Search Documents

By E. F. Ketterer, D. B. Collyer, A. B. Wilder

The microstructural stability of 59 carbon and low alloy steels after 34,000 hr exposure at 900' and 1050°F, including the weld heat-affected zone, is discussed. The tensile and creep rupture properties of the parent metal of many of the steels before and after 10,000 hr exposure are presented. SEAMLESS pipe has been used for many years at elevated temperatures. When seamless first began to be used, operating temperatures and pressures were relatively low and the steel produced adequately met the existing requirements. The need for knowledge of creep properties and graphitiza-tion was nonexistent. Today the requirements for tubular products have changed considerably. Operating temperatures and pressures are increasing continually and corrosion, particularly at high temperatures, presents a problem. Carbon steels have, under these conditions, certain economic advantages particularly in oil refinery use. However, the use of low alloy steels in the generation of steam power has increased appreciably due to the influence of molybdenum on creep strength and the control of graphitization with chromium. The behavior of carbon and certain low alloy steels after long periods of exposure at 900° and 1050°F (480° and 565°C) has been investigated. The steels were examined before and after 10,000 to 34,000 hr exposure. Results obtained with material exposed at 1200°F (650°C) are not presented due to the severe oxidation and resulting decarburiza-tion after long periods of exposure. The graphitization characteristics of carbon and low alloy steels are of fundamental concern to the users of these materials. This is particularly true where welded joints are employed. In order to evaluate properly the behavior of steels at elevated temperatures, it is desirable to employ not only long periods of exposure under controlled conditions, but to use material with known properties and steelmaking practices. The purpose of this investigation has been to study the microstructure of the weld and the tensile and creep rupture properties of the parent metal after long periods of exposure at elevated temperatures. In the report'.' of a previous investigation data were presented on the microstructure, impact strength, hardness, and oxidation characteristics after 10,000 hr exposure at elevated temperatures. When this investigation was planned, methods for controlling the graphitization characteristics of steel were not established and, therefore, a number of special alloy steels were included in the study. During the exposure of these steels, the influence of aluminum in accelerating the rate of graphitization and the inhibiting power of chromium were established by various investigators. Also, the vanadium-bearing steels, because of their outstanding creep properties, received attention. As a result of these developments, considerable progress has been made in the field of high temperature tubular products, and the necessity for special alloys to prevent graph-itization has been restricted largely to the use of chromium. Material Chemical analysis, deoxidation treatment, and austenitic grain size of the 59 steels discussed in this paper are shown in Table I. The steels were forged to 1x1 in. bars with the exception of steels 12B, 12DX, 12DY, 12DZ, 70, 70A, 72 to 78, 82, and 83 which were machined from heavy wall pipe. All bars were surface ground before exposure. Heat treatment before exposure is shown in Table 11. The majority of the steels included were melted in either a basic open hearth or basic electric furnace; how-

Jan 1, 1955

By B. A. Shaw

Historically, microwave tubes have been fabricated from massive metal and ceramic components. The current trend is to lighten tibes for airborne applications. The reqciiremenls of light weight and also reduced cost have created a novel approach to tube structure in which thin-film technology plays a major role. Although the electrical requirements of thin-film circuits in microwave tubes differ from those required or se,niconductor integrated circuits. the technology is basically similar. The stringent requirements of the micvowave tube have created sophisticaled thin-film techniques thut are of interest to the integrated-circuit industry in general. This paper describes a nunzber of thin-jilm techniques recently developed and discusses in detail the application of the technology in microwave tubes. The particular areas of interest are: 1) ceramic mounted thin-film slow-wave structures; 2) thin-film secondary emitters; 3) suppression of tube environnental multipactor by semiconducting' thin films; and 4) age-hardenable and dispersion-hardened thin metal films. SEVERAL thin-film techniques specifically applied to microwave power tubes are discussed in this report. There are two reasons for this work. One is the necessity of reducing weight and cost of microwave tubes and the other is related to overcoming problems in the tube operation by the use of applied thin-film technology. The major emphasis of this work has been on tube slow-wave structures. Other work in the area of secondary emission, either its suppression or its enhancement, is continuing; the most satisfactory results to date have been by utilization of thin-film technology. The requirements of high thermal and electrical conduction together with greater strength than normally obtained with elemental materials have led to the development of dispersion-hardened films. The paper will discuss: 1) ceramic-mounted delay-line microwave tubes; 2) multipactor and secondary emission; 3) hardened films. I) CERAMIC-MOUNTED THIN-FILM SLOW-WAVE STRUCTURES In a conventional crossed-field microwave tube, the slow-wave or delay-line structure is produced from two carefully machined components. One half of the structure is shown in Fig. 1. The other half is the mirror image of the first but is rotationally offset by a half a period. The combined structure now forms an interdigital type of slow-wave structure and is the anode of the tube as shown in Fig. 2. The period and finger length of an interdigital slow-wave structure are prescribed by the desired dispersion characteristics. The typical design is as shown in the first figure; it can be noticed that the finger width is several times greater than the finger thickness. Even assuming that it were mechanically possible to produce free-standing fingers of extremely small cross-sectional dimension, for example, 0.002 in. thick by 0.005 in. wide by 0.500 in. long, decreasing this finger width would increase the tube efficiency but would also decrease the thermal-conduction path, causing an increased temperature rise from intercepted rf current which in its extreme could easily cause finger melting. Hence, for free-standing lines of this type, the design is a compromise between mechanical capabilities, tube efficiency, and thermal dissipation. These structures are also expensive and tend to be heavier than purely electrical considerations would demand. In the present approach, we have transposed the three-dimensional structure previously shown into an essentially two-dimensional structure as shown in Fig. 3. The linear structure is used here for clarity of detail. The support member is a ceramic material and the line is deposited copper. The final tube design is shown in Fig. 4. Because of the backwall sup-

