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By R. W. Armstrong, P. C. Jindal

The hardness dependence on grain size for polycrys-talline cartridge brass and a leaded brass has been measured by Brine11 and Rockwell B testing. In each case, the hardness, H, depends on the average grain diameter, 1, according to: H =Ho + kHl-1/2 where Ho and kH are experimental constants. Diamond pyramid hardness values have also been measured as a function of the indentation size and grain size to give additional information on the nature of the hardness test and the dependence of hardness on micro-structure. The hardness of polycrystalline brass depends on its grain size. Bassett and Davis' demonstrated this as early as 1919 by making Brinell hardness measurements on cartridge brass. Since then, the hardness of this type of material has been measured as a function of grain size by making Rockwell,2'3 Vickers,4 and Brinell5 tests. he hardness dependence on grain size has also been measured for other materials. Angus and summers6 investigated the grain size dependence of the Brinell hardness of polycrystalline copper and a Cu-4.5 pct Sn bronze. In other studies, nickel,? Armco iron,Big an Fe-0.07 pct C alloy,I0 and an 0.39 pct C-12.45 pct Cr stainless steel" have been investigated. In some of the preceding cases, the hardness results have been analyzed to show that the hardness varies with the average grain diameter, 1, according to an l-l\4, l-1/4 or I-2 dependence,11-13 The studies of the influence of grain size on hardness have not been based on any theoretical model. This may be because the hardness of a material is itself a complicated property. However, attempts have been made to correlate, experimentally and theoretically, the hardness of a material with its unidirectional stress-strain behavior.14-l6 On this basis, Hall" proposed that the polycrystal hardness dependence on grain size might follow directly from the Hall-Petch18,19 relation for the grain size dependence of the yield stress. Thus, the hardness-grain size relation was given as: H = Ho + kHl-1/2 [1] where Ho and kH were taken as experimental constants. The relation was applied to the measurements on brass,' copper,6 bronze,= and Armco iron.' More recently, this relation was shown by Armstrong and jindal20 to adequately describe the measurements on cartridge brass made by Bassett and Davis' and Babyak and Rhines.5 In this case, the relationship was taken a step further by independently relating the values of Ho and kH to the values of oyand ky, previously reported by Armstrong, Codd, Douthwaite, and petch21 from measurements of the yield stress dependence on grain size for this type of material. In the present investigation, new Brinell and Rockwell B hardness measurements have been made as a function of grain size for a cartridge brass and a leaded brass. In addition, diamond pyramid hardness values were measured as a function of the indentation size. All these results are applied to a further analysis of the hardness dependence on grain size. MATERIALS AND EXPERIMENTAL METHODS Cartridge brass and a leaded brass were selected for this investigation for two main reasons: it was anticipated 1) that these materials could be cold-worked and recrystallized to a wide range in grain size and 2) that the results to be obtained on these typical industrial materials could be usefully compared with previous investigations. The chemical analyses of the actual materials which were employed are given in Table I. The as-received 1/2- and 3/4-in.-thick plates were given various reductions in thickness by cold rolling. The rolled material was heat-treated at various temperatures between 330" and 850°C for differing time periods from 5 min to 9 hr to achieve a variation in the average grain diameter between 0.0339 and 0.000543 cm.22 During heat treatment, the brass was protected from zinc loss by packing it in chips or foils of the same composition material. Reasonably equi-axed grain structures were obtained in each case. The metallurgical grain sizes of the specimens were determined from measurements of the average linear intercept on a random line. Annealing twin interfaces were not counted along with grain boundaries. The

Jan 1, 1970

By R. M. N. Pelloux

This study of aluminum-copper alloys had two aims: 1) To determine the effect of the amount and distribution of a second phase, CuAl2, on the creep-rupture strength, ductility, and fracture characteristics of the alloys. The work of Gemmell and grant' on single-phase aluminum-copper alloys provided a basis for the present study. 2) To attempt to provide a relation between the microstructure and strength of two-phase alloys deformed at comparatively high temperatures (greater than 0.45 T,). The creep behavior of the two-phase magnesium alloys Mg;Ce and Mg-A1, has been treated by Roberts. 9 In work reported by Sully and Hardy4 and by Underwood, Marsh, and Manning~ on A1-Cu two-phase alloys, and also in a portion of the work of Gemmell and grant,' aging took place during the creep tests. 'In the present work, overaged aluminum-copper alloys were subjected to creep deformation at two temperatures, 500 and 700OF. The overaging treatments to produce the precipitate dispersions were performed prior to the test, at temperatures which were the same as the ultimate respective test temperatures. Hence, the present study is concerned with the creep behavior of stable (in contrast to "underaged") two-phase A1-Cu alloys, i.e., alloys in which no depletion of the solid-solution matrix occurred during: creep. MATERIALS AND PROCEDURE A 2 and a 3 pct Cu alloy, supplied by Alcoa, were studied; Table I shows the compositions. The grain size of the specimens, 0.9 to 1.0 mm, was achieved by annealing the machined test bars for 2 hr at 1000°F, followed by furnace-cooling to 900°F, and homogenizing for 4 hr. Both compositions are in the single-phase condition at 900°F. Two types of overaged dispersions, termed "over-aged I" and "overaged 11" were prepared after the grain size and the homogenization anneals. The overaged I alloys were prepared by quenching to room temperature after homogenization, aging at either 500' or 700°F for 72 hr, and air-cooling to room temperature. The overaged I1 alloys were prepared by furnace-cooling after homogenization, to either 500' or 700°F, and holding at the necessary temperature for 72 hr. The times for furnace-cooling from 900°F to 700° and 500°F were, respectively, about 2 and 3.5 hr. The structures of the A1-2 pct Cu alloys are shown in Fig. 1 (overaged I) and in Fig. 2 (overaged 11). A comparison of Figs. 1 and 2 shows that in the overaged I alloys the precipitate particles along the grain boundaries are much more closely spaced and the grain boundaries are straighter than they are in the overaged I1 alloys. Further, the particle size and spacing in the grains are smaller than in the overaged I1 alloys. Microstructures of the A1-3 pct Cu alloys have not been shown; the structures of these alloys differed from those of the A1-2 pct Cu alloys only in that the distribution density of the particles was greater. The creep specimens had a gage section 1 in. long with a diameter of 0.155 to 0.195 in. Before testing, specimens were electropolished in a solution of 100 cc glacial acetic acid, and 30 cc of 60 pct perchloric acid, at 40' to 50°F, at 24 v. The specimens were kept refrigerated prior to testing to avoid precipitation at room temperature. Constant stress creep tests were conducted; the load was applied 75 min after heating of the specimens to test temperature had begun. EXPERIMENTAL RESULTS Creep-Rupture—Fig. 3 shows the log stress-log rupture life plotfor the overaged alloys studied, and also for the underaged A1-2 pct Cu alloy.' At 700°F, the stress-rupture life relationship is nearly independent of both the amount of precipitate (i.e., composition) and of the type of overaging treatment (i.e., precipitate dispersion). At 500°F it is apparent that the increase in rupture life that was ex-

