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By T. E. Leontis

ONLY a limited amount of information has been published on the effect of thorium as an alloying ingredient in magnesium. McDonald13'2 showed that the addition of thorium in amounts up to 3 pct increases significantly both the ductility and the strength of rolled magnesium sheet. A recent publication by Sauerwald" indicates that thorium contributes strength and creep resistance at elevated temperatures to magnesium in both the cast and wrought states. The observations of Sauerwald are confirmed in this paper, which presents the results of a systematic study of the effects of compositional variation on the tensile properties, creep resistance, conductivity, density, and metallography of Mg-Th alloys containing up to 50 pct Th both in the sand-cast and in the extruded states. The effect of the addition of cerium to Mg-Th alloys is also reported. Experimental Methods The alloys studied in this investigation were pre.pared in small laboratory melts according to the melting practice described by Nelson4 as the crucible method. Electrolytic magnesium was used as the starting material to which the thorium* was introduced in metallic form. It was observed that the behavior of thorium in molten magnesium with respect to reaction with protective fluxes is similar to that of rare-earth metals. In order to obtain the highest possible alloying efficiency, it is necessary to use non-MgC1, fluxes and to apply all the precautions described by Marande6 for melting, alloying, and casting magnesium-rare-earth alloys. .Under these conditions it is possible to obtain an alloying efficiency in the range of 85 to 95 pct. The Mg-Th-Ce alloys were made with cerium of the highest purity available, not with the commercial product "misch-metal" which contains approximately 50 pct Ce. The total rare-earth content of this material was 97.1 pct, of which 0.3 pct was rare-earth metals other than cerium; the major impurities comprising the balance were iron and magnesium. The thorium and cerium contents of each alloy were determined chemically. Test bars 6% in. long with a 2% in. long reduced section of % in. diam were cast in sand molds using a four-baf pattern. In most cases, a 3 in. diam extrusion billet 10 in. long was cast in a steel mold from the same melt used for making the sand-cast test bars. For the higher thorium alloys, it was necessary to remelt the foundry scrap from the test bars in order to make the extrusion billets. The billets were scalped to a diameter of 2 15/16 in. and the ends faced to a length of 9% in. as limited by the size of the extrusion container. The alloys were extruded into % in. diam rod on a 500-ton direct-extrusion press. The details of the extrusion process are as follows: Billet preheat 925°F (2 to 16 hr) Container temperature 900 °F Die temperature 900°F Extrusion speed 10 ft per min Reduction ratio 36:1 Percent reduction 97.3 Alloys containing up to 10.2 pct Th were preheated at 925°F for 2 hr; all alloys with higher thorium contents were preheated for 16 hr. In order to establish the effect of extrusion temperature, billets of

Jan 1, 1953

By E. S. Lenker, H. J. Van Hook

A complete swies of solid solutions has been found between the compounds InAs and GaAs Below the solidus. The melting relations determined by differential thermal and static quenching technzques, indicate that the liquidus and solidus are of the simple ascendant type. No evidence of unmixing of the homogeneous solid solutions was observed at sub-solidus temperatures. A quenching method for locnting the solidus, using X-ray diffraction techniques, is described in some detail. THE semi-conducting properties of compounds formed by various combinations of the less familiar intermetallic elements have created an increasing interest in the phase relations in systems involving these elements. The complete phase diagram of such a system, containing a compound of special interest, will often provide information as to the most favorable conditions for preparing large crystals from a melt, as well as specifying the temperature stability of the crystalline phase or phases produced. In view of the current importance of gallium arsenide in semiconductor research and of the structural similarities of indium arsenide, it was thought that the complete phase relations of the system InAs-GaAs should be investigated. Previous work on the system Ga-As by Koster and homa' and on In-As by Liu and peretti2 has shown that GaAs and InAs are the only compounds formed, having melting points of 1238° and 942°C, respectively. In a survey of various systems of elements from groups IIIb and Vb, spengler3 also re- Mines Ltd., for his continuing encouragement and for permission to publish the results of this work. ports complete miscibility of gallium, indium, and arsenic in the liquid state. In a partial investigation of the InAs-GaAs system, Woolley and smith4 found extensive solid solution throughout the alloy range. Their subsolidus work, however, was inconclusive at temperatures below 900" and they did not determine the liquidus relationships of the system. PRESENT INVESTIGATION The starting materials used were high-purity gallium, indium, and arsenic. The method of preparation of the compounds follows that devised by M. Shafer and is described in detail in a paper by Shafer and eiser.' The end-member compounds, GaAs and InAs, were first prepared by reaction of the elements in the desired proportions in evacuated silica glass vials. The vials were rotated in a furnace as the temperature was slowly raised to insure rapid and complete reaction at low temperatures. Thereafter the starting materials, GaAs and InAs, were melted by heating the sealed vials to 1300" and 1000°C, respectively; the vials in this case were filled as completely as possible to keep the vapor space small and thereby minimize the loss of arsenic to the vapor phase. Ten binary mixtures of these compounds were then prepared by reaction of the powdered material in the solid state just below solidus temperatures. At 900C preparations containing 3, 5, 8, 10, 25, 35, 50, and 75 mol pct GaAs were found to be single homogeneous phases, indicating a complete series of solid solutions between GaAs and InAs. Moreover, it was discovered that the homogeneity of any crystalline binary preparation could be very accurately checked by X-ray diffraction because of the large differences in unit cell dimensions of the end membe5s. The cubic lattice constant ofor GaAs is a = 5.652A and that of InAs is a = 6.061A

Jan 1, 1963

By N. K. Chen, R. Maddin

Single crystals of molybdenum were extended at temperatures from 1300° to 2500°C. It was found that with increasing temperatures, the yield becomes more pronounced and the number of slip bands for equal amounts of elongation decreases. Slip at high temperatures fragments the structure. OTHER than the investigations on sodium and potassium by Andrade and Tsien,&apos; the researches of Steijn and Brick&apos; on a iron single crystals at low temperatures are about the only studies of the influence of temperature on glide of body-centered cubic single crystals. The effect of test temperature on glide has been rather widely investigated with hexagonal crystals" and less widely with face-centered cubic crystals. ~~ a result of these studies it can be said that, in general, the onset of plastic flow as measured by the initial rate of strain hardening becomes more abrupt with increasing temperature, and the value of the yield decreases with increasing temperature. Strain hardening, however, is markedly affected by changes in temperature except at very low and very high temperatures where the strain hardening rate becames constant. In the present investigation it is shown that temperature affects the glide of molybdenum single crystals in much the same manner as crystals of other classes, it., for comparable strains the number of slip bands decreases with increasing temperature; shear along the slip bands increases with increasing temperature; the yield becomes more pronounced with increasing temperature of test; and the strain hardening approaches a constant at very high temperatures. In addition, it is shown that, in agreement with the work of Tsien and Chow, Qlip occurs on (110) planes in <Ill> directions. It is further shown that slip at high temperatures fragments the structure into either irregular sized cells or bent atomic planes which are roughly aligned in crystallographic directions. Experimental Procedure Single crystals 3 mm in diameter by about 25 mm long were prepared using the technique previously described.&apos; The furnace in which the crystals were grown served as the extension apparatus for the tension tests. It consisted of a 4 in. water-cooled brass tube 20 in. long which was continuously evacuated at the bottom. Two water-cooled copper electrodes held the specimen by means of spherical collets secured in place in the electrodes by set screws. These electrodes served also to transmit power and stress to the specimen. The lower electrode was clamped to a stand, while the upper electrode was fastened to one side of a lever arm flexibly supported at the top through a slightly offset pinion. A metal bellows operating elastically was attached to the upper electrode to affect a vacuum seal and allow freedom of motion. The level of the arm was adjusted by rotating a graduated nut. Rotation of the electrode was prevented by a key fitted into a groove. After the specimen was mounted and the vacuum secured, the lever arm was adjusted so that the bellows was at its relaxed position. This insured that the total weight of the specimen, the upper electrode, and the downpull of the vacuum were balanced by the horizontal beam. Since the specimen was heated by its own resistance, expansion of the specimen proceeded freely by this arrangement. During the time of heating the specimen, the beam was maintained in a horizontal position by turning the nut at the top. By graduating the lever arm and using a known dead weight on the lever arm to supply a tensile stress, the graduated nut could be read to 0.0001 in. extension. Since

