1 = K&apos;1 and the following average values are suggested both for K, and K&apos;, at the temperatures 1550°, 1600°, and 1650", respectively, 1.0x10-", 2.8~10-" and 5.5 ~lo-&apos;. Revision of the thermodynamic treatment is necessitated by the recent appearance of new data, based on a combination of combustion and solution calorimetry,&apos; which yields for the heat of formation of low-cristobalite from the elements, the value —209,330 ±250 cal per mol at 25°C. This is about 4000 cal larger than the value previously accepted. The new value for cristobalite is used, together with Kelley&apos;s tables of high-temperature heat contents" and entropies and with Korber and Oelsen&apos;s&apos; heat of fusion of silicon to obtain the following equation for the standard free energy of cristobalite in the temperature range 1700" to 2000°K: Si (1) + 02 (g) = Si02 (crist.); ?F° = -217,700 + 47.OT [4] The free energy of solution of 0, in liquid iron is:8 O2 (g) = 20 (in Fe); AF° = -55,860 - 1.14T [5] and these two equations are combined to give: Si (1) + 20 = SiO, (crist.); AF° = -161,840 + 48.14T [6] ?F°1873 = -71,700 cal. From the experimental value of K, = 2.8x10-5, Si + 20 = SiO2 (crist.); ?F°1873 = -39,000 cal. [7] The combination of Eqs. 6 and 7 yields the free energy change when liquid silicon dissolves in iron to form the dilute solution of unit activity (1 pct). Si (1) = Si; ?F°1873 = -32,700 cal. [8] The heat effect in this process according to Korber and Oelsen&apos; is an evolution of 28,500 cal per gram

Jan 1, 1954

By P. C. J. Gallagher

A number of recmt determinations for the ratio of extrinsic to intrinsic stacking fault energy in fcc solid solutions are examined. Some of these arise from incomplete analyses which can yield only approxi?nate values for the ratio. Reliable results, on the other hand, obtained using extrinsic-intrinsic fault pairs, show that the extrinsic and intrinsic fault energies are essentially equal in several materials. There is some reason to believe that this finding is of general applicability to fcc elements and alloys. A wide range of values has been obtained for the relative magnitudes of the extrinsic and intrinsic stacking fault energies (yext and yint, respectively) in recently published studies in a variety of materials. In contrast, Hirth and Lothe&apos; using a central force model have shown that out to tenth nearest-neighbor interactions the perturbation in energy caused by both types of fault is the same. Although the model used is not completely valid in metals, there is nevertheless some indication that marked variations of yext/nnt should not be observed from one material to another. In early work in Cu-A1, Cu-Ge, Ni-Co, and stainless steel all the deformation faults observed in the electron microscope were found to be intrinsic in nature, which led to an attitude that the extrinsic fault energy must be considerably greater than the intrinsic. Extrinsic faulting arising from deformation has, however, more recently been directly observed in Au-4.8 at. pct n;~ Ag-6 at. pct Sn and Ag-8 at. pct sn; Ag-7.5 at. pct In and Ag-11.8 at. pct 1n;"&apos; pure silwer and Ag-0.5 at. pct ~n;&apos; and Cu-22 at. pct Zn, Cu-30 at. pct Zn, and Cu-7.5 at. pct ~1.l&apos; Multilayer loops containing extrinsic faulting have also been observed in quenched aluminum." While peak asymmetries in X-ray faulting probability studies were generally attributed to the presence of twins,Lelel2 has recently reinterpreted earlier X-ray data in Ag-Sb alloysU in terms of the presence of extrinsic faulting. The determinations of yeXt/yint made from the above studies are shown in Table I, with a brief description of the techniques employed. A number of the methods utilized are deficient in one or more respects, and the reliability of the values listed will be discussed. ~ele&apos;~ recognizes that his approximate determinations of yext/yint assumes equal numbers of extrin-sically and intrinsically faulted dislocations. It is well-known, however, that such an assumption is not at all justified since extrinsic faulting has but rarely been observed in samples studied in the electron microscope. The only conclusion that should be drawn from the X-ray results at present is that the total intrinsic scattering cross section (i.e., the product of the width of the intrinsically faulted dislocations with their density) is approximately ten times greater than for extrinsic faulting in these particular samples. An important point is that the relative magnitudes of the energies cannot be inferred from results of this type, unless the intrinsic and extrinsic faults form with equal ease. One must recognize that, although a formation barrier may restrict the amount of extrinsic faulting which occurs, this in no way implies that the extrinsic and intrinsic energies should be different. It is unlikely that a worthwhile estimate of the relative densities of extrinsically and intrinsically faulted dislocations can be made at the high deformations present in X-ray samples. ~oretto,&apos;~ from a statistical argument applied to the nonobservation of extrinsically faulted tetrahedra out of a large sample, concluded that yeXt/yint could not be less than -4.5. However, the present author feels that a high-energy formation barrier as just supposed also explains this finding satisfactorily and that no conclusion can possibly be drawn concerning the actual extrinsic stacking fault energy. The same argument also serves to explain the fact that extrinsic faulting has been relatively little observed in the electron microscope. Extrinsic-intrinsic node pairs and isolated extrinsic nodes were first reported by Loretto~ and subsequently by Ives and Ruff,&apos; Gallaher,&apos; and Gallagher and Wash-burn.&apos; Ives and Ruff&apos; found a wide spread in the ratio of extrinsically to intrinsically faulted area in the node pairs they observed, and drew the very tentative conclusion that yeXt/yint 2 2. They recognized that a straightforward comparison of the size of the faulted areas could provide no more than a qualitative result without a theoretical analysis of the dislocation geometry associated with extrinsic faulting. A theoretical