Jan 1, 1960

By E. S. Machlin

An extension of the thermodynamic theory has been made for the case of irreversible growth processes occurring by the motion of an interface. The theory is applicable to such diverse phenomena as diffusion, growth in recrystallization, continuous grain growth, growth of carbides, etc., growth of eutectoid products, growth in solidification, recovery, "slipless" flow, etc. THE publication of a recent book1 has served to focus attention on a very powerful means of treating certain irreversible processes. This method which has been formally described as the thermodynamic theory of irreversible processes is applicable to processes which involve an approach to equilibrium and for which the deviations from equilibrium are small. The irreversible processes can be classified into three groups: chemical reactions, transport processes (diffusion, heat and electrical flows), and relaxation phenomena involving a degradation of internal energy to more stable states. The limits of applicability of the theory can be precisely defined1,2 for each type of irreversible process. For example, in a chemical reaction at constant temperature and pressure, the Gibbs free energy released per mol in the process should be less than the thermal energy, RT. Another type of irreversible process, which sometimes involves a combination of the first two of the above-mentioned groups, is treated in this paper. This process is one characterized by the motion of an interface separating two regions having different values of free energy and may be briefly described as a growth process. Prigogine2 and Herring3 have treated special cases of this type of process. Previous conscious applications of the theory in metallurgy have been limited to the field of diffusion, one of the transport processes. Darken,4 Bardeen,5 Prigogine2 and others have made significant contributions in this respect. Some other applications of the theory are described in this paper. The Theory The thermodynamic theory of irreversible processes is based on the work of Onsager,6 DeDonder,7 Prigogine2 and others. A resume of the theory has been given by Prigogine2 and DeGroot.1 A brief description of the theory follows, although for a complete understanding the reader is urged to read the references. It is first assumed that the change in entropy, even for a system removed from equilibrium, is given by dS = [dU + pdV - Si µi, dn, - Sk Pk dxk]T-1 Using this expression, the irreversible entropy production in the system is calculated by subtracting the contribution to the change in entropy of the system by transfer of heat, work, or matter from the surroundings. Thus, for example, the irreversible entropy production of a system at constant temperature and pressure is given by dtS = — — dG (DeDonder7) Now it has been shown by Prigogine,2 DeDonder,7 and DeGroot1 that the rate of irreversible entropy production diS/dt, when calculated in the manner suggested, can be written as a sum of products of conjugate forces XK and fluxes Jk, i.e., d,s/ = Sk Jk Xk [I-1] dt The assumption is next made that a linear relation exists between a given flux and the forces, obtained from Eq. I-1, i.e., Ji = Sk Lik Xk (i = 1, 2, . . . n) [I-2] Generally, there is a degree of freedom in choice of the fluxes and forces. However, for all the choices consistent with Eq. I-1 the Onsager8 relations, based on the principle of microscopic reversibility, namely, Lik = Lki, are valid. The coefficients Lik, depending upon the choice of the conjugate fluxes and forces, may be more or less dependent upon the parameters defining the state of the system. In general, the proper choice of fluxes and forces utilizing Eq. I-1, makes the coefficients Lik independent of time. Also, because many of the three classes of irreversible phenomena have already been treated,1,2 a proper choice can be made by analogy. In any case, the validity of Eq. 1-2, from whatever choice made using Eq. I-1, must be tested by experimentation. The theory, thus, comprises the following steps: 1—The irreversible entropy production is calculated to yield Eq. I-1. 2—The terms in Eq. I-1 are grouped