Jan 1, 1955

By A. Long, A. Silverman, J. L. Kulp

Garth Crosby has written an excellent geologic description of the deposits surrounding the Gem stocks in the Coeur d&apos;Alene district. The ore deposits in the area of the Gem stocks may hold the key to the age and mineralization history of the entire Coeur d&apos;Alene district. A recent isotopic study10 of the Coeur d&apos;Alene district in this laboratory illustrates that a classical geologic interpretation of these deposits, with its implications for the whole district, may lead to erroneous conclusions. For this reason it seems pertinent to submit a summary of these results and an interpretation of the mineralizing history of the Coeur d&apos;Alene districts. Pitchblende from the Sunshine mine has been dated as 1100-1200 million years (m.y.) by Kerr and Kulp,11 and Eckelmann and Kulp.12 This pitchblende is known to predate the major sulphide introduction in the Sunshine mine, but it clearly follows the metamorphism and folding of the Belt Series. Recently, Goldich (personal communication) dated sericite from the Belt rocks as 1200 m.y. by the potassium-argon method. This date establishes a minimum Belt age if the sericite is of metamorphic origin and a maximum age if detrital. The Belt Series, therefore, is not latest Precambrian. Lead isotope ratios of galenas have been measured and model ages calculated by Bate, et all3 for the Sunshine mine, Farquhar and Cummingl4 or the Bunker Hill and Sullivan mine, and Cannonl6,18 for a few other deposits in the district. Galenas from similar deposits in Southern British Columbia have been measured by Bate, et al,23 Farquhar and Gumming,11 and Wanless and Leech." The new work in this laboratory includes leads from ten widely scattered mines north and south of the Osburn fault, and through a vertical distance of over 5000 ft (Star mine). Included in this group are the Hercules, Sunset, and Mountain Goat mines, which are adjacent to the Gem stocks. In addition, galenas from stringers which cut the Gem stocks in the Success and Sunrise mines and the Hercules hanging wall dike in the lower western portion of the Hercules mine, were included in the study. All of the above leads, except one, give model ages of 1300-1400 m.y. for the time of segregation from the parent material. The concordance of the common lead and U-Pb ages, the great horizontal and vertical uniformity of the lead ratios, the sulphur ratios of two Sunshine mine galenas and three galenas from the Edith, Page, and Hercules mines indicating average crustal sulphur, and the U23/Pb204 ratio inferred for the original lead environment, indicate that the entire mineralization of the Coeur d&apos;Alene-British Columbia base metal belt was derived from a deep source and emplaced in the Precambrian. One sample of galena from sulphide stringers cutting the North Gem stock at the Sunrise Prospect mine gave a modern (i.e., Tertiary) lead ratio. This mine is located at the northern tip of the stock. The presence of modern lead suggests mobilization of some rock lead during the intrusion of the Gem stocks and their outliers. Larsen et al.l8 have dated the Gem stocks as Tertiary by the lead alpha method. If Coeur d&apos;Alene mineralization was genetically related to Tertiary magma formation and intrusion

Jan 1, 1961

By M. A. Dayananda, R. E. Grace, P. F. Kirsch

Ternary diffusion experiments were carried out at 750°C with vapor-solid diffusion couples in single-phase copper-rich Cu-Zn-Sn alloys. The Philibert-Guy method was used to calculate intrinsic diffusion coefficients at compositions corresponding to the plane of inert markers imbedded in the diffusion couples. Inter diffusion coefficients were determined at common composition points of intersecting diffusion paths. Intevdiffusion coefficients were also obtained at compositions corresponding to maxima in the tin concentration pvofiles Relations between the interdiffusion coefficients and the expansion of vapor-solid diffusion couples are described in detail. Such relations permit the calculation of constant interdiffusion coefficients in binary couples from expansion data directly. In ternary couples expansion data provide an additional constraint on the interdiffusion coefficzents. ThE phenomenological analysis of diffusion in ternary solid solutions has been developed extensively, and various approaches taken in the determination of diffusion coefficients have been reviewed recently by Guy et al.&apos; Finite,&apos; semi-infinite,3 and infinite4 diffusion couples have been used in studies of ternary diffusion, but most of the work has been done with infinite diffusion couples. Semi-infinite diffusion couples3 (vapor-solid couples) have been used to determine both intrinsic and interdiffusion coefficients in the Cu-Zn-Mn system, in which two diffusing species, zinc and manganese, were supplied from the vapor phase. If only one component has a sufficiently high vapor pressure to be supplied from a vapor source, vapor-solid diffusion couples may still be used. In this case the boundary conditions at the gas/solid interface may be governed by partial equilibria rather than by virtually complete equilibrium between the phases. In the present work diffusion measurements were carried out at 750°C with vapor-solid couples of Cu-Zn-Sn alloys. Only zinc was transported between the vapor source and the diffusion disks, because the vapor pressures of both copper and tin are at least 108 lower than that of zinc. Both intrinsic and interdiffusion measurements were made at several compositions. A secondary objective was to relate expansion of the diffusion couples with the interdiffusion process. Such measurements for binary couples yield average values of the interdiffusion coefficients over composition increments. In ternary diffusion couples ex- pansion data provide an additional constraint on the interdiffusion coefficients. COMPOSITION-DEPENDENT INTRINSIC AND INTERDIFFUSION COEFFICIENTS As shown by Philibert and GUy5 the determination of intrinsic diffusion coefficients in a ternary system requires two independent diffusion couples containing marker planes with identical composition. In the case of vapor-solid couples such a requirement torresponds to two couples set up with the same vapor source exposed to two diffusion disks of different composition. Inert markers placed initially on the disk surfaces become imbedded during diffusion. If the pair of couples exhibits appreciable marker burial with marker planes of virtually the same composition, the intrinsic diffusion coefficient may be evaluated at the composition of the marker planes. Fig. 1 is a schematic diagram of the concentration of of a Cu-Zn-Sn ternary vapor-solid couple after diffusion of zinc from a vapor source into a binary Cu-Sn alloy. The areas, Ai correspond to the cumulative intrinsic fluxes of the three diffusing species across the marker plane:5 where Ji is the intrinsic flux of component i, t is the diffusion time, and D3i are the intrinsic diffusion coefficients. For the determination of interdiffusion coefficients a pair of diffusion couples with intersecting diffusion paths is needed. At the composition point of intersection (C1, C2) the coefficients are evaluated from the equation:3

