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By M. Amsterdam, F. Rothwarf, L. Muldawer

SILVER-cadmium near the composition AgCd shows three equilibrium phases. As with 13 brass, the high temperature phase is disordered body-centered cubic (8) and the low temperature phase has the ordered CsCl structure . However, there is an intermediate temperature phase which is hexagonal close-packed ((). In a recent paper, Speich and Mack' report on a study of the Ag-Cd eutectoid near the AgCd composition. Unfortunately, the phase diagram upon which they base some of their conclusions is incorrect. That diagram is taken from the Metals Handbook' and the error is that the 0 and ( phases have been interchanged. The Handbook gives the low temperature phase as hexagonal (designated 5) and the intermediate temperature phase as cubic ordered (designated . The error may be typographical or it may be one of confusion resulting from the use of 5, ,, and 0 for the intermediate phase in various papers. A careful search of the literature reveals that a number of authors have indicated the correct relative positions of the 13, 5, and 0 phases. The comprehensive work of Fraenkel and Wolf clearly stated that the high and the low temperature phases are either identical or are very similar. olander,' on the basis of electrochemical measurements, showed that the 13 phase is disordered and the 1 phase (designated 8" in his paper and in refs. 3 and 5) is ordered. Further work by Durrant5 using thermal and metallographic analyses provided a more precise phase diagram. A summary of these works was given by Hansen6 and shows the correct relative positions of the phases. Owen, Rogers, and Guthrie7 located correctly the upper two phases by X-ray diffraction. Their failure to find the low tem-

Jan 1, 1954

By R. F. Mehl, J. T. Ransom

For many years the Metals Research Laboratory of Carnegie Institute of Technology has been concerned with the statistical nature of the engineering properties of steel from an experimental viewpoint, particularly those properties representing ductility.' In the past three years new work has been directed toward evaluating the statistical nature of the endurance properties. It has been shown that both the fracture curve and the endurance limit in fatigue are markedly statistical in nature. The S-N curve (and the endurance limit) of ferrous materials is often determined with specimens which number as few as ten. The common procedure is to test the first specimen at a stress well above the expected endurance hmit. Each succeeding specimen is then tested at a progressively lower stress, until, after five or six tests, a specimen runs ten million or so cycles without failing. Two or three more specimens are then used to find the highest stress at which failure will not occur; the limiting stress determined in this way is called the endurance limit. It has now been found, however, that the variability in the fracture curve and in the endurance limit in heat-treated alloy forging steels is so great that S-N curves must be drawn on the basis of distribution curves which can be appraised only by statistical methods. Two methods have been adopted in this study: (1) straightforward statistical studies of cycles to fracture of a number of specimens at each of a series of stress levels, and (2) a new abbreviated statistical method, known as "staircase testing."2 The latter corisists in testing a series of specimens, one by one, with the test stress for any given specimen automatically

Jan 1, 1950

By Gearge C. Wallick

This paper describes experimental procedures for the calibration of capillary tubes to be employed as comparison standards in gas flow-rate measurements and considers several types of flow which were observed in the calibration of seven capillaries of varying diameter. It is shown that under certain experimental conditions deviations from Poiseuille flow are observed which may not be attributed to turbulence, and that this flow behavior may be described empirically by introducing the classical kinetic energy correction into the Poiseuille equation. INTRODUCTION Techniques have been developed for the measurement of the volume rate of flow of nitrogen through glass capillary tubes as a function both of the differential pressure applied and of the absolute gas pressure. Capillary tubes thus calibrated are frequently used to determine the rate of gas flow through a porous sample in the measurement of slip-corrected permeability. The purpose of this note is to describe the calibration procedure and to discuss some observed deviations from the ideal flow behavior predicted by the Poiseuille equation. EXPERIMENTAL PROCEDURE The volume flow rate of nitrogen as a function of the differential pressure was determined experimentally for a series of seven glass capillary tubes of varying diameter. As is shown in Table 1, the capillary radii in the series ranged from 0.004 cm for K1 to 0.07 cm for K7. The capillary tubes were cut from capillary tubing purchased on special order from several manufacturers and the bore radii were determined by microscopic measurement. The gas volume flow rate was measured for each capillary tube at a series of differential pressures in the range from 0 to 3 cm of mercury and at average absolute pressures of 1.0, 2.5, 4.0, and 6.0 atm. Experimental Procedure for Small Capillaries A schematic diagram of the apparatus used to calibrate the three smallest capillaries, Kl, K2, and K3, is shown in Fig. 1. By means of a standard Ruska Instrument Corp. volumetric pump (equipped with a synchronous motor drive, two stages of gear reduction, and a quick-change lathe gear box), nitrogen was displaced by mercury from a metal cell immersed in a constant-temperature bath. The pump, the line to the cell, and a part of the cell were filled with mercury. As mercury was forced into the cell, it displaced nitrogen which passed through the capillary tube being calibrated and into a large container with a volume of approximately 30 liters. Since the volume of this container was very large compared to the total volume change of the gas resulting from the action of the displacement pump, the absolute pressure of the system was essentially constant throughout any one run. Prior to any determination this pressure could be set at any desired level by means of an auxiliary nitrogen cylinder. The differential pressure across the capillary was measured with a Meriam Red Oil manometer and recorded together with the corresponding pump displacement rate which was equal to the gas flow rate. By repeating this process for a series of different displacement rates at each of the absolute pressures of interest, the data necessary for plotting the calibration curves for capillaries K1, K2, and K3 were obtained. All calibration measurements were made in a constant temperature room to minimize errors due to temperature fluctuations. In each run. the flow was maintained until equilibrium was established. Experimental Procedures for Large Capillaries The flow rates through Capillaries K4, K5, K6, and K7 required to obtain the pressure drops desired were larger than could be obtained from available constant displacement pumps, and it was thus necessary to employ an alternative calibration procedure. The arrangement of apparatus used in calibrating these capillaries at an average pressure of one atmosphere is shown in Fig. 2. Each capillary was calibrated by flowing nitrogen through the capillary and recording the differential pressure as a function of the flow rate. 'The differential pressure was measured with a Meriam Red Oil manometer and the flow rate was determined by collecting the effluent gas over water at constant pressure and recording the increase in volume per unit time after an equilibrium had been established. Appropriate corrections were made for the

