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By A. W. H. Morris, G. H. Laurie, J. N. Pratt

Using- galvanic cells of the form Sn(liq)/Sn" (LiCl-KC1-SnCl,)/Sn-Ag (alloy), measurements have been made of relative thermodynamic properties of the a, C, E, and liquid phases of the Ag-Sn alloy system. Partial heats of solution of the components in the liquid alloys lzave also been observed by direct cal-orimetric measurement in an isoperibol calorimeter. The thermodynanzic quantities are disczlssed in relation to structural and other properties and the existence of anomalous minor fluctuations in the partial heats and entropies of solution in liquid alloys is tentatively suggested. In the course of a recent electro motive-force study of the thermodynamic properties of Sn-Ag-Pd liquids,' some measurements were also performed on the Ag-Sn binary system. Most previous thermodynamic studies of this system have been concerned with the liquid state. Measurements confined to the limiting heat of solution of silver in liquid tin have been made by many calorimetric workers2 while high-temperature calorimetric measurements of the heats of formation of the full range of liquid alloys are reported in the early work of Kawakami~ (1323°K) and more recently by Wittig and Gehrin~(1248°K). Electromotive-force studies on liquid alloys have been made by Yanko, Drake, and Hovorka' (606" to 686°K; 86 to 99.4 at. pct Sn) and by Frantik and Mc Donald' (900°K; 30 to 90 at. pct Sn). The only known measurements on the solid state are of heats of formation of the a, £, and c phases; these values were obtained using tin-solution calorimetry, at 723"K, by Kleppa,~ whose investigation also yielded heats of formation of liquid alloys containing more than 64 at. pct Sn. The present experiments on the Ag-Sn alloys include a re-examination of the liquid phase and, because of the dearth of free-energy data for the solid state, attempted measurements on the a, c, and E phases. The principal new feature of electromotive-force results obtained for the liquid phase was an indication of anomalous fluctuations in the partial heats and entropies of solution of tin at certain compositions. However, since the values for these thermodynamic quantities were determined from the temperature coefficients of cell potentials, which are commonly subject to considerable error, confirmation by calorimetric measurements was considered desirable. A detailed investigation of the partial heats of solution of the components in the binary liquids was made using a liquid metal solution calorimeter. I) GALVANIC CELL STUDIES a) Experimental Details. Measurements were made, as a function of alloy composition and temperature, of the potentials of reversible galvanic cells of the form: ~n(liq)/~n++/~n-Ag (solid or liquid alloy) Details of the apparatus and experimental techniques have been given elsewhere.' so that a brief account will suffice here. Molten salt, 58 mole pct LiC1-42 mole pct KC1, containing small amounts (1 to 2 mole pct) of stannous chloride was used as the electrolyte. The salts were dehydrated by pre-electrolysis and vacuum -drying techniques. Cells were established under an argon atmosphere by immersing tin and alloy electrodes in the molten salt contained in a large silica tube, heated in a vertical resistance furnace. The tube was sealed at the top by a head plate provided with openings permitting the simultaneous insertion of six electrodes, a central thermocouple sheath, and connections to vacuum and argon lines. Temperatures were controlled to *0.2"C over prolonged periods, with maximum variation over the electrodes at any time of 0.l°C. Temperatures were measured with a standardized Pt/13 pct Rh-Pt couple. The electromotive force of this and the cell potentials were measured on a Cambridge Vernier potentiometer and short-period galvanometer. Alloys were prepared from Pass "S" tin (99.999 pct) and Johnson-Matthey high-purity silver (99.999 pct) by melting in evacuated silica capsules and quenching in cold water. For liquid phase experiments, pieces of the resulting alloys were remelted into prepared silica electrode units, while solid electrodes were prepared by remelting into 3-mm bore tubing, inserting a cleaned molybdenum lead wire, and quenching to produce uniform rods about 3 cm in length, with soundly attached leads. In all cases remelting was done under an argon atmosphere. The solid electrodes were subsequently annealed in evacu ated silica tubes for 14 days at about 20°C below the solidus and quenched. Analyses showed that these techniques produced uniform electrodes with no significant change from weighed out compositions. b) Results and Discussion. Measurements were made on about forty alloys in the solid and liquid states, over varying ranges of temperature between 550" and 1050°K. Stable, mutually consistent, and reproducible electromotive-force data were obtained with most liquid alloys and these are shown in Fig. 1. Investigations were extended below the liquidus tem-

