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By Nicholas Kowall, K. L. Clark

Maximum furnace efficiency and close control of final steel composition demand that the steel melter be able to follow closely the variations in the carbon content of the bath. For many years, the fracture test has been used by melters for estimating carbon, because it requires only a very short time to pour a sample into a chill mold, cool it in water, break it with a sledge hammer, and observe the fracture. After long experience gained from the observation of such fractures, most melters are able to estimate the carbon content of steel with amazing accuracy, particularly in the lower carbon ranges. Notwithstanding the utility of the fracture test, there has been widespread interest in other methods for rapid carbon determination to supplement it and to ensure against possible errors in human judgment. Several methods, based upon measurement of magnetic properties as functions of carbon content, have been described in the literature1-6 and have been found to give reasonably reliable results in plant practice when scrap composition is known and controlled. A difficulty encountered in the use of analyzers of the magnetic type is that alloying elements do change the relationship between carbon content and magnetic properties and it becomes necessary to establish calibration curves for all the expected combinations of alloy residuals that are not oxidized in the bath. The work reported here is of an investigation of a method that is independent of alloying elements normally present in constructional steels, being based upon the relatively well-known fact that in plain carbon and low-alloy steels martensitic hardness is a function of carbon content alone. Work oF Other Investigators In I938, Burns, Moore and Archer published & curve? that showed that the hardness of martensite is a function of carbon from 0.10 to 0.50 per cent and is independent of grain size or alloy content, at least within the rallge found in construc-tional S.A.E. compositions. Some of the deeper hardening types investigated, however, contained carbon to a maximum of only o.2o per cent. Using this principle, Kern8 developed a method of rapid carbon determination for S.A.E 43xx steels, His procedure consisted of chill-casting a test bar that was large enough to give a a that could be prepared for Brinell indentations. The test piece was quenched immediately after solidi fication was complete and hardness readings were taken, so that the carbon content could he read from an experimentally determined curve giving the relationship between as-quenched hardness and carbon. Experimental Work Although Kern's work had been done with a relatively deep-hardening steel, it

Jan 1, 1944

By K. L. Clark, Nicholas Kowall

Maximum furnace efficiency and close control of final steel composition demand that the steel melter be able to follow closely the variations in the carbon content of the bath. For many years, the fracture test has been used by melters for estimating carbon, because it requires only a very short time to pour a sample into a chill mold, cool it in water, break it with a sledge hammer, and observe the fracture. After long experience gained from the observation of such fractures, most melters are able to estimate the carbon content of steel with amazing accuracy, particularly in the lower carbon ranges. Notwithstanding the utility of the fracture test, there has been widespread interest in other methods for rapid carbon determination to supplement it and to ensure against possible errors in human judgment. Several methods, based upon measurement of magnetic properties as functions of carbon content, have been described in the literature1-6 and have been found to give reasonably reliable results in plant practice when scrap composition is known and controlled. A difficulty encountered in the use of analyzers of the magnetic type is that alloying elements do change the relationship between carbon content and magnetic properties and it becomes necessary to establish calibration curves for all the expected combinations of alloy residuals that are not oxidized in the bath. The work reported here is of an investigation of a method that is independent of alloying elements normally present in constructional steels, being based upon the relatively well-known fact that in plain carbon and low-alloy steels martensitic hardness is a function of carbon content alone. Work oF Other Investigators In I938, Burns, Moore and Archer published & curve? that showed that the hardness of martensite is a function of carbon from 0.10 to 0.50 per cent and is independent of grain size or alloy content, at least within the rallge found in construc-tional S.A.E. compositions. Some of the deeper hardening types investigated, however, contained carbon to a maximum of only o.2o per cent. Using this principle, Kern8 developed a method of rapid carbon determination for S.A.E 43xx steels, His procedure consisted of chill-casting a test bar that was large enough to give a a that could be prepared for Brinell indentations. The test piece was quenched immediately after solidi fication was complete and hardness readings were taken, so that the carbon content could he read from an experimentally determined curve giving the relationship between as-quenched hardness and carbon. Experimental Work Although Kern's work had been done with a relatively deep-hardening steel, it

Jan 1, 1944

By Richard F. Hinds, F. O. Reudelhuber

Application of the conventional depletion drive calculation methods to volatile oil reservoirs results in erroneous estimates of ultimate recovery. In view of the increasing number and importance of volatile oil reservoirs, a special technique has been developed which will result in more realistic predictions using laboratory data obtained from reservoir fluid studies of a specific type. The experimental data are designed to permit continuous material accounting and, therefrom, provide the hy-clrocarbon composition of both the flowing oil and gas phases. The resultant well-stream composition data are then used directly in surface recovery calculations utilizing equilibrium ratios. A step by step procedure, specifically designed for routine use by the practicing reservoir engineer, is presented in an appendix. An actual study performed on a deep Mid-Continent reservoir is used ay an il-lustrathe example. INTRODUCTION It has been a practice for many years to utilize the conventional ma- terial balance methods in conjunction with relative permeability concepts for the prediction of recovery from solution gas drive reservoirs.' Those who have performed such calculations recognize that compromises of several types are necessary in order to reduce the calculations to a reasonable degree of complexity. The most serious assumption involved results from the necessity of treating the produced oil and gas as separate fluids, independent of each other in their behavior. It is further assumed that the gas which is evolved in the reservoir as a result of pressure decline will not yield liquid upon the reduction of pressure and temperature resulting from production through surface equipment. Although these shortcomings have been recognized,' it has been difficult to attempt refinement of calculation procedures since the laboratory data available normally were not of the proper type or extent to permit such calculations. Three general procedures have been available for depletion drive calculations when laboratory fluid data are of the conventional type. Differential Procedure The most simple, and most widely used, method requires use of the formation volume factor and gas sol- ubility data obtained from a differential liberation performed at reservoir temperature. This procedure ignores the differences existing between the fluid behavior in the reservoir and its behavior as it is produced through surface separation equipment. The errors introduced are not serious when dealing with very low volatility fluids and this method may be utilized if the laboratory data indicate only slight differences between the differential data and the flash data obtained from separator tests. Modified Differential Procedure This method was developed when it became apparent that medium volatility fluids evidenced a wide difference between the flash and differential data. The differential data are adjusted by changing from a residual oil basis to a stock tank oil basis. All that is required is multiplication of the differential data by the ratio of residual oil to stock tank oil relative volumes existing for the original reservoir fluid at the determined saturation pressure. This procedure generally results in increased calculated ul-timate recovery; however, such results should be viewed critically. Upon examination it may become apparent that the results are influenced by errors in reservoir liquid