Jan 1, 1954

By L. S. Birks

The bainite transformation in a 3.5 pct Ni-1.25 pct Cr steel was studied under various conditions of cooling and stress. Several characteristics may be specified: 1) transformation in the bainite region (925° to 575°F) is very little affected by the manner of cooling from the austenitizing temperature at 1600°F to 575°F)tothe upper limit of bainite transformation at 925°F; 2) starting time for the bainite transformation is the same order of magnitude for either isothermal transformation or continuous cooling, but the rate of transformation is somewhat greater for isothermal transformation; 3) tensile stress accelerates both isothermal and continuous cooling transformation, and 32,000 psi stress changes the form of the isothermal transformation diagram to correspond in appearance to the continuous cooling diagram; 4) transformation for nonlinear, continuous cooling may not be determined directly from the linear, continuous cooling transformation diagram, but may be predicted by assuming first that the fractional amount of austenite transformed in a given small temperature interval depends on the approximate linear cooling rate during that temperature interval and then by summing stepwise over the whole temperature range. IN a previous publication' an X-ray spectrometer was described with which the X-ray diffraction from a specimen could be observed continuously under controlled temperature and tensile stress. This instrument has now been applied to a study of the austenite-bainite transformation in a Ni-Cr steel for both isothermal and continuous cooling conditions, with and without stress. Certain characteristics of the transformation lead to a method of predicting the amount of transformation to be expected at a given temperature for any type of cooling curve. Material and Specimen Preparation The steel chosen for the investigation was a Ni-Cr steel having the composition in the following percentages: 0.30 C, 0.27 Mn, 0.019 P and S, 3.50 Ni, and 1.25 Cr. In order to fabricate specimens suitable for the X-ray spectrometer, a 1/4 in. plate was ground down to 0.060 in. and then cold rolled to about 0.035 in. Next it was heat treated by quenching in oil from 1650°F and tempering at 1200°F for 1 hr. Then it was etched in dilute nitric acid to reduce its thickness to 0.014 in. and cut into blanks in the shape of flat tensile specimens 3 1/4 Vi in. long, 7/16 in. wide, with a notch % in. long and 7/32 in. wide; see Fig. 1. X-Ray Technique Since the X-ray spectrometer has been described in detail elsewhere,' only a brief outline of the principles will be repeated here. A focusing, pow- der-diffraction arrangement' was used, as shown schematically in Fig. 1, and the specimen was mounted vertically in a vacuum furnace (not shown in the figure). The X-rays, moving in a horizontal plane, enter and leave the furnace through beryllium windows. As shown in the figure, X-rays diverging from the line source A are diffracted by the specimen B and converge at the detector slit C. The detector D and the slit C may be set at the proper angle in the horizontal plane to receive X-rays diffracted by either the face-centered phase (austenite) or the body-centered form (ferrite, bainite, martensite). The specimen is heated by electrical conduction between connectors E, and E,, and a Pt—Pt-10 pct Rh thermocouple spot-welded to the center of the notched region on the side away from the X-ray beam indicates the temperature continuously on a Brown recorder. Temperature control is exercised manually with a variable transformer on the input to E,-E,. Any desired time-temperature relationship is easily obtained by first drawing the desired curve on the temperature recorder chart and then adjusting the variable transformer during the run so that the thermocouple

Jan 1, 1957

By W. W. Mullins

The development, by the mechanism of volume diffusion, of a grain boundary groove on an interface separating a solid phase and a saturated fluid phase is calculated under the following assumptions: 1) isotropy of the interfacial free energy 's, 2) applicability of the Gibbs-Thompson formula relating curvature and chemical potential, 3) a nearly planar groove surface. The groove profile is found to have a .fixed shape and linear dimensions that are proportional to (time)1/3. The constant of proportionality is evaluated and involves ?s in such a way that the latter my be evaluated from grooving kinetics. A grain boundary that intersects an interphase interface will tend to produce a groove along the line of intersection (Fig. 1). The ultimate motivation for the formation of the groove is the reduction in interfacial free energ that occurs as the grain boundary contracts. Smith has discussed the way in which the free energy of the interfaces determines their dihedral angles at the groove root and has given a detailed analysis of the effect of the dihedral angles upon the nature the microstructures developed in polyphase alloys. Herring2 has extended the considerations to the case in which the free energy of an interface depends on its orientation and has thus added torque terms to the condition for interface equilibrium. Although the grain boundary and the interphase interface may quickly achieve the proper equilibrium angles where they intersect, as determined by the balance of equivalent tensions and torques,"2 the groove will generally continue to grow (though with decreasing speed). Thermodynamically, this continued growth reflects the fact that the lowest free energy cannot be achieved until the entire grain boundary has been eliminated; mechanistically, the growth occurs in response to inhomogeneities of chemical potential that are caused by the constraint of fixed dihedral angles at the groove root. The latter point is illustrated in Fig. 1, which shows that atoms* near the groove are on the convex side of a cylindrically curved surface and therefore have a higher chemical potential than atoms on the flat interface beyond. Thus atoms tend to leave the curved groove shoulders and force the groove to deepen. When both phases are solid additional chemical potential gradient may arise from whatever strain fields are necessary to insure continuity of material across the interface. In the discussion that follows, this complication due to strain will not occur since we always assume one phase to be a fluid and the other a solid. The transport processes that may operate to permit growth of the groove are surface (interface)* diffusion, volume diffusion in the phase on either side of the interface, and evaporation-condensation when one phase is gaseous. (Also a melting-freezing process is responsible for groove enlargement on a solid-melt interface as discussed in Sec. VI). The theory of grain boundary grooving has been discussed in detail for the processes of surface diffusion and of one type of evaporation-condensation.3'4 The theoretical predictions for the mechanism of surface diffusion have been confirmed in an experimental study of grooving kinetics in copper.5 In this paper, the theory of groove development by volume diffusion will be presented. Volume diffusion can occur either by atomic migration in the solid S or by diffusion of S atoms in the fluid phase, or solvent, adjacent to the groove surface. As discussed in Sec. V, volume diffusion in the solid should be less important than surface diffusion in forming a groove. Apart from verifying this statement then, the main interest of the present analysis centers on diffusion in an external solvent. The solvent may be either a liquid (e.g., water, or-