Jan 1, 1969

By D. Turnbull, J. C. Fisher

ACCORDING to the "reaction-path" modell,2 of martensite nucleation, the shear angle of the embryonic martensite plate must be treated as a variable, and included in any calculation of nucleus critical size. Also, as can be deduced from this model, the interfacial free energy between austenite and martensite does not reach its final value until the shear is completed. It is zero for zero shear angle. However, in order to account for the kinetics of the martensite transformation, some sort of interfacial energy barrier appears to be necessary even with the reaction-path model, for otherwise the volume and the energy of formation of the critical size nucleus both collapse to zero.3 Cohen independently suggested that surface energy could be incorporated into the reaction-path model, with the overall free energy of a martensite embryo being a function of its volume and shear angle.&apos; It is possible to estimate the energy associated with the formation of a critical-size martensite nucleus starting with the reaction-path model and including a surface free-energy barrier. As the dependence of interfacial free energy upon shear angle is unknown, a simple type of dependence will be assumed, with the belief that the true dependence would not lead to appreciably different results. Consider the work required to form a lenticular martensite plate with radius r, thickness t, and shear angle 8. There are three contributions; one being the interfacial free energy, one being the free energy change in the martensite plate, and one being the free energy increase in the surrounding austenite. The interfacial free energy u is assumed to depend upon the shear angle 0 according to the relationship s=s0(?/?0)n [1] where 8, is the equilibrium shear angle and n is an exponent that may lie in the range 0 n 2. The work required to form the interfaces of a martensite plate then is W. = 2pr² s0(?/?0)n [2] The free energy change per unit volume of martensite is composed of two parts, one the ordinary volume free energy ?f1. which is negative, and the other the elastic strain energy G?m²/2, where G is the shear modulus and 7, the shear strain relative to the martensite structure. This expression for the strain energy is valid only when the shear strain ym, is sufficiently small that the martensite is within its linear elastic range. There is no doubt that ym, lies beyond the linear elastic range for embryos that are considerably subcritical. However, for critical nuclei it will be shown that ym, is 1.5 pct or less, within the linear elastic range of martensite. For embryos of nearly critical size, then, the strain energy of the martensite is correctly given by G?m²/2. The shear strain in the martensite is ym, = 8, — 8, and the work required to form the strained martensite is Wm --= (pr²t/2) [?fv + G(?O - ?)²/2] [3] The free energy change in the austenite is entirely that due to elastic distortion. The elastic strain is not uniformly distributed in the austenite, being large near the martensite plate and small elsewhere. Approximately, however, the energy corresponds to a uniform shear strain ya= (?t/2)/r [4] throughout the volume 4pr³/3 surrounding the plate. The work required to strain the surrounding austenite then is Wa = (4pr³/3) (G?a²/2) = (G?²/6) prt² [51 For simplicity, the same shear modulus G is assumed for each structure. The total free energy for forming a plate then is W = W3 + Wm + Wa. = 2pr² s0 (?/p?0)n + (pr²t/2) [?fr+G(?0-?)²/2] + (G?²6) prt2 [6] This expression is correct for nuclei and for embryos of nearly critical size, where, as will be shown, the strain energy in the martensite is correctly given by the expression G (? — ?)². Having W as a function of r, t, and 8, as in Eq. 6, there is a saddle-point where W has a stationary value, W subsequently decreasing indefinitely as the nucleus volume increases along the reaction path. The stationary value of W is the energy of the critical nucleus. The critical nucleus has radius, thickness, and shear angle such that ?W/?r - awlat: = ?W/?p? = 0. Performing these differentiations and calculating the critical nucleus energy, W* = [8192p(G?/6)²;s/27 ?fv4] [7] where a= (?/?0)3n+1[l +G(8"-8)&apos;/2af.]&apos; [7a] and where 8 is to be determined from the equation (1 + 3n/4) + G8(6O - (9)/[Af. +G(6>o-6>)72] = 0 [8] For ?f, near —200 cal per mol or —10" ergs per cc, and 8, near 1/6, as for iron-base alloys, Eq. 8 gives ?0 - ? ~ - (4 + 3n) ?f1./4G0O [9] as the difference between the equilibrium shear angle and the actual shear angle for a critical nu-