Jan 1, 1953

By L. Guttman

LESTER GUTTMAN* The question of whether classical thermodynamics alone imposes any lower limit to solid solubilities was raised during a discussion among various members of the Institute for the Study of Metals. Although our conclusions are not new,1 they may be worth reiterating, since confusion on this subject seems to persist. In a binary system (A,B), the conditions for equilibrium, at constant pressure and temperature, between a solid solution and a liquid solution are µAs = µAl [la] µBs = µbl [lb] Here µ denotes the chemical potential either of component A or B, as shown by the subscripts, and the superscripts s and l refer to the solid and liquid solutions, respectively. These two conditions are just sufficient to determine the compositions of both phases. Suppose, however, that the solid phase is found experimentally not to contain any of component B; then we cannot evaluate µbs, which is defined by Here nAs and nBs are the number of mols of A and B, respectively, in the solid, whose free energy is Fs. Eq lb cannot be used, but it is no longer needed: we stated at the outset that the solid has the composition "pure A," and only the liquid composition need now be determined, from Eq la. All the equilibrium properties of the system can be derived from Eq la rigorously and simply. Hence there is no purely thermodynamic reason to exclude phase diagrams which show precisely zero solid solubility. Marsh2 has objected to such diagrams as implying that even the transformation of pure A begins at the eutectic temperature. In any case, the user of the diagram must have a certain minimum knowledge of how to interpret it, and it would seem simpler to remember the general rule that eutectic temperatures have no significance for pure components, rather than to show, say, by broken lines, on a scale which will often be exaggerated, a hypothetical solid-solubility about which we know only that it is less than a certain amount. The case of an intermetallic compound in equilibrium with a binary liquid solution does not require a separate treatment since nothing in the foregoing was dependent on the nature of the components. Therefore, thermodynamics alone does not exclude the possibility that (intermetallic) compounds may exist with compositions always precisely those given by their chemical formulas. With the aid of extra-thermodynamic methods, one may conclude that the solubility of one solid in another is never exactly zero. On the other hand, one would generally expect that the solubility will be small unless the components resemble one another (as do the metals), or form weakly-bound crystals. Therefore, it is useful to know that when there is no direct evidence for solid-solubility, one may neglect it without violating thermodynamic principles.