Jan 1, 1961

By Leonard L. Melton, Calvin D. Saunders

The design and performance of many operations common to the petroleum industry depend upon the unique properties of a class of materials known as non-Newtonian fluids. The art of measuring and describing these properties, called rheology, has fallen far behind the field applica-tion of these fluids in this industry. Empirical methods are still employed although theoretically sound methods of analysis are now available. This paper illustrates a completely general method of analysis of the rheological properties of non-Newtonian fluids which id independent of the type of viscometer employed and also the rheological type of fluid encountered except those of a thixo-tropic or rheopectic nature. Values of the rheological properties of a fluid obtained using this method of analysis are based upon an absolute scale of measurement, eliminating the necessity of employ-jng arbitrary concepts of the flow properties of non-Newtonian fluids, The fundamental nature of this method of analysis is further demonstrated by evaluating the precision with which measurements have been made of these rheological properties by employing a dimensionless criteric: —the Fanning friction factor-Reynolds number correlation. INTRODUCTION Non-Newtonian fluids are not new in the petroleum industry. Particular properties of non-Newtonian materials have been recognized and used to advantage in drilling fluids and have found excellent application in the hydraulic fracturing process.'.' While usage of these fluids is not new in this industry, the art of measuring and describing their rheological properties is still in its infancy. This is reflected in the accepted method of evaluating drilling fluids, API RP 29, (1950), which recommends a one point "viscosity" measurement. These shortcomings are recognized by various groups in the industry and more adequate methods have been prposed.3,4 The efforts Of these people are to be commended; but, at the same time, the limitations of their method of analysis and viscometer must be appreciated. This method Of analysis is applicable Only to Bingham plastic fluids as is pointed out early in their articles. The consistency of a Bingham plastic fluid must also lie within the range of the viscometer which is also well defined by the author. It is believed that the apparent simplicity of this method of analysis and the utility Of Operation Of their viscometer will soon make the terms non-Newtonian fluid and Bingham plastic fluid synonymous as used in this industry; a tendency which has already been encountered. Application of this method of analysis to a non-Newtonian fluid other than a Bingham plastic can lead to erroneous results. The field of rheology has long been hampered by the adherence to arbitrary concepts of Of of the flow properties Of non-Newtonian fluids. This has resulted in the design and operation of viscometers so as to fulfill these concepts rather than following the more logical method of analyzing experimental data so as to yield a fundamental truth. completely Bingham proposed the concept Of plastic flow and yield asu rement. data presented by Buckingham could hardly be interpreted so as to substantiate this theory; but rather succeeded in establishing the fact that compliance with this flow concept could never be realized in the capillary tube vis-cometer.5 Bingham, in reply, sug-gested "Rather than complicate our formula, it would seem to me a much better plan to so change the conditions of flow that the formula will be linear... Reiner0 stated .This plan has been followed by me in collaboration with Miss Riwlin. . . . From the present paper (Reiner and Riwlin, 1929) it will be seen that it is possible to choose the conditions of flow so that the formula based on Bingham's law of plastic flow remains linear. This is realized in the rotation viscometer," Thus, a viscometer, with design and operation based on the Reiner and Riwlin equation for plastic flow, is restricted to a specific range of flow

Jan 1, 1958

By Owen Thornton

Recently equations have been presented by Rose and Bruce' and by Rose², showing how the relative permeability of a reservoir rock may be determined from the capillary character of the rock. In particular, equations were developed to show the relationship between capillary pressure and the effective permeability to the wetting phase in a poly-phase flow system. The equations are as follows (nomenclature the same as in the Rose and Bruce paper) Rose and Bruce assume that the average length of path (L,), which the wetting fluid follows in flowing through a porous media is independent of the saturation to the wetting phase, so that 1 is a constant dependent only on the k rock, and the permeability to the wetting phase is a function of the saturation and of the capillnry pressure: In measuring the flow of ekctric current through partially saturated core samples, it has been observed that the electrical resistance usually is not a simple linear function of saturation. This fact indicates that the average length of path in the flow of electric current is not independent of saturation, but rather that the tortuosity of the path depends upon the average saturation to the conducting fluid as well as upon the characteristics of the rock. itself. Inasmuch as the flow of fluid and the flow of electric current in many respects are analogous, it may be indicated further that the length of path for fluid also may not be independent of saturation. The following relationship can be derived to express the resistance to flow of electric current through a core sample partially saturated with conductive wetting phase, the non-wetting phase being non-conductive: where L is the average length of path followed by the current in flowing through a length L of partially saturated core, where L is the length of current path when the core is fully saturated, and where Rs and R, are the specific resistivities of the partially saturated and saturated core sample, respectively. It will be noted that R., the specific resistivity of the core sample when S, = 1.0, is equal to the "formation resistivity factor"' multiplied by the specific resistivity of the saturating fluid. If it be assumed that the average lengths of path for fluid flow and for the flow of electric current are the same, then equation (5) may be combined with equations (l), (2) and (3) to give the following relationship: The above equation suggests including a correction for tortuosity when calculating the relative permeability of a reservoir rock to a wetting phase. The correction factor may be obtained from the resistivity-saturation relationship. For instance, the following calcu- lations are obtained for the unconsoli-dated sands described by Leverett Kw Kw Sw R°/Rs Pt/Pc¹ (Calc.) (Obs.) 0.30 0.08 0.88 0.02 0.0 0.40 0.16 0.94 0.06 0.04 0.50 0.27 0.97 0.14 0.11 0.60 0.40 0.98 0.26 0.21 0.70 0.53 0.98 0.39 0.35 0.80 0.68 0.99 0.57 0.54 0.90 0.84 0.99 0.77 0.76 1.00 1.00 1.00 1.00 1.00 It will be noted that the agreement between the calculated points and the observed data is rather good. Further investigation of the above method for obtaining relative permeabilities may be merited. For many sands within specified ranges of saturations the following relationship has been found to hold approximately': — =SW"......(7) Rs The exponent n in the above equation has been found to equal two for many sands so that equation (6) reduces to the following: The writer acknowledges the permission of The Texas Co. to submit this note for publication. 1. Walter Rose and W. A. Bruce—Jnl. of Pet. Tech., Vol. 1, No. 5, p. 127 (1949). 2. Walter Rose—Jnl. of Petr. Tech., Vol. 1, No. 5, p. 111 (1949). 3. G. E. Archie— -Trans. AIME, 146, 54 (1942). 4. M. C. Leverett— Trans. AIME, 142, 152 (1941). 5. M. C. Leverett—Trans. AIME, 132, 149 (1939).