Jan 1, 1954

By Y. A. Rocher, J. E. Dorn, L. A. Shepard

Creep activation energies for single aluminum crystals favorably oriented for shear by (010) [101] glide were detemined over the temperature range from 78" to 900°K. Observations of slip bands on the specimen surface were made in conjunction with the investigation. From 78" to 780°K, the activation energies obtained in this imestigation agreed closely with those previously found for creep by (111) [101] slip. Between 78" and 140°K, the activation energy was identified with the Peierls process, while between 260°and 780°K the activation energy was close to that for cross-slip. The coarse wavy slip bands nominally parallel to the (010) plane observed above 260°K were attributed to fine cross-slip. From 800" to 900°K, unusually high apparent activation energies ranging from 28,000 to 54,000 cal per mole were obtained. These apparent activation energies were attributed to re crystallization. AS illustrated in Fig. 1, a recent investigation1 has shown that creep of aluminum single crystals by the (111) [i01] mechanism is controlled by three unique processes, each of which is characterized by a single activation energy which is independent of the applied stress and the creep strain. A comparison of the observed activation energies with theoretically calculated values permits a fairly clear identification of the three operative creep processes. Below 450°K, where the activation energy for creep is 3,400 cal per mole, the deformation is controlled by the Peierls process, the activation energy for creep agreeing well with that calculated by seeger2 for the energy required to nucleate the motion of a dislocation loop against the atomic forces of the lattice. Between 590° and 750°K, the observed activation energy for creep of about 28,000 cal per mole agrees well with the energy necessary to induce cross-slip. Seeger and schoeck3 estimate that the activation energy is about 24,000 cal per mole whereas Friedel4 recently calculated this activation energy to be 28,000 cal per mole. Above 800°K the activation energy of 35,500 cal per mole that was observed for creep agrees well with that estimated for self-diffusion in aluminum.= In this range the operative rate-controlling slip process has been clearly identified as that arising from the climb of edge dislocations. The objective of this investigation is to ascertain whether a single crystal of aluminum favorably oriented for simple shear in the [loll direction on the (010) plane might exhibit uniquely different activation energies for creep from those obtained previously for (111) [101] slip. Whereas the exis- tence of such unique activation energies would constitute incontrover table evidence for new mechanisms of slip, the absence of any new activation energies might suggest that slip of aluminum is confined to the (111) [loll mechanism. Several factors prompted the selection of the (010) [101] orientation for study. First, there are more reported observations of (010) [loll slip than of any other nonoctahe-dral mechanism.8-10Secondly, Chalmers and Martius1l have concluded from considerations of the energies of dislocations that (010) slip is the second most favored mechanism in face-centered-cubic metals. Finally, favorable orientations for simple shear by the (010) [loll mechanism provide the least favored orientation for slip by the (111) [101] mechanism. EXPE-RIMENTAL PRO-CEDURE The high-purity aluminum stock, specimen preparation, shear fixture, extensometry, and experimental technique used in this investigation were the same as those previously reported.&apos; Single-crystal spheres grown from the melt of 99.995 pct pure Al* were _ *The high-purity aluminum used in this investigation was graciously given by the Aluminum Company of America. oriented, carefully machined into dumbbell-shaped shear specimens, annealed, and chemically polished. The finished specimen had a central reduced section 0.190 in. wide and 0.590 in. in diam and 1/4-in. grip sections at both sides, 0.690 in. in diameter. The specimen was oriented in the stainless steel grips of the shear fixture with the (010) plane perpendicular to the dumbbell axis and the [loll direction parallel to the stress axis within 2 deg. Creep activation energies were calculated in the previously described manner1 from determinations of the instantaneous change in shear strain rate produced by an abrupt 15 to 20 deg increase or decrease in test temperature. If is the instantaneous strain rate at strain y and temperature T1, and ?2 the instantaneous rate at y and T2,

