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By John Norton

FOR many years the copper-bearing steels have been of considerable interest to the metallurgist because of their corrosion-resistant properties. More recently the discovery of their definite age-hardening characteristics has focused attention on them again. In a recent paper, Smith and Palmer(1)? have given an admirable description of the behavior of a considerable number of steels of this type and a study of their results suggests two questions, of a more or less fundamental sort. In the first place, it has been plainly shown that the hardening effect of added copper does not increase up to the maximum solubility of copper in iron as given by earlier investigators, but reaches its greatest value considerably below this point. This fact suggests that either the solubil-ity is not, so great as previous investigators have stated, or that the age-hardening mechanism is not the simple precipitation phenomenon that has been postulated. In the second place, the nature of the aging mechanism in this partic-ular system should be determined. Recent developments in the study of age-hardening processes have shown that the increase of hardness is often, but not always, accompanied by precipitation and the action of a particular system is not predictable on the basis of its components or type of phase diagram. It would be of considerable interest to study the aging of the iron-rich iron-copper alloys in detail. One would like to know whether the aging mechanism is different at high and low aging tempera-tures, and whether the extreme sluggishness of the system may perhaps represent some new type of aging process.

Jan 1, 1934

By E. P. Abrahamson, S. L. Lopata

A general relalionship between the amount of glide shear (due to slip) and the macroscopic shape change has been developed. Since the deformation can be large, finite strain analysis is employed. In this treatnzent, the shape change is expressed by a deforlnation gradient matrix, F - [axi/aXj/ where X and x refer lo the initial and final positions of a particle. This matrix is readily evaluated in termas of the amounl of glide shear, a , and the direction cosines of the slip-plane normal and the slip direction for a single active slip systena. In the case of deforma tion from slip on several systems, the product F(a) of the several deformation gradient matrices is first calculated. Then, by assuming that the final configuration is reached by a long series of small shears of magnitude a, occurring more or less alternately in the several slip sys- IN problems of crystal plasticity, it is often necessary to relate the amount of glide in the operating slip systems to the macroscopic strain components. This relationship is relatively simple when only small strains are considered. In this case the separate strain contributions from several slip systems are additive. Such a procedure is incorrect in the case of large plastic deformation. To the authors' knowledge, no general treatment of the latter problem has appeared in the literature. In specific instances, Mark, Polanyi, and schmid3 have derived the relationship between glide and axial elongation during tensile pulling of a single crystal when only one slip system is active. A similar relationship for duplex slip was worked out by v. Göler and Sachs.4 Taylor and Elam1 have also studied in detail problems of large plastic deformation. Due to uncertainties as to the slip systems at the time, ! terns, the final deformation gradient matrix can be obtained. Mathematically, the problem is reduced to finding the limit of F(aN as N — m while a — 0 in such a way that the Product Na = a finite conslant designatzng the accumulated amount of shear. It turns out that this limit is simply eafF1, where F, is the matrix whose elements are the coefficients of a in the F(a) twatrzx. Application is made of the present treatment to a fcc crystal of Permalloy compressed on the (110) plane and contrained to elongate in the [112] directzon. In addition, it is shown that one rnay readily obtain from the general analyszs the well-known formulas relating elongation, amount of glide shear, and amount of lattice rotation for crystals deforming by single and double slip under tension. however, they were mainly concerned with proving that slip occurs on {111}(110) systems in fcc metals. The present general treatment arose out of recent investigations of magnetic anisotropy in cold-worked Fe-Ni alloys6 as well as some related problems in strength anisotropy of single crystals.' Detailed application of the general analysis will be provided in the case of a Permalloy single crystal compressed on the (110) plane and constrained to elongate only in the [112] direction. It will be seen that, as expected, the small strain approximation leads to significant errors after moderate straining. It will also be shown that the present general treatment yields the formulas of Mark et al. and of v. Goler and Sachs in those specific cases. GENERAL CONSIDERATIONS Consider a homogeneous deformation in which a material point initially at moves to (xl,xz,x3), both positions being referred to the same set of Cartesian axes. Such a deformation can be

Jan 1, 1967

By R. A. Burton, J. T. Hansford, D. A. T. Donohue

Substantial evidence indicates that many petroleum producing horizons contain naturally occurring, ordered fracture systems and that within a particular geologic zone, vertical fractures induced in wellbores often will be directed along a particular compass direction. Both conditions will seriously alter the fluid displacement behavior within reservoirs. In this study the effect of induced fracture orientation and length on sweep efficiency is determined for a five-spot pattern. In general, it is assumed that all wells are fractured and directed along the same compass direction. Using the electrical analog to steady state, two-dimensional fluid flow in porous media, boundary conditions are obtained from which flood fronts are tracked numerically. The numerical computations require a particle tracking routine for approximating flood front histories. It is shown that recovery is sensitive to the length and orientation of fractures for the pattern studied. with the proper design of fracture-pattern systems, recovery can be enhanced considerably. INTRODUCTION Hydraulic fracturing introduced in 1949l gave the industry a rather inexpensive means of increasing the fluid injection or production capacity of wells. It has been used with particular success to increase the production rate of wells completed in tight formations, such as in western pennsylvania2 where producers have fractured in depleted or near-depleted fields and observed economic responses. Once the natural energy declines in such a reservoir where all wells have been fractured, waterflooding is generally suggested as means of further increasing recovery. Of the dual objective sought in waterflooding — high injectivity and high breakthrough sweep efficiency — the former condition can be obtained if all wells in the flood pattern are fractured; the latter condition should depend on the nature of the fracture system. Considerable theoretical work has been published on the nature of fractures induced in boreholes.3-5 Although discussion persists concerning the possibility of forming a horizontal fracture at a given point within the wellbore, it is generally conceded that only vertical fractures will develop below a given depth, i.e., where the fracturing Pressure is less than the overburden load. Given the fact that fractures will be vertical in most cases of interest, it is also important to know whether there is order to fracture orientations within a given geological region. Kehle has suggested that in tectonically relaxed areas of uncomplicated geology, the stresses are fairly uniform and all fractures in the region should be parallel.5 Dunlap arrived at a similar conclusion in a theoretical investigation of localized stress conditions surrounding the borehole.6 He concluded that most vertical fractures are propagated in a preferred azimuthal direction. Fraser and Pettitt, in extending these theoretical suggestions to a specific field case, used an impression packer to record both a vertical fracture and the orientation of this fracture in the wellbore of a well in the Howard Glasscock field, Tex.7 Use of this information enhanced the waterflood recovery of the field. Anderson and Stahl also used impression packers on three fractured wells in the Allegheny field. N. Y.. and found that the fractures were oriented more or less along the same compass direction.8 Orientation of the fractures in this manner depends on the stress condition within the formation during fracturing. Elkins and Skov have demonstrated that a natural, oriented, vertical fracture system exists within the Spraberry field? Heck suggests

