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By J. E. Hilliard, H. E. Cook

It is shown that for systems having a miscibility gap the spinodal composition (c,) in the vicinity of the critical temperature (Tc) is related to the equilibrium composition (c,) by where cc is the critical composition. This expression is exart for the limit T — Tc and is a good approximation down to (T/Tc) - 0.9. If the miscibility gap meets the composition of the pure components THE recent theoretical treatment by cahn1,2 on spinodal decomposition of solid solutions has revived interest in methods of estimating the chemical spinodal, * i.e., the locus on a binary phase By use of the appropriate expression, the spinodal can be drawn on the Phase diagram almost by inspection with an accuracy comparable to that of lengthy calculations in which a free-energy function is fitted to the phase diagram. Satisfactory agveemenf is also obtained with spinodals comPuted from experimental free-energy curves. where G is the Gibbs free energy of the homogeneous solution and c the atomic fraction of component 2, the derivative being evaluated at constant temperature (T) and pressure (P). (These subscripts will hereafter be omitted from the partial derivatives.) If experimental measurements of G as a function of c and T are available in a single-phase region above the spinodal, then these can be extrapolated to obtain a series of metastable free-energy isotherms in the two-phase region, and from these isotherms a series of spinodal compositions can be calculated. Because the value of is very sensitive to experimental errors, an elaborate analytic procedure is required for

Jan 1, 1965

By C. Ernest Birchenall, Robert F. Mehl

APPLICATION of diffusion laws in the customary form to experimental studies in binary metallic solid solutions has shown the diffusion coefficient to vary with concentration for all systems investigated. The factors determining this variation have not been ascertained. However, the question of whether the diffusion coefficient would become a constant, independent of concentration throughout a single phase if the concentration gradient in the diffusion equation were replaced by an activity gradient has been an attractive subject for speculation. Wagner1 derived an expression for the force acting on a diffusing particle in terms of the chemical potential. This was also the approach chosen by Jost2 in his monograph. From a somewhat different point of view, Eyring3 and his co-workers have used activity gradients when dealing with diffusion in concentrated nonideal solutions. The only actual test with experimental data is that given by Darken,4 though this is more qualitative than quantitative. Many others opposed the application in any way of thermodynamic concepts to kinetic phenomena, including diffusion processes. A rigorous examination of this principle requires good data expressing the relationship between activity and concentration for solid solutions for which reliable diffusion work has been done. The literature provides such information only for the interstitial solution of carbon in gamma iron (austenite) and for the substitutional copper-zinc solutions (alpha brass). Activity data for carbon in austenite at 800°C and 1000°C are available from the recent work of Smiths on the equilibrium of hydrogen-methane and carbon monoxide-carbon dioxide mixtures with gamma iron. Combining these with the diffusion studies of Wells and Mehl6 makes possible a quantitative test for this interstitial solid solution. The vapor-pressure determinations for zinc over brass by Hargreaves7 allowed the calculation of activities in this system over a wide range of temperatures and concentrations. Extensive investigation of diffusion in this substitutional solid solution has been carried out by Rhines and Mehl.8 ACTIVITIES IN BRASS9 If the vapor phase of zinc is assumed to behave as an ideal gas, any solid or liquid solutions that are in equilibrium with the same partial pressure of zinc at the same temperature have the same thermodynamic activity of zinc. In order to assign a numerical value to the activity azn, it is necessary to choose some standard reference state to which an activity value of unity is arbitrarily assigned. It is customary to choose the liquid or solid state of the pure material. Then azn is defined numerically by azn = Pza/Pzn° [I]

Jan 1, 1947

By John S. Crandall

Occurrence: small crystals in alluvial sands from the eroding Belt Series mica schists. Flowsheet: dragline, trommel screen, jigs, drier, crusher, screens. Value: ground, $2.50 per cu yd, garnet sand gross $60. per ton. Costs: production and sales $48. per ton. Uses: blasting sand in aircraft plants, monumental works, foundries. Efficiency comparison: superior to silica sand. Future: possibilities only touched upon, research continuing.

Jan 1, 1950

By F. C. Langenberg

IT is the purpose of this paper to present a limited amount of experimental data obtained on the Charpy impact machine. Several concrete examples will be given showing the relation existing between the results obtained upon the Charpy impact machine and the behavior of the parts tested when in service. Although it is pointed out by G. Charpy and A. Cornu-Thenard1 that it is first necessary to determine a satisfactory working process before studying the correlation between the results of these tests and the behavior of the parts tested in service, this ideal course cannot be strictly adhered to. If a certain part repeatedly fails in service and the available tests give no indication of its cause, advantage must be taken of any possible means that will solve the problem; therefore, even though the reliability of the results obtained by the Charpy impact machine have been questioned by many, it was necessary to use this instrument without giving careful consideration to its possible sources of error. It would seem that the conclusions arrived at by Charpy and Cornu-Thénard justify the assumption that the precision obtained by this machine is comparable to that obtained by, the other more common forms of testing. The second general conclusion arrived at by them, namely, that the impact test upon notching does not offer any direct correlation to the ordinary tests, is also borne out by many hundred determinations made in the laboratories at Watertown Arsenal. This statement, however, should be qualified as follows: Other ordinary tests include the static tensile test from bars taken in a longitudinal .direction and the Brinell hardness. The author agrees that no law is yet known for the computation of the energy absorbed in the rupture of bars of the same material but of different dimensions. Although Charpy and Cornu-Thénard do not refer in their valuable article to the use of the Charpy machine in industrial practice, it should be stated that this instrument has been in constant use in the laboratory at Watertown Arsenal for several