Jan 1, 1950

By Leonard B. Lipson

Boyer, Morgan and Muskat,' with improvements by Morgan, McDowell, and Doty,l and Laird and Putnam,' have described a scheme for the determination of fluid saturatic in porous media by measuring the x-ray linear absorbing power of particular fluids in the media. This method is one of several which depend on the linear absorbing power of the fluids in the porous medium. Other examples of linear absorption methods involve measurement of dielectric constant, gamma ray absorption, and ultrasonic attenuation. It is the purpose of this note to demonstrate by theortical considerations that the absorption versus saturation curve for a linear absorption method is not necessarily a single valued function of the saturation. Such non-unique behavior must be considered and evaluated before suitable saturation determinations can be made by a linear absorption method. To illustrate the discussion, examples will be given only for the simplest cases of combinations of two different dielectrics. The dielectric constant method was chosen for illustration because it was thought to demonstrate most graphically the point in question. According to Argue and Maass,4 the resultant dielectric constant of a combination of two different dielectrics depends on the orientation of the dielectrics in the electric field of the test condenser used to measure the dielectric constant. One ease involves alternate slabs of dielectrics E1 and E2 perpendicular to the electric field of the test condenser, as shown in Fig. 1A. For this case: l/'E, = A/E, + B/E,.......(1) where E,,, is the dielectric constant of the combination, A is the ratio of the path length through dielectric E, to the distance between the plates of the condenser (assuming the dielectrics have the same cross sectional area as the condenser), and B is the ratio of the path length through dielectric E2 to the distance between the plates of the condenser. It will be noted that the constants A and B are numerically equal to the fractional "saturation" of the region between the test plates of the condenser by the two dielectrics E1 and E2, respectively. Another case involves alternate columns of the two dielectrics parallel to the electric field and forming a continuous path between the condenser plates, as shown in Fig. 1B. For this case: E., = AE1 + BE2.........(2) where E., is the dielectric constant of the combination, A is the ratio of the cross sectional area of dielectric E, to the cross sectional area of the condenser plates (assuming the lengths of the dielectrics equal the distance between the condenser plates) and B is the ratio of the cross sectional area of dielectric E2 to the cross sectional area of the condenser plates. As before the constants A and B are the effective "saturation" of the condenser by the two dielectrics. Still another case is described by Lichtenecker5 where dielectric E2 is shown in the form of small particles distributed at random in dielectric E1. This is shown in Fig. 1C. For this case: log Em = A log E1 + B log E2.....(3) where Em is the dielectric constant of the combination. A is the ratio of the volume of dielectric E1 to the volume of the condenser, i.e., the effective "saturation" of the condenser by dielectric E,. B is the ratio of the volume of dielectric E2 to the volume of the condenser, i.e., "saturation" of dielectric El. Equations (l), (2) and (3) are plotted in Fig. 2 for E1 = 2.5 (oil) and E2 = 80 (water). Equations (1) and (2) may he thought of as representing the limiting cases of the configuration of two fluids which might be expected to exist in a porous medium. Equation (3),

Jan 1, 1951

By Leonard B. Lipson

Boyer, Morgan and Muskat,' with improvements by Morgan, McDowell, and Doty,l and Laird and Putnam,' have described a scheme for the determination of fluid saturatic in porous media by measuring the x-ray linear absorbing power of particular fluids in the media. This method is one of several which depend on the linear absorbing power of the fluids in the porous medium. Other examples of linear absorption methods involve measurement of dielectric constant, gamma ray absorption, and ultrasonic attenuation. It is the purpose of this note to demonstrate by theortical considerations that the absorption versus saturation curve for a linear absorption method is not necessarily a single valued function of the saturation. Such non-unique behavior must be considered and evaluated before suitable saturation determinations can be made by a linear absorption method. To illustrate the discussion, examples will be given only for the simplest cases of combinations of two different dielectrics. The dielectric constant method was chosen for illustration because it was thought to demonstrate most graphically the point in question. According to Argue and Maass,4 the resultant dielectric constant of a combination of two different dielectrics depends on the orientation of the dielectrics in the electric field of the test condenser used to measure the dielectric constant. One ease involves alternate slabs of dielectrics E1 and E2 perpendicular to the electric field of the test condenser, as shown in Fig. 1A. For this case: l/'E, = A/E, + B/E,.......(1) where E,,, is the dielectric constant of the combination, A is the ratio of the path length through dielectric E, to the distance between the plates of the condenser (assuming the dielectrics have the same cross sectional area as the condenser), and B is the ratio of the path length through dielectric E2 to the distance between the plates of the condenser. It will be noted that the constants A and B are numerically equal to the fractional "saturation" of the region between the test plates of the condenser by the two dielectrics E1 and E2, respectively. Another case involves alternate columns of the two dielectrics parallel to the electric field and forming a continuous path between the condenser plates, as shown in Fig. 1B. For this case: E., = AE1 + BE2.........(2) where E., is the dielectric constant of the combination, A is the ratio of the cross sectional area of dielectric E, to the cross sectional area of the condenser plates (assuming the lengths of the dielectrics equal the distance between the condenser plates) and B is the ratio of the cross sectional area of dielectric E2 to the cross sectional area of the condenser plates. As before the constants A and B are the effective "saturation" of the condenser by the two dielectrics. Still another case is described by Lichtenecker5 where dielectric E2 is shown in the form of small particles distributed at random in dielectric E1. This is shown in Fig. 1C. For this case: log Em = A log E1 + B log E2.....(3) where Em is the dielectric constant of the combination. A is the ratio of the volume of dielectric E1 to the volume of the condenser, i.e., the effective "saturation" of the condenser by dielectric E,. B is the ratio of the volume of dielectric E2 to the volume of the condenser, i.e., "saturation" of dielectric El. Equations (l), (2) and (3) are plotted in Fig. 2 for E1 = 2.5 (oil) and E2 = 80 (water). Equations (1) and (2) may he thought of as representing the limiting cases of the configuration of two fluids which might be expected to exist in a porous medium. Equation (3),