Jan 1, 1949

By Owen Thornton

Recently equations have been presented by Rose and Bruce' and by Rose², showing how the relative permeability of a reservoir rock may be determined from the capillary character of the rock. In particular, equations were developed to show the relationship between capillary pressure and the effective permeability to the wetting phase in a poly-phase flow system. The equations are as follows (nomenclature the same as in the Rose and Bruce paper) Rose and Bruce assume that the average length of path (L,), which the wetting fluid follows in flowing through a porous media is independent of the saturation to the wetting phase, so that 1 is a constant dependent only on the k rock, and the permeability to the wetting phase is a function of the saturation and of the capillnry pressure: In measuring the flow of ekctric current through partially saturated core samples, it has been observed that the electrical resistance usually is not a simple linear function of saturation. This fact indicates that the average length of path in the flow of electric current is not independent of saturation, but rather that the tortuosity of the path depends upon the average saturation to the conducting fluid as well as upon the characteristics of the rock. itself. Inasmuch as the flow of fluid and the flow of electric current in many respects are analogous, it may be indicated further that the length of path for fluid also may not be independent of saturation. The following relationship can be derived to express the resistance to flow of electric current through a core sample partially saturated with conductive wetting phase, the non-wetting phase being non-conductive: where L is the average length of path followed by the current in flowing through a length L of partially saturated core, where L is the length of current path when the core is fully saturated, and where Rs and R, are the specific resistivities of the partially saturated and saturated core sample, respectively. It will be noted that R., the specific resistivity of the core sample when S, = 1.0, is equal to the "formation resistivity factor"' multiplied by the specific resistivity of the saturating fluid. If it be assumed that the average lengths of path for fluid flow and for the flow of electric current are the same, then equation (5) may be combined with equations (l), (2) and (3) to give the following relationship: The above equation suggests including a correction for tortuosity when calculating the relative permeability of a reservoir rock to a wetting phase. The correction factor may be obtained from the resistivity-saturation relationship. For instance, the following calcu- lations are obtained for the unconsoli-dated sands described by Leverett Kw Kw Sw R°/Rs Pt/Pc¹ (Calc.) (Obs.) 0.30 0.08 0.88 0.02 0.0 0.40 0.16 0.94 0.06 0.04 0.50 0.27 0.97 0.14 0.11 0.60 0.40 0.98 0.26 0.21 0.70 0.53 0.98 0.39 0.35 0.80 0.68 0.99 0.57 0.54 0.90 0.84 0.99 0.77 0.76 1.00 1.00 1.00 1.00 1.00 It will be noted that the agreement between the calculated points and the observed data is rather good. Further investigation of the above method for obtaining relative permeabilities may be merited. For many sands within specified ranges of saturations the following relationship has been found to hold approximately': — =SW"......(7) Rs The exponent n in the above equation has been found to equal two for many sands so that equation (6) reduces to the following: The writer acknowledges the permission of The Texas Co. to submit this note for publication. 1. Walter Rose and W. A. Bruce—Jnl. of Pet. Tech., Vol. 1, No. 5, p. 127 (1949). 2. Walter Rose—Jnl. of Petr. Tech., Vol. 1, No. 5, p. 111 (1949). 3. G. E. Archie— -Trans. AIME, 146, 54 (1942). 4. M. C. Leverett— Trans. AIME, 142, 152 (1941). 5. M. C. Leverett—Trans. AIME, 132, 149 (1939).

Jan 1, 1949

By George C. Gibbons

ALMOST everyone in any of the five counties embracing the great East Texas field depends heavily upon oil for his living whether or not he actually owns a well or piece of royalty himself. Oil is a natural resource that, when utilized, spreads its benefits over a vast area and into many channels. Depending then almost entirely upon agriculture: what is now known as the East Texas oil field a decade ago had a scattered farming population. For many of its people, tomatoes and other vegetable crops coupled with the old southern stand-by of cotton, furnished an adequate living and a small cash surplus. Some farm families on the red hills, however, were not far re- moved from the sowbelly and black- eyed peas, or cornpone and potlikker, standard of living. Kilgore of that day, was a village of less than 850 per- sons. Longview, with just over 5000, apparently had reached the limit of its growth. Tyler was an overgrown farming town of around 17,000 persons, de- pending largely upon the agricultural income of Smith County and surrounding territory for which it was a trading center.