Jan 1, 1960

By N. J. Olson, G. W. Toop

A series of equations previously derived for calculating ternary thermodynamic properties using binary data has been applied to the problem of predicting ternary phase diagrams and quaternary excess free energy. The methods are considered to be rigorous for regular ternary and quaternary systerns and empirical for nonregular systems. The equations have been used to predict ternary phase boundaries in the Pb-Sn-Zn system at 926°K and the Ag-Pd-Cu system at 1000ºK. Calculated quaternary excess free-energy values are presented for the Pb-Sn-Cd-Bi system at 773°K. A method for predicting the location of ternary phase boundaries would be a useful supplement to experimental measurements in ternary systems. This has been recognized with the considerable work that has been done to find models to predict or extend thermodynamic properties and phase diagrams in binary and ternary systems1-18 for which direct experimental measurements are limited. With the access to highspeed digital computers and mechanical plotting devices, it is currently rather easy to compare mathematical models with experimental data. The regular-solution model is consistent with systems which exhibit negative heats of mixing, positive heats of mixing, and miscibility gaps, and therefore it is applicable to simple phase diagrams. The purpose of this paper is to illustrate the use of regular-solution equations to predict, empirically, phase equilibria in some types of nonregular ternary systems. Corresponding equations for regular quaternary systems are given and used to calculate empirical quaternary excess free-energy data. METHOD FOR PREDICTING THE LOCATION OF TERNARY PHASE BOUNDARIES USING BINARY DATA Meijerin1,6 has used the regular-solution model to calculate common tangent points to ternary free energy of mixing surfaces and hence to determine phase boundaries in ternary systems involving miscibility gaps. He used the following equation to calculate ternary excess free energy of mixing values: stants characteristic of the binary solutions, and Ni is the mole fraction of component i. An alternate expression which gives for regular solutions as a function of binary values of along composition paths with constant N1/N2, N2lN3, and N1/N3 may also be derived:15 ternary r xs 1 ?c-*n.Ti*.U*. This expression for is more useful for the empirical calculation of ternary excess free-energy values for nonregular systems because actual binary AFXS data may be used in the expression rather than attempting to find suitable constants for Eq. [I]. The results of this feature of Eq. [2] are illustrated in Table I where calculated excess free-energy values for the Ni-Mn-Fe system at 1232°K are compared with experimental data of Smith, Paxton, and McCabe.19 Although regular-solution equations have been shown to give calculated thermodynamic quantities which agree quite well with experiment for single-phase nonregular ternary systems,14,15 care should be exercised in the use of the equations to predict thermo-dynamic properties of multiphase ternary systems in which strong compound formation is suspected. This precaution is consistent with the simple regular-solution model which for negative values of ai_j will indicate a tendency toward compound formation but even for very large negative values of ai-jwill not give multiphase binary or ternary systems involving a distinct stable compound. Hence, calculated ternary free-energy data using Eq. [2] might be expected to vary between being rigorous and poor, in the following order, for ternary systems which are: a) regular solutions, b) nonregular single-phase liquids in which random mixing is nearly realized, c) nonregular single-phase solids, d) nonregular multiphase systems exhibiting miscibility gaps, e) nonregular multiphase systems with binary compounds but no ternary compounds, f) nonregular multiphase systems with highly stable binary and ternary compounds. The calculated data will be expected to be least accurate for the last two cases. The general method adopted in this paper involves two-dimensional plots of ternary activity curves. The principle used is that tie lines indicating two-phase equilibria join conjugate phases a and B for example, for which a1(a) = a1(B), a2(a) = a2(B), and a3(a) = a3(B). Tie lines may be determined by plotting the ternary activities of two components along an isoactivity line for the third component and the unique points where the above equalities hold may be found graphically.