Jan 1, 1967

By R. Fawley, M. A. Quader, R. A. Dodd

Stacking fault energies and annealing twin frequencies have been measured for austenitic stainless steels having a) constant 20 wt pct Cr and varying nickel contents, and b) constant 20 wt pct Ni and varying chromium contents. The effect of nitrogen has also been studied and, to a lesser extent, so has the effect of carbon. All measured stacking fault energies plot linearly against the corresponding annealing twin frequencies, suggesting that, for constant prior deformation and grain size, twinning frequency can be used to estimate stacking fault energy. Compositions low in nickel possess the lowest fault energy, while the maximum fault energy within the investigated composition range occurs mound 20 pct Cr-20 pct Ni. Nitrogen has practically no effect on stacking fault energy when increased from 0.005 to 0.05 wt pct, although Planar dislocation glide is associated with higher nitrogen contents; this may be a short-range order effect. Carbon may raise the stacking fault energy a little, and causes pronounced dislocation tangling in deformed alloys. The basically different dislocation structures promoted by nitrogen and carbon, respectively, are not associated with large variations in stacking fault energy, and the reason for the difference remains unknown. INTEREST in the dislocation configurations developed in plastically deformed alloys arises principally from a desire for an understanding of mechanisms of plastic deformation and fracture. Comparatively little basic work has been concerned with austenitic stainless steels, although considerable interest has developed in the fundamental aspects of deformation of these alloys since the suggestion that those compositions deforming essentially by planar glide are particularly prone to transgranular stress corrosion cracking.' Certain facts are well-established. An 18 Cr-8 Ni steel (type 304) has a low stacking fault energy which is increased by higher nickel contents, and the structure of these steels when moderately plastically deformed changes concomitantly from planar to less planar to distinctly tangled dislocation configurations. These changes are thought to relate to changes in stacking fault energy, and considerable effort has been expended in measuring stacking fault energies of austenitic stainless steels through the determination of node curvatures2"4 even though the method has limitations due to formula approximations,5 an upper limit of measurement of 50 erg cm-2 at the most,5 and the necessity of an extremely meticulous experimental technique. Therefore, it is not surprising that only qualitative agreement between different investigators is generally to be found.'-' At high energies where node radius measurements are inappropriate, some use has been made of annealing twin frequencies to estimate relative stacking fault energies, although a recent critical evaluation of the method suggests that it should be used cautionsly with due regard to effects of grain size and prior deformation.6 Finally, there is a question as to whether the structures of some deformed steels are due to ordering effects. In particular, the role of nitrogen in promoting planar dislocation motion has been suggested to be due to ordering,' but similar suggestions have been made for steels having low interstitial contents.4 EXPERIMENTAL Small ingots of austenitic stainless steels (-50 g) were prepared from components exceeding 99.99 pct purity, the nickel and chromium being Johnson Matthey "Specpure" metals. Carbon was added as pure graphite, and nitrogen as CrN. The components were accurately weighed, and it was assumed that the final composition was the same as the nominal composition

Jan 1, 1969

By George P. Chapman

Mica is a platy mineral occurring in a variety of complex hydrous aluminosilicate forms with differing chemical composition and physical properties. Principal minerals in the mica group include: Muscovite-potassium mica (colorless or pale green/ ruby) Phlogopite-magnesium mica (dark brown or amber) Biotite-magnesium-iron mica (black or dark green) Lepidolite-lithium mica (lilac) Selected properties are given in Table 1. Muscovite is most important commercially with phlogopite of lesser use. The laminated structure of mica enables it to be split into very thin films which are transparent and tough as well as having outstanding dielectric and insulating properties. Commercially, mica is used in a number of forms (Chowdbury, 1941; Rajgarhia, 1951; Skow, 1962). Sheet mica consists of flat sheets mined from naturally occurring books of mica, free from defects and capable of being punched or stamped into required shapes. Sheet mica is separately classified into blocks, films, or splittings according to thickness. Built-up mica, or micanite, is made by arranging overlapping splittings in layers , cemented with a binder and pressed together at high temperature. Reconstituted mica, or mica paper, is made by depositing fine flakes of high-quality scrap mica in a continuous film impregnated with binder. Scrap and flake mica are normally unsuitable in quality or size for making sheet mica. Originally the term scrap mica referred to the waste byproduct of mining and fabricating sheet mica, and distinct uses were developed for this material. Subsequently it became economically feasible to mine lower quality mica for these uses, and the term flake mica was introduced. Although the two terms are still used somewhat synonymously, it is considered better, at least in the United States, to use the term flake mica in referring to mica mined for uses other than as sheet mica; and to restrict the term scrap mica to mica mined for or with sheet mica, but which will not meet the specifications. Synthetic mica, such as fluorophlogopite, is produced by slow crystallization of a melted blend of pure raw materials. Mineralogy In the true sense the term mica does not relate to, a particular mineral, but to a group or family of minerals of similar chemical composition and to some extent similar physical properties. These minerals are predominantly potassium aluminum silicates with varying amounts of magnesium, iron, and lithium. The precise formulas and isomorphic relationships of the various group members have been studied, but general agreement has not been reached (Grimshaw, 1971; Hurlbut, 1952; Skow, 1962). The general formula describing the chemical composition of micas is [X2Y4-6Z8020(OH, F)4, where X is mainly K, Na, or Ca; Y is mainly Al, Mg, or Fe; Z is mainly Si or Al (Deer, et al., 1962).] These minerals have an internal structure of the layered lattice type where the silicon atoms are in the center of a tetrahedral grouping of oxygen atoms. The groups are linked together in a single plane by three oxygen atoms that lie within the common plane. Each of these oxygen atoms is shared by two tetrahedra. These linked tetrahedral groups, when continually extended, produce a hexagonal network within the plane. This internal structure of the mica has been used to explain the ex-

Jan 1, 1983

By C. W. Phillips, D. N. Frey

A commercial Ti-Fe-Cr alloy, Ti-150, exhibits a martensitic transformation on cooling and two nucleation and growth reactions, one above and one below the Mg-Mf region, on isothermal holding below the single-phase ß temperature range. The reactions were followed by metallographic, X-ray diffraction, and microhardness methods. THE rapidly expanding engineering application of titanium and its alloys makes increasingly urgent an adequate knowledge of the effect of heat treatment on this material. The work herein reported is an attempt to determine certain aspects of the behavior of a commercially available alloy, Ti-150, during heat treatment. The alloy, with a nominal composition of 2.7 pct Cr, 1.3 pct Fe, 0.25 pct 0, 0.02 pct N, and 0.02 pct C, was received in the as-rolled condition as a 3/4 in. round. Slugs 0.11 to 0.12 in. thick were cut under a coolant using a silicon carbide wheel. Preliminary work established that the alloy consists of two phases, a (hexagonal close-packed) and /3 (body-centered cubic), at temperatures below 1750" to 1775"F, and of only /3 phase at higher temperatures. The slugs were heated for 1 hr in air at 1800°F to form a single-phase /3 matrix, then transferred to molten tin (1250° to 1650°F) or lead (1150°F and below) for isothermal holding. Holding temperatures ranged from 700° to 1650°F, times from 0.001 to 23 hr. The treated slugs were then sectioned, one part for metallographic examination and diamond pyramid hardness, the other, after deep etching to remove the high oxygen surface,' for comparative lattice parameter determination and X-ray phase identification. Hardness measurements were taken on the lightly etched surfaces of the metallographic specimens; a 1000 g load on a 136° diamond pyramid was used. Five impressions on each sample were made and the average of the hardness calculated. The use of microhardness measurements to follow the course of an isothermal transformation reaction is undesirable because of the possibility of wide differences in microconstituent hardness.' They were used in this case, however, because of the small amount of material available. At the higher transformation temperatures, where the above-mentioned objection was apparent, the readings were proportioned to correspond to the estimated ratio of transformed and untransformed constituents present. At lower temperatures, resulting in much finer microconstituents, the microhardness measurements were more uniform. The standard deviation of the mean of five impressions calculated from these latter values was 4.2 DPH. Employing 2a limits (probability 0.95) the experimental error of the hardness measurements averages was 8.4 DPH. The etchant used was composed of one part glyc-erol and one part 48 pct hydrofluoric acid." Of a number of etches tried, this one appeared most satisfactory. All micrographs were taken at 500X magnification and with oblique lighting to permit easier identification of the acicular structure resulting from rapid cooling. No advantage was gained by using polarized light for metallographic examination. Phase identification and lattice parameter measurements were made with a North American Philips high angle spectrometer in conjunction with a recording potentiometer. Considerable difficulty was encountered with some of the lattice parameter measurements because of the extreme broadness of the few diffraction lines obtained from samples consisting mainly of strained, untempered, quenched structures.