Jan 1, 1969

By R. N. Thurston, E. A. Nesbitt, G. Y. Chin

A general relalionship between the amount of glide shear (due to slip) and the macroscopic shape change has been developed. Since the deformation can be large, finite strain analysis is employed. In this treatnzent, the shape change is expressed by a deformation gradient matrix, F - [axi/aXj1, where X and x refer to the initial and final positions of a particle. This matrix is readily evaluated in terms of the amounl of glide shear, a , and the direction cosines of the slip-plane normal and the slip direction for a single active slip system. In the case of deformation from slip on several systems, the product F(a) of the several deformation gradient matrices is first calculated. Then, by assuming that the final configuration is reached by a long series of small shears of magnitude a, occurring more or less alternately in the several slip sys- IN problems of crystal plasticity, it is often necessary to relate the amount of glide in the operating slip systems to the macroscopic strain components. This relationship is relatively simple when only small strains are considered. In this case the separate strain contributions from several slip systems are additive. Such a procedure is incorrect in the case of large plastic deformation. To the authors' knowledge, no general treatment of the latter problem has appeared in the literature. In specific instances, Mark, Polanyi, and schmid3 have derived the relationship between glide and axial elongation during tensile pulling of a single crystal when only one slip system is active. A similar relationship for duplex slip was worked out by v. Goler and Sachs.4 Taylor and Elam5 have also studied in detail problems of large plastic deformation. Due to uncertainties as to the slip systems at the time, terns, the final deformation gradient matrix can be obtained. Mathematically, the problem is reduced to finding the limit of F(dN as N — m while a — 0 in such a way that the Product Na = 0, a ftnite conslant designatzng the accunzulated amount of shear. It turns out that this limit is simply , where F, is the matrix whose elements are the coefficients of a in the F(a) matix. Application is made of the present treatment to a fcc crystal of Perlrzalloy compressed on the (110) plane and contrained to elongate zn the [112] directzon. In addition, it is shown that one rnay readily obtain from the general analyszs the well-known formulas relating elongation, amount of glide shear, and amount of lattice rotation for crystals deforming by single and double slip under tension. however, they were mainly concerned with proving that slip occurs on {111}(110) systems in fcc metals. The present general treatment arose out of recent investigations of magnetic anisotropy in cold-worked Fe-Ni alloys6 as well as some related problems in strength anisotropy of single crystals.' Detailed application of the general analysis will be provided in the case of a Permalloy single crystal compressed on the (110) plane and constrained to elongate only in the [112] direction. It will be seen that, as expected, the small strain approximation leads to significant errors after moderate straining. It will also be shown that the present general treatment yields the formulas of Mark et al. and of v. Goler and Sachs in those specific cases. GENERAL CONSIDERATIONS Consider a homogeneous deformation in which a material point initially at moves to both positions being referred to the same set of Cartesian axes. Such a deformation can be

Jan 1, 1967

By H. M. Davis, T. S. Jones

A methodfor accelerating the reduction of a metal oxide by carbon monoxide is to incorporate in the reduction system a nonreducible oxide which has a strong affinity for carbon dioxide and will remove it from the product gases. The effectiveness of this method was investigated by veduction experiments on specially prepared powder mixtures of SrO-ZnO ("active'.) and SrCO3-ZnO (reference). Measurements at 750o and 677°C showed that the rate of reduction of ZnO by CO was as much as an order of magnitude greater in the presence of SrO. Under the experimental conditions at least as much CO2 as generated by veduction was absorbed when SrO was present. Enlzancernent of the veduction rate by SvO resulted from modification of' gaseous djfitsion processes. THE specific question posed in this investigation was whether the reduction reaction CO + ZnO - Zn(g) + COa [1] could be accelerated by incorporating strontium oxide into the oxide charge undergoing reduction. Provided the strontium oxide was active enough, it could remove carbon dioxide from the product gases of ( 11 and form strontium carbonate, thus modifying Reaction [ 1] to CO + ZnO + SrO = Zn(g) + SrCO3 [ 2] This study of the comparative rates of Reactions [ I] and [2] can be considered as a particular case of a general scheme for increasing the rates of reduction of metal oxides by carbon monoxide. The limits of applicability of this scheme are indicated in the simple thermodynamic analysis presented in the appendix. This analysis primarily dictated the choice of the system, CO-ZnO-SrO, employed in this investigation. In addition, it was thought that a study of this scheme by use of the CO-ZnO-SrO reaction system would be of special interest in view of indications in the literature1-3 that the gaseous reduction of zinc oxide is prone to rate control by diffusion in the gas phase. The distinction should be pointed out between this and other efforts to increase the rates of reduction reactions through the use of addition agents. Additions of a wide range of chemicals have been tried with de- grees of apparent success varying from slightly negative to highly positive. The reasons for making additions have included the use of salts to produce effects akin to catalysis,4, 5 the alteration of the microstruc-tural details of the reduction process (including solid-state diffusion),6-8 and the conversion of an en-dothermic reaction into one that is exothermic or autogenous.9-12 The means used to attempt alteration of the enthalpy change has commonly been to incorporate lime into the charge, so that heat is generated by reaction with either of the reaction products, carbon dioxide or water. The use of lime in this way makes endeavors such as that of Edstrom and Wiberg similar to the present one. Furthermore, the basic principle behind the present work has previously been set forth.13 However, a detailed investigation of the type of reaction described in this work does not appear to have been conducted. EXPERIMENTAL PROCEDURE From both conceptual and physical standpoints, Reaction [2] is to be considered as the sum of two reactions:

Jan 1, 1968

By D. T. Peterson, F. A. Schmidt, J. D. Verhoeven

The velocity of mig-ration of these solutes in thorium metal due to a high amperage dc current was measured at several temperatures. All three solutes migrated in the same direction as the electron flow. Diffusion coefficients were combined with the migration velocities to predict the steady-state concentration profile. Electrotransport was shown to be an effective method of removing carbon, oxygen, and nitrogen from thorium and resistance ratios several times larger than for crystal bar thorium were achieved. However, the maxirnum attained purification was well below the predicted values, apparently due to some form of contamination. THE migration of solutes in metals when a high current density dc current is passed has been known for many years. This phenomenon has been the subject of a number of reviews published in recent years.l~* Many of the earlier investigators of electromigration of interstitial solutes interpreted the direction and velocity of migration on the basis of a charge on the solute particle. This interpretation is unclear because, in a given experiment, one cannot separate the contributions to the force moving the solute which arise from the charge on the solute in an electric field gradient and the momentum transfer from the scattering of the electrons or holes. There have been only a few quantitative measurements of interstitial migration velocities and some of these have been characterized by poor accuracy or by errors in the analysis of the experiment. The electrotransport mobilities of carbon, nitrogen, and oxygen in thorium were determined by observing the rate of movement of a discontinuity in the concentration profile. This method was used by Carlson el a~.~ to determine the mobilities of interstitial solutes in yttrium and its advantages are discussed in that paper. The specimen is essentially a pair of semi-infinite, bar-type diffusion couples. The electro-transport velocity was measured by observing the displacement of the mean concentration point in a measured length of time. The diffusion coefficients were calculated by the Grube method from the concentration profile. The transport mobilities and diffusion coefficients can be used to predict the concentration profile in an electrotransport experiment of a given time, current density, and specimen length. At long times a steady state will be reached such that the natural logarithm of the concentration of each solute varies linearly along the bar with a slope which is equal to the velocity of the migrating solute divided by its diffusion coefficient. The estimation of the purification potential of electrotransport is discussed by ~erhoeven.' A comparison of the concentration profile and the purification which should be expected from known solute velocities and diffusion coefficients with that which is obtained in an experiment can be very useful in indicating whether the maximum possible purification has been achieved. EXPERIMENTAL METHOD The apparatus used in this study consisted of a sample chamber which was equipped with two electrodes, a sight glass, and a flange for mounting to a high-vacuum system capable of obtaining pressure of 2 x lo-? Torr. The chamber was made of stainless steel and was 4 in. in diam and 6 in. long. The seal between the electrodes and the chamber was made with "0" rings and compression bushings. The thorium specimens were threaded and screwed into tantalum "U"-shaped adapters attached to the ends of the electrodes. This arrangement is shown in Fig. 1

Jan 1, 1967

By F. W. Luersson

High carbon, low phosphorus steel can now be made from pig iron containing 0.7 pct P or more, in a commercial sized open hearth furnace. No external heat is required for refining, and steel produced is identical with basic open hearth steel. THE classical Thomas process, which requires liquid pig iron containing over 11/2 pct P, yields a product relatively high in phosphorzs and nitrogen. Unless large quantities of recarburizers are added to the refined steel, the product is low in carbon content. Thus, the Thomas process is not well suited to American raw materials, and its product is often not acceptable according to the standards set by American industry. The shortcomings of the Thomas process have long been recognized; with the advent of low cost oxygen, studies were initiated to develop pneumatic processes which would conceivably overcome the inherent objections to Thomas steelmaking. Several such modified basic pneumatic processes have been tested experimentally in commercial trials during the past decade. Probably the most widely publicized of these developments has been the oxygen converter process as practiced in Austrial,2 and in Canada.8 n this process, oxygen is substituted for air and introduced above the liquid bath in order to increase the heat available to the metallurgical system. This avoids the need for high phosphorus raw materials and gives a product low in nitrogen. In this process, the phosphorus content in the final product depends, to a considerable extent, on the total amount of that element in the burden. The rotary furnace4 which is now in commercial operation at Domnarvet Steelworks, Sweden, is producing low phosphorus steel from iron containing 1.8 to 2 pct P. One or more early slags are removed and by this means high carbon steels of open hearth quality can be produced. At this stage of development there is some question as to the applicability of the rotary process to large heats. Another development has been the use of oxygen in combination with either steam6 or carbon dioxide yn the basic bessemer, thus avoiding the introduction of nitrogen gas into the refining system and giving a product relatively low in nitrogen content. A double slag process has been used in Europe7 in conjunction with a regular Thomas converter, by means of which it is possible to obtain a phosphorus content in the product approaching that obtained in basic open hearth steels. The Turbo-Hearth process:' which uses the side blowing principle so as to produce low nitrogen steel from normal American pig irons, has been developed experimentally in this country. A process fitted to U. S. raw materials All of the preceding processes, with the exception of the rotary furnace, suffer from the common shortcoming that they cannot be adapted to the production of high-carbon, low-phosphorus steels unless large proportions of recarburizers are added. In 1947, a program was initiated by the Inland Steel Company1' to study an oxygen steelmaking process specifically designed to utilize the full range of phosphorus analyses encountered in American pig irons and to give finai products with phosphorus and nitrogen contents comparable to steel produced by the basic open hearth process. Some of the objectives of the proposed process are: 1) the process should be able to accommodate molten pig iron conta;rl;rrg up to 1 pct P., 2) sne process should be subject to close control of carbon analysis, 3) the process should be capable of producing high carbon