Jan 1, 1969

By W. A. Backofen, B. B. Hundy

THE pole figure interpretation in a recent paper&apos; on the torsion texture of copper was questioned in discussion,2 nd a simpler alternative interpretation was proposed. In the hope of reaching a positive decision in favor of one or the other, further studies were undertaken with 70-30 brass and Armco iron. This additional work has not answered all the questions about torsion textures, but the new pole figures do offer support for the original interpretation and show that the texture is more complicated than the alternative suggests. From the previous paper,&apos; the appropriate method of describing the texture in a twisted bar is known to be a pole figure plotted on a plane tangent to the surface of the bar. The axes of the pole figure are chosen to coincide with directions in the tangent plane which are parallel and at right angles to the bar axis (the longitudinal direction, L.D., and the transverse direction, T.D.), for these directions define symmetry axes of the texture. Therefore any ideal orientation that might be selected to represent the texture gives the crystallographic plane parallel to the tangent plane and the crystallographic direction parallel to the axis of the torsion specimen. A unique texture was assumed in the original interpretation, and the four ideal orientations, (112) [111], (111) [112], (110) [001], and (112) [131], were used in its description. Of the four orientations, the first three provide possible slip directions along the direction labeled T.D. in the pole figure, which is one of maximum shear stress in a specimen being twisted. The alternative, however, simply considered the texture to be made up of two components, one a [Ill] alignment along the specimen axis with a random orientation about the axis as in the wire texture, and the other a superimposed orientation (110) [0011. Experimental evidence for this simpler interpretation was derived from two observations: 1—twisting did not alter the orientation of a single-crystal torsion specimen of a brass in which an octahedral plane was perpendicular (and a [Ill] direction parallel) to the axis, and 2—deformation bands with approximately the (110) [001] orientation were seen to develop in the crystal during the test. The new pole figures were obtained with a brass and an iron torsion specimen of 3/4 and 1 in. gage length diameter, respectively. After annealing, polishing, and twisting, seven rods, about 0.030 in. in diameter and with different orientations, were prepared from material near the surface of each specimen; these were required for the method of constructing pole figures by using a Geiger counter as developed by Norton.5 Since the shear strain gradient in plastic torsion is linear, it was readily computed that the material supplying the brass rods had been subjected to a shear strain of about 3.2, and that supplying the iron rods had received a shear strain of about 2. All details concerning specimen design, testing procedure, rod preparation, and use of the Norton technique can be found in ref. 1. Only this procedure was followed in working out the (111) and (100) pole figures for brass, Figs. 1 and 2. However, X-ray photograms were also involved in the construction of the (110) pole figure for Armco iron, Fig. 3. The photograms were made according to the conventional transmission diffraction technique using a small sheet taken parallel to the specimen surface and etched to a thickness of about 0.0025 in. They were especially important in locating the boundaries

Jan 1, 1954

By W. A. Wood, H. L. Wain, R. I. Garrod

The mechanical behavior of recrystallized chromil~m of high purity has been studied, principally in torsion and to a lesser extent in tension, at temperatures between —196oand 350oC. Depending upon the conditions of test, the material may show brittle or ductile behavior or an intermediate or subduc-tile state having some of the characteristics of each. This latter state existed at temperatures between approximately ±50°C and was characterized by a) extensive creep at stresses well below the normal fracture stress, b) nonelastic loading/unloading effects during creep, c) strain softening under cyclic loading, and d) final failure of a brittle type. Suggestions are made on the dislocation processes and interactions which give rise to subductile behavior The ductile-brittle transition in bee metals has been studied mainly by tension and bend tests. These methods, however, favor crack propagation which may follow too closely on initiation for detailed study of the transition itself. For work of this nature, therefore, other modes of deformation less favorable to crack propagation may be preferable. This paper describes a study of the ductile-brittle transition in chromium which is based mainly on torsional testing although a few subsidiary experiments were made in tension. It appears to reveal at the transition an intermediate state that cannot properly be described as either brittle or ductile. Torsional tests on chromium have been made by other workers1 but not, as here, primarily for study of this intermediate state. EXPERIMENTAL The chromium, in the form of swaged rod, was prepared by techniques already described.&apos; The particular material used was one in which the main impurities were 0.03 wt pet 0 and 0.006 wt pet N and one in which transition from ductile to brittle states in torsion conveniently fell at about room temperature. For torsion, test specimens were from 5/16-in.-diam rod to provide test portions 1-1/4 in. long by 7/32 in. diam, a twist of 1 deg thereby corresponding throughout this paper to 0.0015 surface shear. The specimens before test were annealed for 2 hr at 1200°C in vacuo, which left them with a re-crystallized grain size of about 0.01 mm, and then electropolished. They were tested under dead-weight loading in an apparatus in which they could be surrounded by a furnace or cooling chamber, tests in practice being made at various temperatures between -196" and +350°C. For tension tests, cylindrical specimens were prepared in a similar manner and tested at room temperature under dead-weight loading. RESULTS (TORSION) Subductile State. The state described above as intermediate between brittle and ductile may be perhaps best defined by reference to torque/twist curves at various temperatures. These are grouped in Fig. 1. Below about -50°C the material was brittle, in the sense that it exhibited little plastic deformation under stress and fractured by cleavage along planes of maximum resolved tension, which in torsion produces the well-known helical type of fracture. The deformation is typified by the curves for -196" and -150°C in Fig. 1; it shows a slight but progressive deviation from linearity above a certain torque, here about 50 lb-in., until fracture occurs at about 95 lb-in. A feature to which it is desired specially to call attention is that under none of the loads did the specimens show significant creep.

Jan 1, 1964

By Robert B. Hall, Charles W. Bauer

Alunite, KA13(SO4)2(OH)6, was used from the 15th century until early in the present century as a source of potash alum and aluminum sulfate. Since early in this century its use for this purpose has declined to virtually nil with acid treatment of bauxite or clay replacing alunite as a source of alum. During the First World War alunite served as an emergency source of potassium sulfate fertilizer in the United States and Australia. More recently, alunite has been investigated as a nonbauxite ore of aluminum, with potassium sulfate and sulfuric acid as recoverable byproducts. The Soviet Union established a commercial-scale plant in the mid-1960s producing cell-grade alumina from alunitic ore and recovering byproduct potassium sulfate and sulfuric acid. Interest in nonbauxite ores, including alunite, is expected to continue in countries that presently are dependent on imports of bauxite or alumina to support their aluminum industries. The US has the largest aluminum producing and fabricating industry in the world but imports more than 90% of its aluminum-bearing raw materials. This chapter reviews the status of alunite as a potential source of aluminum with byproduct fertilizer, and the resources available to support this industry, whenever this becomes economically feasible. Historical Background Alunite has received little attention until recently, yet for centuries it held a higher place than many of the industrial minerals considered essential today. The deposits of alunite at Tolfa, northwest of Rome, were mined almost continuously from 1462 until about the middle of the present century (DeLaunay, 1907; Lombardi, 1977). The potash alum made from the alunite, called Roman alum, was a valued commodity in international trade, being used in the making of paper, in tanning leather, and as a mordant in textile dyeing. The industry at Tolfa is said to have been controlled by the Vatican and was a source of revenue for the Papal State until fairly recent times (Lombardi et al., 1977). Since early in the present century, the preferred method for making alum has been by acid treatment of bauxite, clay, or other aluminous material, so that alunite has fallen into near-total disuse as a source of alum chemicals. Appreciable quantities of mixed alunite-kaolin rock still are quarried in the Tolfa district for use by the Italian cement industry (Lombardi and Mattias, 1979), but the role of this material in the making of Italian cement is not clear. A large deposit of alunite-bearing rock in Chekiang province, mainland China, is said to have yielded a "great quantity" of alum over a period of several centuries (Yih, 1931). During the 19th century, alunite deposits in France, Spain, Australia, and other countries were exploited as raw material for making potash alum and aluminum sulfate. Interest in alunite was revived during the First World War, not for alum, but as an emergency source of potassium sulfate fertilizer. Large veins of nearly pure alunite had just been discovered on Alunite Ridge, 11 km southwest of Marysvale in Piute County, Utah (Butler and Gale, 1912), and these were quickly brought into production for making potash fertilizer to replace supplies cut off from the famous deposits at Stassfurt, Germany. An estimated 225 kt of Marysvale alunite was mined and processed at that time (Callaghan, 1973). Similarly, Australian alunite deposits were mined as a source of potash fertilizer during both world wars (Hall, 1978).