Jan 1, 1953

By F. G. Miller, T. D. Mueller, L. B. Davidson

A mathematical model of reservoir behavior during one cycle of the intermittent steam injection process is presented in this paper. A cycle of the process is considered to be composed of three stages: injection, condensation and production. The model concentrates on behavior during the production stage. The influence of several parameters on production improvement is described, using the results obtained with a numerical equivalent of the model. Reservoir system parameters considered are thickness, reservoir thermal conductivity, oil viscosity, solution gas-oil ratio and the change in oil effective permeability with temperature. Operating parameters investigated are heat injection rate, steam temperature and cumulative injection time. In the face of considerable uncertainty, the model appears to give a fair prediction of the behavior observed during an actual test. This makes the model a useful means of selecting projects. It is shown that the model may also be utilized to select an optimum set of operating conditions for a particular project. Results of this study show the extent to which production improvement depends on each of the parameters investigated and give an indication of the range of system conditions within which the process would be effective. INTRODUCTION In recent years the intermittent steam injection or steam soak process of oil recovery has become a popular method of improving recovery in reservoirs bearing high-viscosity hydrocarbons. Production improvement due to the process results from heating the reservoir near the wellbore. The process is applied on an individual well basis and is executed in a series of cycles, each consisting of three stages: injection, condensation (the soaking period) and production. During the injection stage, high-pressure steam is injected into the reservoir surrounding the well-bore. This study assumes that injection is carried out over the entire vertical section of the reservoir rock that can be exposed to fluid injection. The condition of steam entering the reservoir is considered to fall within the following limits: (1) steam pressures less than 1,000 psig, (2) steam temperatures between 300 and 700F and (3) steam quality less than 90 percent. The last restriction is due to equipment limitations. Normally, injection re maintained for less than 3 weeks. After termination of injection, the condensation stage begins. The well is shut in for several days, supposedly to make certain that the injected steam condenses. This condensation would insure the retention of injected heat. The production stage is initiated when the well is opened again. Reservoir response during this stage determines the effectiveness of the process (response is defined as the oil production rates, the water production rates and the wellbore temperatures observed during the entire production stage). The immediate response of the reservoir is sometimes quite good. Sets of case histories by Longl and by Owens and Suter2 give some typical figures for response. Duration of the production stage is equal to the time needed for the oil production rate to decline to some predetermined value. This usually requires 4 to 6 months. Termination of the production stage coincides with the start of the next cycle. The process is continued, cycle by cycle, until it becomes unprofitable to continue. One simple model2 and two more sophisticated models3,4 of the process have been presented. These are based on fundamentally different assumptions than those used in this investigation. Although the three models might be modified to fit the assumptions used in this study, it is felt that greater rigor would result by developing a

By E. H. Rennhack, J. F. Libsch

Definite transition behavior was found in unalloyed titanium at 0.13 pct 0 equivalent. The addition of 0.5 Sn, 1.0 Al, 0.5 Al, and 1.0 Sn lowers the tvansition temperature of titanium at oxygen equivalents exceeding 0.22, 0.29, 0.40, and 0.51, respectively. Metallographic evidence indicates that progressive amounts of oxygen restrict deformation at low temperatures resulting eventually in brittle fracture. The presence of tin or aluminum is thought to alter the atomic distribution of oxygen within the titanium lattice in such a manner as to facilitate some degree of slip and twinning. 1 ITANIUM-like iron and zinc experiences a transition from ductile to brittle fracture with decreasing temperature. The presence of sufficient quantities of the interstitial elements, carbon, oxygen, and nitrogen in solid solution, has been shown to progressively lower the room-temperature impact resistance of titanium with increasing interstitial content.1"1 Ogden,et al,2 reported finding no transition from ductile to brittle fracture with decreasing temperature in iodide titanium. However, a definite transition was found to occur at 0.36 pct 0 equivalent in an alloy containing 0.47 pct carbon in solid solution. The oxygen equivalent in this case was obtained by assuming the effects of carbon, oxygen, and nitrogen in combination on the impact properties of titanium to be additive on the same basis as their separate effects on tensile strength, namely: Oe = 2/3 (pct C) + pet 0 + 2 (pet N) They concluded that the tendency toward transition behavior is dependent on the total interstitial content in solid solution and not on any one particular interstitial element. Rennhack,4 however, recently found transition behavior in iodide titanium at an oxygen equivalent of 0.17 pct. Ogden, etal3, reported that the strengthening effects of carbon, oxygen, and nitrogen in titanium decrease with the addition of tin. They showed that tin additions increase the tolerance of titanium for the interstitials, that is, 10 pct Sn permitted individual additions of up to 0.4 wt pct of the interstitial elements without any significant loss in ductility. Aluminum tends to decrease ductility and impact strength of titanium for a given interstitial ~ontent.3 Van Thyne and Kessler5 found that the solid solubility of carbon in titanium doubled in the presence of 10 pct Al. The precise effects of tin and aluminum in the nrespncp of rorvfen nn the impact properties of titanium had previously not been determined. The high oxygen tolerance of titanium containing tin may provide a suitable means for improving the impact properties of titanium containing the interstitial elements, particularly oxygen. Unlike tin, however, aluminum has a high affinity for oxygen and will reduce rutile titanium dioxide (TiO2)by a thermit-type reaction.6 Thus, the atomic distribution of oxygen in titanium might be different in the presence of aluminum. The present work was undertaken to: 1) Determine the effect of oxygen on the transition behavior of unalloyed iodide titanium. 2) Determine the effect of small amounts of tin and aluminum on the transition behavior of iodide titanium in the presence of oxygen and other interstitial~. EXPERIMENTAL Three different lots of iodide titanium were employed to prepare the alloys studied in the present work. Their chemical composition is presented in Table I. The compositions of the tin and aluminum used for alloying are shown in Table 11. Oxygen additions were made using calcined rutile titanium dioxide (TiO2)of 99.7 pct purity. Alloy Preparation—Four titanium-base alloys containing separate additions of 0.5 and 1.0 pct each