Jan 1, 1958

By S. J. Rothman, J. J. Hines, D. Rokop, R. Bastar

Self-diffusion has been measured along each principal axis of mosaic-structured and relatively perfect a uvaniuln single crystals. The anisotropy reported before,' D[loo] = D[001] » D[010 , has been confirmed. and is shown to represent volume diffusion. Diffusion along the dislocations in the imperfect crystals increases the measured value of D significantly without changingr either the shapes of the penetvation plots or the anisotropy. SINCE a uranium is orthorhombic, the diffusion coefficients along the principal crystallographic axes need not be equal. A previous measurement of self-diffusion in three mosaic-structured a uranium single crystals1 showed that Dil00| =D[001 >>D[010 This result was deduced from penetration plots similar to those in Fig. 1. That is, the plots for diffusion along [loo] and [001] were the straight lines expected from the solution of the diffusion equation for the boundary and initial conditions of the experiment, while the plot for diffusion along [010] was curved so that the part near X = 0 had a much steeper slope than the straight lines did. The observed anisotropy could have been due either to volume diffusion or to diffusion along the very large number of dislocations in such crystals, according to the model proposed by aart.' The authors of Ref. 1 argued that the latter possibility was unlikely, but did not exclude it. To settle the question, a simultaneous measurement of self-diffusion in mosaic-structured and mosaic-free crystals was carried out. This paper reports the results, as well as a measurement of the temperature dependence of self-diffusion in a uranium. EXPERIMENTAL The single crystals of a uranium used in this experiment are listed in Table I, together with other experimental details. '(Mosaic structured" here means crystals grown by solid-state phase change.3 The Laue spots from such crystals spread over about 6 deg of arc, which indicates that the density of dislocations is very large. "Perfect" crystals are ones grown by Fisher's grain-coarsening tehnique; the Laue spots from these are quite sharp,4 which shows that the dislocation density in these crystals is much lower. All of the crystals were made from high-purity uranium; a typical analysis is given in Ref. 1. The actual diffusion directions were within a few degrees of the nominal. The thin layer-sectioning method was used. The experimental techniques were similar to those described in Ref. 1, except the sectioning. Crystals Za, 2b, 2c, 4a, 4b, and 4c were sectioned on a lathe. Crystals 3a, 3b, and 3c were sectioned by grinding on glass plates, with 1 p diamond powder in butyl alcohol as the abrasive. The use of glass plates eliminated the crowning noted in Ref. 1, and the use of butyl alcohol as a lubricant simplified the chemical processing of the sections. Material from the sides of these three crystals was removed by spark machining before sectioning. The sectioning of crystals 4a and 4c was botched. A small cylinder of metal was extruded from the center of crystal 4a while turning off material from the side of the sample. Crystal 4c was misaligned by 2.1 x 10"3 cm because the dial gage jammed during the alignment. Notwithstanding these errors, useful data were still obtained from these crystals. The points

Jan 1, 1967

By Arthur Taggart

Recent jig practice has shown such marked departures from the pronouncements of the textbooks, particularly as to particle size recovered and size range of feed, as to make it desirable to reexamine the mechanism of jig action. This paper presents the results of such a study. The general conclusions of the Paper are: I. A jig bed is a bi-functioned as well as bi-parted body. The upper layer comprises a plastic stream moving slowly in a substantially horizontal direction from feed lip to tail board. It serves to rough out tailing and light middling and to pick up heavy middling and lift it out 01 the jig box. The lower layer acts as the ultimate separating means by absorbing concentrate and rejecting heavy middling. 2. The separating function of the lower layer is performed in three definitely diflerent ways, depending upon the relative sizes of the grains presented to it and those composing it. Experimental The experimental work consisted of close and long-continued visual observations of operating beds in a plunger jig, eccentric driven, and in determinations of the settling rates of various metal spheres through a quartz bed under various conditions of operation. Falling velocities were measured by an ingenious method devised by A. 6. Dorenfeld, a student in the Mining Department at Colum- bia. Spheres of different metallic alloys, 3/8-in. diameter, were cast with a short piece of fine copper wire frozen in to Serve for suspension-A short piece of black cotton thread was looped to the top of the wire to serve as an indicator. The set-up for a test is shown in Fig. I. The thread should be boiled, if necessary, to make it freely water absorbent. The piece of clean plate glass D is supported rigidly at the proper height in a vertical position. The white scale E is similarly supported behind the glass. At the beginning of a test, D is filmed with water by holding it (best with clean rubber finger cots) under running tap water. It is then clamped in approximate position and C, already wet, is laid across it and drawn straight and vertical with the upper end at or near the top of D, and the ball A slightly above the top of the expanded bed. The water film holds the string to the glass. For a test the string is released, its upper end position noted just after the top of the ball becomes submerged, when the corresponding time is read, and thereafter simultaneous readings of position and time are taken as desired. Results of the visual studies of the bed are given at the pertinent places in the following discussion. Results of the settling tests are summarized in Figs- 2 and 3. Definitions The name bed as used herein refers to the entire mixture of solids and water filling the jig box. A layer is a stratum of a bed composed of particles of substantially the same specific gravities. A granular product is long-range when it approximates a crushed or ground product limited as to upper size only; a short-rafzge product is one closely sized. A bed is loaded when operating with continuous feed and discharge of products; it is unloaded when pulsating norma11y but neither being fed nor