Jan 1, 1967

By R. E. Smallman, I. Milne

The deformation behavior of single crystals of Nb-Mo alloys has been investigated with particular reference to the influence of composition, orientation, and temperature. Strong solid-solution hardening was observed reaching a maximum at the equiatomic cotrlposition and can be attributed to the difference in atomic size between niobium and molybdenutrz. Changes in the form of stress-strain curve, as shown by a high work-hardening rate and restricted elongation to fracture, were observed at a composition of Nb-85 pct Mo and are attributed to the presence of MozC DreciDitate. Conjugate slip was only extensive in dilute alloy samples; at the 50/50 composition deformation rnainly occurred by primary slip, and the onset of conjugate slip gave rise to failure by cleavage on (100). The variation of yield stress of Nb-50 pet Mo with orientation was consistent with slip on (011)(111) slip systems. The temperature deperndence of the yield stress between -196" and 250°C was similar to that of pure bcc metals, but at a much higher stress level; no evidence for twinning %as found. IN recent years the deformation behavior of various pure metals in groups VA and VIA has received considerable attention, but surprisingly little work has been carried out on binary alloys made by mixing metals from the two groups. Such an investigation would be of interest since single crystals of metals of group VA have been shown to deform characteristically with a multistage deformation curve1"3 while a parabolic type of deformation curve has been reported for most of the group VIA metals.4'5 It has been suggested by Law ley and Gaigher~ that the difficulty encountered in obtaining multistage deformation curves for molybdenum in group VIA was possibly because of the presence of a microprecipitate of MozC which they observed even at carbon contents as low as 11 ppm. Recently a multistage deformation curve has been reported for molybdenum ," although the stages are not so definitive as those for group VA metals. The binary alloys of the particular refractory metals which have been investigated in single-crystal form include Ta-w,' Ta- Mo,' and Nb- Na." While a large amount of hardening was observed for alloys of the Ta-W and Ta-Mo systems, associated with room-temperature brittleness for alloys approaching the equiatomic composition, Ta-Nb remained ductile over the complete composition range with little or no solution hardening. Other systems have been investigated by hardness measurements on polycrystalline material and a discussion of the hardening of these alloys has been presented by ~udman." The purpose of the present investigation was to examine the deformation behavior of Nb-Mo alloys in detail, with particular reference to alloy composition and single-crystal orientation. In this way it was hoped to shed some light upon the restricted ductility of these alloy specimens. 1) EXPERIMENTAL PROCEDURE The starting materials were obtained in the form of beam-melted niobium rod and sintered molybdenum rod of suitable dimensions. Since niobium and molybdenum form a complete solid-solution series at all temperatures, alloy single crystals were produced by melting the two constituents together in an electron bombardment furnace (EBM). To produce specimens free from segregation a molten zone was passed over the length of each rod six times in alternate directions at a speed of 10 in. per hr. Typical specimens were analyzed for interstitial impurities by gas analysis and for metallic impurities by spectrographic analysis. The results of this analysis are shown in Table I. Many of the tensile specimens were also analyzed (after testing) by scanning the gage length in an electron beam microanalyzer, from which it was found possible to predict the approximate composition of a specimen from the original proportions of each element in the EBM. The tensile specimens were made with a gage length of 0.5 in. and diameter of 0.075 in., using a Servomet Spark machine. By careful machining on the finest range for the final i hr of this technique, surface cracks could be reduced to the level where they were easily removed by electropolishing in a solution of nitric and hydrofluoric acids. The specimens were strained at a rate of 10 4 sec-' using friction grips designed to prevent accidental straining and maintain a good alignment before straining. The orientations of the individual specimens tested are shown in Fig. 1 and the corresponding compositions listed in Table I1 together with collated experimental data. 2)RESULTS a) General Deformation Behavior. The effect of composition on the room-temperature deformation curves of similarly oriented specimens is shown in Fig. 2. The yield stresses of the pure constituents, while not the lowest reported to date, were at least comparable with existing data. Although the solution hardening was large for alloys at either end of the phase diagram, and comparable with the Ta-W solution-hardening data of Ferris et a1.,8 the low work-hardening rate characteristic of niobium was sustained until a composition of Nb-85 pct MO had been reached. Associated with the peak yield stress ob-

Jan 1, 1969

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's modulus and a value of approximately 0.5 for Poisson's ratio. A value of % for Poison's ratio with finite Young'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 L. W. Holm