Jan 1, 1983

By Richard B. Reese, George R. St. Pierre, Robert A. Rapp

The vapor pressures of pure iron and pure chromium have been measured using a Knudsen cell coupled with a mass spectrometer. The experimental results agree well with some previously reported data; heats of sublimation and vaporization have been calculated. From vapor pressure rr~easurernents, the activities of iron and chromium in their binary alloys have been determined for NcY = 0.10 to 0.65 over a 1400" to 1700~ temperature range. The activity of chromium in the liquid alloys was found to exhibit positive deviation from ideal behavior when referred to solid chromium as the standard state; however, for the activity of chromium referred to nonequilibrium undercooled liquid chromium as standard state, the activity behavior is almost ideal. ALTHOUGH the Fe-Cr system is important as the basic system of alloy steels, the thermodynamic properties of this system have not been thoroughly investigated at elevated temperatures. In view of the potential practical applications of such data as well as their contribution to alloy theory, further study of the Fe-Cr system was undertaken. In addition, further development of experimental techniques for equilibrium measurements at high temperature is required. The present research involved an application of the Knudsen effusion method in conjunction with a time-of-flight mass spectrometer. Belton and ~ruehan&apos; have measured the activities in Fe-Ni and Fe-Co alloys by a similar method. Speiser, Johnston, and lackbburn&apos; have determined the vapor pressure of pure solid chromium between 1283" and 1561°K by a Langmuir free evaporation technique. The vapor pressure of chromium was described by the expression: over the temperature range 1283" to 1561°K. McCabe, Hudson, and paxton3 have measured the vapor pressures of pure iron and pure chromium by the Knudsen cell technique around 1500°K. The vapor pressure and heat of sublimation at O°K, AH,", for pure chromium agreed within experimental error with the measurements of Speiser et al. at 1200°C. Kubaschewski and HeYmer~ determined the vapor pressure of pure solid chromium in the temperature range 1170" to 1400°C by the Knudsen effusion technique combined with a radioactive tracer analysis of crS1. Their results agreed with the work of previous investigators. Edwards, Johnston, and Ditmars5 have measured the vapor pressure of pure solid iron by the Langmuir technique between 1356" and 1519°K. The vapor pressure of solid iron in the temperature range studied was given by: The data of McCabe, Hudson, and paxton3 on the vapor pressure of pure iron around 1500°K by the Knudsen effusion technique were in good agreement with those obtained by Edwards et a~.~ Hultgren, Orr, Anderson, and Kelley give the selected values for the AH: of pure iron and pure chromium as 98,990 *200 and 94,340 * 500 cal per mole, respectively. These values are the average values determined in the several investigations by different methods. The Fe-Cr phase diagram7 is shown in Fig. 1. Previous determinations of activities in this system have been carried out by several investigators, but most of the work has been done on solid alloys. Using a Knudsen effusion method with cr5&apos;, Kubaschewski and Heymer4 reported that the Fe-Cr system exhibits positive deviation from the ideal behavior for compositions ranging from NCr = 0.0398 to 0.699 at 1170"

Jan 1, 1969

By E. P. Miesch, P. B. Crawford

A study was made of the effect of permeable and impermeable lenses in a reservoir on the production capacity of a well. Both steady-state and unsteady-state data were obtained. An electrical resistivity model was used to obtain the steady-state data and thermal models. were constructed to obtain the unsteady-state data. The productivity of a well is affected very greatly only when the lenses are close to the well. The effect of circular lenses on the productivity ratio can be correlated with the distance from the center of the lens to the center of the well divided by the radius of the lens. When this dimensionless distance is equal to six or greater, the effect of the lenses on production capacity will be negligible. The pseudo steady-state productivity of a heterogeneous reservoir can be predicted using steady-state data. INTRODUCTION Many analytical solutions of reservoir behavior assume that reservoir rock is uniform and homogeneous. Although this assumption is used, all of the data from core analyses and well logging indicate that the reservoirs are heterogeneous. Very little work has been done on the performance of heterogeneous reservoirs. The work of Landrum,l et al. showed that transient phenomena in oil reservoirs could be studied with thermal models. Pickering and Cotman2 used thermal models to study flow in stratified reservoirs and investigated the effect of inhomo-geneities in oil reservoirs on transient flow performance. Loucks3 made a mathematical study of the pressure build-up in a system composed of two concentric regions of different permeability. Root, Silberberg and Pirson4 studied the effect of the growth of the flooded region on water influx predictions using a thermal model consisting of three concentric cylindrical regions of different thermal properties which simulated the aquifer, the flooded region and the unflooded portion of the original hydrocarbon region. Tomme, et a1.5 made a mathematical study of vertical fractures. The object of this investigation was to study the effect of highly permeable and impermeable lenses in the vicinity of the wellbore on the pressure depletion history of the well. Steady-state data were obtained for both conductive and nonconductive lenses that completely penetrated the formation. The lenses were symmetrically located at various distances from the wellbore. The unsteady-state data were obtained on seven thermal models. EXPERIMENTAL EQUIPMENT AND PROCEDURE STEADY-STATE DATA The steady-state data were obtained from an electrical resistivity model 30 in. in diameter and approximately 11/2 in. deep. The outside of the model was lined with a 30-in. diameter copper strip, which served as the outer boundary of the reservoir. The bottom was covered with a sheet of plexiglass so that it would be nonconductive. The model was filled with a slightly saline solution. The well size was varied from an 0.064-in. diameter copper wire to a 10-in. diameter copper cylinder. Readings were taken with an impedance bridge using AC current to prevent polarization at the contacts. Copper and wax lenses were used to represent infinitely conductive and nonconductive lenses, respectively. The resistance was first measured for each well diameter with no lenses in the reservoir. Then the conductive and nonconductive lenses were spaced symmetrically at various distances from the well and the resistance read from each lens location. The diameters of the conductive lenses were 3, 1.022 and 0.624 in., and those of the nonconductive lenses were 3, 2.25 and 1.563 in. The ratio of each resistance reading to the resistance reading with no lenses in the reservoir

Jan 1, 1965

By R. A. Swalin, L. A. Neimark

The research work presented in this paper had initially a two-fold goal. First, further data concerning the low-temperature recovery of cold work was desired. Recovery phenomena have been extensively studied in face-centered-cubic metals but at the time of initiation of this research, no investigation concerning the low-temperature recovery in body-centered-cubic metals had been made. During the course of the investigation a paper by Martin on the recovery of point defects in molybdenum appeared.&apos; Comparison of our results on tungsten with Martin&apos;s results on molybdenum will be made. Secondly, knowledge concerning the influence of a particular type of impurity addition on the recovery kinetics was desired. It has been known for a long time that extremely small amounts of certain impurity additions exert a profound influence on the recrystallization behavior and the resulting microstructure of tungsten. Small amounts of potassium silicate and aluminum chloride added prior to the reduction of tungsten oxide to the metal have been found by Smithells to raise the recrystallization temperature markedly,2 and yield an ultimate microstructure in which grains several millimeters long are produced in fine wires of say 10 mil diam. If the impurities are added singly, ordinary secondary recrystallization results with none of the spectacular properties of the wire to which special additions were made. Swalin and Geisler3 and Rieck4 have studied the recrystallization behavior of such doped wire in some detail. The former workers found that small amounts of these impurities raised the recrystallization temperature over 400°C and electron microscopic examination revealed no obvious inclusions in the microstructures. In fact. chemical analysis showed that there was <0.001 pct K, <0.002 pct Al, trace of Si, and <0.0003 pct 0 in the wire studied. The possibility that the role of the special impurities is to keep the structure open by void formation and that submicroscopic porosity acts as the inhibiting agent has been discussed.2&apos;3 Meijering and Rieck5 have suggested that the impurities are strung out as second-phase particles in a direction parallel to the drawing direction. It was thought that a kinetic study of recovery could perhaps elucidate the role of the impurities to some extent. When a metal is deformed by cold work three basic types of defects are thought to be introduced into the crystal lattice, namely, interstitials, vacancies, and dislocations. Van Bueren6 has proposed that recovery of cold-worked metal is a four-stage process, each step being the result of the annealing of a primary defect or a combination of defects and having a unique activation energy. The steps in order of increasing activation energy are attributed to a) the diffusion of interstitials recombining with vacancies, b) diffusion of vacancy pairs, c) the diffusion of single vacancies, and d) climb of dislocations. In metals with relatively low- or medium-range melting points the temperatures for recovery are low enough so that the first three steps may occur during room-temperature deformation. For tungsten, because of the high melting point and subsequently high recovery temperature, it was calculated, using Nowick&apos;s approach7 that this recovery would occur in the temperature range 200" to 600°C. It is also known that recovery of X-ray line broadening, presumably due to dislocation climb, occurs at about 600°C.8 EXPERIMENTAL METHOD Two types of cold-rolled 10-mil-diam tungsten wire were used in the investigation; a) pure tungsten, (called undoped) and b) G. E. No. 218 wire (called

