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By J. S. Brown, A. G. Guy

With the exception of the work of Tammann and Hartmann,1 no published information has been found on the structural changes produced in eutectic structures as the result of heating following plastic deformation. In part this lack of information may be due to the fact that many eutectic structures contain an intermetallic compound as a prominent phase, and as a consequence have been considered to be unworkable. For example, Tammann and Hartmann were able to obtain useful data only on those alloys that they could greatly reduce in thickness by cold rolling. This restriction placed on the investigation of alloys containing intermetallic compounds has been largely removed by the work of Savitskii2 which showed that large deformations of such alloys can be produced by relatively slow compression at temperatures near the melting range. It was possible, therefore, to carry out the present work on a range of binary eutectics including one composed of two intermetallic compounds. The essential results obtained on the alloy systems studied are illustrated by the Pb-Mg eutectic containing 33.2 pct Mg, Fig 1. The cast structure, Fig la, was obtained by melting together magnesium of 99.8 pct purity and chemically pure test lead, casting into a heated, small steel mold, and furnace cooling in the mold from about the eutectic temperature. The fairly coarse eutectic structure thus obtained was too brittle to work at room temperature without cracking. Fig 16 shows the worked structure obtained by compressing a 1/2-in. cube 70 pct in about 15 sec at 550°F and then water quenching. The pronounced changes in the distribution of the two phases produced by heating the worked alloy at 850°F for 1 hr are shown in Fig lc. Recrystallization of both phases appears to have taken place, and the mechanical properties of the cast alloy must have been significantly changed by the working and heat treatment. Similar results were obtained with the Mg-59.5 pet Bi, Mg-36.4 pet Sn, Mg-65.4 pet Cu, and Bi-40 pet Cd eutectics, only the last of which could be worked at room temperature. Tammann and Hartmann reported a thickening and shortening of the needles of the eutectics which they heated about 10°C below the melting range for 1 hr after drastic cold rolling. They found the following eutectics, given the indicated amounts of reduc- tion, to have a granular structure after heat treatment: Sn-9 pet Zn (98 pet); Cd-82.5 pet Pb (60 pet); and Bi-43.5 pet Pb (90 pet). On the other hand the alloy Al-11.7 pet Si (60 pet) showed no change after heating. Tammann and Hartmann observed a distinct shrinking of the needles in unworked eutectics subjected to heat-treatment. In the present work inappreciable change in the eutectic structure was found on heating undeformed alloys. In summary, it appears that eutectic structures can be recrystallized into a "spheroidized" condition by heating near the eutectic temperature after severe deformation. If the eutectic contains one or more brittle phases the necessary deformation can be accomplished by pressing at high temperatures. It is reasonable to expect that this tendency towards equiaxed grains from the plate- or needle-like eutectic structure should be general since the energy relations and mode of growth in recrystallization are so different from those that hold for eutectic crystallization. References 1. G. Tammann and H. Hartmann: Ztsch. Melallkunde (1937) 29, 141-144. 2. E. M. Savitskii: Doklady Akad. Nauk S.S.S.R. (1940) 62, 349-351. Abstr. in Melal Prog. (July, 1949) 56, 126, 128.

Jan 1, 1950

By B. Welber, R. Webeler

A CCORDING to accepted theory, fatigue in A] metals is connected with the occurrence of local strain hardening even at applied stresses below the yield point as a consequence of stress concentrations created by the presence of structural inhomogeneities.1 It seemed possible, therefore, that

Jan 1, 1954

By P. A. Albert

THE to a transformation has been investigated by Newkirk1 in sponge titanium alloys which had been relatively slow-cooled so that several grains formed in a former grain. For a nucleated from , Newkirk assumed the following relationships and found them consistent with his experimental results: (00.1)a (110)Pll.01. II [111] Liu and Margolin,' in their investigation, found that the habit planes of martensitic in titanium consisted of planes of the families (3341, and (3441,. Using Newkirk's orientation relationship, the (3341 habit plane is found to correspond to the (1450) plane of a.