Jan 1, 1958

By A. E. Back, W. Wyman, K. E. Tame, S. F. Ravitz

In 1940, when it appeared that the United States soon might be cut off from foreign sources of high-grade manganese ore, the Bureau of Mines began an extensive series of investigations on the production of ferro-grade products from low-grade domestic ores by ore-dressing, pyrometal-lurgical, and hydrometallurgical methods. Among the hydrometallurgical processes for oxide ores investigated was a sulphur dioxide process in which the manganese was recovered from solution by precipitation with lime;' this process is essentially as follows: The ground ore is suspended in water and leached with SO2 gas to extract the manganese as manganese sulphate. Calcium chloride is then added to the slurry to precipitate calcium sulphate and form manganous chloride solution, and the resultant slurry is filtered to remove the calcium sulphate together with the insoluble portion of the ore. Calcium hydroxide is added to the filtrate and the mixture is agitated with air to precipitate hydrated oxides of manganese and regenerate calcium chloride. The precipitate is calcined, and the calcium chloride is recycled. To determine manganese extraction, reagent consumption, grade of product, and similar data for this process, a labora- tory investigation was started. Two minor modifications in the process were soon made: (I) the ore was suspended in calcium chloride solution instead of in water in order to extract the manganese and precipitate the calcium sulphate in one step, and (2) the agitation with air after the addition of slaked lime to the filtrate was omitted because manganese hydroxide is readily precipitated without air agitation and can be nodulized or sintered to a satisfactory product. When the process was carried through a series of cyclic tests, it was noted that the concentration of dithionate ion (which is one of the products of oxidation of SO2 by MnO2) in the cycled solution gradually increased; at the same time the chloride content of the solution gradually decreased, owing to soluble losses in the leach residue and in the precipitate. After a number of cycles, the calcium chloride became virtually completely replaced by calcium dithionate, the quantity of dithionate ion formed during the leach being more than enough to make up for the losses of dithionate in filtering. The calcium chloride process thus developed into a calcium dithionate process. Since the latter eliminated the need for make-up calcium chloride, and the dithionate solutions appeared much less corrosive than the chloride solutions, work on the calcium chloride process was dropped in favor of the calcium dithionate process. Acknowledgments The dithionate process was developed by the Bureau of Mines as part of a

Jan 1, 1949

By W. O. Philbrook, K. Natesan

A mathematical model was derived for the temperature change in a particle undergoing heterogeneous chemical reaction and heal exchange with a stream of fluid. The model has been applied specifically to the exothermic oxidation of spherical particles of zinc sulfide. Very good agreement was obtained between the theoretical prediclion and experimental observation. It was found that at no stage of the reaction was the particle subjected to a state of thermal instability. In studies of gas-solid reactions, it is generally assumed that the gaseous and the solid phases are at the same temperature throughout the reaction period. This is not strictly true since most of the reactions are either exothermic or endothermic in nature. This paper deals only with heterogeneous gas-solid reactions of noncatalytic type. In the case of exothermic reactions (e.g., roasting of sulfides), there may result an increase in temperature of the particle due to the release of the heat of reaction, and this increase in temperature may enhance the reaction rate and thus cause further release of heat. Such a "spiralling" effect may lead to a thermally unstable situation within the particle. On the other hand, in the case of endothermic reactions (e.g., calcination of limestone), there may occur a decrease in temperature of the particle as the reaction proceeds, leading to a virtual "quenching" of the reaction front. A general discussion of autothermic processes with emphasis on properties and reactor design is given by Van Heerden. 1 Levesque and cubicciotti 2 observed self heating of the sample in the oxidation of thorium. Anous et al. 3 observed self cooling of the sample in their dehydration studies on chrome alum. Cannon and Denbigh, 4 and Ong et al.5 reported self heating of the sample in their studies of the kinetics of oxidation of zinc sulfide. A typical plot of heat generation and heat loss rates with reaction temperature is shown in Fig. 1.'14 The Sigmoid curve represents the heat generation rate while the straight lines represent the heat loss rate. The main objectives of this analysis are to estimate the temperature increase of a single particle undergoing an exothermic reaction and to study the possibility of a thermally unstable situation within the particle. Also, a study of the dependence of the tempera- ture increase on different process variables has been attempted. A "she ll-by-shell" method has been proposed to analyze the problem. The shells may be made as small as necessary, and equations may be set up for heat transfer by various mechanisms. Such equations will have to be solved for each shell, with the boundary conditions for ith shell being obtained from the (i - 1)th shell, using a high speed digital computer. The oxidation of spherical particles of zinc sulfide is considered for this analysis, but the treatment is general enough to be applicable to other reactions and particle shapes. The oxidation reaction can be written as AH =« -115 kcal/mole ZnS [1] Such a reaction has been found to proceed in a topo-chemical manner; i.e., as the reaction proceeds, a progressively thicker outer shell of zinc oxide is formed, while the inner core of unreacted sulfide decreases. It has been found experimentally, both in the present work and in the previous investigations,4-6 that the particle retains its original dimensions. Therefore, at any given time, the particle may be

Jan 1, 1970

By C. S. Herzig

In the Engineering and Mining Journal of Jan. 27, 1900, there appeared an article by Fred T. Greene, describing a method of measuring stopes by the use of strings, a clinometer and a tape. In the early part of 1899 I had occasion to use a somewhat similar method, for the purpose of accurately ascertaining the volume of a very irregular drift connecting two mines. This drift was an important factor in a lawsuit for $150,000, in which it was necessary to determine accurately the volume originally occupied by the material extracted from the drift. While it is unnecessary to give all details of the controversy, some explanation of the conditions is required for a clear understanding of the following description. This drift was started by the a E." Co. from its workings, in about 7 ft. of ore, and headed toward the " G " property, the plan being to extract all the ore between foot- and hanging-walls, but to take out nothing but ore. As the " G." workings were approached; the ore-body became very irregular and much thinner. It was, however, very closely followed, and where the drift broke through into the " G." workings, the hole was only 11 inches high by 14 inches wide, or just about the size of a man-hole in a boiler.. Thus, this connection-drift tapered sharply; and the very irregular foot-wall sloped toward the " G." workings, and entered them at a place where the stope was only about 3 ft. high, and the ground had already commenced to cave. It may be added that the ore-body was a nearly flat deposit of lead carbonate in limestone, the ore and gangue being quite soft. I was called upon by the " G." people to make the survey