Laboratory flooding experiments on linear flow systerns indicated that high oil displacement, approaching that obtained from completely miscible solvents, can be attained by injecting a small slug of carbon dioxide into a reservoir and driving it with plain or carbonated water. Data are presented in this paper which show the results of laboratory work designed to evaluate this oil recovery process, particularly at reservoir temperatures above 100°F and in the pressure range of 600 to 2,600 psi. Under these conditions CO2 exists as a dense single-phase fluid. It was found that a bank, rich in light hydrocarbons, was formed at the leading edge of the CO? slug during floods on long cores. Formation of this bank is probably due to a selective extraction by the C02 and, it is believed, partially accounts for the attractively high oil recoveries. In crddition to the efficient displacernerlt of oil from the pores of the rock by this process, the favorable rnobility ratio related to a C0 2-water flood also contributes to high oil recovery. A further advantage of this process is noted on limestone and dolomite rock, in that the CO1 reacts with the porous medium increasing its permeability. Flooding experiments were conducted on sandstone and vugular dolomite models. The results of this experimental work show the effect on oil recovery of type of porous medium, pore geometry, flooding length, and flooding pressure. The porosity of the cores and rilodels varied from 16 to 21 per cent and their pern~eabilities ranged from 100 to 200 md. A reconstituted West Texas reservoir oil, a West Texas stock tank oil, an East Texas stock tank oil and Soltrol were used to represent reservoir oils in this study. Oil recoveries ranging from 60 to 80 per cent of the original oil in place in these cores were obtained by CO2,-carbonated water floods at pressures between 900 and 1,800 psi, compared with conventional solution gas drive and water-flood recoveries of 30 to 45 per cent on the same cores. Oil recoveries greater than 80 per cent resulted frorn f1oods at pressures above about 1.800 psi. There high recoveries were noted from both the sandstone and the irregular Porosity carbonate cores. In all floods, additional oil was recovered by a solutiorr gas drive resulting from blowdown following the flood. Oil recoveries of 6 to 15 per cent of the original oil in place were obtained during this blowdown period. This additional recovery was found to be a function of oil remaining after the flood, decreasing with decreasing oil saturation. It was also noted that highest oil recoveries by blowdown were obtained when carborlated water rather than plain water followed the CO, slug. INTRODUCTION Miscible phase or solvent flooding processes, which are designed to increase oil recovery -from petroleum reservoirs, involve the injection of small quantities of a petroleum solvent into the reservoir, followed by an inexpensive scavenging fluid which is miscible with the solvent. Essentially complete displacement of oil from the pores of reservoir rock has been obtained by this technique. CO,, although not completely miscible with most reservoir oils at moderate pressures, is highly soluble in these oils at pressures above about 700 psi; there is appreciable swelling and reduction in the viscosity of oil when CO, is dissolved in it. Therefore, CO, could be expected to perform similarly to other oil solvents as a displacing agent. CO, is also highly soluble in water at elevated pressures, so water should be a satisfactory material to drive a slug of CO, through an oil-bearing reservoir. A favorable mobility ratio would be obtained through the reduction in viscosity of the oil and the use of water as a final displacing agent. A number of investigations of the use of CO, to improve oil recovery have been reported in the literature.2,3,4,5,6 These studies, however, have been conducted on uniform porosity sandstone at relatively low temperatures and pressures. The behavior of CO1 as a flooding agent at temperatures above its critical temperature could not be predicted adequately from these studies, particularly for the case of non-homogeneous rock. The purpose of this work was to evaluate the oil recovery efficiency of a process involving the injection of a CO2 slug followed by carbonated water, at reservoir temperatures above 100°F and in the pressure range of 600 to 2,600 psi, and to compare this process with conventional water flooding. The investigations were primarily designed to provide information on the efficiency of the process in irregular porosity carbonate rock. The effects of flooding path length, the presence of free gas, the type of oil to be recovered, and the amount of solvent required were also determined. The essential results of static phase behavior studies and experimen-

By Lloyd Pollish, Robert N. Breckenridge

SUCCESS in any underground mining operation is determined by accessibility of the orebody, which in turn is dependent upon maintenance of passageways to the mining zones and temporary support of the voids caused by extraction of ore. This is accomplished by one or a combination of the following methods: timbering, back-filling, pillaring, or, more recently, rock bolting. Timbering has usually been the principal means of maintaining these underground openings necessary for mining operations. Timber, however, does not prevent ground movement beyond the scope of localized sloughing, which is indicated by the gradual failing of the timber itself. Besides this, timbering has always been a costly process, and with the decline of available supplies of timber close to the mining areas, mining men have constantly sought other methods of controlling ground. Rock bolting is now replacing timbering at an ever increasing rate. Experience has proved that this form of ground support is just as applicable to blocky igneous rock as to stratified rock. Besides preventing sloughing of the walls and back of underground openings, Fig. 1, rock bolting has a stabilizing effect on the surrounding ground in much the same manner that steel reinforcing rods add to the strength of concrete structures. Further, rock bolting is flexible and may be applied to any shaped excavation, whereas timber sets are in a fixed pattern and the ground must often be changed to conform with this pattern. Rock-bolting installations were made in metal mines of the Northwest as early as 1939. An exhaust air crosscut was driven that year in one of the Butte mines of the Anaconda Copper Mining Co. The crosscut was rock-bolted and gunited at the time it was driven and is still being used to exhaust hot humid air from the 3400 level of the Belmont mine. It is interesting to note that no sloughing or caving has taken place in the 14 years it has been open. Even though these early installations of rock bolts were successful, few men recognized their potentiality until recent years, when the coal mines started their programs of mechanization and the great trend toward roof bolting began. In some areas of the Northwest stopes that previously required heavy timbering and close backfilling are now being mined by the more economical cut-and-fill and shrinkage methods. When used in conjunction with timbering, rock bolting increases the efficiency of the operation by decreasing hanging wall dilution and by making it possible to blast larger rounds. Most of the rock bolts installed to date in mines of the Northwest have been the 1-in. diam slot and wedge type, but there has been a recent trend to- ward using the 3/4-in. diam expansion shell bolt shown in Fig. 2. In addition to these commercially manufactured steel bolts, wooden bolts have been used with considerable success by the Day Mines of Wall'ace, Idaho. Installation of the slot and wedge type requires three distinct operations, with tools for each operation: 1—drilling the hole to proper diameter and depth, 2—setting the bolt, and 3—tightening the nut. Holes are drilled and bolts set with pneumatic rock drills. A number of setting or driving tools have been used successfully, but most follow the same general pattern. Usually the driving tool is designed to accommodate a short length of drill steel on one end and the rock bolt on the other end. In this manner the hammering effect of the rock drill is transmitted through the steel and driving tool to the bolt. When machines not having stop rotation are used, slippage is allowed between the driving tool and bolt or between the drill steel and driving tool. The rock bolt nuts are tightened either with pneumatic impact wrenches or with hand wrenches. Impact wrenches are desirable because they are faster and assure adequate tightness. Expansion shell bolts have the following advantages over slot and wedge rock bolts: 1—No special equipment other than a wrench is needed for their installation. 2—Installation is faster. 3—They are removable. 4—Holes need not be drilled to a specific depth as the expansion shell will anchor anywhere along the length of the hole. These advantages are offset somewhat by the lesser strength of the bolt, since expansion shell bolts are generally made from 3/4-in. diam steel as compared to 1-in. diam steel for the slot and wedge type. One manufacturer, however, is now fabricating expansion shell rock bolts from steel of high tensile strength, which gives this ¾-in. bolt a much greater strength than that of the mild steel bolt. Table I illustrates tests made by the Anaconda Copper Mining Co. to determine the proper hole size to use with various types of bolts and to determine