Jan 1, 1941

By D. K. MACKAY

The production of oil and gas in Arkansas is confined to two distinct and widely separated regions of the state; namely: (1) South Arkansas in the Gulf coastal plain, where 49 fields-many containing two or more reservoirs or pools-yield oil, condensate and gas from beds in the Cretaceous and Jurassic, and (2) Northwest Arkansas, a part of the Arkansas Valley, where only dry gas is produced in 21 fields from sandstones of Pennsylvanian age. Exploration during the year 1945 centered largely in these two producing regions, but some of the geophysical surveys were made and wildcat drilling was done a considerable distance outside these regions.

Jan 1, 1946

By Arthur F. Hagner

The titaniferous magnetite deposit at Iron Mountain, Wyoming, is in Precambrian anorthosite. Individual ore bodies are lenses, commonly arranged en echelon, conformable to the platy crystal structure and compositional layering of the anorthosite; a few transect these features at various angles. The ore bodies are on the east flank of the principal anticline in the anorthosite mass. Magnetite and ilmenite, accompanied by spine!, are the ore minerals. The principal gangue minerals are olivine, which was introduced with the ore, and plagioclase, the chief constituent of the anorthosite. The anticlinal region appears to have been a structurally weak zone, and westward-bowing curves of the axis were especially favorable sites for localization of the two largest massive ore bodies. These bodies are synclinal and plunge southeast. The proportion of magnetite-ilmenite to olivine and to anorthosite appears to be related to structural features. Where magnetite-ilmenite is present with olivine, the magnetite-ilmenite is encountered along the most pronounced parts of a fold where anorthite content is highest, whereas olivine is associated principally with more gently folded portions. During granulation and recrystallization of the anorthosite mass, temperature and pressure changes furnished the energy required to release and mobilize iron and other elements that migrated to areas of low pressure, the ore zone. Some iron and magnesium may have combined with silica from partly dissociated plagioclase to form olivine. The ore formed by replacement of anorthosite as indicated by: (1) the marked changes in mineralogy along strike, dip, and plunge of an ore body; (2) the concentration of massive ore in folds and olivine on limbs; ( 3) the halo of low-grade mineralized rock that transects the structure of the anorthosite in the hanging wall; and ( 4) the layering in the large southern ore body, that strikes more easterly than the trend of the body.

Jan 1, 1968

By PAUL M. Tyier

NOW that analytical chemistry has gone so far to debunk early misconceptions about minerals, the fact that the light of exact knowledge still fails to illuminate many dark corners is often overlooked. By combining the skills of the physicist with those of a chemist, the identification of minerals has become an exact science and the presence of even minute traces of impurities and extraneous elements is readily revealed by spectrographic means, Granted that we can learn all there is to know about the composition of a substance and even about its physical propertied (which latter assumption is somewhat far-reaching) it still does not follow that we clearly understood its commercial designation or utility.

Jan 1, 1941

By H. Rosenthal, A. L. Jamieson

The action of mercury on stressed brass to produce cracks was known before Moore, Beckinsale and Mallinson1 showed that actual season cracking did not occur spontaneously but could be induced by ammonia. These investigators studied other substances, including diphenylamine, without finding that anything other than ammonia could cause season cracking Grimston2 reported season cracking in cartridge cases stored in wooden boxes wetted with dilute sulphuric acid pickling solution. Season cracking associated with sulphur dioxide, water vapor and air has been reported by Johnston,3 although he reported that trimethylamine and pyridine did not cause cracking. Jevons4 has ascribed season cracking of brass in certain instances to trimethylamine, "aldehyde amine," "ketone amine" and pyridine, but no experimental work was done evidently to prove this definitely. Pyridine was investigated by Morris,5 who found it to have considerable cracking power. In the present investigation, the object was a qualitative evaluation of a number of representative amines with respect to their ability to cause season cracking. Thus it was desired only that an appreciable vapor pressure of each amine be obtained in order to make the test as severe as possible, without attempting to test equivalent concentrations for comparative purposes. MEthods Specimens TWO types of specimen were used: 1. Unannealed 70-30 brass CUPs formed from 0.040-in. thick sheet. Height of cup Was 13/8 in. and diameter was 17/8 inches. 2. First draw pieces of caliber .50 cartridge cases in the unannealed condition (70-30 brass)- The cups were representative of a thin wall and thin base specimen, whereas the draw pieces have a thick base (1/4 in.) and a thick wall (approximately 3/32 in.). Both types of specimens contained high residual stress and cracked in less than one minute in a solution of I per cent mercurous nitrate and I per cent nitric acid provided that this was receded by a 30-sec. pickle in 40 per cent nitric acid. Specimens were prepared as follows: (1) degreased in trichlorethylene, (2) rinsed in H2O, (3) pickled 5 min. in 10 per cent by volume H2SO4 (1.84 SP. gr.), (4) rinsed in H2O, and (5) dried. Amirtes Tested In selecting the amines, representatives of the three series of amines, and one series of substituted amines were chosen. The aliphatic series was represented by the methyl and ethyl primary, secondary and tertiary amines. These are the simplest aliphatic amines. For the aromatic series, the phenyl primary, secondary and tertiary amines were selected as being the simplest. The heterocyclic series was represented by pyridine, which is a simple heterocyclic base (tertiary amine).