Jan 1, 1901

By M. S. Azun

M.S. Azun I have many objections to the content of the author's paper. Before discussing it, however, I would like to repeat the property of semivariogram function. Second order stationary properties of regionalized variables (ReV's) such as semivariogram function ?(h) are perfectly known in geostatistics. Also, the kriging equations in the language of mathematical statistics using second order stationary properties are well understood. However, the way to use the sample (estimated) semivariogram function in any one of the kriging procedures is vague. The sample semivariogram function is given as follows: [1 N-hy*(h) = 2(N h) i21 {Xi-Xi+h}Z, h=0, 1, N-1] where N is the total number of samples, Xi is the sample value at the i - th location, X i+h is the sample value at the i +h - th location, and h is the distance among the samples. An estimation variance of sample semivariogram function of first lag is smaller than that of higher order lag. The theoretical semivariogram function reaches the variance of samples asymptotically. But this is not easily observable because of the larger variation involved in the estimate of semivariogram function. In general, an estimation procedure is done for h = 0, 1, 2,…., up to the greatest integer less than N/2, even though sample semivariogram function can be computable through N-1. After estimating semivariogram function, the critical question of how to model sample semivariogram function arises. As seen in the above equation, sample semivariogram function is discrete and can be smoothed by the model being selected. Therefore, modeling of sample semivariogram function is the most important step in geostatistics. It not only smoothes a discrete function but also affects the results of the kriging procedure. When the only aim is to model the semivariogram function, which is the basic point of the author's paper, one can employ any fitting techniques, such as curve fitting, or any ar¬bitrary functions, which are called submodels in the paper. The term "arbitrary function" is used rather than "submodel" because there is no basic understanding of developing them. The author suggests that the sum of those submodels can also be used for the modeling of sample semivariogram function. The combination of any arbitrary functions brings many problems instead of giving an insight of the domain structure considered. The author used two arbitrary functions and the nugget effect in response to sample semivariogram function (Fig. 10). For the same example, he stated that the parameters involved in the mixed arbitrary function model can be accepted when the discrepancy between sample semivariogram function and the model is small visually. For verifying the fitting behavior of any selected model, one should not be contented with the visual satisfactory. Some statistical measure such as goodness of fit has to be used. The author's practice is no more than an exercise in curve fitting without any fundamental understanding or conceptualization of the underlying physical mechanism. Furthermore, the selection of any model is not an easy task if the purpose is the search for the "best" response to the observed second order properties of ReV's. I suggest that the Markovian model (Azun, 1983), on the basis of a theoretical understanding of underlying mechanism, which gives more information about the occurrence of regionalized variables, is used to respond all properties of ReV's. There are a lot of problems for modeling of onedimensional sample semivariogram function. Thus, it is not appropriate to go to higher order dimensional sample semivariogram function modeling. In the meantime, I would recommend that one can connect the values of standardized sample semivariogram function rather than simple values of semivariogram function in the two-dimensional estimation. The standardized values can be computed in dividing the semivariogram function value by the number of sample pairs involved in each lag regardless of the directions. In conclusion, geostatistics is an interdisciplinary area in mining that uses the principles of mathematical statistics. Thus, it should not violate any probabilistic and statistical rules. When Matheron was developing the theory of geostatistical study in the early years of geostatistics, many mining people had a reservation accepting the geostatistical tools. However, this does not mean that we, the geostatisticians, might try to convince those people using some "strange" tools or rules as some authors implied (Baafi and Kim, 1984). Instead, we have to develop and explain the geostatistical tools staying only in the framework of statistical concepts and properties. ? References Azun, M.S., 1983, "Stochastic Process Modeling of Spatially Distributed Geostatistical Data," Columbia University, Ph.D. Thesis. Baafi, E.Y., and Kim, Y.C., 1984, "Discussion - Comparison of Different Ore Reserve Estimation Methods Using Conditional Simulation," Mining Engineering, Vol. 36, No. 3, p. 280. Reply by J.M. Rendu The interactive method proposed by Rendu allows practitioners to develop semivariogram models that take into account not only the numerical information obtained by sampling, but also highly significant additional information that often cannot be quantified. The geology of the deposit - including hypotheses concerning its genesis, sampling methods, assaying methods, and mathematical methods used to calculate the semivariograms - all have an influence on the numerical results obtained and on how these results should be interpreted. If all the information concerning the spatial distribution of values in a mineral deposit was contained in the sample values, it could be argued that statistical techniques alone would produce optimum models. However, this is rarely, if ever, the case. Methods that allow the user to take into account his experience and his geologic understanding of the deposit should not be rejected for the sake of theoretical statistical purity. ?

Jan 1, 1986

By Arthur B. Cummins

Diatomite is a siliceous rock of sedimentary origin, which may vary in degree of consolidation, but which consists mainly of the fossilized remains of diatoms. These are microscopic algae of the order Bacillaria. Diatomite is a unique form of silica, there being nothing else found in nature or produced by the manufacturing arts, that has its characteristic physical structure. There are numerous sediments which contain some diatom residues, admixed with a substantial amount of other materials-clay, carbonates or silica. While these are classified as diatomaceous silts, shales, or mudstones, they are not properly diatomite, a designation which is restricted to material of such qualities that it is suitable for commercial uses. The terms diatomaceous earth and kieselgur are synonymous with diatomite. The expressions infusorial earth and tripolite are obsolete. Diatomaceous silica is a definition best used to distinguish the basic component of diatomite, that is, the substance of the silica shell itself and is the major constituent of beneficiated diatomite or processed diatomaceous products. Some highly indurated materials, such as cherty shale, porcelanite, and opaline cherts which have resulted from diagenetic changes cannot be considered as diatomite although they may have been derived therefrom. On the other hand, diatomaceous oozes or loose sediments consisting mainly of diatom residues with or without much organic matter are source materials in process of becoming diatomite. Composition and Properties Pure diatomite is composed of opaline or hydrous silica, with small amounts of associated inorganic components-alumina, iron, alkaline earths, alkali metals, and minor constituents, all of which may occur in solid solution or as an essential part of the opal complex. Crude diatomite on the other hand may contain variable amounts of organic matter and soluble salts, and the usual contaminants of sedimentary formations-particles of rockforming minerals, sand, clay, or carbonates. As occurring in nature, diatomite contains an unusual amount of free water, which may vary from 10 to 60 pct or more. Diatomite, in the dry deposits which are characteristic of most of the important world deposits, occurs as a lightweight, comparatively light colored, "chalklike" material. The apparent density (dry basis) in situ varies from 20 to 40 lb per cu ft. The structure may be either massive or finely stratified. The earth is highly porous, usually soft and easily friable. It is nonreactive with acids and may be tentatively identified by the above characterizations. Confirmation is by microscopic examination which readily reveals the nature of the material. In deposits which contain organic matter the appearance of the material is totally different. The color may vary from light tan or gray to brown, greenish or nearly black. There is frequently difficulty in distinguishing it in the field from peatlike materials, but the difference is readily apparent after calcination. Powdered diatomite or diatomite products have an apparent density (loose weight) of 5 to 16 lb per cu ft, wet densities of 10 to 30 lb per cu ft, specific gravities 1.9 to 2.35, index of refraction 1.42 to 1.48. Diatomite is essentially micro-amorphous, but does show some tendency toward orientation in structure after a cristobalite pattern. Amorphous silica has been considered as a random association of cristobalite crystallites, the size of which are only slightly larger than a unit cell.20 The prop-