Jan 1, 1970

By T. H. Janes

NATURAL abrasives of some type are found in all countries of the world. In order of their hardness the principal natural abrasives are diamond, corundum, emery, and garnet, which are termed high grade, and the various forms of silica, including pumice, pumicite, ground feldspar, china clay and, most important, sandstone. The properties qualifying materials for use as abrasives are hardness, toughness, grain shape and size, character of fracture, and purity or uniformity. For manufacture of bonded grain abrasives such as grinding wheels, the stability of the abrasive and its bonding characteristics are also important. No single property is paramount for all uses. Extreme hardness and toughness are needed for some applications, as in diamonds for drill bits, while for other purposes the capacity of the abrasive to break down slowly under use and to develop fresh cutting edges is of greatest importance, as with garnet for sandpaper. In dentifrices, soaps, and metal polishes, of course, hardness and toughness are objectionable. First among the natural abrasives, industrial diamonds are essentially of three types: l—bort, which includes off-color, flawed, or broken fragments unsuitable for gems; 2—carbonado, or black diamond, a very hard and extremely tough aggregate of very small diamond crystals; and 3—ballas, a very hard, tough globular mass of diamond crystals radiating from a common center. Bort comes from all diamond-producing centers, carbonados only from Brazil, and ballas chiefly from Brazil, although a few of this last group come from South Africa. By far the largest producer of industrial diamonds is the Belgian Congo; the Gold Coast, Angola, the Union of South Africa, and Sierra Leone supply most of the remainder. There is no production in Canada, which imports $6 to $9 million worth of industrial diamonds annually. Industrial diamonds find innumerable uses in modern industry. They are used for diamond drill bits for the mining industry; in diamond dies for wire drawing; in diamond-tipped tools for truing abrasive wheels and for turning and boring hard rubber, fibers, and plastics; and in diamond-toothed saws for sawing stone, glass, and metals. High-speed tool steels, cemented carbides, and other hard, dense alloys can be cut, sharpened, or shaped efficiently only with diamond-tipped tools and diamond grinding wheels. .. Second only to the diamond in hardness is corundum, an impure form of the ruby and sapphire gems consisting of alumina and oxygen (Al²O³) with impurities such as silica and ferric oxide. Corundum generally crystallizes from magmas rich in alumina and deficient in silica, as in the nepheline syenites of eastern Ontario. Grain corundum is used in the manufacture of grinding wheels; very coarse grain is used in snagging wheels. Both types of wheels are employed in the metal trades, where the hardness of corundum, coupled with its characteristic fracturing into sharp cutting edges, makes it an ideal cutting tool. The finest corundum (flour grades) is used for fine grinding of glass and high-precision lenses. From 1900 to 1921 Canada was the world&apos;s leading producer of corundum. Following this period the deposits located in northern Transvaal of the Union of South Africa supplied more and more of the world&apos;s requirements, and since 1940 South Africa has provided almost the entire output, which has ranged between 2500 to 7000 tons a year during the last decade. Minor amounts have also been produced in Mozambique, India, and Nyassaland. Opportunities for Mining Corundum Corundum deposits in southeastern Ontario are of three types, which may be described as follows: 1—Scattered, irregularly-shaped deposits of coarse-grained corundum which could be mined by means of small pits. About 10 groups of such deposits are known. Although the tonnage of individual deposits of this type is not great, it has been estimated that several years&apos; ore supply is available for a small tonnage operation. Deposits average about 9 pct corundum. 2—Large irregular deposits of coarse-grained corundum which would require mining by adit with possibly a scavenger operation on the remains of former surface deposits. The Craigmont deposit of this type produced about 20,000 tons of corundum concentrate during operations between 1900 and 1913. Most of the readily available surface ore was removed by operators during that time. Reserves of ore above road level have been estimated to average 7 pct corundum, but none of the so-called reserves have been blocked out, or even indicated, by diamond drilling. From 1944 to 1946, 2025 tons of