Jan 1, 1944

By Shiou-Chuan Sun

There are several postulations for the mechanism of slime-coating. Incel proposed the electrostatic hypothesis, del Giudice2 suggested the chemical theory; Bankoff3 reported that slime-coating is inhibited whenever the surfaces of the slime particles are ionized sufficiently for Brownian movement to occur, and is facilitated when they are not. These postulations were examined by experiments involving the Burton tube, the cataphoretic cell, and slime-coating. The techniques involved will be described elsewhere in this paper. The electrostatic hypothesis, supported by migration experiments in a Burton tube, was abandoned by del Giudice.2 Experiments of mineral migration in a Burton tube. after the idea of Ince with modification, indicated that this apparatus was inefficient for accurate observation. A cataphoretic cell was constructed. The experimental data, as shown in this paper, enable the correlation and advancing of this hypothesis. Del Giudice's chemical hypothesis considered that slime particles are attached to the galena surfaces by a cement formed as the result of a metathetical reaction between the sulphide and the slime particles. Applying this hypothesis, the calcite slime particles were cemented to the galena surface by the formation of a cementing lead carbonate. In a similar way, lead silicate was considered as the cement of quartz slime coating on galena. Experiments verifying this hypothesis were carried out according to the following procedure: Fresh mineral particles selected from the central part of the broken lumps and examined first under a microscope for ascertaining a clean surface were placed in a small beaker (1.5-in. dia. by 2.5 in. deep) half filled with one kind of slime pulp. The dilution of all slime pulp was 4:I and the particle size of slime was minus 400-mesh. After agitation for 5 min. the specimen was removed by a sharp-end tong and washed gently three times in three separate distilled water baths. It was dried before a small electrical fan and examined immediately under a microscope. A photograph was made of the observation. With reference to the published solubilities,' several of these experiments, which contradict the chemical hypothesis, are listed as following: I. The coating of fluorite slime on the galena surface was light but the coating of galena slime on the fluorite surface was heavy. In a similar way, the coating of quartz slime on the galena was fairly light, but the coating of galena slime on the quartz particle was heavy. According to the chemical hypothesis, using the same constituents and regardless of which is the slime, the density of the coating should be expected to be the same. This, however, as shown above, is not true. Moreover, fluorite (CaF2), having a solubility of 16 mg.4a per liter of water, should not be

Jan 1, 1943

By Shiou-Chuan Sun

There are several postulations for the mechanism of slime-coating. Incel proposed the electrostatic hypothesis, del Giudice2 suggested the chemical theory; Bankoff3 reported that slime-coating is inhibited whenever the surfaces of the slime particles are ionized sufficiently for Brownian movement to occur, and is facilitated when they are not. These postulations were examined by experiments involving the Burton tube, the cataphoretic cell, and slime-coating. The techniques involved will be described elsewhere in this paper. The electrostatic hypothesis, supported by migration experiments in a Burton tube, was abandoned by del Giudice.2 Experiments of mineral migration in a Burton tube. after the idea of Ince with modification, indicated that this apparatus was inefficient for accurate observation. A cataphoretic cell was constructed. The experimental data, as shown in this paper, enable the correlation and advancing of this hypothesis. Del Giudice's chemical hypothesis considered that slime particles are attached to the galena surfaces by a cement formed as the result of a metathetical reaction between the sulphide and the slime particles. Applying this hypothesis, the calcite slime particles were cemented to the galena surface by the formation of a cementing lead carbonate. In a similar way, lead silicate was considered as the cement of quartz slime coating on galena. Experiments verifying this hypothesis were carried out according to the following procedure: Fresh mineral particles selected from the central part of the broken lumps and examined first under a microscope for ascertaining a clean surface were placed in a small beaker (1.5-in. dia. by 2.5 in. deep) half filled with one kind of slime pulp. The dilution of all slime pulp was 4:I and the particle size of slime was minus 400-mesh. After agitation for 5 min. the specimen was removed by a sharp-end tong and washed gently three times in three separate distilled water baths. It was dried before a small electrical fan and examined immediately under a microscope. A photograph was made of the observation. With reference to the published solubilities,' several of these experiments, which contradict the chemical hypothesis, are listed as following: I. The coating of fluorite slime on the galena surface was light but the coating of galena slime on the fluorite surface was heavy. In a similar way, the coating of quartz slime on the galena was fairly light, but the coating of galena slime on the quartz particle was heavy. According to the chemical hypothesis, using the same constituents and regardless of which is the slime, the density of the coating should be expected to be the same. This, however, as shown above, is not true. Moreover, fluorite (CaF2), having a solubility of 16 mg.4a per liter of water, should not be

Jan 1, 1943

By George J. Bancroft

INTRODUCTION. IT is unnecessary to repeat here the contents of many valuable contributions to this subject which have appeared in the Transactions and in the publications of the U. S. Geological Survey. As a basis for the further suggestions of this paper, the following are the most important: 1. The investigation of J. R. Don,1 showing the gold of certain Australasian veins to have been deposited by ascending solutions, and not by lateral secretion. 2. The theory of Prof. Posepny,2 distinguishing the vadose from the deep circulation, and ascribing the origin of certain classes of ore-deposits to ascending solutions of the latter class. 3. The theory of Prof. Van Hise,3 as to the underground circulation and the primary enrichment of veins thereby. 4. The paper of Prof. J. F. Kemp,4 showing that ore-deposits are largely the products of " expiring vulcanism." Many of Prof. Kemp's, ideas have been widely adopted by mining men. 5. The theory of secondary enrichment, so lucidly expounded by Mr. S. F. Emmons.5 This theory, dealing with, the rearrangement of ore-bodies after primary mineralization, has been generally adopted, and seems to me to have been as completely proved as the nature of the case permits. There are two facts which I think should be constantly borne in mind in formulating a theory of the genesis of ore-