Jan 1, 1960

By R. A. Morse, W. W. Owens, D. R. Parrish, T. M. Geffen

Laboratory studies of several factors affecting measurements of relative permeability were made using the three-section plastic-covered core technique. Results show that the core assembly, properly constructed, will perform as a single unit, and that the testing technique will, under suitable conditions of pressure gradient, gas expansion, and migration of partial water saturation, permit measurement of flow characteristics not affected by technique. Wettability equilibrium is readily established in cores exhibiting strong wetting preference to water or oil when initially saturated with water. Laboratory tests must be conducted so that saturation changes represent those that occur in the reservoir. Immediate implications of saturation history are (1:) that the possibility exists of increasing the displacement efficiency of solution gas drive reservoirs over the natural process, and (2) residual gas saturations following water flooding in gas or gas condensate reservoirs will be 15 to 50 per cent pore space rather than 1 to 11 per cent as generally believed. INTRODUCTION Solutions of petroleum reservoir problems pertaining to production performance require the use of true relative permeability characteristics. 'This relationship of fluid conductivity and saturation has been obtained by reservoir engineers in four ways, namely: 1. From past gross reservoir performance and the extrapolation of this data based on experience,1,2 2. By using published fluid flow relationships obtained in laboratory studies on general type porous materials,3, 4, 5 3. By attempting a mathematical derivation of flow behavior," using some experimentally obtained characteristics of reservoir rocks, and 4. By laboratory flow tests using representative rock samples of a reservoir. The first three methods listed above have shortcomings which make their use limited or questionable. Production characteristics of only certain processes are obtained from field data and these are not available at the beginning of a reservoir's producing life, at which time they are desirable. It is fortuitous if general fluid flow characteristics obtained experimentally have accurate application to specific field problems. Also, it is felt that at this time there is not sufficient knowledge of the flow behavior of oil, water, and gas in porous materials to enable applicable analytical description of this to be made based on other measured rock characteristics. Measurement of relative permeability in the laboratory offers the only direct method subject to adequate checking for determination of flow characteristics applicable to field problems. Primarily, this paper deals with laboratory experiments to establish the effects of several factors on the measurement of relative permeability and the practical significance of this knowledge. Laboratory flow tests are essentially model studies; the gross reservoir being represented by a small rock sample. It is necessary to simulate in experiments all the factors of importance which influence flow in the reservoir, as well a.; to eliminate effects peculiar to the model studied to assure measurement of valid flow behavior. Factors which affect the measurement and behavior of fluid flow in porous materials have been studied by other investigators.3,7,8,9,10,11 This analysis is not intended to evaluate fully all factors involved, but to establish first the validity of measurements by the technique used and then study flow behavior under various conditions. The studies reported are as follows: 1. Effects of pressure gradient, 2. Effects of gas expansion in tests conducted at near atmospheric pressure, 3. Effects of migration of a partial water saturation in oil-gas-water systems, 4. Effects If wettability characteristics of the system. and 5. Effects of the fluid saturation history. The first three are important only in laboratory measure-

Jan 1, 1951

By N. K. Chen, R. Maddin

In the extension of molybdenum single crystals at room temperature, the slip planes were found to be of the type (1101; the slip direction <111>. Theories of plasticity of body-centered cubic metals have been examined, and an explanation based upon planes of highest atomic density seems plausible to explain the plastic behavior of molybdenum single crystals. IN body-centered cubic metals, slip has been reported to occur on several planes; these are of the type {110), {112), and (123). Andrade has correlated&apos; the operative slip planes in body-centered cubic metals with the testing temperature relative to the melting point. In this correlation, if T is the absolute temperature at which slip takes place and Tm the absolute melting point, then the acting slip planes in body-centered cubic metals may be arranged as shown in Table I. However, deviations from this correlation have been reported in iron and iron-silicon alloys2 and also in molybdenum deformed at a temperature around 2400°C." In the case of iron and other body-centered cubic metals or alloys in which all three slip planes have been reported to be active at any one temperature, the crystallographic mechanism of slip is not well understood. Numerous investigators in this field have assumed that the resolved shear stress is a deciding factor. Such considerations were given by Gough in his experiments with repeated torsion of iron single crystals4 and recently by Opinsky and Smoluchowski in their study of iron-silicon alloys," and will be dealt with later in this report. A third possibility is that slip lines in body-centered cubic metals may be formed by alternate slip on nonparallel (110) planes and not by slip on any plane of higher indices. This was advanced by Elam in the case of ß brass." Since (1101 planes are planes of highest atomic density in the body-centered cubic structure, this hypothesis would be in accordance with the plastic behavior of metals in other systems, namely, face-centered cubic and hexagonal close-packed. Experimental evidence in support of this hypothesis is lacking. Nevertheless the work of Barrett, Ansel, and Meh12 has definitely demonstrated that the slip resistance on {110} planes in iron is very much smaller compared with that on (112) and (123) planes. In the present investigation, molybdenum single crystals were carefully documented as to the operative slip planes and lattice reorientations after plastic extension at room temperature. In three crystals studied, (110) planes were found to be active invariably rather than the (112) planes, which were previously reported for molybdenum at this temperature&apos; and predicted by Andrade&apos;s theory.&apos; In two other cases (112) and (123) planes seemed to operate together with (110) planes as active slip planes. However, it is believed, after careful analysis of crystallite and lattice rotations, that slip on (112) and (123) planes may be spurious. Particular reference will be made to the formation of asterism, lattice rotation, and crystallite rotation in an attempt to show that slip apparently observed on {1121} and (123) planes is actually slip on nonparallel {110} planes. Materials and Treatment Sintered molybdenum rods ? in. in diam, obtained from the Fansteel Metallurgical Co., were reported to have a purity of 99.9 pct.* One specimen, Mo-13, ¼ in. in diam, was supplied by Westinghouse Electric Corp. Single crystals were prepared, using the technique devised by Chen, Maddin, and Pond." Mo-13 was ¼ in. in diam x 7 in. long with a reduced gage section of 0.200 in. in diam x 3 in. long. The center of