Jan 1, 1961

By A. D. Rovig, D. W. McGlashan, Donald M. Podobnik

Crystal-chemical and stntctural properties of sulfide minerals are considered. The information gained is to be used to interpret (I ) freshly broken mineral surfaces, (2) modifications of the mineral surfaces, and (3) reactions at the mineral surfaces. From these basic disciplines, concepts with regard to the changes that surfaces undergo, reactions that might take place, the geometry of the interface, the state of different atoms and ions in the interface, and other physical and chemical properties of an interface must be developed, weighed and applied. The authors first deal with these conceptual considerations from which hypotheses are set forth to describe the environ men tal-interfacial relationships for several sulfide minerals. Qualitative and quantitative explanation of par-ticulate solid separations are unknown entities because of the lack of adequate models and mathematical relationships to explain the activity occurring between the solid and liquid phases. It is a transitional region in which it is difficult to ascertain the mechanisms of adsorption of ions, molecules, etc., on mineral surfaces, as well as other secondary reactions which occur in interfacial regions. Thus, in this paper the authors deal with conceptual considerations from which hypotheses are set forth to describe the environmental-interfacial relationships for sulfide minerals. GENERAL CONSIDERATIONS Interfacial Reactions:Interfacial reactions are the cruxes of flotation schemes as well as other processes such as thickening, filtration and hydrometallurgy. However, as noted by Klassen and Mokrousov: 1 "The problems concerning the surfaces of natural minerals, the laws governing simultaneous adsorption from aqueous solution on these surfaces of a whole series of reagents, the laws of the surface reactions and the properties of water layers separating the minerals, are all known to a first approximation only." An investigator has the privilege of postulating methods of solid-liquid interfacial reactions. REACTIONS WITH WATER - Water consists of hydronium (H3 O 4) and hydroxyl (OH-) ions in the ionized state. That this is so forms the basis for the postulated reaction of the hydrated hydrogen ion with net-negative mineral surfaces as depicted in Fig. 1. In this case water is bonded to mineral surfaces through hydrogen-bridge-type bonds - possibly hydrogen bonds. Although bonding of the van der Waal type may be responsible for this reaction, it is most likely that stronger bonds are involved. Once firmly bonded to the surface, the water layer is known to be quite tenacious. It is further speculated that a shear plane exists at some distance (see Fig. 1) away from the mineral surface. Exact location of this plane is not known, but in all probability it will be positioned across a weak bond of the hydrogen-bond type where the surface-attached water is coordinated to the original hydrated hydrogen ion. REACTION WITH METAL IONS - Klassen and Mokrousov &apos; state: "The presence of an ion in water leads to an immediate formation around that ion of a highly condensed atmosphere of water dipoles and thus to hydration of the ion." The fact is known that multivalent cations are strongly hydrated, usually by six or eight molecules of water, and that anions are not so strongly hydrated. Conceding the fact that thermodynamics, concentration, pH, and physical considerations are of utmost importance in truly explaining a mechanism of metal ions reaction with a hydrated mineral surface, it does seem logical that the mechanism illustrated in Fig. 2 is feasible. In this reaction, the metal ion (M) is coordinated in one dimension - to the mineral-surface hydration layer. Note also that explanation of this reaction requires that the shear plane move to a less stable bond configuration; that is, the shear plane has moved to a position between the metal ion and the other coordinated water molecules which are more free to dissociate. Reactions as depicted in Fig. 2 should cause the formation of an apparent mineral surface which is net-positive. Immediately, it must be noted that measurements of apparent-mineral surfaces serve - within limits - to indicate a degree of ion-surface reaction capability. The major limiting factor he re is one related

Jan 1, 1970

By Charles C. Peterson, Ronald E. Enstrom

Significant improvements have been made in the ursine systern for epitaxial vapor gvowtlz of Gds. The electron concentration has been reduced to below 1015 cm-3 with electron-mobility values as high as 7200 sq on per v-sec at 30PK and 60,000 sq cw7 per v-sec at 77°K. These high-purity layers have been successfully gvown on n&apos; layers with thicknesses as snzall as 1 p and as large as 125 p. Furthermore, high-purity layers have been incorporated into an structure without degradation of electrical properties. Different impurity gradients at the n&apos; to n interface were achieved. Using these structures, Gunn oscillators have been operated at frequencies as low as 0.4 GHz and as high as 40 GHz, which equals the highest valzle yet reported. The frequencies nleasured are in reasonable apeenlent with those calculated fron7 the n-layer widths and the transit times. CW operatiolz has been achieved from 3 to 20 GHz. In Gunn devices for >40 GHz operation (i.e., witk an n-layer tkickness below 2.5p), the n layer has been generally too pure to permit oscillations to occuv. ThE mechanism of the Gunn oscillator&apos; is now generally understood.2-5 Electron transfer from the (000) minimum to the ( 100) minima leads to a voltage-controlled negative resistance, which results in the formation of domains of high and low electric fields which travel through the crystal with a characteristic velocity of about 107 cm per sec. When a constant voltage is applied to the sample, this domain motion generaliy leads to oscillations at the transit time frequency, fT = 107/L, where L is the thickness of the active n layer.&apos; In this case, a single high-field domain is nucleated at the cathode and grows until it reaches the anode, where it is absorbed; a new domain then forms at the cathode.5 There are related modes of oscillation of the same device in which a tuned circuit causes a periodic variation of the voltage across the device. The frequency then may be either above or below fT. It has been shown that oscillations will occur when n • L 2 1012 cm"2, where n is the carrier concentration in the active region. At lower doping densities, 10" 5 n . L 5 lo&apos;&apos;, the doping is said to be subcritical for oscillation and the description of the device operation changes since the domains become comparable in thickness to the device thickness, L. Nevertheless, such devices have been found to be "active" and, in fact, are useful as amplifiers.778 For CW operation, one wishes to minimize the power dissipation, which is related to the electric field, E, and the low-field resistivity, p. Below threshold, the power dissipation density is approximately Typically, at threshold where E -- 3 x 103 v per cm, the dissipation density is 107/p watts per cu cm, p in ohm-cm. Furthermore, it is desirable to provide good conduction of the heat generated in the active region. The temperature rise, AT, across the active layer of a sandwich structure, with a heat sink on one side, is given by AT = (E&apos;/P)(L~/~~) where it is assumed that the thermal conductivity, u, and resistivity, p, of GaAs do not vary appreciably over the range of temperature and electric fields existing in the layer. This expression shows that, subject to maintaining an appropriate (n . L) product, CW operation is favored by a higher resistivity, a lower threshold field, and a thinner device. The above device requirements place some severe restrictions on the materials to be used, especially for high-frequency (>10 GHz) operation. Here, it is necessary to prepare very thin (<10 µ) layers of GaAs, in a state of high purity (-1 ohm-cm), complete with very low-resistance ohmic contacts. Problems of handling such thin and fragile samples become inereasingly severe as the frequency is raised. Furthermore, while good low-resistance ohmic contacts are easily applied to low-resistivity GaAs, contacting difficulties are encountered for these higher-resistivity materials.