Jan 1, 1954

By W. R. Aufricht, E. H. Koepf

The theory, measurement, and application of capillary forces in reservoir rock have been treated ex-tensively in the various petroleum publications.1,2,3,4 These forces are of prime importance in oil production, and data on capillary properties are among the most important tools used in the study of reservoir mechanics. The principal application of measured capillary pressure data by the production and reservoir engineer is in the determination of the initial distribution and mobility of fluids in the reservoir. The distribution refers to the magnitude of the oil and interstitial water saturations under capillary equilibrium conditions and to their variation throughout the reservoir as a result of changes in rock properties and nearness to free water. The magnitude of the water (or oil) saturation, as well as the porosity, is required in volumetric calculations of oil in place. In low permeability reservoirs, where long transition zones are common, the magnitude of the oil content, even below the depth interval where commercial rates of flow of oil can be obtained, must be evaluated since this oil contains energy available to the production of the remainder of the reservoir. The mobility of the water phase is of particular importance in water-flood calculations since mobile water may condemn what would otherwise be a successful water flood. In reservoirs with predominantly small pores, high immobile water contents are possible. Conversely, reservoirs with predominantly large pores may contain mobile water even though the interstitial water contents are relatively low. This presentation reviews the distribution and mobility of interstitial water contents as determined from capillary pressure data and shows typical data for various types of carbonate reservoirs. A discussion of the variations found in different types of carbonate reservoirs is given. DISCUSSION Interpretation of Laboratory Data Fig. 1 is a typical laboratory capillary Pressure curve where water saturation as Per cent of Pore space is plotted vs capillary Pressure (psig) for an air-water system. This par- ticular curve was obtained by measurement on a sample of San Andres dolomite with intergranular-type porosity. The sample studied had a permeability of 10.0 md and a porosity of 18.8 per cent. The capillary pressure-saturation relationship illustrated is an inherent property of the rock (a function of the size and distribution of the pores) and represents the ability of this water-wet rock to retain water against the pressure differential exerted by a non-wetting fluid (oil or gas) to remove it. In the laboratory a known pressure differential is exerted from a pressure source; in the reservoir the pressure differential is controlled by the density difference between the hvdrocarbons and the water. The laboratory capillary pressure values may be converted into terms of equivalent height of water column using known values of reservoir oil and water density and measured or average values of interfacial tension

Jan 1, 1958

By Henry A. Stiff

The classification and correlation of water analysis data presents many problems which can be solved by graphic methocis. The pattern system, a new type of graphic procedure described in this communication, is believed to have several advantages over older methods. Examples of the application, of the pattern system to the solution of problems encountered in petroleum production are given. INTRODUCTION Several graphic methods for presenting analytical water data have been developed and are now in use.1,2,3,4 It is believed, however, that a recently developed type of graph called the "pattern" offers several advantages over other methods. This system presents a better picture of the total salt concentration than is usual in such graphs. The effect of dilution or concentration has been reduced to a minimum, and at the same time distinction between various types of water has been improved. The system is extremely versatile, yet so simple it can be plotted on ordinary graph paper and adapted to almost any type of filing system. DISCUSSION The essential feature of the pattern system is the graph shown in Fig. 1. Horizontal lines extending right and left from a vertical line at zero form the graph. Positive ions are plotted to the left while negative ions are plotted to the right. The figure immediately beneath each ion gives the scale. Most oil field waters can be plotted on a scale where 100 milli-equivalents of sodium and chloride and 10 milliequivalents of each of the other ions are represented by one scale unit. For highly concentrated brines, 1,000 milliequivalents of sodium and chloride and 100 milliequivalents of each of the

Jan 1, 1951

By Henry A. Stiff

The classification and correlation of water analysis data presents many problems which can be solved by graphic methocis. The pattern system, a new type of graphic procedure described in this communication, is believed to have several advantages over older methods. Examples of the application, of the pattern system to the solution of problems encountered in petroleum production are given. INTRODUCTION Several graphic methods for presenting analytical water data have been developed and are now in use.1,2,3,4 It is believed, however, that a recently developed type of graph called the "pattern" offers several advantages over other methods. This system presents a better picture of the total salt concentration than is usual in such graphs. The effect of dilution or concentration has been reduced to a minimum, and at the same time distinction between various types of water has been improved. The system is extremely versatile, yet so simple it can be plotted on ordinary graph paper and adapted to almost any type of filing system. DISCUSSION The essential feature of the pattern system is the graph shown in Fig. 1. Horizontal lines extending right and left from a vertical line at zero form the graph. Positive ions are plotted to the left while negative ions are plotted to the right. The figure immediately beneath each ion gives the scale. Most oil field waters can be plotted on a scale where 100 milli-equivalents of sodium and chloride and 10 milliequivalents of each of the other ions are represented by one scale unit. For highly concentrated brines, 1,000 milliequivalents of sodium and chloride and 100 milliequivalents of each of the