Jan 1, 1951

By William H. Hartwig

A paper by Rose1 has called attention to some of the problems of wetting-liquid relative permeability measurement. The premises and conclusions set forth by Rose, namely the applicability of the Hassler scheme of measurement, will be accepted. In addition, it will be concluded that certain electrical analog circuits can be used as a pattern for consideration of possible hydraulic systems of measurements. NEW SCHEME OF MEASUREMENT The object of this note is to propose a new scheme of wetting liquid relative permeability measurement. It is significantly different from those heretofore described, nonetheless it is based on Hassler concepts. The scheme is illustrated in Fig. 1 in terms of the corresponding electric circuit analog. It may be designated descriptively as the "comparison" method of wetting-liquid relative permeability measurement. In this circuit, R, represents the resistance of the core sample which is being studied for relative permeability characteristics, R represents a "standard" resistance, R represents the combined series resistance of the barrier pads, R R2 represent the combined series resistance of barrier pads in the manometer circuit, C, C represent the capacitance of the manometers, E is a constant voltage source, S is the switch or stopcock. The following conditions are imposed upon .the network: Rb » R, and R, R,» R, R, » R., and the condensers C, and C,

Jan 1, 1953

By Paul A. Beck

IN several recent investigations1 ' considerable evidence was accumulated to show the predominance in various face-centered cubic metals of a certain relative orientation, corresponding to a rotation of 30" to, 40" around a [111] axis, between a matrix with a strong single orientation texture and grains growing in this matrix." This relative orientation was found to occur both in recrystallization and in coarsening, "secondary recrystallization", so that one is inclined to look for an explanation applicable in both cases. The abundance of growing grains in the described orientations proves that suitable "nuclei" are present in the matrix material and that they have the capacity to grow. The scarcity of growing grains in other orientations may be explained in one 'of two ways. Either the number of nuclei or the rate of growth must decrease strongly for orientations deviating from that predominating among the growing grains, Fig. 1. Both the "oriented nucleation" and the "oriented growth" theory found support in the literature. Because the frequency of nuclei as a function of orientation is in most instances not amenable to direct experimental investigation, a definitive decision is difficult to achieve. However, it is now known with great certainty that the rate of boundary migration is strongly dependent on the relative orientation of the two grains meeting at the boundary and that the orientation favored by high boundary mobility closely corresponds to that predominating in most cases of recrystallization and coarsening. Thus, it was found that, in general, the mobility is very low for boundaries between grains of nearly identical orientation, or for coherent twin boundaries. On the other hand, the boundaries between two grains of a relative orientation correspending to a [1111 rotation of 30" to 40" have the highest mobility in face-centered cubic metals. If a large variety of nucleus orientations are produced grow- by means of a highly inhomogeneous local deformation, nuclei close to the above orientation are found to grow fastest.z4 In view of this evidence and of the fact that the preferred orientation relationship is the same in recrystallization and in coarsening, the oriented growth theory appears by far the more promising one. Since the origin of nuclei in primary recrystallization is certainly different from that in coarsening, the occurrence of the same orientation relationship in the two processes would be difficult to explain on the basis of oriented nucleation. other advantages of the oriented growth theory are its capability of accounting for the often observed sharpening of the texture in coarsening, and its suitability for explaining the role in the formation of the ''cube texture,, of the most important variables, such as the degree of rolling, the penultimate grain size, and the time and temperature of the last anneal: No similarly consistent explanation of all these effects has ever been offered in terms of oriented nucleation. An important problem in connection with the oriented growth theory is the following: In the ce-c entered system there are four [111] axes and