Jan 8, 1919

By L. H. Schwartz, S. K. Lahiri, M. E. Fine, D. Chandra

WHILE the yield stress of solution treated Fe-Cu alloys increases rapidly with aging, a precipitate has only been directly observed in overaged samples.'-" This precipitate is essentially pure fcc copper, the E phase. Hornbogen2 suggested that the initial hardening is due to clustering of copper atoms in a bcc iron matrix. Hornbogen was not able to obtain direct confirmation for such bcc clusters by either X-ray diffraction or electron microscopy; however, he did observe analogous clustering in Fe-Au alloys7 where the scattering factor difference between iron and gold is more favorable than that for iron and copper. Fujii, Nemoto, Suto, and Monma4 recently observed diffuse electron diffraction scattering in a 2.5 pct Cu alloy aged at 500°C: for 30 hr. They suggested that part of the diffuse SCattering was due to a modulated structure of 26 to 42 wavelength parallel to the (110) matrix plane. This disappeared with further aging. However, 30 hr at 500°C is well beyond the peak strengthening in this alloy which occurred at less than I hr at 500oc.4 By transmission electron microscopy they could not distinguish between quenched samples and samples aged to maximum strength. The purpose of the present investigation was to try to obtain further confirming evidence for a precipitation stage preceding the formation of the fcc E phase. Change in Young's modulus was selected for study be- EXPERIMENTAL PROCEDURE The Fe-1.67 at. pct Cu alloy was supplied by the U.S. Steel Corporation in the form of a hot forged rectangular bar. The carbon and nitrogen contents of this alloy were 70 ppm and less than 10 ppm, respectively. The samples for Young's modulus measurements were made by cold swaging to & in. diam and cutting to 2 in. lengths. Tensile test samples 1 in. long were prepared by cold rolling to a thickness of 0.012 in. and then machining to gage dimensions of 0.5 by 0.012 in. For Mijssbauer studies, foils 1 mil thick were prepared by cold rolling. During fabrication the alloy was given intermediate anneals at 845OC followed by quenching. The specimens after preparation were solution treated at 1000°C (y field) or 845°C (a field) for 1 to 2 and 5 to 6 hr, respectively, in a dynamic vacuum of about 2 x lom6 torr. The tensile and modulus specimens were drop-quenched into iced brine through an aluminum foil which vacuum-sealed the bottom of the furnace tube. The MOssbauer foils were drop-quenched into helium gas cooled by passing through N2 (liq) in a copper coil. The grain diameter of the modulus and tensile specimens was between 0.025 and 0.035 mm. The samples were aged from 400" to 500°C in a dynamic vacuum of 2 x 10-6 torr and cooled by pulling into a water-cooled portion of the vacuum system. The dynamic Young's modulus was measured at room temperature using electrostatic excitation and detection of longitudinal vibrations.' Neglecting any length change during the aging, (this is expected to be comparatively small), the fractional change of Young's modulus (?Et)/Eav, is equal to twice the fractional change of the resonant frequency (?ft)/fav . ?ft =ft —fo where fo and ft are the resonant frequencies of a specimen before aging and after aging to time t. The measured f's, approximately 51,000 cps, were corrected to 25°C for any variation in the ambient temperature. The tensile tests reported were carried out at room temperature in an Instron with a 1000 lb full scale load cell. The flow stress reported herein corresponds to a strain of 0.002. The Massbauer spectra were taken in a constant acceleration model AM-1 NSEC spectrometer. The