Jan 1, 1952

By D. R. Parrish, T. M. Geffen, R. A. Morse, W. W. Owens

Laboratory studies of several factors affecting measurements of relative permeability were made using the three-section plastic-covered core technique. Results show that the core assembly, properly constructed, will perform as a single unit, and that the testing technique will, under suitable conditions of pressure gradient, gas expansion, and migration of partial water saturation, permit measurement of flow characteristics not affected by technique. Wettability equilibrium is readily established in cores exhibiting strong wetting preference to water or oil when initially saturated with water. Laboratory tests must be conducted so that saturation changes represent those that occur in the reservoir. Immediate implications of saturation history are (1:) that the possibility exists of increasing the displacement efficiency of solution gas drive reservoirs over the natural process, and (2) residual gas saturations following water flooding in gas or gas condensate reservoirs will be 15 to 50 per cent pore space rather than 1 to 11 per cent as generally believed. INTRODUCTION Solutions of petroleum reservoir problems pertaining to production performance require the use of true relative permeability characteristics. &apos;This relationship of fluid conductivity and saturation has been obtained by reservoir engineers in four ways, namely: 1. From past gross reservoir performance and the extrapolation of this data based on experience,1,2 2. By using published fluid flow relationships obtained in laboratory studies on general type porous materials,3, 4, 5 3. By attempting a mathematical derivation of flow behavior," using some experimentally obtained characteristics of reservoir rocks, and 4. By laboratory flow tests using representative rock samples of a reservoir. The first three methods listed above have shortcomings which make their use limited or questionable. Production characteristics of only certain processes are obtained from field data and these are not available at the beginning of a reservoir&apos;s producing life, at which time they are desirable. It is fortuitous if general fluid flow characteristics obtained experimentally have accurate application to specific field problems. Also, it is felt that at this time there is not sufficient knowledge of the flow behavior of oil, water, and gas in porous materials to enable applicable analytical description of this to be made based on other measured rock characteristics. Measurement of relative permeability in the laboratory offers the only direct method subject to adequate checking for determination of flow characteristics applicable to field problems. Primarily, this paper deals with laboratory experiments to establish the effects of several factors on the measurement of relative permeability and the practical significance of this knowledge. Laboratory flow tests are essentially model studies; the gross reservoir being represented by a small rock sample. It is necessary to simulate in experiments all the factors of importance which influence flow in the reservoir, as well a.; to eliminate effects peculiar to the model studied to assure measurement of valid flow behavior. Factors which affect the measurement and behavior of fluid flow in porous materials have been studied by other investigators.3,7,8,9,10,11 This analysis is not intended to evaluate fully all factors involved, but to establish first the validity of measurements by the technique used and then study flow behavior under various conditions. The studies reported are as follows: 1. Effects of pressure gradient, 2. Effects of gas expansion in tests conducted at near atmospheric pressure, 3. Effects of migration of a partial water saturation in oil-gas-water systems, 4. Effects If wettability characteristics of the system. and 5. Effects of the fluid saturation history. The first three are important only in laboratory measure-

Jan 1, 1951

By Thomas L. Kesler

Present Raw Materials The lithium industry has had exceptional growth since publication of the last edition of this volume, and the present scale of mining and consumption of raw materials is a great many times that of 1949. The materials of present economic importance consist of four pegmatite minerals and lithium-bearing brine. Spodumene, a lithium pyroxene, occurs in greatest abundance, and is the chief source. It has the formula LiAlSi2O6 and theoretically may contain 8.03 pct Li2O, but in the more important deposits the content is 6.5 to 7.5 pct. The hardness is 6.5, the specific gravity 3.1 to 3.2, and the color mostly pale green to white although deep green, lilac, and yellow varieties exist. The crystals are prisms with strongly developed longitudinal cleavages, and crushing characteristically produces lath-shaped particles. Giant crystals up to 47 ft long are known, but in most occurrences the predominant size range is 0.5 to 12 in. long and 0.1 to 2 in. wide. Hypogene* alteration has formed lithia-bearing sericite and coarser muscovite and rarely eucryptite, while supergene* alteration yields kaolinite and hydrous mica. Lepidolite, of second importance, is a mica of varying composition approximating K2Li3-A14Si7O21(OH,F)3. It has lamellate cleavage, book structure, and a specific gravity of 2.8 to 3. The books range in size from microscopic to a diameter of several inches. The color is mostly violet, but other colors include pink, gray, yellow, and white. Most commercial lepidolite contains 3 to 4 pct Li20 and chemically is in the higher grade range of a series of lithium micas that includes polylithionite, zinnwaldite, and protolithionite. In this series, the content of Li2O is exceptionally as high as 7 pct. Petalite and amblygonite are also of economic importance, but are used in smaller amounts. Petalite has the formula LiA1Si4O10 and is white, gray, or pink. The hardness is 6, the specific gravity 2.4, the cleavage in two planes 114° apart, and the Li2O content commonly 3 to 4.7 pct with a maximum of 4.88. Amblygonite has the formula LiA1FPO4 in which OH may substitute for F to form montebrasite. It is white and has polysynthetic twinning in two directions at 90°. Amblygonite superficially resembles potash feldspar, but has a bluish or grayish tint unlike the cream or salmon tint of the feldspar.[t] The hardness is 6 and the specific gravity 3 to 3.1, and the content of Li2O is the highest among lithium minerals that occur in significant quantity, ranging mostly from 7.5 to 9 pct with a maximum of 10.2. The brine of Searles Lake in California30 has been a commercial source of lithium since 1938. See Chap. 7, p. 108. The "lake" is a saline evaporite deposit, and the exposed part has an area of 12 sq mi. To an average depth of 71 ft, this part of the deposit consists of crystalline salts with 50 pct interstitial voids. The voids are filled with brine that contains mainly sodium and potassium compounds, but the brine also contains 0.015 pct Li2O, which is recovered as dilithium sodium phosphate containing 21 pct Li20. This deposit overlies a