Jan 1, 1943

By Arthur Taggart

Recent jig practice has shown such marked departures from the pronouncements of the textbooks, particularly as to particle size recovered and size range of feed, as to make it desirable to reexamine the mechanism of jig action. This paper presents the results of such a study. The general conclusions of the Paper are: I. A jig bed is a bi-functioned as well as bi-parted body. The upper layer comprises a plastic stream moving slowly in a substantially horizontal direction from feed lip to tail board. It serves to rough out tailing and light middling and to pick up heavy middling and lift it out 01 the jig box. The lower layer acts as the ultimate separating means by absorbing concentrate and rejecting heavy middling. 2. The separating function of the lower layer is performed in three definitely diflerent ways, depending upon the relative sizes of the grains presented to it and those composing it. Experimental The experimental work consisted of close and long-continued visual observations of operating beds in a plunger jig, eccentric driven, and in determinations of the settling rates of various metal spheres through a quartz bed under various conditions of operation. Falling velocities were measured by an ingenious method devised by A. 6. Dorenfeld, a student in the Mining Department at Colum- bia. Spheres of different metallic alloys, 3/8-in. diameter, were cast with a short piece of fine copper wire frozen in to Serve for suspension-A short piece of black cotton thread was looped to the top of the wire to serve as an indicator. The set-up for a test is shown in Fig. I. The thread should be boiled, if necessary, to make it freely water absorbent. The piece of clean plate glass D is supported rigidly at the proper height in a vertical position. The white scale E is similarly supported behind the glass. At the beginning of a test, D is filmed with water by holding it (best with clean rubber finger cots) under running tap water. It is then clamped in approximate position and C, already wet, is laid across it and drawn straight and vertical with the upper end at or near the top of D, and the ball A slightly above the top of the expanded bed. The water film holds the string to the glass. For a test the string is released, its upper end position noted just after the top of the ball becomes submerged, when the corresponding time is read, and thereafter simultaneous readings of position and time are taken as desired. Results of the visual studies of the bed are given at the pertinent places in the following discussion. Results of the settling tests are summarized in Figs- 2 and 3. Definitions The name bed as used herein refers to the entire mixture of solids and water filling the jig box. A layer is a stratum of a bed composed of particles of substantially the same specific gravities. A granular product is long-range when it approximates a crushed or ground product limited as to upper size only; a short-rafzge product is one closely sized. A bed is loaded when operating with continuous feed and discharge of products; it is unloaded when pulsating norma11y but neither being fed nor

Jan 1, 1943

By P. Dayal, L. S. Darken

THE migration of carbon in austenite under the influence of an electric current has been observed qualitatively several times.14 Lebedev and Guterman5 recently have reported quantitative measurements; their method consisted of welding a low-carbon to a high-carbon wire, passing current, and later estimating the carbon distribution metal-lographically. We believe the method reported in this paper is superior in principle since electrolytic migration and ordinary diffusion are not necessarily coupled as in the weld method; also for the first time the extent of migration is determined by combustion analysis for carbon. A uniform tubular specimen (S.A.E. 1045 or 1095) was mounted as illustrated in the figures. the whole assembly being in an atmosphere of purified nitrogen. Direct current (129 to 226 amp at 0.65 to 1.0 v) served as source both of heat and of potential gradient for carbon migration. The duration of experiment was 7.5 to 12 hr, during which time the temperature was controlled (±10°C) manually. The experimental conditions are indicated in the first five columns of table I. With this experimental arrangement, the temperature initially has a maximum value at the central plane. Also, in this vicinity (by virtue of the symmetry), the carbon entering any volume element is equal in quantity to that leaving; the loss or accumulation of carbon occurs near the electrodes since the carbon moves uniformly near the center and is "frozen" at the cold ends. Hence, providing the time of experiment is not sufficiently long to seriously influence the conditions at the central plane, carbon crosses this plane only under the influence of the electrical potential gradient and not under the influence of temperature or concentration gradient. The amount of carbon which has crossed this plane was determined by combustion analysis of the two halves of the specimen. The results of these analyses are shown in the sixth and seventh columns of table I. It will be noted that substantial amounts of carbon migrated from the anode portion to the cathode portion (except at 920°C, which temperature was too low to exhibit the effect in the allotted time). In spite of precau-tions taken, considerable decarburization occurred as may be seen by comparing cols. 8 and 5. In three cases (indicated by asterisks in table I) the specimen was ground on one side, polished, and examined metallographically before analysis. One specimen was normalized and re-examined. Micrographs of selected areas in specimens 4 and 6 are shown in figs. 1 and 2, respectively. Evidence of carbon migration from the anode toward the cathode is quite apparent. Fig. 2 shows abundant graphite as well as cementite in a region near the cathode. The temperature of this zone is estimated at about 800°C. In fig. 1, particularly in the micrograph on the extreme right (the right side of which is of unaltered carbon content), there is evidence of slight depletion of carbon in the immediate vicinity of the cathode as contrasted to the general increase in carbon of the cathode half of the specimen. Although this may be attributed in part to decarbur-ization, it is believed that it is occasioned also by thermal diffusion—migration (of carbon) from a cool to a hot zone4—a phenomenon superimposed upon the electrical migration. Evidence of carbon migration was visible particu-larly during the course of the high-temperature,

Jan 1, 1951

By C. R. Criss, R. J. McCormick

ThiS paper .summarizes the development and perform. ance of the Coldwater Oil field, Isabella County, Mich. Production is obtained at a depth of 3750 ft from a dolomite reservoir, which is probably both Rogers City and Dundee. There appears to be no persistent barrier to vertical fluid movement between the Rogers City and Dundee, and both formations are believed to have a common original oil-water contact. No we1ls are open to production at the level of the Dundee. The discovery of the field in 1944 was followed by the drilling of 81 producing wells and nine dry holes. By the end of 1952, the field had produced 12,763,000 bbl of oil, at which time 69 active wells were producing 3600 B/D oil and 21,000 B/D water. The reservoir has an effective natural water drive, and bottom-hole pressure has declined 75 psi from an original pressure of 1453 psi. Oil is undersaturated at reservoir conditions with a solution GOR of 512 cu ft/bbl and a saturation pressure of 1190 psi. INTRODUCTION Although the Coldwater Field is now in its ninth year of production, it ranks seventh in cumulative recovery, and second in current daily oil production in the State. Following complete development of the field in 1946, it has consistently contributed approximately 11 per cent of Michigan's daily production. Coldwater appears to have a greater pay thickness than most fields producing from the Rogers City forma- tion in the west central part of the Michigan basin. Except as influenced by the extent of closure and the thickness of the oil column, reservoir performance is believed to be representative of Rogers City fields in this part of the basin. For this reason, it is felt that the following presentation of factual data for the field will be of general interest. HISTORY AND DEVELOPMENT Discovery of the Coldwater field during Aug., 1944, followed favorable subsurface geological correlations and core tests drilled to a shallow stratigraphic marker horizon. The field is located in the west central part of the Michigan Basin in Coldwater Township (T16N-R6W), Isabella County. It is 60 miles west-northwest of Bay City, and near the geographic center of the southern peninsula of Michigan. The discovery well flowed 200 bbl of oil the first 24 hours from the Rogers City dolomite at a depth of approximately 3750 ft. Field production is principally from the Rogers City with a minor amount assumed to come from the underlying Dundee dolomite, although none of the wells are open to production at the level of the Dundee. Both the Rogers City and Dundee formations belong to the Devonian system (See Geologic Column-Fig. I.) In addition to Rogers City-Dundee oil production, sweet gas is produced from the Michigan Stray sand of the Mississippian system at a depth of 1400 ft. The gas reservoir has approximately the same areal extent as the underlying oil reservoir. Although gas production is an important feature of the Coldwater field, this report is concerned only with the oil reservoir. The productive area is approximately 3200 acres. The pool is developed on a 40 acre spacing pattern with wells drilled in the center of the north half of 40 acre tracts, except for a few off-pattern wells drilled along