Jan 1, 1960

By T. E. Leontis

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

Jan 1, 1953

By Oliver Bowles

Dimension stone is a term applied to stone sold in blocks or slabs of specified shapes and usually of specified sizes, contrasted with crushed, broken and pulverized stone covered in another chapter. Dimension stone includes cut stone, rough building stone, ashlar,* rubble, monumental stone, paving blocks, curbing, flagging, and many types of ornaments and novelties carved from stone. Riprap-large, irregular blocks used for shore protection-is classed with crushed and broken stone. Composition, Varieties, and Properties Dimension stones are of many kinds. The principal varieties are granites, trap rock (diabase, basalt, and gabbro), sandstone, limestone, and marble. Slate is covered in a separate chapter. Granite is a visibly granular crystalline rock consisting essentially of feldspar, quartz, and mica or hornblende. The basaltic rocks are darker in color than the granites. They contain little or no quartz and consist largely of plagioclase feldspar, augite, pyroxene, and hornblende. They are classed commercially as black granites. Limestone consists essentially of calcium carbonate. Dolomites and magnesian limestones used as dimension stone are classed with the high-calcium limestones. Marble is a crystalline form of limestone, but in the trade, any carbonate rock which will take a polish is called a marble. Many limestones which are fossiliferous but which will take a polish are sold as a decorative stone for lobbies of hotels and office buildings. Sandstone consists essentially of silica in the form of sand grains cemented into a coherent mass. Although rock occurrences are numerous and widespread, the exacting requirements of use condemn all but a small fraction of them for commercial use as dimension stone. No deposit that has closely spaced joints or planes of weakness can be used because sound blocks of moderate to large size are demanded. Uniform texture and grain size, constant and attractive colors or color pattern, and freedom from impurities that may cause stains or deterioration usually are demanded. Hardness is a variable property. Granites and diabases are as hard as or harder than steel, while limestones and marbles may be scratched with a knife. The hardness of sandstone depends upon the degree of cohesion of the grains. Workability depends to a considerable extent on hardness, but the degree of hardness has little influence on use except where stones are subjected to abrasion as on steps or floors. "Texture" as applied to stone relates to the arrangement, uniformity, and size of the constituent grains. Stones are of many colors and thus can satisfy a variety of tastes. For monumental stone, a marked contrast between polished and tooled surfaces is preferred in order that inscriptions may be read easily. Strength requirements usually may be disregarded because any sound structural stone suitable in other respects is almost invariably many times as strong as would be required for any ordinary use. The pressure on the base course of the Washington Monument, Washington, D. C., is less than 700 psi, and highgrade granites, limestones, sandstones, and marbles will sustain a crushing load of 10,000 to 25,000 psi. A structure made of stone with a crushing strength of 15,000 psi would have to be nearly 21h miles high before crushing of the lower courses would occur. However, stone disintegrates more readily under severe

Jan 1, 1960

By C. S. Matthews, M. J. Fischer

Distortions caused by dip on five-spot sweep pattern were determined by visual experiments on a model composed of parallel plates of glass with holes drilled at the well positions. This model war designed to simulate a reservoir depleted of its primary oil and containing a gas phase. Prior to interference, it was found that the injected fluid took a nearly circular shape about the injection well for the cases studied. However, these circles moved down-dip considerably under the influence of gravity. It was concluded that pattern flooding should be practical for many dipping reservoirs. A quantitative measure is given of how much the well position should be altered to allow for dip. Experimental deternzinarions of injectivity showed this to be about the same in a dipping reservoir as in a horizontal one. INTRODUCTION This investigation was undertaken at the suggestion of the Pacific Coast area, Shell Oil Co., where a pilot water flood in a dipping reservoir was being carried out at the time this paper was in preparation. Prior to the undertaking of this flood there had been considerable speculation as to how gravity would distort a flood pattern in a dipping reservoir. The thought was expressed in some quarters that a five-spot flood would not be applicable to a dipping reservoir because the flood pattern would elongate in the direction of dip and would never form a "seal" around each five-spot. If the flood pattern elongated sufficiently, both the oil and the water might flow largely downdip rather than into the pattern producers. In view of the importance of the California water floods, it was deemed important to determine the effects of gravity on a five-spot pattern in a dipping reservoir. Previous work had also been carried out in this laboratory,1 but only for the single-fluid case. The present investigation extends these results to multifluid cases. Several sets of pictures of flood fronts are presented so that the process can be visualized. From these pictures, curves are obtained which show the correct drilling position for achieving equal times of oil-bank breakthrough. Several injectivity curves are also presented which may aid in prediction of injection rate. ASSUMPTIONS The present results were obtained with a model composed of two parallel plates of glass spaced about 1 mm apart. When the inertial forces are small, as in these experiments, the flow between the plates follows Darcy's law and is analogous to flow through porous media. In using these plates, it is not possible to scale effects of capillarity correctly as regards a transition zone between injected and displaced fluid. Calculations show, however, that effects of such capillarity should not be important in determining the gross flooding pattern in the field. In fact, in this model the capillary forces tend to circularize the pattern to a greater degree than in the field. To preserve a large ratio between the viscous forces and the circularizing capillary forces in the laboratory model, viswus glycerine was used as the flooding liquid and the rate of flooding was very high. The circularizing force is believed negligible in these experiments. In addition to the effect of the surface tension y, which tends to circularize the pattern, another capillary force must be considered. This is the adhesion tension y cos, which acts at right angles to the circularizing term y. If the plates in the model are "wetted" the same all around the periphery, then the adhesion tension,