Jan 1, 1960

By W. D. Robertson, A. S. Tetelman

The technique of decorating dislocations was employed to investigate deformation and fracture resulting from Precipitation of hydrogen in Fe-3 pet Si single crystals. It is shown that cracks are produced on (100) planes inside crystals, as a consequence of the precipitation of hydrogen gas, either when crystals are quenched from a hydrogen atmosphere at elevated temperatures or cathodically charged with hydrogen at room temperature. Plastic deformation in the vicinity of cracks, observed as arrays of decorated dislocations, is in conformity with the calculated stress distribution about a crack containing an internal pressure, and the observations provide information permitting a detailed analysis of the mechanics of crack growth. The fracture characteristics of crystals containing internal cracks were evaluated at 25o and -196°C and the results are related to the mechanism of hydrogen embrittlement in terms of the growth of preexisting cracks. HYDROGEN in bee iron or steel produces two characteristic changes in mechanical properties: I), a decrease in ductility (macroscopic strain at fracture) that depends on temperature and strain rate, and 2), spontaneous fracture under static load that depends on time and apparent stress. Resolution of these phenomena into the microscopic processes that combine to produce the macroscopic effects is especially difficult in the Fe-H system in which the active component cannot be directly observed and only maintained in equilibrium with great difficulty in the temperature and pressure range in which embrittlement phenomena appear. As a result of these complications, verification of the numerous hypotheses&apos;-5 that have been proposed to explain the microscopic mechanism of embrittlement depends on self-consistency with measured changes in macroscopic properties that are averaged over the volume of a specimen. It is obviously important to obtain a more direct evaluation of the microscopic processes that combine to produce embrittlement. Accordingly, the present investigation was designed to identify and observe, as directly as possible, the microscopic effects of introducting hydrogen into a bee crystal. It was concluded from a previous investigation6 of X-ray line broadening, produced by introducing hydrogen into pure iron at room temperature, that the only effect that could be associated with the introduction of hydrogen was plastic deformation; in particular, dilation of the lattice was not observed, within ± 0.01 pet, and no evidence was found that could be interpreted to support the idea7&apos;* that hydrogen occupies tetrahedral interstitial sites in the iron lattice. The absence of lattice dilation is consistent with the extremely small solubility of hydrogen in bee iron9,10 (0.015 at. pet at 900oC and 1 atm pressure), and the evidence of plastic deformation is consistent with the fact that hydrogen, introduced by cathodic charging, eliminates the carbon yield point.11-13 Following this investigation, the immediate problem was to devise a method by which plastic deformation could be observed directly. The technique employed by Hibbard and Dunn14 to observe the movement of dislocations during bending and subsequent polygonization of Fe-3 pet Si single crystals was adopted and modified for the present purpose to include the observation of dislocation arrays in the volume of the crystal, and their association with the fracture process. EXPERIMENTAL PROCEDURE Single crystals of a high purity Fe-3 pet Si alloy, containing 0.007 pet C, were grown in vacuum by

Jan 1, 1962

By J. L. Huitt, IM. L. Slusser, E. E. Glenn, M. L. Slusser

This paper is concerned with: (1) an analysis and interpretation of the filtration characteristics of drilling muds on filter paper, and (2) an interpretation of early stage "filtration" on consolidated synthetic porous media, herein referred to as the "surge loss" period. It is shown that water-loss data can be plotted so as to disclose the existence of a surge period, a non-uni-form cake thickness period, and a constant pressure filtration period. The same periods occur during exposure of consolidated porous media to muds. The data on consolidated porous media indicate that: (1) mud particles bridge pores inside porous media during the surge period, and (2) "filter cake" build-up inside porous media occurs during subsequent filtration. The data also show that the surge loss increases with sample permeability and with pressure differential. INTRODUCTION The phenomenon of mud filtrate invasion into porous sands of a drilling well has been recognized for many years.1,2,3,4 Part of API Code 29 is concerned with the filtration testing of a drilling mud to yield data on this subject. In a number of investigations "plastering properties" of muds were studied,5,6,7,8 "plastering" apparently meaning cake forming properties. In such studies the characteristics (thickness, permeability, and toughness) of the cake and the rate at which the liquid phase of the mud was separated from the solids (filtration rate through the cake, commonly referred to as water loss) were measured or at least considered. From the standpoint of its effect on well productivity, filtrate invasion into "clean" water-wet pay sands (i.e., those containing no clay minerals) may not necessarily be a serious problem. An increase in water saturation in the zone immediately around the wellbore would cause loss of oil permeability. However, in such a system, much of this water may be removed by oil production. If filtration occurs into "dirty" sands (i.e., those containing appreciable clay minerals), clay swelling or other mechanisms may cause losses in oil permeability which cannot be overcome by oil production.&apos;.&apos; The phenomenon of mud particle invasion into the pay sand of a drilling well was considered to be a possible serious factor in the early days of rotary drilling. Opinions varied as to whether drilling fluids "mudded up" and "sealed" oil sands. In 1932 Rubel,9 Gill,10 and Parsons," in separate papers, presented differences of opinion together with some laboratory and field data concerning loss of oil production caused by drilling fluid invasion into pay zones. These papers, and the discussions, furnish a large background on this subject and indicate the very clear thinking of many men at a time when petroleum production technology was in its infancy. Jones and Babson,6 and Silent,&apos; experimentally found that the depth to which mud particles invaded water-saturated sand packs was small (no greater than 1/16 in). Arn-quist12 in 1937 observed loss of water permeability due to invasion of mud particles into water-saturated, consolidated, sandstone samples. Williams and Cannon5 studied the filtra-tion properties of drilling muds and mentioned "sludge" which penetrated a short distance into the water-saturated filtering medium (sand pack). Byck5 concluded that formation permeability had no effect on the plas-