Jan 1, 1970

By A. S. Venkatadri, H. B. Bell

The equilibrium sulfur distribution between molten iron and Ca0-Mg0-Al203 slags containing iron oxide was investigated at 1550°C. The results were used to derive the iron oxide activities at low iron oxide concentrations in the slag by combining the sulfide capacity data obtained from gas-slag work with the free energies of both the sulfur solution in iron and the iron oxide formation in slag. The derived ferrous oxide activities were compared with values based on Tem-kin's kin's and Flood's ionic models. One difficulty in using these models is that the nature of the aluminate ion in slag is uncertain. Nevertheless, such indirect methods, in particular, those described in the present paper, are of value because of the difficulty of measuring small amounts of oxygen in liquid iron in equilibrium with slag. It is shown that these methods confirm the consistency of thermodynamics data on liquid iron and slags. It is well established that decreasing the iron oxide activity in the slag increases the desulfurization of molten iron at constant slag basicity. This effect is most pronounced at the very low iron oxide activities, characteristic of blast furnace slags. Yet a precise quantitative determination of the significance of low iron oxide contents in slag in blast furnace desulfuri-zation is not possible for the following reasons: a) difficulty of separation of iron "shots" from the slag, and b) errors in chemical analysis of small amounts of iron oxide in slags. In view of these obstacles, one must resort to indirect methods of calculating iron oxide activities. EXPERIMENTAL TECHNIQUE The apparatus for providing the sulfur equilibrium data has been described previously1 and was similar to that used by ell' in connection with the study of slag-metal manganese equilibrium. The procedure consisted of: a) melting about 50 g of Armco iron in a magnesia crucible in a platinum furnace, b) adding a mixture of about 15 g of lime-alumina slag and varying amounts of Fe2O3 and CaS, and c) maintaining the temperature at 1550°C for more than an hour in an atmosphere of argon to enable the sulfur equilibrium to be attained. Several melts were made using lime-alumina slags with basic composition 55, 50, and 45 pct lime. During the experiment the temperature was controlled manually using a Pt/10 pet Rh-Pt thermocouple. After the experiment, the Power was shut off and the flow rate of argon was increased to freeze the melt as quickly as possible. The analysis of sulfur in the metal was carried out by the oxygen combustion method3 using uniform drillings from the top and bottom of the metal button. After crushing and grinding and removal of any iron particles with the aid of a hand magnet, the slag was analyzed for sulfur by the CO2 combustion method.4 The E.D.T.A. method was employed for the analysis of lime5,6 and magnesia,= the ceric sulfate method7 for the analysis of slag iron oxide, and the perchloric acid dehydration method5 for the analysis of silica. The remaining amount was taken to be Al2O3 precipitation with ammonium hydroxide in several preliminary melts had confirmed the propriety of using this simple procedure. RESULTS The activity of iron oxide in binary, ternary, and more complex slags has been the object of numerous investigations, and the two experimental methods for its determination are: 1) Equilibrating the metal with the slag in question and measuring the oxygen content of the metal. The ferrous oxide activity is then given by aFeO L%OJSat where [%0]sat is the oxygen content of the metal in equilibrium with pure iron oxide slag. This method was used by Chipman et al.8,9 2) Equilibrating the slag in iron crucibles with known partial pressures of H2/H2O or CO/CO2 mix-tures.10-12 This method is limited to temperatures between 1265" and 1500°C. The very low oxygen content of the melts in this investigation made it impossible to derive the ferrous oxide activity by the first of these methods. Therefore, the iron oxide activities were computed by means of: Sulfide capacity data from the gas-slag work" Temkin's concept14 Flood's approach15 a FeO from Sulfide Capacity. The method of calculating the aFeO involves the sulfide capacity of the slag (c,), the sulfur distribution coefficient (Ls), the free energy of dissolution of sulfur in iron, and the free energy of formation of iron oxide in the slag. Bell and Kalyanram13 have investigated the sulfur absorption characteristics of lime-alumina slags containing magnesia by the Carter-Macfarlane method16 (based on comparing the sulfide capacity of the slag in question with that of a standard slag of unit lime activity) and have derived lime activity values. The relation between sulfide capacity and their lime activity a'CaO is given by: Cs= 3—: Xa'CaO at 1500°C

Jan 1, 1970

By W. Rostoker, R. P. Elliott, B. W. Levincer

Phase equilibria in the Ti-Cr-Mo system have been investigated for alloys containing 100 to 40 pct Ti in the temperature range 550° to 1300°C. Five experimental isothermal sections and a surface of incipient melting are presented in addition to a summary projection of the space. Seven vertical sections have been constructed from the isothermal sections. A STUDY of the system Ti-Cr-Mo was undertaken as part of a program sponsored by Watertown Arsenal toward the development of titanium-base phase equilibrium diagrams of potential technical importance to alloy development. The scope of the investigation included the composition range contained by the titanium corner and the line of 64 pct Ti (all compositions are by weight) and the temperature range 550" to 1100°C. A surface of incipient melting was constructed from measurements on a large number of alloys. The system Ti-Cr has been established.&apos;-? The phase diagram is characterized by a wide miscibility field of the solid solution at elevated temperatures and a eutectoid reaction of the type: (15 pct Cr) + TiCr, (685C). The a solid solution has a very limited capacity for solution of chromium (< 0.5 pct Cr). The intermediate phase TiCr2 has at best a very narrow composition range. It has been shown that two allotropic modifications of this phase exist. However, this behavior does not appear to be perceptibly reflected in the form of phase boundaries of the type + TiCr,. In the system Ti-Mo,9-10 the phase is stabilized to successively lower temperatures with increasing molybdenum content. There are no known intermediate phases. The a solid solution is limited to less than 0.5 pct Mo. Because of the very extensive range of the phase, the ternary system was ideally suited to the determination of the phase boundaries by the parametric method of Andersen and Jette." A parametric surface was constructed to provide the necessary basis for the application of this method. Preparation and Treatment of Alloys More than 60 alloy compositions were prepared for the study of this system. Alloy buttons of 10 grams were arc-melted in a nonconsumable electrode furnace using inert atmosphere protection and a water-cooled copper crucible. The construction and operation of this type of melting unit have been adequately described elsewhere.&apos;&apos; To insure complete solution of alloy additions, the buttons were remelted alternately on top or bottom as many as five times. This was accomplished by a suitable mechanism for "flipping" over the ingots. Iodide titanium (99.97 pct Ti) was used as the alloy base. An especially high quality chromium (99.9 pct Cr) was obtained from the National Research Corp. Molybdenum sheet (0.005 in.) of 99.9 pct purity was used.