Jan 1, 1952

By M. J. Sinnott

WITH the advent of nodular iron as an engineering material, considerable interest has been shown in developing this material for various applications. Generally the strength, hardness, or ductility are the more common properties used for design purposes but occasionally applications involving a knowledge of the thermal conductivity of the material is required. A search of the literature showed, rather surprisingly, that relatively little work has been done on this property for all types of cast iron. Insufficient data are available on thermal and electrical conductivities to develop the Weidemann-Franz ratio, or the Lorentz relationship, for estimation purposes. There are no data on nodular irons and the published data on malleable irons are quite sketchy. For these reasons the conductivity of the group of nodular irons listed in Table I were measured. Irons I to IV were made in such a fashion as to maintain the carbon and alloy content essentially the same while varying the silicon content. Test specimens were cut from the mid-section of 4-in. keel castings. Iron V is a commercial casting of nodular iron. The test specimen of this iron was cut from the center of a large cast billet 3x10x26 in. All alloys were tested in the as-cast condition. A microstructural examination showed that each iron had spheroidal graphite but the size and distribution varied with the silicon content of the iron. The spheroid size decreased while the number of graphite nodules increased as the silicon content of the iron was increased. The matrix structures of each iron consisted of pearlite and ferrite with the proportions varying from predominantly pearlite in the low-silicon iron to mostly ferrite in the high-silicon iron. The commercial heat, iron V, was predominantly pearlite probably because of its higher manganese and phosphorus content. Two methods for measuring the thermal conductivity were used. The first was a modification of the techniques described by Powell and Hickman and Van Dusen and Shelton,² the second method was a simpler technique described by Jakob and Hawkins." Since the agreement of both methods as tested on two sets of duplicate samples was excellent, the simpler experimental technique was used. The results of the measurements are given in Table II along with a summary of the microstructural constituents. These conductivity data indicate that as the percentage of silicon increases there is a corresponding decrease in the thermal conductivity even though the structure is changing from pearlitic to ferritic. Such a change in microstructure is usually accompanied by an increase in conductivity. A third factor involved in the behavior of these irons is the size and distribution of the graphite nodules. The relative amounts of graphite do not change greatly but the size and distribution do. Generally graphite improves the conductivity but in the present case such an effect is probably masked by the alloying effect from the silicon and its dispersion through the matrix. The thermal conductivity of the nodular irons studied is less than that of regular foundry irons by some 10 to 30 pct and is less than that of regular malleable irons.' The cause of the decreased conductivity is probably the more highly alloyed fer-rites obtained in these irons and the changed mode of distribution of the graphite as compared to the regular foundry irons. References R. W. Powell and M. J. Hickman: Journal Iron and Steel Inst. (1946) 154, No. 2, p. 99. 'M. S. Van Dusen and S. M. Shelton: U. S. Bur. Standards Journal of Research, RP668 (1934) 12, p. 429. ³M. Jakob and G. A. Hawkins: Elements of Heat Transfer and Insulation. 2nd Ed. (1950) New York. John Wiley and Sons. ' J. W. Donaldson: Journal Iron and Steel Inst. (1933) 128, No. 2, p. 255.

Jan 1, 1954

By J. L. Weeks

THERMAL conductivities of several samples of uranium and uranium alloys were determined using an apparatus previously described.' The value previously reported for uranium,' 0.035 cal per sec per cm per "C at 70°C, is in error due to the failure of a thermocouple during the determination on uranium. The defective thermocouple was detected after a reanalysis of the data obtained during the run and since has been replaced. Subsequently, runs on several samples of uranium show the thermal conductivity of uranium to be 0.069 cal per sec per cm per 'C at 70°C. The accuracy of the determinations was checked by measuring a sample of synthetic sapphire whose thermal conductivity was previously reported and found to be in agreement with other values."-" The values given in Table I are believed correct to % 3 pct or 0.003 cal per sec per cm per "C, whichever is larger. The samples were provided by J. H. Kittel of the Argonne National Laboratory, Metallurgy Div. References J. L. Weeks and R. L. Seifert: Apparatus for the Measurement of the Thermal Conductivity of Solids. Review of Scientific Instruments (1953) 24, pp. 1054-1057. J. L. Weeks and R. L. Seifert: Note Regarding the Thermal Conductivity of Synthetic Sapphire. Journal American Ceramic Society (1952) 35, p. 15. :' J. Francl and W. D. Kingery: Thermal Conductivity: IV, Apparatus for Determining Thermal Conductivity by a Comparative Method; Data for Pb, Al2O3, BeO, and MgO. Journal American Ceramic Society (1954) 37, No. 2, Part 11, pp. 80-84. (Part 11: special issue on thermal conductivity.) ' W. D. Kingery, J. Francl, R. L. Coble. and T. Vasilos: Thermal Conductivity: X, Data for Several Pure Oxide Materials Corrected to Zero Porosity. Journal American Ceramic Society (1954) 37, No. 2, Part II, pp. 107-110. (Part 11: special issue on thermal conductivity.) Edwin Ruh: New Jersey Ceramic Research Station, Rutgers University. Private communication.

Jan 1, 1956

By J. L. Weeks, K. F. Smith

IN order to determine the magnitude of thermal conductivity changes resulting from alloying vanadium with titanium and a few other elements, several sam~les were PrePared and measured. The thermal conductivity -values reported herein in Table I were determined with an apparatus previously described.' As in recently reported2 determinations on uranium and uranium alloys, whose thermal conductivities are in the same range as vanadium," the accuracy of the values was checked by using synthetic sapphire." The error in the measurement is estimated to be '-3 pct or 0.003 cal sec-1 cm-l "C-1, whichever is larger. The vanadium used in preparing the samples was the calcium-reduced type and was supplied by the Electro Metallurgical Co. as 99.6+ pct pure. All alloying elements used in the preparations were 99+ pct pure. A nonconsumable tungsten electrode arc furnace was used for melting the alloys and, without opening the furnace, each ingot was re-melted a number of times to insure homogeneity. The samples as prepared by the Armour Research Foundation were machined from as forged material without annealing. Acknowledgment The note is based on work performed under the auspices of the AEC. References 'J. L. Weeks and R. L. Seifert: Apparatus for the Measurement of the Thermal Conductivity of Solids. Review of Scientific Instruments (1953) 24, pp. 1054-1057. 2 J. L. Weeks: Thermal Conductivity of Uranium and Several Uranium Alloys. Trans. AIME (1955) 203, p. 192; Journal of Metals (January 1955). 3C. A. Hampel: Rare Metals Handbook. (1954) p. 593. New York. Reinhold Publishing Corp. Thermal conductivity of vanadium is given as 0.074 cal sec-1 cm- '°C-1 at 100°C. 4 J. L. Weeks and R. L. Seifert: Note Regarding the Thermal Conductivity of Synthetic Sapphire. Journal Amer. Ceramic Soc. (1952) 35, p. 15. At 70°C, K = 0.071 cal sec-l cm-l °C-1.