Jan 1, 1955

By J. A. Bailey, J. H. Tundermann

The dihedral angles of the solid-liquid interfaces were measured at various temperatures above the solidus and the interfacial energies calculated when small additions of copper, indium, lithium, magnesium, antimony, and silicon were made to an aluminum alloy containing 3 pct Sn. When the results were compared with those of the Al-Sn alloy some differences were found which could be interpreted in terms of the ability of the added element to enter into solution or form intermetallic compounds with the aluminum and tin. It was shown that in some cases considerable changes in the shape of intergvanular liquid films can be brought about by comparatively small compositional changes in the alloy. DURING the melting or solidification of an alloy a temperature range is usually found where the presence of a liquid phase may be detected at the grain boundaries of a solid. It is believed that the presence of this liquid phase is responsible for hot tearing in castings and welds and hot shortness in the working of some alloys at elevated temperatures. Rosenberg, Flemings, and Taylor1 in a study of the solidification of aluminum castings have indicated the importance of intergranular liquid films and shown that their shape and distribution at the end of solidification effect the hot tearing characteristics of the material. The shape of such intergranular liquid films are determined largely by the ratio between the solid-liquid interfacial energy (yLS) and the grain boundary energy (ySS). A measure of this ratio (yLS/ySS , relative interfacial energy) is the dihedral angle 8. The dihedral angle 0 is related to the relative interfacial energy by the following expression: Rogerson and Borland 2 have also suggested that the shape of the intergranular liquid is an important factor in determining the susceptibility of a material to hot shortness. They showed that on a comparative basis materials having the lowest dihedral angles at a given temperature gave the greatest severity of cracking. They stated that liquid in the form of globules should be less harmful than liquid in the form of extensive films as more intergranular cohesion should be possible. Rogerson and Borlland 2 also showed that the susceptibility of an A1-Sn alloy to hot cracking can be reduced by small additions of cad- mium. It was found that the cadmium gave an increase in the dihedral angle at all temperatures. Ikeuye and smith3 investigated changes in the dihedral angle and relative interfacial energy with temperature for a number of ternary alloys formed when small additions of bismuth, cadmium, copper, lead, and zinc were made to an A1-Sn alloy. They found that in most instances changes in the dihedral angle were caused by compositional changes in the liquid phase; as the composition of the liquid approached that of the solid the dihedral angle decreased. They noted that the addition of a third element which was soluble in both the liquid and solid phases at a given temperature may decrease the dihedral angle (e.g., the addition of copper or zinc) but otherwise the ternary alloys formed exhibited dihedral angles between those of the A1-Sn binary alloy and those of the binary alloy of aluminum with the added element. Dwarakadasa and Krishnan4 investigated the changes in dihedral angle and relative interfacial energy with temperature when small additions of magnesium, iron, silicon, manganese, sulfur, cobalt, and silver were made to a copper alloy containing 3 pct Bi. They found that in all cases the added elements gave an increase in the dihedral angle and relative interfacial energy when compared with the values obtained for the simple binary alloy at the same temperature. It was noted that an increase in temperature gave a decrease in dihedral angle and relative interfacial energy in each of the ternary alloys studied. Similar results have been obtained by Ramachandran and Krishnan5 for the addition of small quantities of lead. This paper describes the application of dihedral angle measurement to the determination of the shapes of liquid phases at various temperatures above the solidus when small additions of copper, indium, magnesium, lithium, antimony, and silicon are made to an aluminum alloy containing nominally 3 pct Sn. An attempt is made to correlate the measurements with the relative solubility of the added elements in tin and aluminum. The work was undertaken to provide more data concerning the effects of temperature and composition on the shape of liquid films above the solidus. EXPERIMENTAL PROCEDURE In the present work ternary aluminum alloys containing nominally 3 pct Sn and small additions of high-purity copper, indium, lithium, magnesium, antimony, and silicon were made. The alloys were melted in a graphite crucible under an inert atmosphere of argon and cast into ingots 6 in. long by 0.5 in. diam. The ingots were then cut into rods 1.5 in. long, given a 50 pct cold reduction, and machined into test pieces 0.5 in. long by 0.5 in, diam for heat treatment. The alloy samples were annealed at the various test temperatures between the liquidus and solidus for approxi-

Jan 1, 1967

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' 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'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's minimum work problem imply the solutions of Bishop and Hill'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 Benny J. Nelson