Jan 1, 1954

By Paul M. Tyler

MUCH has been said in print, and much more that was unprintable, about burdensome controls, taxation, and multiplying restrictive, regulatory, or taxing activities of the Federal Government, but not so much has been said about ways and means whereby the Government can and does render economic assistance. Economics has been defined as the study of men earning a living, and economic assistance to industry as well as to individuals properly should take the form of helping enterprisers to help themselves rather than charity. Proposals to have the Government play Santa Claus must be examined carefully if -only to avoid undue favoritism to politically important persons and downright venality by potentially crooked public officials. Thomas Jefferson is credited with the remark that the best government is the one which governs least. Paternalism is abhorrent to most Americans.

Jan 1, 1947

[ ] DISCUSSION F A LORIA*-The method of testing gun steel for resistance to surface cracking described in this paper was restricted to the examination of small, rod-shaped specimens The writer would like to point out the importance of other factors in producing defects in forged and bored gun tubes which would not be apparent in this investigation because of the nature of )he test Actual section size would accentuate the possibility of internal wall (bore) defects arising from unequal expansion between the internal and external wall surfaces on firing, resulting in internal tearing Checks and tears on the inside walls arise from internal tensions and nonuniformity on cooling, but the internal tearing can be reduced by using alloys of low expansion and of good thermal conductivity so as to reduce the difference between the outer and inner wall surfaces Also, the possibility of the location of inclusion segregates within a machined gun tube becomes more likely than in a small test specimen The effect of these nonmetallics on gun life and performance is evident when one realizes that the inclusions are soft yet brittle They reduce the amount of plastic deformation which can take place before cohesive failure occurs Once localized fracture has occurred at the position of a chain of these inclusions, a sharp notch (crack) is formed which produces stress conditions more favorable to cohesive failure than to plastic deformation These cracks aid erosion by providing channelways for the explosive gases, eventually leading to the tearing out or spalling of blocks of metal Oxidation of the surface may be partly responsible for the change in the surface of gun steel during firing observed by the author The appearance of burn on the surface is an indication that high temperatures were reached on firing, resulting in a slight oxidation of the surface Since the color of the oxidized film depends on both temperature and time, a higher temperature is required for a given color to form when it is caused by explosive heat, which acts for only an extremely short time at a given spot, than when it is caused by ordinary tempering The cross section of the gun steel specimen, Fig 16, illustrates that the repeated firing temperatures were high enough to cause

Jan 1, 1948

By James P. Sloss

A PERMANENT assay office is commonly established as part of the general plant equipment of operating gold and silver properties, but during the development stage of a mine, the cost of such an office is usually so assay work must be done elsewhere. In most instances only a few samples will be taken each day, but if the mine is to be developed scientifically, the analyses of those samples will guide further development. Under such circumstances, the time element in assay returns is important, since the lapse between the taking of the samples and the receipt of results may determine the success or failure of a small-mine operator. The following description of fur-