Jan 1, 1968

By Pradeep K. Rohatgi, Clyde M. Adams

Structures obtained on freezing of several hypo-and hypereutectic Al-Cu alloys over a range of solidification rates have been examined. Dendrite spacing, L, increases linearly with solute concentration and with the square root of the inverse freezing rate. The relationship for hypoeutectic alloys is: where rate of change of fraction solid with time, is freezing rate, C is solute concentration, (pct Cu)=1. Mass transport in inter dendritic liquid during solidification is analyzed; the experimental observations suggest maximum concentration differences and constitutional supercooling in the inter dendritic liquid increase with an increase in the solute concentration. The dendrite morphology changes with freezing rate and alloy composition. The dendrites of the a phase are parallel, uniformly spaced plates with slow freezing and rods with rapid freezing. Nonor-thogonal side branching has been observed in phases with cubic and tetragonal structures. Side branches in a dendrites are orthogonal with slow freezing and at 60 deg with rapid freezing. Formation of second-phase envelopes around the Primary phase is also discussed. DENDRITIC structure is characteristic of many types of phase transformation. The most extensively studied so far has been solidification of liquid solutions. chalmersl and coworkers have interpreted the formation of dendrites in terms of the breakdown of a planar interface. Most of the work done concerns itself with the development of an instability at the interface. Little theoretical work has been done quantitatively to relate the parameters of dendritic structure to mass transport in the liquid phase. A few empirical relations based on the experimental2&apos;3 observations exist in the literature. Several workers2 including Brown and Adams1 have studied dendrite spacing in A1-Cu system as a function of solidification variables. In most cases, dendrite spacing has been found to increase linearly with the square root of some parameter proportional to the freezing time. The effect of solute concentration is not clear; some workers report the dendrite spacing increases with solute concentration4 whereas others report vice versa.&apos;&apos;&apos; ~ohatgi&apos; has observed an increase in the spacing between ice dendrites with an increase in solute concentration in water. Tiller has also suggested that dendrite spacing should increase with solute concentration. In the present work dendrite spacing and morphology have been examined as a function of solute concentration and freezing rate. The freezing rate is defined as the fraction of liquid solidified per unit time, dfs/dß?, where f, is the fraction solid and 8 the time. The fastest freezing rate studied was 4550 times the slowest freezing rate. THEORETICAL CONSIDERATIONS It is of interest to analyze the concentration distribution in the liquid phase between growing dendrites during solidification, Fig. 1. Since this distribution is a direct consequence of the rejection of solute by the growing solid, a diffusional process, the concentration gradients increase with the freezing rate. However, when solidification rate is the only variable in a series of experiments, the interdendritic liquid regions become smaller (i.e., the dendrites become more closely spaced) with an increase in freezing rate. The main purpose of the analytical treatment of interdendritic liquid diffusion will be to reveal a tendency for dendrite spacing to decrease with increasing solidification rate in just such a way that the maximum concentration differences developed in the liquid phase are remarkably independent of freezing rate. Two rather different analyses are set forth, one pertaining to the one-dimensional diffusion which obtains in the interdendritic liquid between parallel plate-shaped dendrites, and the other to the cylindrically symmetrical diffusion around rod-shaped dendrites during early stages of solidification. The results of the two analyses are quantitatively similar, correlating dendrite spacing, maximum concentration difference, and freezing rate. First consider the simpler one-dimensional case. Two parallel plate-shaped dendrites are separated by a distance, L, between centers, Fig. 1. Solidification takes place by the thickening of these plates, with solute being rejected into the liquid. It is assumed there is no diffusion in the solid. This thickening process is slow enough and the dendrite spacing small enough that the concentration differences which develop, although interesting and important, are very small (an important assumption which is verified ex-

Jan 1, 1968

By J. F. Pierce, S. M. Enterline

Since January 1959 a zinc refiner of novel design has been in operation at Blackwell, Okla., producing 99.995+ zinc from the output of the Blackwell horizontal retort smelter. The refiner is a continuously operated, pyro-metallurgical unit with principal dimensions horizonhl permitting one floor operation. It is very ruggedly constructed. Furthermore it is not subjected to deterioration from high concentrations of iron in the feed metal because the boiling units are separate from the rectification columns and constructed with silicon carbide brick arches through which the heat is transferred radiantly to the zinc. A zinc refiner of novel design has been in operation since January 1959 at the Blackwell, Okla. plant of the Blackwell Zinc Co., Inc., a wholly owned subsidiary of American Metal Climax, Inc. Developed by the company&apos;s technical and operating staffs, the new refiner produces special high-grade zinc (nominally 99.995+ pct Zn) from the prime western1 slab output of the Blackwell horizontal retort smelter. The refiner is a continuously operated, pyromet-allurgical, high-capacity unit employing fractional distillation to separate zinc from its impurities, consisting principally of lead, cadmium, and iron. In prime western slab, these elements may vary in concentration from 0.005 to 1.6 pct. Table I shows the impurities usually encountered in the Blackwell prime western metal fed to the refiner together with their boiling points and vapor pressures at 907oC. The commercial pyrometallurgical smelting processes for extracting zinc from ore include distillation from retorts and a limited degree of refining can be accomplished by redistillation in similar retorts. To achieve special high-grade purity, an impractical number of batch redistillations would be required, however, with an accompanying loss of much metal. A continuously operated and integrated unit is required in which fractional vaporization and condensation can take place in a large number of stages. The first commercial continuously operated unit was developed by the New Jersey Zinc Co.4 In the separation of any two substances the degree of separation is limited if a mixture exists having a constant boiling point. The Zn-cd5 and Zn-pb6 systems contain no constant boiling points and hence these metals may be separated to any degree of purity. Basically, the pyrometallurgical refining of zinc involves three steps: a) iron, copper, and other metals having no appreciable vapor pressures at 907ºC concentrate in the bath when the impure zinc is boiled, b) lead, bismuth, antimony, and other metals having boiling points above but closer to that of zinc are selectively condensed from the vapor boiled from the bath, and c) cadmium and other metals having lower boiling points than zinc are fractionally distilled by reboiling and subsequent condensation of the zinc from the vapor. The boiling and condensation of zinc must be conducted in vessels constructed of materials which are refractory at the temperature involved (907 ºC) and it is highly desirable that they also be resistant to attack by the various metals. This requirement dictates construction from relatively small, simply shaped pieces which limits the pressures which may be employed to avoid leakage through the numerous joints. Stresses induced must be limited essentially to compressive ones and suitable provision must be made to permit thermal expansion of the components in order to minimize these stresses. Where heat is to be added for boiling or removed for condensation, refractory material through which the heat flows must have a high thermal conductivity. Silicon carbide is highly conductive but is subject to attack by iron and is expensive compared to other commonly employed refractories. A hard, dense aluminous fireclay is well suited to contain these metals where high thermal conductivity is not required. Zinc will penetrate the pores of fireclay brick but only to a limited depth in an exterior wall and has little effect other than an increase in weight and conductivity. The design objectives of the Amax refiner were: a) to achieve a long life by heavy, rugged construction and by employing silicon carbide refractories only where required for heat conductivity and not in contact with liquids of high iron concentrations, b) to simplify operation, manning and control by essentially horizontal construction, and c) to obtain high capacity in a single unit. DESCRIPTION Flow of metal through the Amax refiner is shown diagrammatically in Fig. 1 and schematically in Fig. 2.