Jan 1, 1958

By F. Forscher

Pronounced porosity, decreasing with distance from the fracture surface, is found in the necked region of tensile specimens tested at room temperature or liquid nitrogen temperature. A hydrogen solution treatment followed by a quench prevents pore formation in tests at —196°C, but has little effect on tests made at room temperature. Reduction of area values at —196°C are strikingly improved by the same treatment, but show no improvement in room temperature tests. The experimental results support the hypothesis that strain-induced porosity results with hydride initially present or, in material containing less than 50 ppm H, with hydride precipitated by strain aging. ZIRCONIUM&apos;S advent as an engineering material in nuclear reactor construction has brought forth many investigations concerned with the properties of this metal and its alloys. Some attention has been given to the ductility of the metal.1, 2 Particularly, the effect of hydrogen on the impact strength was noted," indicating a pronounced dependence of ductility on the hydrogen content and its distribution in the metal. Micro graphic:&apos; and X-ray diffraction studies&apos; have shown that a precipitated hydride phase causes embrittlement in zirconium,&apos; which implies a distinctly different mechanism from that causing hydrogen embrittlement in steels."-&apos; In the latter case, it is assumed that atomic hydrogen diffuses to rifts, where it forms molecular hydrogen under such internal pressures that it causes the rifts to enlarge, leading to fracture. Thermo-dynamic studies of the Zr-H system8, 9 also indicate that the internal pressure of molecular hydrogen would be too low to cause any damage to the zirconium at room temperature, and the formation of a zirconium hydride (d phase) is favored." It is noteworthy that this phase has a face-centered-cubic structure and nearly 18 pet larger molar volume than close-packed-hexagonal a-zlrconlum&apos; Other features of the ductility of zirconium are the absence of a typical cup-cone failure upon tensile testing, a pronounced strain-induced porosity in the necked region of a tensile bar, Fig 1, and the associated spongy appearance of the fracture surface A tremendous improvement in ductility at liquid nitrogen temperature can be observed following a heat treatment that retains the commonly present quan- tities (10 to 50 ppm) of hydrogen in solution. Such tests show a typical cup-cone failure and the absence of strain-induced porosity, Fig. 2. The present paper reports results of an investigation into the causes of strain-induced porosity in zirconium. Room temperature tensile fractures of mild steel, aluminum, and titanium have also been examined for strain-induced porosity. In each case porosity could be detected, but the amount was orders of magnitude less than was found in zirconium. Of the three metals, titanium showed the strongest effect. Material, Specimens, and Preparation The greater part of this investigation was done on Westinghouse crystal bar zirconium, are-melted, forged, and hot-rolled. Chemical analyses of the hot-rolled plates are given in Table I, along with those of the Foote crystal bar zirconium used in this work. The specimens were machined from the hot-rolled plate (1550°F) of 1/2 in. thickness and subsequently heat-treated according to one of the treatments shown in Table IS. All specimens were machined round, the longitudinal axis in the rolling direction, with a gage

Jan 1, 1957

By H. C. Fiedler

A high degree of cuhe-on-edge grain orientation and good magnetic properties were obtained in Si-Fe strip processed from laboratory heats containing vanadium nitride inclusions. The higher the nitrogen content the greater was the restraint on normal grain growth and the greater was the ability to undergo secondary recrystal-lization. The degree of restraint in a heat containing magnanese sulfide inclusions was slightly greater than that in the lowest nitrogen vanadium nitride heat. The high rate of diffusion of nitrogen in the temperature range in which the texture is developed makes it necessary to retard the loss of the inclusions until the texture has been developed. MAY and Turnbulll have shown that to develop the cube-on-edge secondary recrystallization texture in Si-Fe it is necessary that inclusions, such as manganese sulfide, be present to prevent normal grain growth. They showed that the driving force for the growth of the secondary grains is inversely proportional to the diameter of the matrix grains, and that the function of the inclusions is to maintain a small matrix grain size. Fast3has developed cube-on- edge texture in Si-Fe by nitriding the hot rolled band. The silicon nitride thereby formed promotes secondary recrystallization during the anneal of the final gage strip. To obtain the best magnetic properties, the inclusions must be removed from the strip after the grain orientation has been developed. Nitride inclusions have an inherent advantage over sulfide inclusions in that the greater diffusivity of nitrogen as comared to sulfur permits the use of shorter times and or lower temperatures for the purification heat treatment. The purpose of the work to be described was to examine the usefulness of vanadium nitride inclusions in developing the cube-on-edge texture and to determine the magnetic properties of oriented strip made from heats containing these inclusions. A comparison is made with a heat having had iden-

Jan 1, 1962

By H. R. Stahi

THE ore of the Southeast Missouri lead district consists essentially of galena in dolomitic limestone. The galena usually is in a very finely disseminated condition. The experience of recent years in the concentrating plants of the St. Joseph Lead Co. has shown that dry crushing carried to a point where about 90 per cent of the ore passes a 14-mesh screen liberates the larger portion of the galena, and minimizes further necessary reduction in rod or ball mills. Concentration practice has attempted to carry size reduction to a point where economic unlocking of the galena is obtained, without causing undue sliming of the very friable galena. While 60 per cent of the tonnage of the district is treated by the flotation process, only 40 per cent of the total concentrates is produced by that means, as efforts have always been made to keep the grade and tonnage of flotation feed as low as possible. The milling practice of the district for some years has recognized the generally accepted idea of better selective grinding in rod mills as compared with ball mills, with the attendant decrease in production of fines. The function of rod and ball mills in the various concentrating plants is the grinding of table middlings and coarse tailings that carry lead values too high to be discarded. The simplified flowsheet in Fig. I illustrates the place of grinding mills in the circuit. The arrangement of classifiers, tables and mills constitutes a closed circuit within somewhat flexible limits. In 1937 experiments were conducted in replacing the ball charge in a 6 by 4-ft. ball mill with rods 2 in. in diameter and 51 in. long. This step was taken with some hesitancy, as it was easy to picture a mass of tangled and crossed rods. However, no difficulties developed, and after a short trial period, six more ball mills were converted to rod mills. These mills are of the spur gear and pinion, belt-driven type, using in most cases a 75-hp. motor and having a 9 1/2 -in. open trunnion discharge. As ball mills, they carried a charge of 16,000 to 20,000 lb. of balls, 2 in. in original size. The feed to the mills was dewatered by dewatering wheels and introduced at 70 to 75 per cent solids, with a single scoop feeder. One change in mill design was found advisable when rods were introduced. The existing end liners had an outward flare of 3 ½ in. in 12 in. These were replaced by linings having vertical interior faces, in order to prevent undue end travel of the rods. This change gave an effective working length of 5 2 ¾ in. inside the mill. No alterations were made in the shell liners, which are of the smooth type, made of manganese steel 2 in. in original thickness. The rods at present in use are 51 in. long and 1 3/4in. in diameter. The composition has been varied at times; at present they contain 0.70 per cent carbon and 0.70 per cent manganese. Some breakage and etching occurs as the rods become small, but this is considered preferable to using softer rods, which may kink and cause tangling of the charge. The mill charges are renovated occasionally, broken pieces being removed and the charge brought up