AS a part of the fundamental research program of Aluminum Research Laboratories, some data were obtained on the ternary system Mg-Al-Mn. As very little information on the magnesium corner of this diagram has heretofore been published, it seems desirable to make available the values found for the liquidus and solidus surfaces of this system. Procedure The settling procedure was used for the determination of the liquidus compositions. Metallo-graphic examination of quenched samples, and stress-rupture upon incipient melting, were used for the solidus determinations. The settling procedure has been described in a previous paper.' Briefly, this method involved saturating the alloy with manganese at a temperature substantially above that at which the sohbility was to be determined, then cooling the melt to the latter temperature, and holding it at that temperature for a substantial period of time. Samples for analysis .were carefully ladled from the upper portion of the melt at hourly intervals during the holding period. After the ladling of each sample, the melt was stirred to redistribute some of the manganese that had already settled, because it appeared that when the latter particles of manganese again settled, they aided in carrying down more of the manganese and thus hastened the attainment of equilibrium. The melts were prepared and held in a No. 8 Tercod crucible holding approximately 4 lb of metal. The manganese was added either in the form of a prealloyed ingot (Dow M) containing about 1.5 pct Mn or by the use of a flux (Dow 250) containing manganese chloride. In calculating the flux additions, it was assumed that the manganese introduced would be equal to 22 pct of the total weight of the flux. Temperatures were measured with an iron-constantan thermocouple enclosed in a seamless steel tube, the lower end of which was welded shut. This protection tube also served as a stirring rod. The samples ladled from the upper portions of the melts at the various intervals were analyzed for aluminum, manganese, and iron. When making the alloys which were to be used for the determination of the solidus, 2½ in. diam tilt mold ingots were cast, scalped to 2.0 in. in diam, and extruded into ? in. diam wire. The principal impurities in the melts for this investigation were iron and silicon; their total not exceeding 0.03 pct. Portions of the wire, approximately 2 in. in length, were enclosed in stainless steel capsules for protection from the atmosphere. Bundles of these capsules, with a dummy capsule containing an iron-constantan thermocouple, were heated inside a large steel block (acting as a heat reservoir) in a closed circulating-air type electric furnace. At ap- propriate times, the capsules were removed and quenched in water. The wires were examined metallographically to determine the temperature of initial melting. Short times at temperature were used at the beginning for wire specimens of all alloys to obtain quickly the approximate temperatures at which melting could be first observed. When approximate solidus temperatures had thus been determined, equilibrium heating was attempted. This equilibrium heating consisted of an 8 or 16 hr period at a temperature, about 50 °F below the lowest temperature at which melting occurred when short heating cycles were used, followed by further heating for 1 hr periods at consecutive 10" higher temperatures. The theory for the method of stress-rupture at incipient melting has been well covereda and its limitations are recognized. Thus, if the interfacial tensions are such that the first minute quantity of liquid is "bunched up" at the grain boundary junctions instead of spreading out along the grain boundaries,³ temperatures higher than the solidus are required before melting will be manifested by rupture of the specimen. This point will be elaborated later. Specimens of the wires with a reduced section (approximately 1/16 in. diam) were suspended vertically in a tubular furnace. The setup used is shown in Fig. 1. The clamp holding the specimen was made from alumel thermocouple wire and the thermocouple was thus completed across the specimen by attaching a chrome1 wire to its lower end. Temperatures were read from a Speedomax recorder used in conjunction with a calibrated thermocouple. The small weight attached to the specimen and a vibrator attached to the furnace tube, to aid in distributing the molten constituent along the grain boundaries, were used to bring about rupture at a temperature closely approximating the solidus. The specimens were heated at a rate of about 5°C per min. The rupture of the specimens was indicated both by sound and by the action of the recorder. An argon atmosphere containing a small amount of SO² was used for protection of the specimen. The assembly was taken out of the furnace immediately following rupture and the specimen removed. Some of the broken specimens were examined metallographically and will be referred to later. Results and Discussion Fig. 2 shows a set of typical time-composition curves for liquid samples of the Mg-Al-Mn alloys used for the settling tests. The data as presented