Jan 1, 1956

By G. J. Wolga, W. W. Tyler, A. C. Wilson

THE physical properties of uranium have been reviewed by Katz and Rabinowitch.1 Their review includes thermal conductivity data for ternperatures above 375°K. Recently, Mendelssohn and Rosenberg' have published data on the thermal conductivity of uranium from 2" to 20°K. Our measuremerits indicate the temperature dependence of the thermal conductivity in the temperature interval from 20" to 300°K. Electrical resistivity and thermoelectric power were measured on the same sample. The material studied was normal uranium which had been heated at 700°C in a lead bath for 10 min and then quenched in a water bath held at 50°C. From this material a rod M in. in diameter and 2 1/2 in. long was machined. Two 0.040 in. holes were drilled into the rod 1 3/4 in. apart. Copper-constantan thermocouples for temperature and potential measurements were soldered to copper pins which were pressed tightly into these holes. Details of the equipment and experimental techniques used in making the measurements have been described elsewhere." Fig. 1 shows micrographs of a section of the sample studied. Fig. la was taken with unpolarized light and shows impurity inclusions, probably uranium carbide. Fig. lb, showing the same field, was taken with polarized light and gives some indication of the grain size and twinning within the grains. Experimental Results Thermal conductivity and electrical resistivity data are shown in Fig. 2. Table I shows values of

Jan 1, 1954

By E. E. Duncan, G. Derce

REVIEW of the literature on hydrogen in steels indicates that inadequate consideration has been given to the influence of temperature gradients on segregation of this element. Even when segregation has been taken into account, the interpretation of the data has been seriously handicapped by incomplete understanding of the mechanism by which it occurred. Recognition of a mechanism which will be described as "thermal segregation" appears to rationalize many of the observed effects so well that it will be reported here with some preliminary experimental evidence. The complete quantitative evaluation of the factors controlling the mechanism will require extensive experimentation. The operation of the mechanism can be described in relation to fig. 1, which shows the temperature dependence of the solubility of hydrogen in iron at

Jan 1, 1951

By A. T. Corey, J. H. Henderson, M. R. J. Wyllie, C. H. Rathjens

The results of three-phase relative permeability tests on nine water-wet consolidated Berea sandstone samples are presented as composite ternary diagranls showing isoperms of oil, water and gas. Capillary pressure control was exercised over the flow of gas and oil in the presence of water. The water saturations ranged from 17 to 71 per cent pore volume. A method of calculating both the oil and water permeabilities of a three-phase system from the easily measured gas relative permeability is presented. EXPERIMENTAL PROCEDURE AND RESULTS A renewed interest has been shown in three-phase relative permeability as a result of recent developments involving underground combustion processes, steam injection, and other multiphase displacement processes. The experiments and results described here involved simultaneous flow of oil and gas in consolidated Berea sand with brine present as the wetting phase. Gas and oil relative permeabilities were measured on nine cores with CaC12 brine present as the wetting phase in saturations ranging from 17 to 71 per cent. The average residual liquid saturation of the cores was approximately 20 per cent. In order to make certain that brine was the wetting phase, the test cores were saturated with brine before contact with hydrocarbons. As an added precaution to avoid having oil displace brine from the wetting position as a result of changing wettability, each core was only used twice, i.e., first with a fixed percentage of brine and then for a gas-oil permeability determination with no brine present. The results, therefore, are presented as composite ternary diagrams representing the flow tests on nine individual cores having very similar properties. All tests were made using a modification of the capillary pressure techniquc described elsewhere. The effective oil permeability was measured before gas was introduced using a very small pressure gradient (a few centimeters of oil). This determination was made without selectively wet barriers in contact with the core. The cores were then placed between capillary barriers and gas-oil relative permeability curves obtained. The capillary barriers had been made water repellent with a silicone treatment. In determining gas-oil-water relative permeability in this fashion, control was exercised over the capillary pressure existing between the gas and oil. No control was exercised over the pressure difference existing between the oil and water. Athough an equal pressure gradient was applied to the gas and the oil phases, this pressure gradient does not exist in the water phase. Since the pressure gradient across the core was always much less than the displacement pressure of the fully saturated core, the pressure gradient can have caused only a very slight distortion of the oil-water interfaces. This slight distortion of the oil-water interfaces had a negligible effect on the validity of the oil permeabilities measured. The oil permeability, measured in the presence of water but with no gas present, was in every case equal. within experimental error, to the gas permeability of the gas-oil system when the oil saturation was the same as that of the water. Gas and oil relative permeabilities were plotted as a function of total liquid saturation. It was found that the gas relative permeability curves obtained on cores with brine present were identical with those obtained on the same cores with no brine present. The denominator for calculating oil relative permeabilities was the permeability found by extrapolation to infinite mean pressure (A la Klinken-berg). Fig. 1 illustrates gas-oil relative permeability results obtained on a typical core. The solid permeability curves represent the experimental data. The dashed oil relative permeability curve was calculated using the relationship;