Jan 1, 1935

By G. A. Beske, P. Hilsch, J. Wulff

The effects of the growth precipitates on the su-perconduching properties of an Al- 15 al. pel Zu alloy have been studied using magneization, transition lem-perature, and residual resistivity measurements. Aging at 230C for 1/2 to 11 he produces an increase in Hfp, Ike field of first penetration, and tut increase in trapped flux. The upper critical field, Hc2 remains constant for such aging tunes. Aging at 200°C produces a decrease in Hfp and an increase in trapped flux. The transition temperature remains constant at Tc - 1.227° ± 0.02°K for aging at 220°C for tims of from 1/2 to 10 hr, and for aging at 200°C it remains constant at Tc. = 1.18° i 0.02°K for times from 1/2 hv to 26 hr. The observed behavior indicates that the superconducting matrix when aged at 220°C behaves tike a type U su-perconducior, but when aged at 200°C behares like a type I superconductor. The magnetization changes after aging can be attributed to the growth and clutnge in distribution of the precipitate in a matrix of fixed composition. IT has been realized for some time that the superconducting properties of alloys are highly structure-sensitive. This is evident in the work of Mould and Mapother1 who examined the properties of an aluminum alloy. Precipitation effects have also been briefly mentioned in other studies.2-4 Bonnin and coworkers5 have observed a sharp inc rease in trapped flux in an A1-Mg alloy when the residual resistivity reaches a value that indicates it is a type II superconductor. Recently Blanc, Goodman, and Nemoz5p have reported on precipitation effects in A1-Ag alloys. Detailed studies of precipitation in Pb-Sn and Pb-Cd alloys made by Livingston6 serve to show that the upper critical fields are enhanced by quenched-in solute. Furthermore. at various stages in the precipitation process? the upper critical field is determined largely by the remanent solute. The observed magnetic hysteresis and trapped flux in such alloys result from the interaction between precipitate and the flux filaments in the mixed state. The flux trapping appears to depend largely on the precipitate distribution and is greater if the superconductor is type II than if it is type I. To examine the effect of precipitation in another alloy system, particularly one in which the composition of the superconducting phase does not change significantly during the course of precipitation, the Al-Zn system seems interesting, especially in view of the transition temperature and resistivity studies of Chiou and seraphim.&apos; Furthermore, the recent detailed electron-microscope studies of an Al-Zn alloy by Richards and Garwood8 provide a guide for relating superconducting properties to changes in structure. For these reasons, magnetization, transition temperature, and residual resistivity measurements for varying times of heat treatment at two temperatures were made with a -15 at. pct Al-Zn alloy. The results are reported in this paper. I) EXPERIMENTAL The alloy used was prepared by Cominco Products Inc. from 99.9999 A1 and 99.999 Zn. It was chill-cast, swaged, and drawn to 0.125-in.-diam rod. The analyzed composition was 15.6 at. pct Zn (31.1 wt pct). A jeweler&apos;s saw was used to cut the 0.125-in.-diam rod into the 0.875-in. lengths needed for magnetization measurements. The ends of the cylinders were slightly beveled to remove the sharp edges. A portion of the original 0.125-in.-diam rod was drawn into 0.010-in.-diam wire and used for transition temperature measurements. Specimens were suspended from wires within a vertical furnace during heat treatment. All were homogenized at 500°C for a minimum of 3 days and subsequently solutionized for times in excess of 6 hr. The solutionizing temperature was held constant to +3°C. Individual specimens were homogenized, quenched, and aged several times and no effects indicating loss of zinc were noted. The suspended specimens were quenched by cutting the wires and allowing the specimens to fall into a silicone oil bath held at the aging temperature. They were then isothermally transforked by aging in the same bath used for quenching. After aging for the required time (approximately 10 min aging was necessary before the upper critical field reached a fixed value), they were briefly (1 to 2 sec) dipped into an acetone bath at room temperature to remove adherent oil and then immediately transferred to liquid nitrogen where they remained until inserted into the helium bath (usually within an hour). The temperature of the aging bath was held constant to +3°C for longer aging times. The cryostat used for the measurement of superconducting properties consisted of outer and inner dewars for liquid nitrogen and liquid helium, Stokes 6-in. booster diffusion pump and Stokes Model 212 mechanical pump, temperature controller to measure and control the temperature of the helium bath, and a superconducting solenoid with inserted search coils to provide the magnetic field and measure the magnetic moment of the specimens. A schematic diagram of the cryostat is shown in Fig. 1. An ultimate temperature of 0.85°K was reached with this apparatus. The temperature controller used is similar to the one described by Blake and chase.&apos; A 0.5 pct Allen-Bradley carbon resistor and a nichronle heater (200

Jan 1, 1968

By Jacques B. Wertz

Both the San Andreas fault complex and the Murray fracture zone are apparently found to be contemporaneous with the Laramide mineralization period. Their compounding effects certainly have disturbed the Texas lineament belt and its components with serious lateral offsets and most probably have been instrumental in allowing intrusives to be emplaced as well as mineralization to accompany these intrusions at some of the fracture intersections. While the main fracture centers can be almost accepted as being structurally linked together, the Texas lineament trend definitely predominates, exerting a prevailing direction to graben (Silver Bell) and to elongated depressions (Bisbee). That this lineament belt also influenced the concomitant mineralization seems a logical inference. The orebodies are generally found at intersections near the most centrally-located intrusive with a distance varying from contiguity to one or two miles. The Southeast Arizona copper province owes its existence primarily to a particularly favorable structural setting of broad semi-continental scope. Thus, various regional structural elements are to be considered as possibly direct or remote cause for the widespread mineralization, although the one or the ones really responsible may never be singled out. There arc three basic regional elements: (1) The north-northwest-trending anticlinorium that diagonally crosses Arizona is quite obvious because many mountain ranges follow this direction. This anti- clinorium, which merges northward into the Wasatch-Jerome Belt, marks a broad zone of weakness where tension seems to prevail. Mineralized trends such as Jerome-San Manuel-Bisbee may give some weight to the economic value of this structural element. (2) Northeast-trending fractures, parallel to the Colorado Mineral Belt (Landwehr, 1967), appear troincident with mineralization as evidenced by the Questa-Grants-Morenci and the Lordsburg- Tyrone-Santa Rita alignments. This structural direction is accepted as one of the most economically significant in the Southwestern United States. (3) The Texas Lineament.