Jan 1, 1913

By E. F. Steeb, P. C. Rosenthal

BlANKS 8 in. long were cut from the as-received bar stock and austenitized at 1560° F for 1 hr, oil quenched, tempered at 1140°F for 1 hr, and water quenched. The heat-treated blanks were machined into tensile specimens which were subsequently used for the straining operation. Some of the tensile specimens were temper embrittled at 900°F for 24 hr and air cooled prior to or following the straining operation. The specimens were strained in tension up to 5 pct total strain (elastic plus plastic) either at room temperature or at 900°F. The reduced sec- tion of the tensile specimen employed was 5 in. long and 0.600 in. in diam. This size specimen was sufficiently large to permit two standard Charpy impact bars to be machined from it. One group of specimens was temper embrittled at 900°F for 24 hr under stress of about 20,000 psi applied with a hydraulic tensile testing machine. Approximately 0.34 pct plastic strain occurred during this treatment. A comparison of series "A" and "B" data in Table I at 0 pct strain, reveals that the steel was rather highly susceptible to temper embrittlement, the embrittling treatment causing the transition temperature to rise 165°F. The 28 ft-lb level, which was near the center of the sharp-rising portion of the transition curve, was selected as the

Jan 1, 1959

By D. L. Luffel

This paper presents two main developments: (1) a short, constantly accelerated centrifuge method of measuring drainage capillary pressure properties of cores, and (2) a new analytic method of treatment of centrifuge measurements to obtain saturation-capillary pressure relations. Toward the first objective, a clever experimental method is presented which is certainly more rapid than previous centrifuge methods. Toward the second objective, a new analytic method is derived to eliminate the approximate method of Hassler and runner. The derivation of this new analytic method, however, appears to be in error. The new analytic solution is developed as Eq. 5 in Appendix A. At the beginning of this derivation, the average wetting phase saturation of a core is expressed as, where is the centrifuge angular velocity. Eq. D1.2 makes explicit the dependence of S and S upon The second equation shown in Appendix A expresses the relation between the three variables Since for a given porous medium the saturation is uniquely related to capillary pressure, the functional dependence of S upon P is trivial, i.e., Pc.ri does not actually appear. Thus, the function 5 (r, ) may be expressed as a new function, S*, of PC, , alone The author transforms the variable of integration in Eq. Dl through use of Eq. D2 and writes

Jan 1, 1965

By Richard Miller

WORK was undertaken two years ago at the Hammond Laboratory for the purpose of determining the magnitude of the elastic range in single crystals of pure metals by means of creep tests, the assumption being made that if a true elastic range exists, the elastic limit represents the maximum stress for no creep. A sensitive extensometer was constructed, and creep tests were made on zinc single crystals at a variety of loads and temperatures1. It was soon discovered that there is tip measurable elastic limit in ductile zinc single crystals at, or above, room temperature. The inference that pure metallic single crystals may not possess a definite elastic range was not justified, however, since zinc had been tested in creep only above its recrystallization temperature, and several investiga-tors2,3,4 had already shown that above the recrystallization temperature polycrystalline metals will flow under very small stresses, while below that temperature stresses of a much larger magnitude are required. For that reason, it was decided to extend the study of the elastic limit to other metals having a higher recrystallization temperature than zinc. Aluminum and silver were selected, because of the ease of obtaining pure materials and of preparing large single crystals, and because the crystallo-graphic glide system of these metals is well known. Owing to the limited time available, the elastic range was investigated by slow tensile tests rather than by creep tests.

Jan 1, 1937

By O. J. C. Runnalls, L. M. Pidgeon

J. M. Blocher, Jr. and I. E. Campbell (Battelle Memorial Institute, Columbus, Ohio)—Since the de Boer-Van Arkel process for making titanium metal involves a number of steps in a fairly compact unit, it is difficult to determine simply which of the steps is rate controlling. In any statement as to which step constitutes the rate-controlling process, qualifications appear to be in order. It is possible to design a reaction bulb in which any one of a number of steps is made to be controlling. I—With the filament removed some distance from the crude, as in the case of the authors' experiments, the interdiffusion of iodine and iodide may be controlling. 2—If, as is usually done, the crude metal is placed in a perforated cylindrical basket, or as a briquetted mass, in close proximity to the filament, the rate of deposition is increased (we obtained rates of deposition 5 to 10 times those cited in the authors' paper), and another rate-limiting factor, such as the reactivity of the crude, may take over. In this regard, we have noticed radically different rates of deposition with different crudes, and with crudes in various stages of exhaustion. 3—With a very reactive crude metal and with optimum practical geometry, still another process may be controlling. It is felt that this is a diffusion process in the immediate vicinity of the filament involving the fundamentally adverse situation of a net flow of particles away from the filament. The separate experiments on the reactivity of iodine with titanium are interesting but somewhat inconclusive. Data is still needed on the partial pressure of iodine in an operating decomposition bulb. A knowledge of the gradient of iodine partial pressure from the crude to the filament would be particularly enlightening. Optical absorption may be a useful technique here. Accurate measurements of the total pressure within a decomposition bulb under various conditions would be quite revealing. Preliminary measurements have been made at Battelle in following this line of attack. It is interesting to note that the authors' data on the temperature dependence of deposition rate indicate that the overall rate is not controlled by the kinetics of the decomposition reaction at the filament: TiI1 ? Ti + 4I Any reasonable estimate of the activation energy of this reaction would, if its kinetics were controlling, dictate a much greater temperature dependence than is observed here. The authors apparently attribute the drop in deposition rate (eventually to zero) with increased TiI4 pressure solely to a decrease in diffusion rate. However, there is an equilibrium factor involved here that must not be overlooked. As the partial pressure of TiI4 is increased, a point is reached where, due to the competing reaction of the tetraiodide with titanium to form lower iodides, the equilibrium partial pressure of titanium is reduced to the point that it equals the vapor pressure of titanium at the filament temperature and the deposition rate falls to zero. This effect would

Jan 1, 1953