Jan 1, 1957

By L. R. Page, J. J. Norton

EFFECTIVE methods for determining grade and reserves of pegmatites in advance of mining have been developed in recent years. When intensive work began on the economic geology of pegmatites during the early years of World War 11, it was widely believed that grade and reserves could be estimated only in a most general way. The literature indicated that not all pegmatite deposits are unpredictable, but statements emphasizing unpredictability and irregularity seem to have been more widely accepted. Many standard references reflect the prevailing opinion that minerals: are unsystematic in their occurrence in pegmatites. Pegmatites have been described as "notorious for their irregular structure," and minerals within pegmatites as "irregularly distributed." "irregularly disseminated," of "erratic occurrence," "proverbially erratic in distribution," "characterized by extreme irregularity in ... size and distribution of the essential minerals, and variety and proportion of the accessory minerals," and "spotty.'"" Over many years, however, geologic techniques have been applied with increasing success to economic analysis of pegmatites. Investigations, chiefly since 1939, have shown that mineral distribution and structure of pegmatites are largely systematic and that detailed geologic study can be used to predict the size and shape of mineral deposits in pegmatites. Because the writers are most familiar with the pegmatites of the Black Hills, S. D., examples cited are from that area." Pegmatites mined in other dis- * All examples are described more cornpletely elsewhere.: tricts are similar to those in the Black Hills," and the techniques described here have been applied by geologists and engineers working in other districts. In actual practice few pegmatite mine operators attempt to make accurate estimates of grade and reserves in advance of mining. Many deposits are too small for mining except on a very small scale; few pegmatite mines have more than ten employes. Hence there is little systematic preparation for mining, and the capital outlay may be so small that only a general knowledge of reserves is necessary. Technical personnel are rarely employed by pegmatite mine operators to make such estimates. In the future, however, as capital outlay becomes larger, estimates of grade and reserves will have to be more accurate. Geologic Aspects of Determining Grade and Reserves Estimating grade and reserves requires that the type of pegmatite, the size and shape, and the internal structure be determined by detailed geologic mapping and careful mineralogic study. The wide variations in the texture and distribution of minerals within many pegmatite deposits make a thorough geologic study of this kind necessary before it is possible to decide what sampling methods should be used to determine mineral content or grade. Types of Pegmatites: The first step in economic appraisal of a pegmatite is to determine the min-eralogical and structural type. In general, pegmatites may be classified into two groups: 1) those in which component minerals are more or less evenly distributed throughout the entire body and show relatively minor variations in texture, and 2) those in which component minerals have been segregated into units with recognizable differences in texture, mineralogy. or both. Johnston" has classified these types of pegmatites as homogeneous and heterogeneous, respectively. Cameron et al.10 have used the terms ~inzoned and zoned for similar types. The difference between the homogeneous and heterogeneous types is of great commercial importance. Homogeneous pegmatites can seldom be mined where the products are concentrated by the hand methods now commonly used, but they have been mined in a few places where a milling process has

Jan 1, 1957

By M. C. Miller, M. R. Tek, D. L. Katz

Previous studies have shown the influence of geometric variations on the drawdown and buildup behavior of a well completed in a homogeneous, porous medium containing a single-phase fluid. Other papers have shown the influence of leakage across caprocks on drawdown tests on water wells and aquifers. This paper presents two additional cases: the influence of an adjacent, expansible source of fluid, and the effect of caprock leakage on the measured in situ permeability and compressibility. Methods are developed for evaluating the influence of these two deviations from a uniform aquifer upon the in situ permeability and compre.ssibility indicated by pump tests. INTRODUCTION In relatively uniform porous media, saturated with a single-phase fluid, the effective reservoir permeability and compressibility of the water porous bed system may be obtained from drawdown and build-up data on wells, such as the initial wells drilled in aquifer storage reservoirs (Homers and Katz et al.7). In considering the drawdown and build-up behavior of wells adjacent to storage reservoirs, or of wells in an aquifer adjacent to an unknown gas field, questions arise as to the quantitative effect of the presence of compressible fluid on the measured permeability and compressibility of the formation. The solution to this problem is presented, using a constant pressure line source at some distance from two wells, one of which is pumped and the other used as the pressure observation well. The solution is presented in terms of the geometry of the wells and their relationship to the constant pressure line. It is known that caprock leakage can interfere with the determination of an aquifer in situ permeability and compressibility (Mantush4, Hantush and Jacob3 and Witherspoon and Muellerll). This paper presents an added case of the effect of leakage through a caprock of known thickness and permeability on well tests starting with a reservoir of constant pressure above the caprock and contributing to the aquifer as a result of the pump test. Again, both a pumping well and an observation well are postulated. These two cases are presented together since both a compressible fluid nearby and. caprock leakage show similar deviations from expected in situ permeability and compressibility results, and the solutions are similar in form. EFFECT OF A NEIGHBORING CONSTANT PRESSURE SOURCE ON IN SITU MEASUREMENTS Bixel, Larkin and van Poollenl presented a paper showing the influence of a discontinuity of the properties of a fluid formation system on drawdown and build-up performance. Their case is related to the present study but may be distinguished from it in that their numerical work and resulting graphs relate only to the performance of the pumping well itself. Incorrect values for in situ reservoir properties may be obtained from pump test data if the skin effect of the well and after-flow are not considered. Analysis of this problem by the authors indicated that the more reliable method of evaluating the influence of an adjacent gas field or expansible source was to use one well for pumping and another well at some distance from it for observing the aquifer pressure performance. An expansible source of hydrocarbon near a pumping well may be approximated by a line of constant pressure for a pump test. Fig. 1 illustrates a pumping well and an observation well near a line of constant pressure. Pressure behavior of an observation well during a drawdown pump test near a line of constant pressure is given by the diffusivity equation:

Jan 1, 1967

By C. A. Stout, S. W. Nicksic

The materials that stubilize emulsions of some Southern California crude oils were isolated from the produced crude. These substances were separated into acidic and nonionic fractions by ion exchange chromatography. Each fraction was further broken into groups of homogeneous molecular weight composition by gel permeation chromatography. Both ionic character and molecular weight of the individual fractions are reflected in the properties of the original crude oil emulsion. Specifically, the more acidic and the higher molecular weight fractions appear to be the most effective stabilizers. INTRODUCTION The treatment of oilfield emulsions is a continuing problem for the oil industry. In almost all cases, these are water-in-oil emulsions. Much more is known about the formation and stabilization of oil-in-water (O/W) emulsions than of the water-in-oil (W/O) type. To understand W/O emulsions, more information is needed on the materials responsible for their formation and stabilization. This is especially true in the case of oilfield emulsions where the stabilizing materials are complex mixtures of large asphaltene-like molecules. To study the chemical and physical properties of these emulsion stabilizers, it is necessary first to separate them from crude oil. This separation was achieved in the case of two Southern California crude oils. The materials that were isolated appear at first to be little different from an asphaltene mixture. However, if a mixture of distilled water and mineral oil containing about 1 percent of the natural emulsion stabilizers is passed through a colloid mill, the W/O emulsion formed may be stored in the laboratory for many months without any sign of breaking. This could not be done using undifferentiated asphaltenes from the same wells, indicating that there is a real difference between these materials and ordinary asphaltenes. The colloid mill used to generate the emulsion was required because tile natural emulsion stabilizers had very little effect on oil-water interfacial tension. The one characteristic — complexity of composition — that emulsion stabilizers share with asphaltenes makes virtually impossible the exact structure determination of the components of the mixture. For this reason, it was decided to investigate first the influence of molecular weight on the ability of these materials to stabilize emulsions. The emulsion stabilizers were first separated into acidic and neutral fractions according to whether or not the material was retained on a weakly basic ion exchange column. The extraction procedure was not designed to remove basic components from tile oils, and no attempt to isolate such a fraction was made. Following this separation, selected fractions were analyzed by gel permeation chromatography. Gel permeation separates according to molecular size, largely independently of chemical or polar characteristics. A heterogeneous mixture is separated into a number of fractions having much more homogeneous molecular weight distribution. A number average molecular weight of each fraction is therefore close to the true molecular weight of the principal component of that fraction. The fraction weights, expressed as weight percent of the sample, and the number average molecular weight of a representative selection of the fractions, will be referred to in this paper as the molecular weight profile of the original sample. DESCRIPTION OF GEL PERMEATION ANALYSIS The first reported gel permeation analyses were for separating partially hydrolyzed protein molecules in an aqueous system using expanded starch granules. Most of the theoretical work on gel permeation has been done by biochemists.1 This theoretical treatment is still incomplete, but the