Jan 1, 1970

By M. Prats, D. G. Russell

The performance of a well in a bounded, layered reservoir with interlayer crossflow has been investigated mathematically. The system studied comprises a centrally located well in a bounded cylindrical reservoir composed of two layers of contrasting physical properties. The reservoir contains a single fluid of small and constant compressibility. In the case of a well producing at constant pressure, the production rate of the crossflow system declines exponentially after the early transient behavior dies out. For wells which produce with constant rate, the pressure-time relationship is linear following the transient. For very early production time, the production rate of the two-layer crossflow system behaves as that of the two-layer stratified system (the case in which the layers are in communication at the well only). Except for early time, in most practical cases the performance of a two-layer reservoir with cross-flow can be duplicated by that of a single-layer reservoir. The equivalent single-layer reservoir must have the same pore volume and the same drainage and wellbore radii as in the two-layer case. In addition, the equivalent reservoir must have a "kh" (permeability x thickness) product equal to the sum of the "kh" products of the respective layers in the crossflow system. If the porosity and permeability distributions are known, the production and pressure behavior of a well with and without crossflow can be predicted. From a comparison of the observed pressure or production performance of a well and the theoretical behavior, the occurrence of interlayer crossflow can be detected. INTRODUCTION When flow is possible across the bedding plane from a low-permeability layer into an adjacent layer of moderate or high permeability, the earlier depletion of the more permeable layer will cause such flow to occur. If this situation exists, the oil recovery from tight layers can be appreciable; thus, the economic ramifications of interlayer crossflow are apparent. The possible importance and extent of flow between adjacent and connected layers — whether resulting from capillary, gravitational, or viscous forces — have been the subject of considerable speculation for many years. Jacquard1 presented a rigorous analysis of the crossflow due to single-fluid expansion occurring between two adjacent and connected layers when the well produces at constant rate. His presentation was entirely mathematical, however, and no numerical results from evaluation of the mathematical solutions were presented. Our objectives in the preparation and presentation of the present paper are essentially twofold— (1) to analyze the behavior of a well which produces a single compressible fluid from a bounded, layered reservoir with interlayer crossflow, and (2) to present practical numerical results and simplified formulas to facilitate engineering analysis of reservoirs with crossflow. The constant-terminal-pressure case was analyzed rigorously, whereas the constant-terminal-rate case was treated only for semisteady-state conditions. DESCRIPTION OF THE IDEALIZED TWO-LAYER RESERVOIR The reservoir to be studied is assumed to be bounded and cylindrical in shape, with a completely penetrating well at its center. The reservoir is composed of two adjacent horizontal layers between which fluid is free to flow. Each layer is assumed to be homogeneous, isotropic and completely filled with a fluid of small and constant compressibility. The total thickness of the reservoir is small enough

By F. R. Hensel

P. R. Kalischer.*—I should like to amplify a little one of the points made by Dr. Hensel, and rather violently disagree with him at the same time. He brought out the point that when the higher forming pressures are used on the green compacts there is a marked decrease in the density as sintered. We found that to be true and, of course, many of you notice that that is true with copper compacts also. But, in my opinion at least, it is not true that the expansion is due to entrapped air. We have vacuum-pressed both silver and copper compacts and obtained almost exactly the same numerical expansion as we secured by pressing in air. The powder, however, that is vacuum-annealed does show a slight decrease in expansion on sintering, but almost the entire increase on expansion can be overcome by very slow rates of heating. And it is our opinion that a majority of the expansion is due to dissolved oxygen in the discrete metal particles themselves rather than to entrapped gases. Another interesting observation that we have made is that often with silver or copper compacts it is desirable to silver solder or braze the compact into some part of a piece of equipment after completing powder metallurgical operations on it. If such a compact is sintered and coined, say a silver compact, given an initial forming pressure of 10 to 15 tons per square inch, and sintered, there is an adequate amount of shrinkage and it can be coined at about 50 or 60 tons per square inch and bring up the density nearly to theoretical. If, then, that compact is silver-soldered into some part of a fixture or a machine, it will expand very beautifully, and the only way that this can be overcome. as far as we know, has been to reanneal after the coining operation at a temperature higher than is to be used in any subsequent operation. In that way, a density very nearly theoretical can be achieved, but the coining operation cannot be carried to the excessively high pressures or expansion and bubbling of the compact will occur again.

Jan 1, 1945

By E. S. Davenport

WHEN annealed carbon, or low-alloy, steels are suitably heated the ferrite (alpha iron solid solution) and the carbide, of which they are composed, react together to form a single solid solution of carbon (and other elements) in gamma iron (austenite). This reaction may begin only at a certain minimum temperature called the eutectoid temperature. The first ferrite and carbide thus to react together do so in definite proportions known as the eutectoid composition. With further heating the original constituent that is present in excess is dissolved in the austenite until exhausted. Whether the excess constituent be ferrite (hypoeutectoid steels) or carbide (hypereutectoid steels) the procedure is much the same, and upon slow cooling the homogeneous austenite expels the excess of either (proeutectoid ferrite or carbide) until the eutectoid composition is reached. Thus the reaction upon heating is strictly reversed upon cooling and accordingly an equilibrium diagram of this process may be constructed. Such an equilibrium diagram concerns itself only with the tempera¬tures involved and with the proportions and compositions of the phases developed under conditions that suffice to permit equilibrium. Specifically it has no concern for the type or mode of distribution of these constituents nor with any extra-equilibrium conditions such as undercooling, which is almost universally encountered in metals. Actually, however, of great importance is the sluggishness toward equilibration caused by the not inconsiderable time involved in diffusion. Thus instead of the theoretical transformation point AE, we find for a certain rate of heating or cooling the use of the designations Ar and Ac (transformation temperature found on cooling and upon heating). These figures obviously have no particular meaning except as measured and expressed for a definite heating or cooling rate, and represent the apparent temperature displacement caused by an inadequate time allowance. In this paper are presented the results of a study of the time required for&apos; the transformation of austenite to ferrite and carbide at a variety of temperatures and also of the time required for the reaction austenite ?martensite at the temperatures at which this reaction occurs instead of