Jan 1, 1955

By H. K. Najarian

This paper describes recent development work on the Wheaton-Najarian Vacuum Condenser for Zinc at Josephtown Zinc Smelter, wherein, to dissipate the heat of condensation, the "airlift" action of gases bubbling through the molten zinc in the condenser is utilized to circulate the zinc through an outside "cooling well" and cooling it continuously. AN earlier paper1 gave an account of initial development of the Wheaton-Najarian Vacuum Zinc Condenser at the Josephtown Zinc Smelter of the author's company. This paper is a progress report of further development work over the years directed toward improving the efficiency and increasing the capacity of the condenser. In this type of zinc condenser, zinc vapor with accompanying noncondensable gases from electro-thermic zinc smelting furnaces is passed upwardly through a mass of molten zinc confined in a refractory-lined U-tube. The zinc vapor condenses in the molten zinc and the noncondensable gases are drawn out of the condenser by suction applied over the surface of the molten zinc. The heat of condensation of zinc, amounting roughly to 1000 Btu per lb of zinc condensed, is absorbed by the molten zinc and, in turn, is dissipated continuously to keep the temperature of molten zinc in a range to permit effective condensation. At the time of publication of our first paper, we had at Josephtown Smelter five units of 69-in.-bore metal furnaces and one larger metal furnace having 96-in. bore. Each 69-in. metal furnace had a condenser with 22-ft overall length. The 96-in.-bore furnace had a condenser with overall length of 31 ft. Condensers were of circular cross section, with corrugated steel outer shell and carborundum lining. Diameter of these condensers was 32 in. inside the refractory lining. Molten metal in the con- denser was kept cool by spraying cold water on the outside of the condenser shell. Under good operating conditions, 22-ft condensers produced some 12 tons of metal per day; and the 31-ft condenser, about 22 tons. When the furnaces produced zinc vapor at higher rates, invariably the condenser temperature would rise to levels where excessive blue powder would form and accumulation of accretions in the condenser would be accelerated. We found that, with the system of cooling in use, we had to provide heat-exchange surface of some 150 sq ft to condense 1000 lb of metal per hr with reasonable efficiency. The wall of the condensers was made up of 5/8-in.-thick corrugated-steel shell having next to it several layers of mica and inner refractory lining of special carborundum shapes to fit the corrugation in the steel shell, and having a minimum thickness of about 2 in. Relatively low rate of heat transfer through the thick condenser wall and slow internal circulation of the molten zinc limited the rate of heat exchange between hot metal within the condenser and the cold water flowing over the outer steel shell. The thickness of the condenser wall was about minimum that we considered suitable for continuous operation. As we learned to operate the electrothermic furnaces with higher power input, producing zinc vapor at higher rates, it became apparent that we needed condensers having larger heat-exchange surfaces. Our 96-in.-bore furnace had 6 single-phase power circuits with transformers rated at 500 kva each and normally good for power input of 3000 kw.

Jan 1, 1959

By N. K. Chen, C. H. Mathewson

Single crystals of high purity aluminum of various orientations were carefully documented after plastic extension. Special attention was given to the formation of slip lines, deformation bands, and asterism. An explanation for the geometry and mechanism of formation of deformation bands is considered. WHILE the general process of plastic extension of face-centered cubic metals is well understood,' the accompanying structural changes due to slip and rotation are far more complex than ordinarily assumed. In the case of stretched single crystals of aluminum, the complicated behavior is especially marked by the formation of deformation bands, as first indicated by Collins and Mathewson." Such bands were believed by them and also by others,".'7 who have discussed banded structure in general, to represent one of the important modes of lattice reorientation and to be intimately connected with the recrystallization process. Yet, despite their fundamental importance to the understanding of the mechanism df both plastic deformation and recrystallization, practically no study of the crystallographic features of these bands in their relationship to the conventional slip process has been attempted. This paper describes part of an extensive investigation on the structural behavior during plastic deformation of aluminum single crystals and is especially concerned with the characteristics of deformation bands. The investigation of the subsequent re-crystallization of deformed aluminum single crystals will be discussed in a later publication. Experimental Procedure Single crystal specimens of 99.996+ pct pure aluminum, Yz in. in diam and 5 to 6 in. in length were made both by the Bridgman method5 nd by a modified temperature gradient method.'* Crystals were selected in which the lineage deviation did not exceed 2"; i.e., as determined from the back-reflection Laue X-ray photograms. These crystals were radiographed to insure that no internal porosity was present. The orientations showed good coverage of the whole area of the Taylor and Elam triangle.' Orientations of the crystals were obtained by the back-reflection Laue technique described by Greninger." Crystals so selected were tapered very carefully in a lathe to obtain a linear decrease in diameter from 0.500 to 0.350 in. along a gage length of 3 in. This is considered desirable because it permits a strain gradient to be introduced in a single specimen at one initial orientation. The advantages of tapered crystals for studying the development of slip lines and recrystallized grains have been pointed out by previous investigators." The cold-worked layer resulting from the machining operation was removed by alternate etching in aqua regia and careful polishing with 2/0 emery paper until undistorted Laue back-reflection spots were obtained. A homogenization treatment at 600 °C for 24 hr was then introduced to insure the removal of residual stress. Two of the crystals so prepared were also checked by use of a glancing angle technique. Using a copper target, at 30 kv and 10 microamperes, a monochromatic beam was positioned at right angles to the axis of the crystal about which it rotated. The time of exposure was 24 hr. From these X-ray photograms, it was concluded that the present method of preparation of single crystals is satisfactory. Following this procedure, the crystals were elec-trolytically polished in a 2:l solution of methyl alcohol and concentrated nitric acid. Intermittent