Jan 1, 1952

By D. H. Thompson, A. W. Tracy

Season-cracking is a type of failure of brass that results from the simultaneous effect of stress and certain corrodants. The object of this paper is to present data that will aid in a more complete understanding of the mechanism of season-cracking and related phenomena. Results presented show that certain high copper alloys are susceptible to season-cracking or stress-corrosion cracking, and possible explanations are discussed. Starting at least as far back as 1906, many papers have been devoted to this subject but the symposium1 held in Philadelphia in 1944 is the richest source of information. In order to study season-cracking, several of the many variables were held constant so as to learn the effects of others. Season-cracking is generally understood to refer to the corrosion cracking of brass having internal stresses;²,³ it is a special case of the general stress-corrosion cracking. Inasmuch as applied stresses are more readily produced and controlled, they were used exclusively in this research and the resulting phenomenon must he called stress-corrosion cracking.²,³ Only constant tensile stresses were used. The agents believed to be most frequently responsible for season-cracking are ammonia. amines and compounds containing then]. Both moisture and oxygen also appear to he necessary. Therefore, an atmosphere containing ammonia, water-vapor and air was selected for these tests. Briefly, the work consisted of exposing sheet metal specimens, having a reduced section ¼ by 0.050 in., of copper-base alloys to the effect of static tensile stresses between 5,000 and 20,000 psi and simultaneous contact with a. continuously renewed atmosphere containing 80 pct air, 16 pct ammonia and 4 pct water vapor at 35°C. The gas mixture and the speci- mens were maintained above the dew-point. The time-to-failure in minutes was the primary measure of results. In order to limit the experiment to finite time, it was considered that a specimen which had neither failed nor undergone microscopically detectable cracking in 40,000 min. (4 weeks) while under a stress of 10,000 psi or more could be considered immune to cracking. This is merely a convenient limit and is not to be considered proof of immunity. Supplementary tests in the absence of stress using weight loss or microscopical appearance as measures of attack were made. Apparatus The apparatus used in this research is shown in Fig 1. To facilitate the description it may conveniently be divided into six parts: stress-producing units, test chamber, gas train, electrical controls, timers and gas analysis device. A stress-producing unit is shown in an exploded view at the left in Fig 2. At the right is an assembled unit with a specimen in place in the lower portion; it is this part that remains in the ammonia atmosphere during a test. The upper part contains a spring, a central threaded rod, a large nut and necessary washers, pins, and so forth. Stress is produced in the specimen by screwing down the top nut against the spring, thus putting a tensile load on the central rod and so on the specimen. The wrench that turns the nut by extending through the upper cap, is seen at the upper right of the figure. The magnitude of the load is gauged by measuring from the pin that extends through the side of the tube, to a fixed point on the large flange. Measurement is made with a vernier beam caliper, shown at the right of the figure. The necessary spring compression to give a desired stress is calculated from the calibration curve of the spring and the dimensions of the specimen. The test chamber, center Fig 1, consists of a thermally insulated steel box 32 in. long by 10 in. high by 7 in. wide. A horizontal baffle reaching nearly to each end divides the chamber equally. Below this baffle are inlets for air and ammonia, a heating coil and a fan. Thus the gases are warmed and mixed in the lower level and flow past the specimens in the upper level. A thermo-regulator and thermometer project into the upper space. The top is pierced by 12 ports flanked by 3/8 in. threaded studs. A test starts when a port is opened and a unit containing a stressed specimen is thrust through it and bolted down against a neoprene gasket. The test chamber is held at 35°C. The gas train, right rear Fig 1, carries ammonia and air continuously to the test chamber. Tank ammonia passes through two reducing valves, a needle valve, a flow meter and into the test chamber. The air from either the plant compressor or a small laboratory compressor passes through wool towers and flow controls to the flow-meter. It then bubbles through water at 34°C and through a heated line to the test chamber. Electrical controls, left rear, Fig 1, provide rectifiers and mercury relays for the test-chamber and humidifier-heating-control circuits and outlets for

Jan 1, 1950

By F. W. Glaser

Metal-carbon-boron powder mixtures were hot pressed and the resulting specimens were studied by X-ray diffraction. It was found that regardless of the starting combination of the metal, carbon, or boron powders, a metal boride phase was always the major component in these samples. In the absence of carbon the boride phase formed on hot pressing depended only on the amount of boron present. Two new phases of the system Ti-B were found. They are Ti2B and Ti2B5. The existence of a controversial face-centered cubic phase of formula TiB was confirmed. Electrical resistivities were measured for various boride phases. It was found that the diborides are generally better conductors than the monoborides of the same metal. THE carbides and borides of the transition elements have very high melting points, in the range 2500° to 4000°C, and are therefore of interest as high temperature materials. The literature on the stability or chemical reactivity of these carbides and borides is very scarce. Various investigators'-" have demonstrated a relative instability of certain carbide phases in the presence of boron or boron-containing substances. In a recent publication, Glaserl demonstrated the stability of zirconium-boride (ZrB,) in the presence of carbon at temperatures in excess of approximately 2900°C, while during a preliminary investigation of boride phases, Steinitz' concluded that the diborides are stable in the presence of carbon while the monoborides of the fourth and fifth group are not, forming diborides plus carbides instead. Nelson, Willmore, and Womeldorph" have elaborated on the reaction B,C + 2TiC = 2TiB, + 3C, which was known to occur because of a relative instability of B,C and the great tendency towards TiB, formation at relatively low temperatures (approximately 1200°C). A similar study, involving as starting materials TiO, and B,C and resulting in TiB,, was recently described by Honak4, who observed the beginning of an exothermic reaction of a Ti0,-B,C powder mixture, which, when preheated in a hydrogen atmosphere to approximately 950°C, was carried to about 1600 °C by the heat of reaction. To shed more light on reactions of this type (Metal-C-B), the final product apparently always resulting in a boride phase at the expense of a carbide phase," a systematic investigation was started * Boride phases of various metals, as reported to date, are listed in Table I. and the following is an account of some of the results that were obtained. Materials, Preparation of Samples, Testing Methods The raw materials employed for this work consisted of various carbide, boride, and metal powders. as well as of boron and graphite powders. In cases where commercial grades of carbides were considered unsuitable because of low purity or excessive amounts of graphitic carbon, such carbide powders were prepared by this laboratory. The procedure for the preparation of carbide powders (zirconium carbide, titanium carbide, tantalum carbide, and niobium carbide) consisted of mixing graphite and the respective metal hydride powders in stoichio-metric proportions and subsequent heating of such mixtures in a hydrogen atmosphere in carbon crucibles. The heating was by high frequency to temperatures ranging between 1700" and 2100°C. The resulting carbide was then comminuted and screened to the desired particle size. ZrB, and TiB, powders were produced by the electrolysis of fused salt baths, according to the method described by Andriex.. The borides of niobium, vanadium, tantalum, molybdenum, chro-ium, and iron were obtained by mixing the respective metal and boron powders in the desired proportions. Such metal-boron mixtures were heated in a high frequency furnace to form boride powders. For each metal-carbon-boron group (Tables I1 through XI) a metal, its hydride, carbide or boride were mixed with carbon, boron or boron carbide powders. The additions of carbon, boron or boron carbide powders to any of these metals or metal compounds were calculated to satisfy a particular carbide or boride phase that according to the literature (Table I) had definitely been established by X-ray diffraction work. Samples of powder mixtures were hot pressed in graphite molds that were heated by direct conduction. The specimen dimensions were approximately 2.5X1X1 cm. Hot pressing temperatures were measured optically and maintained for approximately 30 sec under a constant pressure of about 1.3 ton per sq in. Wherever possible, an attempt to obtain maximum specimen density was made by temperature variation. Electrical resistivity testing was done by measuring potentiometrically the voltage drop over a length of 1.5 cm for a current of 10 amp, at room temperature. To obtain electrical resistivities for specific carbide or boride phases, values were plotted as a function of the respective sample densities