Jan 1, 1957

By R. I. Jaffee, H. R. Ogden

AT the present time, there appear to be two conflicting opinions on the solubility of boron in titanium. P. Ehrlich' has indicated from X-ray diffraction work that boron is soluble in titanium up to TiB0.8 (17.8 wt pct, 44 atomic pct). The X-ray diffraction pattern for titanium was found in compositions up to TiB0.05_0.07 (1.1 to 1.6 wt pct); then, without a phase gap, superlattice lines appeared up to TiB0.8 On the other hand, Craighead, Simmons, and Eastwood' have estimated the solubility of boron in both alpha and beta titanium to be less than 0.1 wt pct, based on results of metallographic analysis. In some recent work done at Battelle, results were obtained which shed more light on the titanium-rich end of the titanium-boron system. Iodide-type titanium and high-purity crystalline boron were used in this investigation. The boron was prepared by hydrogen reduction of boron tri-bromide and deposition on a hot tungsten wire. The alloys were prepared by arc melting in an argon atmosphere of 10 cm Hg pressure on a water-cooled copper hearth. The ingots were hot rolled to strip at 850°C. Alloys containing up to 1 pct B could be hot rolled. Those containing 2 pct or more B could not be hot rolled. Metallographically, it was found that a second phase was present in alloys containing as little as 0.4 pct B, and that the quantity of second phase increased with increasing boron content. This is illustrated in Figs. la and lb, which show the microstructures of a Ti-0.4B and a Ti-1B alloy annealed in argon at 850°C. X-ray diffraction patterns of alloys containing 1 and 5 pct B revealed the presence of extra lines which correspond to the superlattice lines reported by Ehrlich.' However, no evidence was found of a shift in the lattice constants of alpha titanium indicating that there is very little, if any, solubility of boron in alpha titanium. This fact, coupled with the fact that the alloys were definitely two-phase, indicates that the extra lines are not superlattice lines, but are more probably the result of a second phase of a hexagonal structure almost identical in cell

Jan 1, 1952

By H. Margolin, E. Ence

Two versions of the Ti-Mn binary diagram have been published recently.' , -0th diagrams show two compounds in the region between 40 and 70 wt pct Mn, but disagree as to the reaction in which these compounds are involved. The investigation of the manganese-rich portion of the Ti-Mn binary diagram was undertaken at New York University as part of an investigation of ternary systems with titanium and manganese in order to determine which of the proposed diagrams is correct. A number of alloys between 31 and 70 pct Mn were prepared in a manner similar to that described by Cadoff and Nielsen; except that low currents (110 amp in argon atmosphere) and long melting times (up to 20 min) were used to prepare the alloys. Compositions were determined from weight-loss data, assuming all loss as due to manganese. Heat treatments were carried out with relatively large pieces, since there was a tendency for manganese to be lost during heat treatment. When X-ray diffraction data was to be obtained, the central parts of heat-treated specimens were used to make filings or powders which were not heat treated. Specimens were heat treated from the as-cast state. Heat-treatment times were as follows: 1150°C, 1 day; ll00°C, 2 days; 1000°C, 5 days; and 900°C, 15 days. It should be noted that equilibrium was not attained at 900°, 1000°, and in one case, at 1150°C. Metallographic specimens were electrolytically polished and strain etched by a technique described elsewhere.' At least four, and possibly six, phases were found in the region investigated. On the basis of information available at this time, a completely self-consistent diagram cannot be constructed, and therefore data are presented only for those phases which have been identified by both X-ray and microstruc-ture. Of the compounds detected, the one highest in manganese is the Laves phase, TiMn,, which is hexagonal with a MgZn, type of structure.V he diffraction data for TiMn2 from a 70 pct Mn alloy annealed at 1150°C are shown in Table I. The c/a ratio and parameters of TiMn2 agree well with those of Wall-baum hnd Rostoker et al. The values obtained here are c/a = 1.641, a = 4.825A. Another compound is the y-phase which is estimated to contain about 60 pct Mn. The y-phase has a structure which is identical to that of TiMn, with c/a = 1.639, a = 4.906Å. The fact that y has a Laves-type lattice would suggest that TiMn, has a range of solubility which extends from the composition of TiMn2 (69.6 Mn) to that of y (60 pct Mn). However, this could not account for microstructures which, in the 60 to 70 pct Mn region, show several phases in both the as-cast state and after annealing at 1150°C. Fig. 1 shows a two-phase structure of a 60 pct Mn alloy annealed at 1150°C. The phases present are y (white) and e (dark). If y were TiMn, then, according to Rostoker et al.,' the second phase of Fig. 1 should be P-Ti. The diffraction data for the 60 pct Mn alloy of Fig. 1 are shown in Table I. The starred d-values are from the e-phase and these lines do not correspond to those of &Ti. Comparison of as-cast and 1150°C microstructures of the 60 pct Mn alloy indicates that e precipitated from y. Since y has a