Jan 1, 1930

New York Meets first Wednesday after first Tuesday of each month. J. E. JOHNSON, JR., Chairman EDGAR RICHARD, Vice-Chairman D. M. LIDDELL, Secretary, 7 Wall St., New York, N. Y. C. A. BOHN, Treasurer JOHN V. N. DORR LEWIS W. FRANCIS Boston Meets first Monday of each winter month. R. L. AGASSIZ, Chairman JAMES G. CARLETON, Vice-Chairman E. E. BUGBEE Secretary-Treasurer, Mass. Inst. of. Technology, Cambridge, Mass. W. E. C. EUSTIS G. A. PACKARD Columbia Holds four sessions during year. Annual meeting in September or October. W. H. LINNEY, Chairman OSCAR LACHMUND, Vice-Chairman LYNDON K. ARMSTRONG, Secretary-Treasurer, P. O. Drawer 2154, Spokane, Wash. STANLY A. EASTON S. SHEDD Puget Sound Meets second Saturday of each month SIMON H. ASH, Chairman I. F. LAUCKS, Vice-Chairman PERCY E. WRIGHT, Secretary-Treasurer, 2012 L. C. Smith Bldg., Seattle. Wash. GLENVILLE A. COLLINS JOHN N. POTT

Jan 11, 1917

By B. S. Tani, R. V. Schablaske, M. G. Chasanov

In the Ti-Cd system two intermediate phases, TiCd and Ti Cd, have been found and characterized by X-ray diffraction powder techniques. An earlier reference&apos; had reported the existence of the compound Tisd. No structural details, however, were given nor was there any indication of the possible existence of other binary compounds. Studies of the solubility of titanium in liquid cadmium2 led to the discovery of both TiCd and Tisd. The solid phase in equilibrium with saturated solutions of titanium in liquid cadmium at temperatures below 620°C is TiCd, whereas TizCd is the equilibrium solid phase above 620°C. Both thermal analysis and X-ray studies show that a peritectic reaction between the y phase (~isd) and cadmium to form the 6 phase (Ti Cd) occurs at 620°C. X-ray diffraction powder photographs of material isolated from the ingots used in the solubility measurements as well as material prepared by a direct heat of the appropriate stoichiometric amounts of titanium and cadmium can be indexed on the basis of a tetragonal unit cell with a = 2.904 ± 0.002A, co = 8.954 * 0.004A, c/a = 3.083. No variation of lattice parameters indicative of a range of composition is evident. With four atoms in the unit cell the calculated density of the intermetallic is 7.05 g per cm3; the observed value is 7.07 g per cm3. The TiCd lattice is primitive as indicated by the fact that there are no systematic absences among hkl reflections. The absence of all hko reflections for which h + k = 2n + 1 is also evident. This systematic absence indicates the following two space groups, C\h — P4/n and D&~4/nmm; both groups, however, have the same two- and four-fold positions. Stoichiometry, symmetry and space group indicate two likely structure types. They are the PbO-litharge3 (B10) type and the Ti CU (B11) type. Spatial considerations favor the B11 structure with atoms placed in the following positions: 2Ti (c) 0, 1/2, Z; l/2, 0, Z 2Cd(c) 0, 1/2, Z; 1/2, 0, Z The TiCd structure may be summarily described as a layered structure in which double cadmium layers alternate with double titanium layers along the c-axis. The best agreement between calculated and observed intensities is obtained for the values ZTi = 0.608 and ZCd = 0.130. Calculated and observed powder intensities as well as other pertinent powder data are recorded in Table I. Interatomic distances for the proposed structure are recorded in Table II and are to be compared with the distances of closest approach for titanium and cad-