Jan 1, 1953

By J. W. Spretnak, D. A. Chatfield, G. W. Powell, J. R. Eifert

In nzost cases, the driving force for a lattice transformation is produced by supercooling below the equilibriunz transformation temperature. The interfnce reaction in isothermally annealed, multiphase diffusion couples may involve a luttice transformation which also requires a driving force. Direct experinzental evidence has been obtained for the existence of the driring force in the form of a supersaturated phase at the aocc)-0@cc) interface in Cu:Cu-12.5 ult pct A1 couples; the super saturation is equivalent to an excess free energy of approximately 3 cal per mol at 905. A tentatiue interpretation of the dynanzic situation a1 the interface based on the free energy-composition diagram is proposed. THE presently accepted theory of diffusion in multiphase couples1 states that there will be a phase layer in the diffusion zone for every region which has three degrees of freedom and which is crossed by the diffusion path in the equilibrium phase diagram. For binary systems, this restriction excludes all but single-phase fields and, for ternary systems, only one- and two-phase fields are included. In addition, Rhines"~ as well as other investigators3 6 have reported that the compositions of the various phases adjacent to the interfaces are, for all practical purposes, the compositions given by the intersections of the diffusion path with the solubility limits of the single-phase fields of the equilibrium phase diagram. Some studies of the rate of thickening of these intermediate diffusion layers indicate that the thickness of the layer changes para-bolically with time, or: where x is the position of the interface relative to an origin xo, t is the diffusion time, and k is a temperature-dependent factor. crank7 shows mathematically that, if the compositions at an interface are independent of time and the motion of the interface is controlled by the diffusion of the elements to and from the interface, then the segments of the concentration penetration curve for a semi-infinite step-function couple will be described by an equation of the form: hence, Eq. [l] follows from Eq. (21 if the interface compositions are fixed and if the motion of the interface is diffusion-controlled. Although the concept of local equilibrium being attained at interfaces has assumed a prominent role in the theory of diffusion in multiphase couples, experimental evidence and theoretical discussions which challenge the general validity of this concept have been reported in the literature. arkeen' has stated that strict obedience to the conditions set by the equilibrium phase diagram cannot be expected in any system in which diffusion is occurring because diffusion takes place only in the presence of an activity gradient. Darken also noted that it is usually assumed that equilibrium is attained locally at the interface although the system as a whole is not at equilibrium, the implication being that the transformation at the interface is rapid in comparison with the rate of supply of the elements by diffusion. ISirkaldy3 indicates agreement with Darken in that he believes the concept of local equilibrium is at best an approximation because the motion of the phase boundary requires that there be a free-energy difference and, hence, a departure from the equilibrium composition at the interface. Seebold and Birks9 have stated that diffusion couples cannot be in true equilibrium, but the results obtained are often in good agreement with the phase diagram. The initial deviation from equilibrium in a diffusion couple will be quite large because alloys of significantly different compositions are usually joined together. Kirkaldy feels that the transition time for the attainment of constant interface compositions (essentially the equilibrium values) will be small, although in some cases finite. Castleman and sieglelo observed such transition times in multiphase A1-Ni couples, but at low annealing temperatures these times were quite long. Similarly, ~asing" found departures, which persisted for more than 20 hr, at phase interfaces in Au-Ni and Fe-Mo diffusion couples. Braun and Powell's12 measurements of the solubility limits of the intermediate phases in the Au-In system as determined by microprobe analysis of diffusion couples do not agree with the limits reported by Hiscocks and Hume-Rothery13 who used equilibrated samples. Finally, Borovskii and ~archukova'~ have stated that the determination of the solubility limits of phase diagrams using high-resolution micro-analyzer measurements at the interfaces of multiphase couples is not an accurate technique because of deviations from the equilibrium compositions at a moving interface; diffusion couples may be used to map out the phase boundaries in the equilibrium diagram, but the final determination of the solubility iimits should be made with equilibrated samples. The purpose of this work was to investigate the conditions prevailing at an interface in a multiphase diffusion couple and to compare the interface compositions with those associated with true thermodynamic equilibrium between the two phases. Microanalyzer techniques were used to measure interface compositions in two-phase Cu-A1 diffusion couples annealed at 80@, 905", and 1000°C for various times.