Jan 1, 1969

By A. O. P. Casbarian

An analytical method is developed to determine the variation of the ultimate lateral resistance of a plate in a cohesionless soil with depth. This analysis is based on a modification of Rankine's classical earth pressure theory and the theory of plasticity as applied to soils. The ultimate resistance is defined as the product of the effective stress at the midpoint of the plate, the area of the plate and a dimensionless variable termed the ultimate resistance factor. This variable has been plotted us the depth ratio: i.e., the ratio of of the depth of embedment us the height of the plate. The resistance of a plate may then be calculated using the values af the ultimate resistance factor from the chart provided or the equation may be programmed for use in an analysis of anchor systems in cohesionless soils. It is emphasized that the analysis is semitheoretical. The theory has been compared with experimental results reported in the literature and results indicate general agreement. Actual field tests are necessary to further verify this theory. INTRODUCTION With the exploration for oil offshore in waters all over the world, it is of importance to determine the behavior of the various soils in relation to their ultimate resistance to deformation. Examples of such problems are the holding capacity of anchors and the lateral resistance of piles. Very little information is available in the published literature on the design and performance of anchors, in either cohesive or cohesionless soils. The analysis developed in this report is the first step in obtaining a solution for the determination of anchor holding capacity in a cohesionless material. DISCUSSION The theory used in the analysis is based on the ultimate strength of the soil and is the maximum resistance developed by the plate against further movement. In such a state the elastic deformations are disregarded in comparison with the plastic deformations. Hence, the plate can be considered as completely rigid. The theory of plasticity determines the three unknown stresses at any point by means of two equilibrium conditions for a small earth element in combination with the failure condition. However, the exact solutions can only be carried out in a few simple cases such as, for example, when the rupture or failure lines are straight (Rankine theory) or with spiral and straight rupture lines (Prandtl theory).l Kiitter 2 derived a single equation expressing the variation of the stress in any given rupture line. To utilize this equation, it is necessary to know the stress in the rupture line at a certain point. Unfortunately, this is difficult to obtain unless the rupture line intersects the free surface at a certain angle or when the earth is cohesion-less and unloaded. A method to overcome this is to consider only the boundary conditions at both ends of a rupture line without investigating the equilibrium of the earth above the rupture line. This assumes that the rupture lines meet the surface at statically correct angles, so that boundary stresses may be determined. As Kiitter's equation furnished a relation between these stresses, the unit earth pressure may be calculated at the point where the rupture line meets the wall. Another way in which Kotter's equation may be applied is in investigating the equilibrium of a soil mass above a rupture line. This method assumes that the failure or rupture line is known and that the boundary stresses in the rupture line at the ground surface can be determined. In this case it is possible to determine the earth pressure from the equations of equilibrium.

Jan 1, 1967

By M. C. Flemings, T. S. Piwonka

Pore formation is examined analytically in cellu-larly solidified single crystals, in cylindrical castings of pure metals and alloys, and in unidirectionally solidified castings. Effects are considered of fluid flow. dissolved gas, and surface tension. Experimental results show that flow through a partially solid "mushy" aluminum alloy obeys relations similar to those applicable for flow through other types of porous beds. Flow rate is proportional to the square of the fraction liquid (fL) for fL less than 0.3. Results indicate models chosen for mathematical description of pore formation in alloy solidification are valid. ONE of the solidification variables which is influential in determining mechanical properties of castings and of wrought material produced from cast ingots is porosity. This porosity may result from shrinkage, dissolved gases, or a combination of both, and may take the form of either macroscopic pores in localized areas of the casting or microporosity evenly distributed throughout large areas of the casting. In alloys which freeze over a range of temperatures some microporosity is generally found after solidification. There has been much discussion as to whether the micropores are caused primarily by shrinkage, by gas, or by a combination of both.'-3 There has, however, been little experimental or analytical work performed to delineate the relative contributions of shrinkage and gas in causing microporosity or to quantitatively describe the influence of processing variables on microporosity. Porosity other than microporosity (e.g., center line shrinkage) has also received only limited quantitative treatment.495 The aim of this work is to examine analytically the general problem of pore formation in solidification and to perform limited confirmatory experiments. Consideration is first given to shrinkage porosity in pure and nearly pure metals (shrinkage in cellular growth, centerline shrinkage in cylinders). Next, a discussion is given of formation of shrinkage-caused microporosity in unidirectional solidification and in "mushy" solidification. Finally, influences of dissolved gas and surface tension on microporosity are examined. Numerical results are given for aluminum and an aluminum alloy. Typical examples of microporosity are shown in Figs. 1 to 3, for 1) cellularly solidified aluminum, 2) sand-cast aluminum alloy, and 3) low alloy steel. SHRINKAGE POROSITY IN PURE AND NEARLY PURE METALS 1) Cellular Growth. In cellular freezing of an impure liquid, liquid grooves may exist over a considerable length of the growing crystal.6 The cross-sectional area of the grooves decreases with increasing distance from the cell tips; the root of the groove is blunt if the liquid at this point reaches eutectic composition. As a result of volume contraction during solidification, flow occurs down the groove, parallel to the growth direction; hence, there must be a pressure drop from the groove entrance to points within the groove. The geometry of the groove is simplified to that of a circular cylinder of radius r and length L, Fig. 4, L » r, and a simple and useful limiting case is obtained. This is that, in the circular cylinder freezing at constant velocity, the pressure at the root of the groove is lower than that pressure at radius r in grooves of other geometries where r decreases continuously to a lower limit at L. As discussed below, a pore resulting from a given pressure difference