Jan 1, 1951

By N. P. Reddy, L. Adler

The valuable Maximum Utilization Factor (MUF) concept has been extended to other rotating excavators beyond Stripping Shovels and Draglines. In this concept the boom reach and bucket capacity are multiplied to get an MUF, then normalized by dividing by the equipment weight. Statistical analyses were applied to the remaining shovels (hydraulic and cable), draglines, and backhoes. Positive correlations were found. Stripping Shovels and Draglines were also re-examined. The results provide an estimate of equipment diggability and encourages versatility by the interchange of the boom and the bucket. The concept further clarifies the existing equipment classification by delineating General Excavating, Loading, and Stripping kinds. The results also forecast trends, and noted innovative advances and possible retrogression. Extension to other boom excavators, such as front-end loaders, is recommended. The MUF concept provides one of the few indices of gross external characteristics available to the engineer-user of equipment.

Jan 1, 1991

By J. H. Palm

Experiments have shown12 that the formula -S = St - (St - Se')e ne [1] expresses very well the relation between the true stress S and the true form monotonic deformation of plastic metals in single tension and compression (Fig 1). St (asymptotic or final stress), Se' (threshold stress) and ne (characteristic or specific strain) are constants, the significance of which immediately follows from Fig 1. Only at the initial stages of deformation the experimental curve runs below the theoretical curve. This may be due, at least partly, to the uneven stress distribution caused by the anisotropy of the crystals. It is now obvious that a similar formula H = Ht- (Ht- He)e ne' [2] might be valid for the relation between the hardness and the strain. The hardness can be only a function of the strain and must therefore be independent on the hydrostatic tension present in the neck during straining. Hence, if Eq 2 is correct it will also represent the relation between hardness and strain in the middle section of the neck, the strain of which is generally assumed to be almost or fully homogeneous. For aluminum, copper, and several copper alloys it is indeed observed that Eq 2 agrees very well with the experimental Vickers hardness-strain relation from zero strain on up to the strain at fracture. Moreover nc' is, for several metals fairly equal to nc- Hence H = C1 + C2S [3] C1 and C2 are constants during uniform uniaxial tension. Eq 3 was also obtained for copper by Voce.3 According to Hencky's theory4 the ratio of the Brinell or Vickers hardness and the yieldstress (expressed in kg per mm2) of a non-strainhardening metal is approximately equal to 2.8. If Eq 1, 2 and 3 are correct the ratio Ht/S, must accordingly be the same for all plastic metals and be equal to 2.8. It is now experimentally established that this ratio varies between 2.7 and 3.1 with a mean value of 2.9. Taking into account that Ht and especially St can be obtained only by extrapolation from the range of rather low strains, the agreement with the theory is very satisfactory. References 1. J. H. Palm: Appl. Sci. Res. Al (1948) 198. 2. E. Voce: Jnl. Inst. of Met. (1948) 74, II, 537. 3. E. Voce: Metal Treatment (1948) 15, 53. 4. H. Hencky: Zlsch. f. angew. Math. and Mech. (1923) 3, 241.

Jan 1, 1950

By P. A. Beck, W. D. Manly

In a recent note Sully and Head1 showed that the Cr-Fe sigma phase is isomorplious with the Cr-Co gamma phase, and that the lattice constants are also nearly identical. In a preliminary investigation of the ternary Cr-Co-Fe system at 800°C at this laboratory the above findings were confirmed, and it was found by microscopic techniques, using various etching reagents, that the two binary phases form an urinterrupted series of solid solutions with each other. These solid solutions occupy a straight narrow band which cuts across the 800°C isothermal section of the ternary system, connecting the two binary phases. A detailed investigation of the Cr-Co-Ni ternary system at 1200°C disclosed that here, too, the Cr-Co gamma phase extends deep into the ternary system in the form of a long narrow lip. The fact that this sigma type lattice is sustained even when well over half of the Co atoms in it are replaced by Ni atoms, with relatively little change in the Cr content, clearly indicates that Ni itself has a certain tendency to form the sigma phase with chromium. This tendency is hidden in the binary Cr-Ni alloys, where the sigma phase is not known to occur, but it becomes operative in the presence of a suficient amount of Co. The interpretation of these facts in terms of electron concentrations is rendered difficult by the uncertainty of our present knowledge of the valency electron structure of the transition elements in their alloys. However, Sully and Heal's results and the present work suggest that intermetallic phases with signla type lattice may occur more frequently in these little investigated alloys than heretofore suspected. In particular, it is expected that a similar phase may exist in the V-Co and perhaps in the V-Ni system, in analogy to the known sigma type phase in the V-Fe system, and that all these sigma type phases may form extensive solid solutions with one another.

Jan 1, 1950

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