Jan 1, 1962

By S. T. Wlodek

The surface and subscale oxidation reactions were followed by means of continuous weight-gain and metallographic techniques over the range 1600" to 2200°F (871° to 1204 °C) for up to 400 hr. Full identification of all scale and subscale reaction products was obtained by electron and X-ray diffraction. At or below 1800°F (982°C) a linear rate of reaction (QL = 46.0 kcal per mole) governed the oxidation process, extending for up to 100 hr at 1600°F (871 "C). During linear oxidation the surface scale consisted of an amorphous SiO2 film overgrown with Cr 2O 3 and NiCr204. This initial linear process was followed, and above 1800°F completely replaced, by two successive parabolic rate laws (Qp = 60 and 57 kcal per mole). This parabolic reaction involved the formation of a complex scale consisting of Cr2 O3 and smaller amounts of NiCr2O4. Parabolic oxidation appeared to coincide with the disruplion of the silica film present during linear oxidation and was followed by subscale (internal) oxidation of crystobalite and NiCr2O4. The balance between the subscale and surface oxidation reactions controls the oxidation of this commercial alloy. The amorphous silica film appears to result in the linear rate and diffusion through Cr2O3 is the more likely rate-limiting step during parabolic oxidation. THE oxidation of a multicomponent composition is a complex phenomenon not presently amenable to a rigorous classical interpretation. Nevertheless, even a qualitative understanding of the scaling and subscale reactions that occur in a commercial composition can illuminate the reactions that limit its high-temperature stability in an oxidizing environment. This study of the oxidation of Hastelloy Alloy X presents the first of a series of studies with the above approach in mind. Hastelloy X exhibits one of the best combinations of strength and oxidation resistance available in a wrought, solution-strengthened, nickel-base alloy. Although during long time exposure some precipitation of M6C and M23C8 carbides as well as a complex Laves phase occurs, the amounts are probably small enough to have no appreciable effect on the chemistry of the matrix. Radavich has identified the oxidation products on Hastelloy X oxidized for 5 min to 10 hr at 1115°F as NiO and the NiCr2O4 spinel. Oxidation for 5 to 15 min at 1500°F produced a scale of spinel, NiO, and a rhombohedra1 phase, probably Cr2Os. Sannier et 2. have reported continuous weight-gain data for Hastelloy X at 1650" and 2010°F and internal-oxidation measurements after 150 hr at 2010°F. In addition, much of the data on binary Ni-Cr alloys recently reviewed by Kubaschewski and okins&apos; and Ignatov and Shamgunova4 as well as studies of binary Ni-Mo alloys5 are also pertinent to the oxidation of this composition. EXPERIMENTAL Continuous weight-gain measurements and metallographic measurements of subscale reactions were the main experimental techniques used in this study. X-ray and electron diffraction backed up by a limited amount of electron-microprobe analysis served to characterize the nature of the scale- and subscale-reaction products. Two heats of commercial sheet of the composition given in Table I and identified as A and B were used in the bulk of this study. Internal-oxidation measurements were made on a third heat of material in the form of a 0.5-in.-diam bar. In order to assure homogeneity, all heats were reannealed 4 hr at 2175°F prior to sample preparation. weight-Gain Measurement. All specimens (1.5 by 0.4 by 0.03 in.) were abraded through 600 paper, electropolished, and lightly etched in an alcohol-10 pct HCl solution. An electrolyte of 150 cu cm H,O, 500 cu cm HsPO4 (85 pct conc), and 3 g CrO3 at a current density of 0.9 amp per sq cm or a solution of 10 pct HaW4 in alcohol used at 4 v and 0.3 amp per sq cm was used for electropolishing. The resultant surface exhibited a finish of 3 ± 1 p rms. Continuous weight-gain tests were made at 1600°, 1700°, 1800°, 1900°, 2000", and 2200°F on auer&apos; type balances capable of recording a total weight change of 110 mg with an accuracy of k0.1 mg. All tests were made in air dried to a dew point of -70°F and metered into the 2-in.-diam reaction

Jan 1, 1964

By Frederick T. Williams

THE purpose of this paper is to discuss the relative merits of the large 31/8 in. machine and the small 21/4-in. tappett machine in driving development-headings ; and although the . data here presented were obtained from cross-cut headings alone, experience has shown that the results are equally true in drifting, raising and winning. Recently we drove two parallel cross-cuts through the same formation, using a 3k-in. machine at the breast of one cross-cut., and a 2k-in. machine of the same make at the breast of the other. The results of this work afforded an ideal comparison, since in both cases the headings were advanced through rock practically of the same hardness and breaking-properties ; the amount of sludging was equal, and there was no difference in the condition of the steel or the machines, in the air-pressure or in the experience of the operating-crews. Some operators in the Cripple Creek district contend that there is ground which cannot be handled with the small machine, the holes being too small to contain enough powder to pull the ground, etc. The results obtained in working the property of the Portland Gold Mining Co., however, show that the ground worked by them does not fall in this class. During a period of two years there have been driven, with the small machine, 4 miles and 308 ft. of development-headings, through a diversity of ground, including Pike&apos;s Peak granite (a coarsely porphyritic type of granite), highly indurated, andesitic or phonolytic breccia, true massive andesite, trachytic phonolyte, tuffas, and along dikes of decomposed basalt and hard phonolyte; in every instance a satisfactory record was made. The headings here described were driven through highly indurated, andesitic breccia, having a hardness of from 5.2 to 7.2

Mar 1, 1906

By J. T. Ryan

FIGURES for the first 11 months of 1935 indicate that the total coal production of the United States for 1935 will be approximately 416,000,000 tons, or almost identical with the production figures for 1934. Bituminous production will show a gain of about six million tons, and anthracite production a loss of about the same tonnage, compared with the previous year. This does not take into account so-called "bootleg" anthracite coal amounting to approximately 5,000,000 tons. Twenty-nine years ago, in 1906, the production of coal was almost identical with this year&apos;s production. At that time, 626,000 men were employed in producing this tonnage, which took a toll of 2138 lives from accidents. In 1935, approximately 540,000 men were required to produce the same tonnage with an estimated loss of 1155 lives. This shows definite safety advancement in the industry, but even so accidents are still costing an average of 3c. a ton more than they should.

Jan 1, 1936