Jan 1, 1967

By A. J. Griest, P. D. Frost, J. R. Doig

During the past 5 years, research directed toward the development of titanium alloys having improved strength-ductility relationships and heat treatability has been carried out at Battelle for the U. S. Air Force.1"3 In the course of this work, a method of heat treating ß-stabilized titanium alloys was developed which produced a wide range of useful properties.4 The heat treatment consisted of two steps: a) solution treating at temperatures in the a-ß phase region, and b) overaging at a lower temperature in the range 800°to 1100°F. Corollary to the alloy development work, research was conducted on the mechanism of the heat-treatment reaction. The investigations of Frost and co-workers on isothermal transformation in Ti-Cr5 and Ti-Mn8 alloys disclosed the existence of the transition phase, w, during the course of the decomposition of metastable ß phase. Subsequent work at Battelle7,8 'and at Case Institute by Brotzen and co-workerss further clarified the nature of the decomposition process. Beta decomposition was found to proceed by the following series of reactions: 1 2 3 4 a + Ti, My (in eutectoid systems). ßo, ßr, and ßU refer to ß phase of original, enriched, and ultimate alloy contents, respectively. Omega is a transition phase having a complex structure. 10-13 Step 4, of course, occurs only in ß-eutectoid systems. This paper presents data correlating transformation behavior with mechanical properties for the following alloys: Ti-8Mn, Ti-8Mn-2A1, Ti-4Mn-4A1, Ti-6Al-4V, and Ti-4Fe. The isothermal decomposition of ß in titanium-manganese alloys of similar composition has been investigated by Frost and coworkers8 and the effect of various annealing treatments on alloys in this system has been studied by Holden, Ogden, and Jaffee.14 The compositions Ti-8Mn-2Al, Ti-4Mn-4A1, and Ti-6A1-4V, were studied in the present work in an effort to define more clearly the effect of aluminum on the response to solution and aging treatments. Ogden, Holden, and Jaffee15 have invesitgated the effect of aluminum on the response of a similar alloy (Ti-8.8Mn-2.46A1) to annealing treatments, and Luini and Lee16 have made an exploratory investigation of the heat-treatability of the Ti-4Mn-4Al alloy. The Ti-4Fe alloy was studied as an example of a moderate1y active eutectoid system. Holden, Ogden, and Jaffee 17 have studied Ti-Fe alloys and have presented some hardness data for aging at 400°C for alloys of Ti-2.56, 5.01, and 7.35 iron after quenching from the a-ß field (750°C). EXPERIMENTAL PROCEDURES The experimental procedures generally used in the precipitation-hardening study are outlined in the following sections. Departures from these techniques are noted in the discussions of the individual alloys. Table I presents the nominal and actual compositions of the alloys studied, together with the swaging and rolling temperatures. In all cases, these temperatures were in the a-ß field and the microstructures consisted of an equiaxed a-ß mixture. Melting and Fabrication—Except for the commer-

Jan 1, 1960

By H. R. Ogden

The notch sensitivity of titanium alloys is affected by impurity content, microstructure, and heat treatment. Using notch tensile properties to evaluate notch sensitivity, three commercial titanium-base alloys were investigated over the temperature range of -320o to 390°F. The alloys studied were Ti-5Al-2.5Sn, Ti-6Al-4V, and Ti-2Fe-2Cr-2Mo. Six interstitial levels were studied for each alloy in four mi-crostmctural conditions. The ff- 0 alloys were studied in both the annealed and heat-treated condition. All tests were conducted using 1/4-in. diam round tensile samples. The notched samples had a 50 pct notch with a notch sharpness (a/r) of 53, corresponding to Kt 6.3. Notch sensitivity was increased by increased interstitial content, low temperature, and acicular-type microstructures. The heat-treated, high-interstitial content - 13 alloys were more notch sensitive than the same alloys in the annealed condition. In addition, minima in the notch tensile-temperature curves were observed at temperatures near 32°F. These minima became more pronounced with increasing interstitial content. 1 HE increaseduse of titanium alloys in high strength applications at subzero temperatures requires that a better under standing of the low-temperature behavior of the alloys be obtained. At low temperatures, metals generally exhibit increased strength with lowered ductility and tohness. Notch sensitivity and the factors which influence it become more important as the strength level is increased and the temperature is decreased. Some of the factor s which affect notch sensitivity in ti- tanium alloys are composition, interstitial content, microstructure, and heat-treatment condition. In this paper, the results of a study of these variables on the notch sensitivity of three titanium alloys at temperatures from —320o to 390o are reported. The notch geometry selected for this program was chosen to provide a severe test of notch sensitivity. The ability of the metal to flow without initiating fracture under these severe conditions is reflected in the notch-strength values. Since notch strength is, in part, determined by the constraint exerted by the combined tensile stresses, the behavior of notch specimens reflects the properties of the material under combined stresses. For example, a material with a high notch-unnotch strength ratio may be expected to withstand the biaxial stresses encountered in a pressure vessel better than a material with a low ratio of notch-unnotch strengths. This implies that maximum strength alone is not a sufficient criterion for applications of this type. It further may be concluded that the various conditions that promote poor notch behavior also will affect adversely the performance of materials under combined stresses. In the alloys studied, these included low temperatures, high interstitial levels, and hasformed microstructures. EXPERIMENTAL PROCEDURES Three alloys, Ti-5Al-2.5Sn, Ti-6Al-4V, and Ti-2Fe-2Cr-2Mo, were purchased from commercial producers as 2-in.-dam rod stock. Oxygen and nitrogen were added to these alloys by remelting to obtain a variety of interstitial contents as shown in Table I. In order to Compensate for the much more potent strengthening effect of nitrogen compared with oxygen, an oxygen equivalent content is used to describe the total oxygen plus nitrogen contents studied. It has been suggested previously1 thatnitro-gen is approximately twice as effective in strengthening as oxygen, and carbon, to the extent it is in so-

Jan 1, 1962

By W. B. Hickman, J. J. Pickell, B. F. Swanson

Many physical properties of the porous media-immiscible liquid system are dependent upon the distribution of fluids within the pores; this in turn, is primarily a function of pore structure, liquid-liquiri interfacial tcnsion and liquid-solid wetting conditions. The cnpillary pressure hysteresis process provides a means of investigating the influence of pore structure upon fluid distribution for consistent sur/acc conditions. Invcstigntiot2s indicate that residual non-wetting-phase saturations /ollozuir,g the imbibition process (i.e.,wetting phase displacing nor2-wctting phase) are dependent upon both pore structure and initial non-raetting phase saturation and suggest that residual fluid is distributed as Discontinuous ,globules, one to a few pore sizes in dimension, thrnugh the entire range 01 pore sizes originally occupied. It clppears that air-mercury capillary pressure dala adequntely rellect the distribution of fluiris in a water-oil system when strong wetting condition preliczil. An oil-air counter-current imbibition technique has also been found to provide a rapid rneans of obtaining residual-initial saturation data. In a majority of cnses, rcsidual saturations detf-rniinecl from the oil-air or air-mercury process reasonably approximate residual oil saturation following water drive of a strongly water-wet medium. INTRODUCTION A reliable estimate of recoverable reserves depends not only on the amount of original oil-in-place but also on pore geometry and distribution of fluids within the pores. A critical parameter determining the recovery from a reservoir under waterflood, for example, is the amount and distribution of residual oil within the various rock types present. The purpose of this paper is to investigate the mechanism of capillary trapping and assess its importance in laboratory measureqents of residual oil saturation. The degree of wettability of a reservoir rock is recognized as an important factor in waterflood or imbibition experiments. In this paper, however, only the water-wet case has been considered. Considerable experimental evidence1 suggests that for water-wet rocks, capillary forces predominate in tile distribution of fluids and that viscous forces in the range normallv of interest in the reservoir have a minimum influence on residual oil saturation. It follows that if the ultimate recovery is controlled by pore geometry, a unique residual non-wetting phase saturation should exist for a given set of initial conditions. Two laboratory procedures.found to be extremely useful in the study of pore structure and degree of fluid interconnection at various saturations are decribed. Although air-nercury capillary injection curves have been used2 previously to characterize the drainage case, the withdrawal or imbibition case can provide valuable supplementary data. The air-mercury process, however, has several disadvantages; it is difficult to run in a sufficiently accurate manner, mercury does not always act as a strongly non-wetting liquid and in the air-mercury process the sample is rendered unsuitable for future analyses. An alternative process is described in which air is the non-wetting phase and naptha, hentane, octane or toluene is the wetting phase. INTERFACIAL TENSION AND CAPILLARY PRESSURE Interfacial tension between immiscible fluids is due to the difference in attraction of like molecules as compared with their attraction to molecules of the neighbouring fluid. This net attraction results in a tension at the interface. To extend the interface; thus, interfacial tension s can also be thought of as free surface energy. Interfacial tension is normally expressed as dynes/cm, and interfacial energy is measured in ergs/cm2 hence, both have dimensions ml A 2 and are numerically equal.