Jan 1, 1955

By S. A. Lever, R. Hultgren

The solidus is usually the least satisfactorily determined portion of a phase diagram. Cooling curves, which succeed well with the liquidus, show the solidus inaccurately or not at all because of segregation which occurs during freezing. Heating curves of carefully homogenized alloys might be expected to indicate accurately the solidus, but they are seldom used. Dynamic methods involving heating or cooling are never completely satisfactory because of uncertainty as to whether equilibrium is attained. A static method in which the specimen may be allowed hours, days, or even weeks to attain equilibrium is to be preferred. In a static method a solid solution, for example, is first made thoroughly homogeneous, then heated to successively higher temperatures. After sufficient time at each temperature to assure equilibrium, some property is measured which should alter strikingly when melting begins. Microscopic examination can be used to detect the beginning of melting, but the method is tedious since the specimen must be quenched, sectioned, polished, and etched before each examination. Of all the physical properties which change on melting, electrical resistance is probably the most satisfactory to measure. The measurement may be made while the specimen is at temperature without damage to the specimen. It may be repeated indefinitely to ascertain when equilibrium has been achieved. Measurements may be made on a single specimen over the whole range of temperature. Most metals approximately double their resistance on melting. Since an accuracy of a few tenths of a percent is easy to achieve, the method is highly sensitive to the beginning of melting. In spite of these advantages, which have been perceived for a long time,l,2 a reasonable search of the literature has failed to reveal a single case in which the method has been satisfactorily applied in practice to the determination of solidus temperatures. The use of electrical resistance measurements appears to have been confined in practice to changes in the solid state. In the work described in the following pages we have applied the electrical resistance method to the solidus of the lead-tin system. We have found the method to be convenient, reproducible, and highly sensitive. We chose the lead-tin system because it leads to few technical difficulties. Furthermore, a number of determinations of solidus have been made in this system by various methods and results could be checked against them. However, all published results are not in good agreement with one another, so this work should help in determining the solidus more precisely. The Lead-tin Diagram Because of its commercial importance, there have been numerous investigations of the lead-tin diagram. The results of the most recent work on the solidus are indicated in Fig 7, as well as the results of the present work. The works of Honda and Abe3 and of Stockdale4 agree fairly well with each other and with the present work. Jeffery&apos;s5 data indicate the solidus to be about 50°C lower. Honda and Abe3 used differential thermal analysis on both heating and cooling cycles. Stockdale4 used the microscopic method and also differential heating curves. Stockdale&apos;s results were about 4" higher than those of Honda and Abe at low tin contents and lower at higher tin contents. These results also agree with those of Rosen-hain and Tucker.= Jeffery5 used electrical resistance measurements of the alloy as it was being heated or cooled. Apparently he did not attain equilibrium as his results are about 40°C lower than those of Stockdale4 or Honda and Abe.3 MATERIALS AND METHODS The lead and tin used were of high purity. They were supplied by the American Smelting and Refining Co., who gave the following analyses: Lead: silver, 0.0016 oz per ton; copper, 0.0008 pct; cadmium, 0.0007 pct; zinc, 0.0002 pct; arsenic, 0.0003 pct; antimony, 0.0002 pct; bismuth, 0.0005 pct; tin, 0.0001 pct; iron, 0.0020 pct; lead (by difference), 99.995 pct. Tin: antimony, 0.037 pct; arsenic, 0.020 pct; bismuth, 0.004 pct; cadmium, trace; copper, 0.025 pct; iron, 0.004 pct; lead, 0.020 pct; nickel and cobalt, 0.005 pct; silver, 0.0005 pct; sulphur, 0.005 pct; tin (by .-difference). 99.88 pct. One hundred grams of metal with the desired proportions of lead and tin was weighed out to the nearest one-tenth of a milligram. The mixture was placed in a silica crucible, covered with charcoal, and melted in a reducing atmosphere in a gas-fired furnace. The alloy was well stirred. Chemical analysis of two of the alloys checked closely with the weighed portions. The compositions of the remainder of the alloys were taken directly from the weighings, without chemical analysis.