Jan 1, 1963

By O. R. Morris, G. L. Hawkes

A galvanic cell, using as electrolyte a fused salt solution of calcium carbide and as electrodes carbon and a Fe-C alloy of known composition, has been set up to study the thermodynamics of Fe-C alloys in the temperature rmzge 800" to 1000°C. Time independence and reproducibility of the cell electromotive force were taken as evidence of the reversible behavior of the cell. Carbon was believed to be present in the electrolyte as the so-called acetylide ion, C;-. The plots of the cell electromotive force us temperature for a specific alloy composition were straight lines within the limits of experimental error. The average Partial molar enthalpy of carbon in iron relative to pure carbon was found to be +10,610 i 93 cal per g-atom C. Thermodynamic analysis of the data has led to the following equation for the carbon activity, ac, based upon pure carbon as the standard state: In ac = In Zc + 10,560/RT + (10.02 + 77O/T)ZC - 2.350 where ZC is the lattice ratio [nC/(nF, - nc )] and T is the absolute temperature. This equalion gives carbon activity values generally slightly lower than those from gas equilibration studies reported in the literature. METAL LOGRAPHIC examination of a polished cross section of the steel anode used in the electrolysis studies of fused salt solutions of calcium carbide by Morris and Harry revealed extensive carburization of the steel by the electrodeposited carbon. This carburization was reflected in the variability, with time, of the applied potential to the electrolysis cell, necessary to maintain a constant current density at the electrodes. This observation suggested the setting up of a galvanic cell of the "alloy concentration" type to study the thermodynamics of some metal-carbon alloys. Cells of this general type have been widely used for the study of alloy systems.2 In view of the availability of published data in respect of the austenite phase of the Fe-C system, it was decided to carry out measurements upon these alloys before proceeding to studies of less well documented systems. The galvanic cell may be written: where [C] is carbon dissolved in iron. The electrolyte was a fused salt solution of calcium carbide, containing some 5 to 10 mol pct of carbide. The cell reaction is believed to be: C(s)-[CI [I1 Carbon forms an interstitial solid solution in iron, with the atoms located in the octahedral interstices. In the fcc crystal structure of austenite there is one octahedral interstice per iron atom. Thus, the lattice ratio, ZC, shown by Gurney3 to be the fundamental concentration parameter in the context of interstitial solutions, is given by: where nc and nFe are the number of carbon and iron atoms, respectively. chipman4 has recently shown empirically the advantages of using this concentration parameter instead of the more usual atom ratio or atom fraction. The cell electromotive force, E, assuming reversible behavior, is related to the carbon potential or the partial molar free energy of carbon in the solid solution relative to pure carbon at the same temperature and pressure, GP at the composition ZC, by the equation: where z is the carbide ion valency and F is the Faraday constant. An activity of carbon, ac, in the solution relative to the value of unity assigned to pure carbon, and an activity coefficient, qC , are defined such that: where R is the gas constant and T the absolute temperature. GF is further related to the relative partial molar enthalpy Hm, and the temperature coefficient of the cell electromotive force, (aE/aT)Zc, by the equations: Measurement of the cell electromotive force thus enables calculation of the relative partial molar thermodynamic properties of carbon in iron, if z is known. At E = 0, the solid solution is in equilibrium with pure carbon. More convenient for many purposes is the standard state based upon the infinitely dilute solution, Henry&apos;s law. The relationship between the activity coefficient of carbon based upon this standard state, and that based upon the pure carbon standard state, qC , may be obtained by considering the free energy of transfer of carbon from the latter standard state to the former. The relationship is: where +:H is the activity coefficient of carbon in the hypothetical standard state based on a reference of

Jan 1, 1969

By W. E. Newell

The basic principles and assumptions involved in D. L. White&apos;s solution5 for ultrasonic wave amplification in piezoelectric semiconductors are summarized. If the gain per unit length is maximized at each frequency without regard to the drift-field power density, the gain increases linearly with frequency. Therefore it would seem that very high gain is possible for frequencies in the hundreds of megacycles. However, with present materials the resulting drift-field power density is so large that cooling would be a major problem. For this reason it is more realistic to judge the capabilities of an ultrasonic amplifier in terms of the gain that is possible with a specified power density. In this case the gain at high frequencies does not increase but decreases more rapidly than l/f. The calculation of the gain us frequency at a fixed power level involves the repeated solution of a cubic equation and is therefore tedious. For the purpose of comparing different materials, sufficient accuracy can be obtained from an approximate solution which may easily be plotted as three straight lines on logarithmic graph paper. This method is used to compare the Performances of CdS, CdSe, ZnO, and GaAs. At a power density of 10 watts per cu cm, the first three give maximum gains of 60 to 80 db per cm in the vicinity of 60 megacycles. At the same power density, GaAs has a maximum gain of about 7 db per cm near 150 megacycles. Although an increase in mobility usually increases the gain for a specified power density, it is shown that there is an optimum mobility above which the gain decreases. An approximate expression for the optimum mobility is established. It is well-known that the interaction between charged particles and an electromagnetic wave can be used to amplify the electromagnetic wave. In the conventional traveling-wave tube, electrons in a vacuum are caused to move at a velocity slightly greater than the wave velocity, thereby coupling energy into the wave.&apos; In principle, the same effect would be evident in a solid except that repeated collisions prevent the electrons from attaining a velocity greater than that of an electromagnetic wave. However, the drift velocity of electrons can be made to exceed the velocity of an acoustic wave in a solid. In 1956, weinreich2 noted that the deformation potential provided one means of coupling energy from drifting electrons into an acoustic wave, but the effect was too small to be of any practical importance. It was not until 1961 that White and Hutson demonstrated that the piezoelectric effect provided a strong enough coupling to give appreciable amplification of an ultrasonic wave and awakened wide interest in electron-phonon interactions. Qualitatively the effect may be described as follows. An acoustic wave propagating through a piezoelectric material is accompanied by an electric-field wave. If the vibrations are properly oriented with respect to the crystal axes of a piezoelectric semiconductor, the local electric fields are axially directed and cause bunching of the charged carriers. If the drift velocity of these carriers is less than the velocity of sound, they tend to be dragged along by the acoustic wave. This electroacoustic effect results in a net potential appearing across the material and in attenuation of the acoustic wave. On the other hand, if the drift velocity exceeds the velocity of sound, energy is coupled from the carriers to the acoustic wave and amplification results. Related effects which are being investigated include ultrasonic amplification in semimetals6-&apos; and semi-conductor, and current saturation in piezoelectric semiconductors.&apos;4-17 There are various problems which hinder the immediate application of ultrasonic amplification in a practical device. First, there are the traditional problems encountered in the design of acoustic delay lines: attenuation in the electromechanical transducers, reflected waves (which can lead to self-oscillation in an amplifying device), mechanical tolerances necessary to maintain phase coherence, and so forth. Second, there is the problem of selecting the best material from among the various piezoelectric semiconductors as they become available in single-crystal form with a wide choice of characteristics. This paper deals with the second problem and shows that the most realistic way of comparing materials is in terms of the gain which can be obtained without exceeding a