Jan 1, 1967

By R. I. Jaffee, F. C. Holden, H. R. Ogden

Ti-Mn alloys were studied in order to determine the factors affecting the mechanical properties of &stabilized titanium alloys. The principal compositional factors have been found to be solid-solution strengthening, the martensitic transformation, and instability of the P phase. Structural factors, such as grain size and shape, were found to have more influence on ductility and toughness than on strength. THE alloys of titanium with the &stabilizing elements offer the chief hope for developing useful heat treatments. Conversely, the heat-treatment response possible with the p-stabilizing elements causes difficulties such as weld embrittlement and thermal instability during service at elevated temperature. Therefore, it is of considerable technical importance to understand the factors that govern the heat-treatment responses in these alloys, so as to be able to soften the alloys if they are embrittled by an adventitious heat treatment, to render them stable in service, or to harden them while maintaining adequate ductility and toughness. The Ti-Mn system is a good example with which to demonstrate the factors that govern strength and heat-treatment response in. a P-stabilized system. The region of the a-j3 transformation, after the work of Maykuth, Ogden, and Jaffee,' is shown in Fig. 1. The a solubilities are low. This means that, in the two-phase a-p field, partition of manganese between the two phases occurs practically only to the P phase. The solid-solution effects are therefore chiefly the result of solution in the ,8 phase. The eutectoid occurs at 20 pct Mn and 550°C, and proceeds very sluggishly. It can be ignored in heat treatments in hypo-eutectoid alloys, except for long-time storage at low temperatures below the eutectoid temperature. Even here, there is some question that diffusion proceeds far enough to involve eutectoid decomposition. Three compositional factors bear on the mechanical properties and structure of titanium a-P alloys. These are: 1—solid-solution strengthening, 2—mar-tensite transformation, and 3—P instability. Combined with the purely structural factors of grain size and shape, these govern the properties of the alloys. Perhaps the most important factor is solid-solution strengthening. The facts that manganese dissolves in a titanium to a maximum of only 0.5 pct and most of the manganese partitions to the p phase dominate the structure and properties of the a-/3 alloys. Because of the overwhelming preference of manganese for the ,3 phase, the P phase is harder and the a phase is softer. The relative amounts of both phases may be modified by heat treatment in the a-P field as application of the lever rule in the two-phase field clearly shows. A critical temperature in the Ti-Mn diagram is 800°C. This is the P transus temperature of the 6.4 pct Mn alloy, which has the lowest manganese content which will form all retained-P phase on quenching to room temperature. Any quench performed from below 800°C will produce a structure consisting of only a, a plus retained P, or retained p, for alloys of the compositions used in this work. For alloys containing less than 6.4 pct Mn, any quench from above 800°C will always result in structures

Jan 1, 1955

By John W. Cahn

Tile avevage value of the mean curvature of surfaces in a specimen can be precisely delermined by sitrlple measurements performed on random sections or on 1 vojectiotzs of these surfaces. For surjaces enclosing particles, the quanlity is sllown to be velated to the probable tlurrrhev ot particles intevcepted by a random platne and, under certain conditions, to the perimeter of their Projected image and to the increuse in surjace area when the particles grow. Many of the velalionsl~ips are valid for any shape or size of the particles. THE recent growth of the field of stereology or quantitative microscopy is largely the result of the discovery of a limited number of rigorously defined geometrical parameters that can be precisely measured on random sections or projections of a structure without assumption about particle shape.' Such parameters have been the volume fraction and surface area and line length in a unit volume. The present paper introduces the average of the mean curvature of surfaces in a volume, and shows that it can be rigorously measured by counting methods alone. AVERAGE CURVATURE ON A PLANE Consider a curve y = v (x) on the xy plane. The curvature Kp in the plane at any point is given by Kp = (dZy/dx2)/[1 + (dy/dx)2]3/2. The average curvature along the curve may be defined as Kp = (1/L) fKpdl |1] where dl = [(dx)' + {dy)2]1/2 is the length of an element of the curve and .(dl = L is the total length of the curve. The integral on the right-hand side of Eq. [l] will be called the total curvature, It is dimensionless and readily evaluated by substituting d = arctan (dy/dx) to give ah which is the change in direction of the tangents to the ends of the curve, Fig. 1. Hence, Kp = (1/L)(?h) [2] It can also be seen that Eq. [2] is applicable in the limit of sharp corners. Even though the curvature is infinite at a corner, f Kpdl remains integrable and equal to the change of angle. The signs of the quantities Kp and dl are arbitrary and, if the areas adjoining the curve are equivalent, there seems to be no compelling reason to fix the signs. For a closed curve, however, it becomes worthwhile to use the signs to distinguish among different types of areas or phases enclosed. For such a closed curve AO = t2r and As a convention, we shall take the direction of the integration along the curve in such a way that the area or phase under consideration (henceforth called a) is kept to the left side of the curve, Fig. 1. Then Kp is positive where the curve is concave and negative where the curve is convex. For a closed curve Ad - +2n if the curve encloses a, and Ad = —2n if the curve is surrounded by a. PLANAR SECTIONS OF THREE-DIMENSIONAL STRUCTURE OF ISOLATED a PARTICLES Consider next a planar section of a microstructure containing particles of a in a matrix. We place no restriction on shape of connectedness of these particles, and begin by considering the curvature of only the boundary between a particles and matrix' Clumps of contiguous a particles are then treated as a single a particle. The two-dimensional section will show in a unit area na simple closed curves enclosing a particles and nh closed curves of holes, in-

Jan 1, 1968