Jan 1, 1950

By C. L. Magee, H. W. Paxton

The effects of testing temperature, frorn 77" to 420" K, and volume fraction of martensite on the micro-plastic response of unaged Fe-31Ni martensite-austenite aggregates have been determined. The kinetics of the aging phenomena which lead to a decrease in the microplastic response were also characterized. These determinations, supplemented by other experimental results, show that at least two mechanisms of plastic deformation give rise to the apparent softness of the quenched structures. Only one of these mechanisms is fully discussed in this paper The transformation of retained austenite to martensite during the application of stress leads, in specified conditions, to large microplastic strains. This deformation behavior cannot be described by normal transformation plasticity theory but is shown to result from the fact that stress-assisted formation of martensite is a possible deformation mode. The present results and further considerations of previous work lead to the conclusion that it is unnecessary to postulate a special work-hardening mechanism to explain the mechanical properties of unaged martensite. It is now generally accepted that dislocation motion can occur in many solids at stresses very much below the L&apos;macroscpic" yield stress, e.g., 0.1 pct offset. This phenomenon has been investigated by a variety of techniques including measurements of elastic limit,&apos; effective static elastic modulus,~ and irreversible deformation following stressing at low levels.3"5 Of particular interest to the work to be described are exper -iments conducted on the deformation of martensite in attempts to decide whether freshly quenched ferrous martensites are "hard" or "soft".6 Muir, Averbach, and cohenl and McEvily, Ku, and ~ohnston&apos; have shown that as-quenched ferrous rnartensites can be plastically deformed at relatively low stresses. A difference between these two sets of experiments exists in that some diffusion of carbon would take place before testing in the experiments of Muir et a1. because the plain Fe-C alloys which they have tested transform to martensite well above room temperature. McEvily et a1. examined Fe-Ni-C alloys with Ms of about -30"~ and tested the alloys directly after quenching to — 195" ~ —a technique which obviates any appreciable carbon diffusion. Unfortunately, a characteristic of the alloys which transform below room temperature is that they do not transform entirely to martensite. The results discussed below will show that, because the transformation of this retained austenite under stress leads to plastic deformation, one cannot investigate the properties of martensite by such experiments. The existence of a second deformation phenomenon, which is not caused by retained austenite, is also established in the present work. In line with a previous suggestion,&apos; it is believed that the second microdefor-mation mode is principally due to the internal stresses generated by the formation of martensite. To avoid confusion in the present report, the evidence we have found for this interpretation will be discussed separately in a brief note.7 EXPERIMENTAL Materials. The alloys were induction-melted and cast under vacuum; the resulting compositions are given in Table I. The ingots were hot-swaged to 2-in.-diam bar and further cold-swaged and/or cold-rolled prior to specimen preparation. The standard tensile specimens were machined from sheet. The gage section was 0.05 by 0.2 by 5 in.; 0.75-in.-wide ends had 0.2 5-in. centered holes for pinloading. The three-point bend samples were 0.075-in. thick and 0.6 in. bide. The distance between the outer loading points was 5.5 in. In order to establish a standard starting condition, all specimens were quenched to 77°K prior to annealing in vacuo for austenitizing. The temperature of the austenitizing anneal was controlled to + 5"~. The testing and aging temperatures were maintained by various liquid baths (nitrogen, 77"~; freon, 130° to 200°K; acetone, 200 to 300°K; silicone oil, 300&apos; to 450°K) to better than il°K. Strain Measurement. The results herein were derived from both uniaxial tension and three-point bending experiments. For bending tests, the stresses and strains reported are those corresponding to the maximum fiber values. Normally, because of the small strains involved, very sensitive strain measurements are necessary to make microplastic measurements. However, because of the magnitude of the dilatation and shear involved in the martensitic transformation, the requirements in the present experiments proved to be less rigorous. In most experiments the plastic strain was evaluated by measuring stress relaxation and modulus defects. In this method, specimens are loaded rapidly to some predetermined load on an In-

Jan 1, 1969