Jan 1, 1945

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

Some observations on the kinetics of the iodide process are reported. The deposition rate is geometry-sensitive in a system containing a finely divided titanium charge. Further, results indicate that the iodine diffusion rate influences the velocity of the process. The nonvolatile iodide, Til,, forms in the hot filament zone, thus removing iodine from the cycle. TITANIUM metal of 99.9 pct purity may be prepared using a refining technique originated by Van Arkel and de Boer.&apos; The purity of this metal, commonly called iodide titanium, exceeds that produced by any known process. In a recent application, the method was employed by Gonser et al.² to prepare titanium rods up to 2 to 3 cm in diam. In the Van Arkel-de Boer system, the relative influence of the fundamental mechanisms: l—production of titanium iodides, 2—gaseous countercurrent diffusion, and 3—decomposition, on the deposition rate have not been clearly established. Blocher and Campbell" have indicated that the controlling step in the process under practical conditions of operation may be the reaction rate of iodine with the crude metal. Fast&apos; reported that crude titanium metal reacted with iodine rapidly, even at room temperature, in his apparatus. Little has been reported on the effect of gaseous diffusion or decomposition on the deposition rate. It is these aspects of the process about which this investigation is centered. An attempt has been made to separate these latter effects from those due to the formation of the iodides at the crude metal surface by a division of the experimental program. Reaction of Iodine with Titanium Apparatus: In the investigation of gas-metal reactions of this type, the chemical reactivity of the halogen and halide vapors dictates the use of all-glass apparatus. In such a system standard techniques for measuring reaction rates are difficult to employ. Here, a simple apparatus was devised (Fig. 1) so that some indication of the reactivity of titanium powder with iodine vapor could be obtained. A stream of iodine gas was evolved from a bulb of controlled temperature and passed over a sample of titanium powder heated in a horizontal tube furnace. The product of the reaction, TiI4, volatilized and was condensed outside the furnace in a series of four glass bulbs, each cooled to room temperature in turn. Preliminary experiments indicated that distillation was retarded in a sealed evacuated system due to a pressure build-up in the condensing end of the apparatus. Hence, the system was pumped continuously using a mechanical pump and two oil diffusion pumps in series, through a liquid air trap. The iodine bulb was made large and a capillary restriction was inserted between the titanium bulb and the condensers so that the iodine pressure over the metal would approach the equilibrium pressure over solid iodine crystals. The effect of this restriction on the evaporation rate of TiI4, was determined separately. The iodine bulb was heated in an oil bath controlled to ±2°C. The titanium bulb temperature was automatically controlled to ±5°C. Procedure: About 200 mg of —30 mesh titanium powder, weighed to 0.1 mg, was placed in the reaction bulb after part B had been joined to part A. The powder was tapped into a long (5 cm) shallow mass along the bottom of the tube. Two chromel-alumel thermocouples were inserted into the magnesium radiator which was clamped to the reaction

Jan 1, 1953

By A. D. Marlin, A. J. Gentile, E. F. Jordan

Metallurgical changes in SAE 52100 ball-bearing components resulting from overload testing are described. Changes in microstructure, hardness, and resiclctal stresses crre discussed zuitlz re.ference to material cleanliness obtained by various steel-melting practices and are compared with work by otlzer investigators. Evidence is presented to show that the initialion and development of microstruc-tural alterations are characterized by two separate reactions: the appeavance of a "dark etchingJ&apos; constituent, and "gray lines" or a light etclzing constituent. The dependency of these tzvo reactions on material cleunliness, running tirne, and contact stresses is discussed and a failure mode related to material cleanliness and microstructural transformation is proposed. THE study of ball- and roller-bearing contact fatigue has been paced by a strong emphasis on bears ing application performance. Particular attention has been paid to conditions that effect the spalling-type failure that is characteristic of rolling contact fatigue in through-hardened components. Some of the conditions investigated are lubrication and atmosphere,1-3 material characteristics and finish,475 and speed and design fa~tors."~ A typical spalling-type failure is shown in Fig. 1. The arrow shows the motion of the ball relative to the inner-ring race surface. The leading edge of the spall is usually sharper than the trailing edge. The race surface near the trailing edge also shows small dents caused by debris from the spall. In this type of testing very little metallurgical investigation is done on failed bearings. Emphasis is placed on test conditions and statistical analyses of endurance data. More basic work has been done relating micro-structural changes to fatigue performance. Dyer" and Wood, Cousland, and sargant9 have used mostly simple materials, such as single crystals and single-phase polycrystalline specimens, under simple alternating strain to identify a systematic process of fatigue damage. drutowski" was concerned primarily with the relationship between steel structure, contact stress, and energy losses in rolling contact. dones11 and Bush, Grube, and Robinson12 utilized changes in microstructure and residual stress in overload-tested rolling contact elements as a means of investigating the fatigue process. Work is being done on an ASME-sponsored contract,13 using both simple and complex materials, but there is still a long way to go before such theories as pore and void growth in simple structures can be applied to the relatively complex bearing steel microstructure. The purpose of this paper is to report on an investigation into the effect of steel cleanliness on the structural alteration and residual stress changes found in overload-tested ball bearings. Using these results and those of previous investigators, we will propose probable failure mechanisms in both overload- and normal load-tested ball bearings.14,15 PROCEDURE Ball bearings? 3208 size, were fabricated from SAE 52100 steel obtained by five different melting practices. The melting practices, chemistry, and inclusion ratings for the five lots of steel are summarized in Tables I and 11. The nonmetallic inclusion ratings were determined by the Jernkontoret method described in ASTM E45-51 Method A. This technique consists of microscopically examining a series of polished samples taken from specified locations in the ingots, billets, or bars. Each sample is surveyed at XlOO magnification and the inclusion types and sizes are compared to standard fields. Because of the nature of these ratings all values in Table I1 are rounded to the nearest half. The elec-

Jan 1, 1965

By J. J. Becker

BEAN1 has discussed the magnetic behavior of mixtures of small ferromagnetic particles on the order of 20 to l000A in diam. As he points out, there are three size categories with characteristic properties: 1) Particles large enough to contain many ferromagnetic domains magnetize initially by the motion of domain walls. The initial susceptibility of such particles, if domain-wall motion is assumed to be perfectly easy, depends only on their shape. It is equal to the reciprocal of the demagnetizing factor (and is thus 3/4 tt for a sphere) and is independent of temperature. 2) Smaller particles find it energetically undesirable to contain domain boundaries. They are always spontaneously saturated, and reverse their magnetization only by rotation of their entire magnetic moment. As assemblage of such particles has a remanence which is a large fraction of the saturation of the assemblage; its coercive force is on the order of 2K/1,, where K indicates magnetic aniso-tropy from any source, and I, is the saturation magnetization of the substance of which the particles are made. 3) Particles which are still smaller continue to be single-domain, but the direction of their magnetization fluctuates thermally, as first pointed out by Neel.&apos; They have no remanence and no coercive force and possess the temperature-dependent magnetization curve of a paramagnetic substance with a very large moment. Bean calls this superpara-magnetism. All of these kinds of behavior are observable in alloys consisting of a precipitate of ferromagnetic phase in a nonferromagnetic matrix. Fig. 1 shows a typical aging curve for the room temperature coercive force of a sample of 98 pct Cu-2 pct Co alloy

Jan 1, 1958