Jan 1, 1952

By Harvey T. Kennedy, Charles R. Olson

In many investigations of the performance of petroleum reservoirs the assumption is made that the liquid, if below its bubble-point pressure, is at all times in equilibrium with gas. On the other hand, observations by numerous investigators have indicated that gas-liquid systems including hydrocarbon systems, may exhibit supersaturation to the extent of many hundred psi in the laboratory. Up to the present, there has been no reliable data on which ti judge the actual extent of supersaturation under conditions approaching those existing in petroleum reservoirs. The work reported here deals with observations and measurements on mixtures of methane and kerosene in the presence of silica and calcite crystals. Bubbles were observed to form on crystal-hydrocarbon surfaces in preference to the glass-hydrocarbon interface or to the body of the liquid. Statistically, it was found that the number of bubbles formed per second per square centimeter of crystal surface was a function of the supersaturation only. and the function was evaluated graphically. Supersaturations were observed up to 770 psi, under which condition bubbles formed quickly and with considerable violence. With decreasing degrees of supersaturation, the frequency of bubble formation became less, until at 30 psi supersaturation and lower, no bubbles were observed to form, even though the observation at 30 psi was continued for 138 hours. It was found that silica and calcite crystals had identical effects, within experimental error, in accelerating the formation of bubbles, and that small amounts of water and crude oil had no effect on the results. It is shown that the maximum supersaturation that can exist in a reservoir may be calculated from the data presented and from the area of the rock surface. It is also shown that the number of bubbles formed in the reservoir, in order of magni- tude, may be calculated for any rate of pressure decline imposed on the reservoir by production. The bearing of the number and distribution of bubbles on reservoir performance is discussed. INTRODUCTION A liquid system is supersaturated with gas when the amount of gas dissolved exceeds that corresponding to equilibrium at the existing pressure and temperature. The degree of super-saturation may be conveniently expressed as the difference between the bubble-point of the mixture and the prevailing pressure. Thus, if a mixture having a bubble-point of 1,000 psi at a given temperature exists in single liquid phase at 700 psi at the same temperature. it is supersaturated to the extent of 300 psi. There are many examples of high supersaturations, mostly in aqueous solutions, reported in the literature. Thus, Kenrick, Wismer and Wyatt1 showed that water may be saturated with oxygen, nitrogen or carbon dioxide at 100 atmospheres, and the pressure reduced to one atmosphere without producing bubbles immediately. When liquids are in a state of tension, they may be considered as supersaturated at least to the extent of the tension. The tensile strength of water has been reported as 30 atmospheres by Meyer,1 60 atmospheres bv Budgett. 30 to 50 atmospheres by Temperley and Chambers,4,5 200 atmospheres by Dixon6. and 223 atmospheres by Briggs.7 Vincent8,9 determined the tensile strength of a mineral oil as 45 psi. Gardescu1 maintained pressures for short times in a model reservoir at 115 psi below the bubble-point. It should be noted that the high supersaturations observed were obtained on systems carefully purified to remove particles or surfaces which might promote the formation of bubble; These "nuclei" were considered as contaminants which interfered with the determination of a property of the liquid. In

Jan 1, 1952

By W. A. Stickney, J. W. Town

Tests demonstrated that aqueous solutions of sodiu~n sulfide would dissolve over 95 pct of the cinnabal- in 5 pct Hg flrotation concentrates and 60 to 90 pct of the cinnabav in low-grade ol-es. Double-leach tests showed that potassiutn sulfide would dissolve 90 pct of the avsenic sulfide in Hg-As satnples and only 1 to 10 pct of the Hg; the sodium sulfide would then dissolve 80 to 90 pct of the rernaining Hg and 30 to 70 pct of the vemaining As. 1 HIS paper describes the extraction, by alkaline sulfide solutions, of mercury from cinnabar-bear ing ores and flotation concentrates. Leaching time and solution temperature had minor effects on mercury extraction when compared to the effects of reagent quantity and ore type and grade. Cinnabar, although readily soluble in sodium sulfide, was only partially soluble in potassium sulfide and essentially insoluble in ammonium sulfide. A double leach process was developed to extract selectively the arsenic from Hg-As products with K2S and to treat the residue with sodium sulfide-hydroxide solutions to extract the mercury.' Mercury was then recovered from the pregnant solutions either by precipitation with metallic aluminum or by electrodeposition. The solubility of HgS in alkaline sulfide solutions was first reported by Volhard in 1878.' The first reported commercial application was made in 1915 when Thornhill applied the method to the treatment of an amalgamation tailing.3 Mullhollen, in 1911. described the chemical reaction of HgS with Na,S and alkaline hydrate to be:4 Most investigators have reported using a 4-pct sodium sulfide and a 1-pct sodium hydroxide soluti~n.3-4 An increase in temperature or excessive dilution of the solution causes the reaction to be reversed. Church Holmes described a similar process used for the extraction of antimony from silver concentrates at the Sunshine Mining Company's mill at Kellogg. Idaho.5 More recently. Erspamer and Wells reported the results of leaching studies on a Hg-Sb ore from Alaska.6 EXPERIMENTAL PROCEDURE Leaching tests were made on samples of mercury ore from eight deposits in Oregon, Washington, and Idaho. In addition. tests were made on flotation concentrates from seven of the samples as well as a flotation concentrate from an operating mill. Since previous investigators reported reagent requirements greatly in excess of that required by the equation HgS + Na2S = HgS . Na2S, initial studies were made on chemically pure HgS. Results showed that the reaction actually required about 1 g of Na,S per g of HgS in an aqueous solution rather than 0.338 g of Na,S as indicated by the equation. To check further the matter of reagent requirements, Na2S and HgS were mixed together in equal mole ratios. Water was then added, a drop at a time, until the components reacted; X-ray diffraction analyses showed no HgS nor Na,S present. The yellow hydrate compound which formed would not redissolve until about three additional mole equivalents of Na,S were added to the solution. This indicated that a stable solution would require at least 4 moles of Na2S for each mole of HgS. While these implications may be valid for pure HgS, the possibility of entirely different results caused by the existence of other elements present in ores and concentrates was recognized. Consequently, experiments of the same order were made on samples of a flotation concentrate from a producing mill. The concentrate, containing about 18 pct