Jan 1, 1964

By D. D. Smith, D. P. Squier, E. L. Dougherty

A system of differential equations describing the temperature behavior of fluid injected at constant surface temperature in a well is derived and .solved analytically. A formula for the fluid temperature at any time and depth is given, as well us a special formula valid for very large times. These formulas are used to calculate temperatures for several typical cases. The results indicate that, initially, the temperature of the water entering the formation is considerably lower than the injection temperature. This condition lasts for only a short period— less than three days for most cases of practical interest. Following this highly transient period, during which the temperature of the fluid entering the formation builds up to about 50 to 75 per cent of the injection temperature. the system enters a quasi-steady state in which the temperature changes are very slow. After severl years, the bottom-hole temperature will still be 50" to 100°F lower than the injection temperature, hilt the heat losses may he tolerable. INTRODUCTION Predicting the behavior of a hot-water flood requires that the temperature of the water entering the injection interval be estimated. This report describes the development and solution of a system of equations which describes the temperature behavior of the injected water in the wellbore with certain simplifying assumptions. The only previous means known to the authors for describing such a process is that of Moss and White.&apos; Their results appear to be close to those obtained by our method in the practical cases which were compared; this agreement is largely due to the fact that in our method temperature soon approaches a quasi-steady state, as was assumed in their method throughout. However, our model covers all times, is continuous (whereas the Moss-White model depends on breaking the depth into discrete intervals) and. we feel. more closely describes the physical problem. FORMULATION OF THE PROBLEM PHYSICAL SYSTEM AND ASSUMPTIONS The injection procedure consists of pumping water at a fixed surface temperature T., down an infinitely long cylindrical well or tubing of inner radius Any material exterior to the water column such as mud, casing, or cement is regarded as part of the formation. The general behavior of the system may be described qualitatively as follows. When the hot water is first introduced into the system, the temperature difference between the formation and the water is large, resulting in a high rate of heat transfer. As a result, the temperature adjacent to the wellbore rises very quickly. Because the segment of the formation adjacent to the wellbore largely controls the heat transfer rate, the heat transfer rate will become relatively constant when this portion has reached a temperature close to that of the water opposite it. The temperature of the water and formation then increase very slowly with time. The length of the initial highly transient period and the temperature of the water at its conclusion will be functions of depth, injection rate, injection-string radius, surface injection temperature and the physical properties associated with the water-formation system. The following additional assumptions were made. 1. There is no heat transfer by radiation in the system. 2. There is no heat transfer by conduction in the vertical direction in either the injection stream or the formation. 3. The linear volumetric and mass flow rate of the water is constant throughout the injection stream. 4. No horizontal temperature gradient exists in the injection stream. 5. The product of density and heat capacity is constant for both the water and the formation, and the formation thermal conductivity is constant. 6. Initially, both the water in the wellbore and the reservoir are at a temperature given by the (constant) ambient surface temperature plus the product of depth and geothermal gradient (assumed constant). At large distances for the wellbore (r m), the formation will remain at this temperature. 7. The water temperature and the formation temperature at r — r,, are equal for all depths D. DERIVATION OF EQUATIONS The differential equation satisfied by the fluid temperature T,(D, t), which is obtained by writing a heat balance on a cylindrical differential of volume dV of the injection string between the depths D and D i dD, is

By C. W. Allen, B. D. Cullity

The proportional limit of iron crystals in torsion is governed by the resolved shear stress in the most highly stressed slip systems, averaged around the specimen circumference, and does not obey a critical resolved shear stress law. Crystals of most orientations exhibit a stage of easy plastic deformation, akin to easy glide in tensile or shear specimens. Transient deformation, similar to that which occurs in single crystals of other materials, is also observed. THE torsional deformation of single crystals of magnesium (hcp) and aluminum (fcc) has been described recently by Choi et al.,&apos; especially with respect to the criterion for the orientation dependence of the onset of plastic flow in these materials. The purpose of this paper is to present results of torsion tests of iron single crystals and thus to extend this yield criterion to a bcc metal. In addition to considering the variation of proportional limit with crystal orientation, this paper also briefly treats work hardening, transient deformation, and the mechanism of plastic flow in iron. The effects of the method of surface polishing and the chemical purity of the iron have been investigated. STRESS DISTRIBUTION It is convenient to express the stress at any point of a cylindrical crystal stressed in torsion in terms of t0, which is the shear stress acting at the surface on a plane normal to the axis of the cylinder and in a direction tangential to the cylinder. This stress is given by To = 2T/pr3 [1] where T is the applied torque and r the specimen radius. The shear stress t, resolved in any chosen slip system is given in terms of 7, by1 Ts/TO = sin 0, cos d sin (0, -) + cos , sin d sin d - ) [2] where 0 and d are the angles between the specimen axis and the slip plane normal and slip direction, respectively; h is the angular circumferential position on the specimen at which t, is being determined, measured from an arbitrary reference plane which includes the axis;o and d are the angular coordinates of the projections of the slip plane normal and slip direction on a transverse section with respect to this same reference plane. Slip in iron occurs in a <1ll> direction on the {ll0}, (1121, and (123) planes, which together comprise 48 slip systems. A complete evaluation of the stress distribution in an iron crystal stressed in torsion would therefore require a calculation of Ts/T0 as a function of for 48 different slip systems. Fortunately Gough,&apos;who studied the behavior of iron crystals in alternating torsion, was able to simplify this problem considerably. He showed that it was sufficient to consider a kind of average slip plane for each slip direction, namely the mathematical plane of maximum resolved shear stress containing the slip direction considered. This simplifying approximation is possible because, for each slip direction, the active slip plane or planes lie very near this mathematical plane of maximum shear stress. Vogel and rick&apos; have critically reviewed the early work of Taylor and Elam,13 Taylor,14 and Fahrenhorst and schmid8 from which the identification of the above crystallographic planes as slip planes in the bcc lattice largely stems. While their criticism is clearly justified, their own results do little to clarify the issue. The role of cross slip (screw dislocations changing glide planes) is evidently so important in this case, as Read3 has suggested, that methods for deducing slip systems from observations of gross slip traces are inadequate, such traces commonly arising from complex dislocation motion. Thus the treatment given here involving the plane of maximum resolved shear stress seems a logical simplification especially in view of Gough&apos;s2 study of a iron. There is, however, an assumption built into the subsequent treatment the comparative validity of which is difficult to assess, namely, that slip in all slip systems in iron may be characterized by a common critical resolved shear stress. The shear stress 7, resolved in a slip direction defined by d andd, and on the plane of maximum shear stress containing this direction, is found by first maximizing 7s/70 with respect to either Oo or 4,. The slip plane coordinates are then eliminated by using the relation between 0, ,o and d, d, namely,

Jan 1, 1963

By Axel Hultgren

IN ingots of silicon-killed carbon steel made without addition of - aluminum, transparent spherical or nearly spherical inclusions, up to about 0.15-mm diameter, are generally present. They may be glassy or crystallized, wholly or partially. In steels of high carbon contents they consist of silica,4,12 in steels of lower carbon contents arid, in consequence, higher oxygen contents, of iron-manganese-silicate with higher iron and manganese contents the lower the carbon content. Small silicate inclusions, about 0.01 mm or smaller, may occur, just as sulphide inclusions do, in portions that have been the last or nearly the last to freeze,10,12,17 this location being verified by primary etching.10 Hence, it may be concluded that they have separated from liquid steel that has become enriched in oxygen through segregation during freezing. Silicate inclusions with a diameter larger than about 0.02 mm appear, at least in ingots of moderate size, to be distributed at random in relation to the primary structure and therefore may be assumed to have existed as droplets in the liquid steel before freezing started at the point in question. The average size of such large inclusions has been found to increase toward the axis17 and their amount to increase from the top downward in the axial region .2,10 It has been assumed that this accumulation is a result of the droplets being brought down by the slowly settling metal crystals.2 It has been suggested that large silicate inclusions generally form,6 or may form," by coagulation of smaller ones, or by small drops being caught by larger ones during the rising of the latter.9 The occasional occurrence of a large inclusion surrounded by a swarm of small ones has been taken as a proof of this mechanism but, as suggested later, may be explained in another way. It has been pointed out that an inclusion droplet in the liquid steel may grow at the expense of an adjacent one, which implies diffusion of soluble inclusion-forming elements in the liquid steel.15 Further, it has been pointed out that, on cooling in ladle or mold, the metal-silicate equilibrium is displaced in the direction of separation of silicate. Thus inclusions may grow in size and amount.2,3,8,12,13,17,19,20 The exposure of the liquid steel to the oxygen of the air during tapping and pouring, and the consequent reaction, has been mentioned as a source of the formation of inclusions19,20 but this possibility has not received particular attention. Further, the admixture of furnace slag during tapping&apos; or of refractory material from various sources1,20 has been considered. The inclusions due to the latter may be recognized, however, through their resistance to hydrofluoric acid, imparted by the alumina content. Silicate inclusions, are often referred to as. the natural and inevitable product of reaction on adding silicon or silicon

Jan 1, 1948