Jan 1, 1969

By AIME AIME

FOUR separate groups of conveyors are installed in the Morenci Reduction Works as follows: (1) Ore-handling conveyors from the primary crushing plant to the coarse ore bin, from the coarse-ore bin to the secondary crushing plant, and from the secondary crushing plant to the ore bin in the concentrator plant. (2) Conveyors in the mill section of the concentrator plant. (3) Conveyors handling concentrate from the filter plant to the bedding plant, and from this plant to the smelter. (4) Conveyors handling flux and custom ore in the smelter crushing plant and to the bin at the bedding plant.

Jan 1, 1942

By R. D. Coleman, A. E. McIlhinney, C. E. Capes

tentially valuable. These losses will probably increase with the expansion of production and will require the development of effective disposal and utilization processes under pressure of the lack of adequate disposal areas, the enforcement of air and stream pollution laws, and the economic need to obtain the maximum yield of salable product.1 Fine Coal Treatment Processes Most coal cleaning methods depend upon the density difference between coal and its impurities to effect separation. These gravity concentration methods, however, are not practical for particles finer than about 100 mesh and cleaning methods dependent upon the differences in

Jan 1, 1971

By J. E. Kemp

1. Situation.—From Monterey in the State of Nuevo Leon, the Sierra Madre mountains stretch away to the southeast and present a steep front to the northeast. The Monterey and Mexican Gulf railway. which connects Monterey with Tampico. follows their general line with its road-bed a few miles out from the foothills. At a distance of 100 miles from Monterey it passes through the town of Linares. and from Linares one can see far away to the southeast the peaks of another group of mountains rising from the general plateau and forming a more eastern

Jan 1, 1906

By M. A. Bryant, J. C. Goodwin, T. B. Faddies, L. D. Kornze

The Mercur Gold Mine is located 56 km (35 air miles) southwest of Salt Lake City in north central Utah; In July 1981 Getty Mining Company made the decision to put Mercur into production. The first gold bar was poured in April 1983. This paper provides details on: 1) the history of the camp, 2) past production, 3) geology of the deposit, 4) the exploration and development program, 5) ore reserve estimates, 6) detailed geologic pit mapping, 7) production blasthole sampling techniques and 8) the use of geostatistics (kriging) in handling assays and gold extractions to produce the required mill feed.

Jan 1, 1985

By John Peperakis

Coal mine bumps are normally associated with pillar mining under moderate or deep cover. Severe bumps at Sunnyside, however, have not been confined to pillar lines. Many have occurred in virgin development and in localities a long way from active pillar workings. As early as 1918 bumps in virgin territory were attributed to the faulted structure in the Sunnyside area.1 Sunnyside is an old property, mined for more than 60 years. Both man-made and natural conditions contribute greatly to bump occurrences, and loss of life and great destruction of workings have resulted from some unusual bumps in recent years.

Jan 9, 1958

By John V. Beall

Many Americans will judge the energy crisis by the picture shrink on their TV screen. And they are right to make this assessment considering the large areas of the country with marginal generating capacity, (See Fig, 1). The Federal Power Commission (FPC) recommends 20-25% reserve generating capacity above peak summer loads and 15-20% as minimal. The New York metropolitan area is the most concentrated power service area in the United States, and a spot check with Consolidated Edison, serving this area, revealed that on Friday, August 18, the company was operating at 5% reserve.

Jan 10, 1972

By Joseph A. Gill, Ernest A. Curth

The Government and Leeco concluded a cost-sharing agreement in 1976 to demonstrate longwall mining of a thin coalbed, 1 m or less, in a mine near Hyden, Ky. A premining investigation laid the groundwork for mine design and equipment specifications. Four- legged shields, a face conveyor, a stage loader and an in-web shearer were selected to operate on a 183 m face. Lengwall mining began in 1979 and initially was slowed by low mining height and equipment problems. A rock mechanics program provides early warning capability and criteria for future mine design. Monitoring of surface effects is included.

Jan 1, 1981

By Waldemar Lindgren

I. Character of the Deposits, 226: Principal Features, 226 (Form, 227; Posi tion, 227 ; Constituent Minerals, 227 ; Exceptions, 228) ; Literature, 228 ; Geo graphic Distribution, 230 ; (California, 230 ; Idaho, 231 ; Arizona, 233 ; British Columbia, 233; Northwest Territory, 234 ; Mexico, 234; Other Countries, 235). 11. Origin oF the Deposits, 236 : Contact-Metamorphism, 236; Caw of Contact Metamorphism, 237 ; Similar Deposits of Different Origin, 240; Genetic Classifi cation, 240 ; Relation of Pegmatite- Veins to Ore-Deposits, 242. I.—Character of the Deposits. 1. Principal Features. In many schemes of classification and description the term contact-deposit has been somewhat loosely applied to all accumu-

Jan 1, 1902

By Roderick K. Davey

Introduction in any business, it is essential that we select those alternatives which are not only technically feasible, but will be the most profitable to the business m terms of corporate objectives Some of the studies and activities requiring support of financial analysis to select the alternatives which most closely satisfy the management objectives and technical considerations are as follows 1 ) Cutoff grade determination. 2) Ore reserve estimation. 3) Production forecasts (long- and short-term) for an operating mine, development of a new mine, or expansion of an existing mine. 4) Evaluation of haulage alternatives. 5) Evaluation of equipment.

Jan 1, 1979