Jan 1, 1955

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

THE pole figure interpretation in a recent paper' 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,' 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 Nicholas J. Grant, Chih-Chung Wang

TO phase of the Ti-0 system has the structure of NaCl and has a wide range of solid solubility.' In the course of studying the Ti-Cr-0 ternary system, binary alloys were made of iodide titanium and high purity TiO,. It was found from X-ray studies of the binary alloys that a transformation of the TiO appears to take place at a temperature near 925°C. Evidence of this phase change is best seen in Fig. 1. Fig. 1A shows the X-ray spectrometer pattern (CUKa radiation) of an alloy of 25 wt pct 0 corresponding to the stoichiometric composition of TiO.

Jan 1, 1957

By W. C. Ellis

IN an ingot of germanium solidified progressively from the bottom by a method' devised by J. H. Scaff and H. C. Theuerer, examination discloses ex- IH. C. Torrey and C. A. Whitmer, Crystal Rectifiers. p. 364. 1948. New York. McGraw-Hill Pub. Co. tensive twin relationships. A slice taken about midway in a cylindrical ingot approximately 3/4 in. in diameter and 1 1/2 in. in length, after etching and polishing to delineate different orientations, is shown in fig. la. The orientations of the regions designated with letters were determined by Laue X-ray back-reflection methods and plotted on stereograms. The orientation relationships of the designated components were determined by comparing the values for the nine angles between the three respective cube poles of each orientation with the values calculated in a formal treatment of octahedral multiple twinning in cubic crystals. Germanium, diamond cubic in structure, has the octahedral twinning habit. I am indebted to K. H. Storks for the calculation of the angular relationships of cube poles in octahedral twinning to four orders. The set of values for the nine angles is distinctive of the order of twinning. Confirmation for a multiple twin relationship is obtained from the determined indices of the mirror planes. These exist for all orders of twinning through the third and for some of the fourth." If the orientations are not those for twinning, then the nine angles for the cube poles do not correspond in value and distribution to those formally calculated. Since all nine angles must correspond in values and distribution of values to the calculated ones, the Laue method with a precision of one or two degrees is adequate to establish or deny with confidence the existence of multiple twins. Regions of the same orientation can also frequently be identified by the optical reflections. For example, the narrow twin bands in A at 2: 00 o'clock have orientation B1. The interesting twin relationships shown schematically in fig. lb were found for the section in fig. la. Most of this slice was made up of orientation, A, appearing in widely separated regions. Of the four possible first order twins of A, three were present in this slice and are designated by B with subscripts. Four second order twins of A are designated by C with subscripts. It is worth emphasizing that two of these, C, and C,, are second orders of A through the first order missing in this section. Two regions, designated by D with subscripts are third order twins of A. D2 is a sixth order twin of D,. All orientations found were ascribable to multiple twinning, as if the orientations in this section originated earlier in solidification from a single nucleus. The presence of extensive multiple twinning to- gether with the absence of other orientations appears to be a characteristic result in many instances of solidification of germanium. Fertile conditions for twinning probably exist in the array of atoms in the diamond cubic structure. The high order twins in the section shown, it is reasonable to presume, are the result of progressive octahedral twinning through several generations in the material freezing earlier. Some of these generations do not appear in this section, it is suggested, because their orientations with respect to the growth direction were unfavorable for survival. The extensive twinning is probably promoted during solidification by constraint imposed by volume increase, and to an irregular growth front. Twinning may also be due, in part, to the attempt of the solidifying region to attain the orientation most favorable to the growth direction (maximum thermal gradient). The nucleus for a twinned orientation could have its origin in a "stacking fault" on the close-packed octahedral plane. Further work is being done in which the course of twinning throughout an ingot is being studied. The results appear to be important in the general theory of solidification.

Jan 1, 1951

By Peter Haasen

INDIUM antimonide has the zincblende structure. A possible defect that does not disturb the indium tetrahedron surrounding any antimony atom in this lattice (or vice versa) is obtained when neighboring

Jan 1, 1958