Jan 1, 1962

By B. H. Kear

All the possible ways of forming simple two-dislocation boundaries in multiple slip orientations are deduced. It is shown that the principal differences in work hardening behavior of crystals plastically deformed in these orientations can he accounted for in terms of the likelihood of formation of diffuse boundaries, or deformation bands, consisting of the products of dislocation reactions of the Lomer type. Also, it is pointed out that the break-up of boundaries under the applied stress is more likely to yield interstitial jogs than vacancy jogs, whereas glide dislocations cutting throuqh dislocations trapped in particularly stable boundam'es can acquire both types of jogs. USING Frank's' grain boundary formula, Ball and Hirsch2 determined the parameters of all the possible boundaries that can be built from two sets of glide dislocations in the fee structure. This paper deduces the geometrical possibilities for the formation of these two-dislocation boundaries in the different multiple slip orientations, and discusses the role of boundaries in work hardening and in jog formation. Formation of Two-Dislocation Boundaries in Mutiple Slip Orientations. The parameters of the possible two-dislocation boundaries for any crystal orientation can be deduced most conveniently using the boundary formulae due to Amelinckx,3 in conjunction with the stereographic projection shown in Fig. 1. Suppose that slip occurs in a-BC and ß-CA. According to Amelinckx, when the two systems of glide dislocations are parallel, the rotation axis, u, of the boundary is parallel to (a x ß) and the unit normal, u, defining the boundary plane is parallel to (a x ß) x (BC x CA). On the other hand, when the glide dislocations form a crossed grid, u is parallel to (BC x CA) and u is parallel to (a x CA) x (ß x BC). In Fig. 1, (a x ß) is the pole of the great circle passing through a and ß, so that u is parallel to DC, i.e., parallel to [110]. Furthermore, (a x ß) x (BC x CA) is the pole of the great circle passing through DC and 6, so that u is parallel to [110]. Hence, when all the glide dislocations are parallel, the boundary is pure tilt with parameters u = [110], v = [ 110]. Similarly, it may be shown that the corresponding crossed grid of dislocations is a mixed boundary with u = [111], u = [111]. Consider the case of a crystal compressed in the [001] orientation. In this orientation, according to Fig. 1, there are eight available slip systems. In what follows, the different types of two-dislocation boundaries that are possible in this orientation will be examined by taking different combinations of two slip systems out of the available eight, with a-BC always one of the systems. Case (i)—Slip Systems a-BC and d-CB. The formation of a tilt boundary in (101), which consists of a crossed grid of edge dislocations with vectors BC andCB, is illustrated in Fig. 2(a). As the figure shows, slip is required in the system a-BC in one part of the crystal and in d-CB in the other part, with both sets of dislocations entering the boundary from opposite sides. The rotation axis of the boundary lies in (101), depending on the relative densities of the two sets of edge dislocations in the boundary. Case (ii)-Slip Systems a-BC and ß-CA. The two possible boundaries are shown in Figs. 2(b) and (c); boundary (b) is tilt with u = [110], u = [110], and

Jan 1, 1962

By E. D. Gardner, E. M. Sipprelle

The Synthetic Liquid Fuels Act (58 Stat., 190; 30 U.S.C. Sup., Secs. 321-325) was approved by Congress April 5, 1944; it directed the Bureau of Mines to build demonstration plants to produce synthetic liquid fuels from coal, oil shale, and agricultural products. The most important oil-shale deposits in the United States are in the Green River formation of Colorado, Utah, and Wyoming. The oil shale of western Colorado generally is more amenable to exploitation, more persistent, and apparently richer than elsewhere in the Rocky Mountain Region. It occurs at the top of a high plateau surrounded by bold, nearly vertical escarpments 500 to 600 ft in height. The top 400 to 500 ft of these escarpments comprises an oil-shale measure that averages 15 gal of shale oil per ton; the bottom 70 90 100 ft of the measure, called the Mahogany Ledge, averages over 30 gal per ton. The full measure in a 1000-square-mile area is estimated to contain 300 billion barrels of shale oil;' the Mahogany Ledge is estimated to contain 100 billion barrels of oil. These estimates are based on numerous surfac,e samples and on core-drill holes drilled by the Government and by private enterprise. The oil-shale beds are undisturbed and lie nearly horizontal. The name "oil shale" is unfortunate, as the rock is a tough, strong marlstone. Organic matter named "kerogen" is a constituent of the rock. The oil-shale demonstration mine is on Naval Oil-Shale Reserve No. 1; it is about 5 1/2miles by mountain road from the plant site, which, in turn, is 2 miles from U.S. Highway 6 and 10 miles west from Rifle, Colo. The highway parallels the Colorado River, the Denver and Rio Grande Western Railroad, and a 66,000-volt public-utility power line. Early in the program it was realized that an oil-shale enterprise would have to be on a large scale to be commercial, and that unusually low mining costs would be necessary. The physical characteristics of the Mahogany Ledge and an overlying roof stone are unusually favorable both for large-scale operation and low mining costs. Quarry practices largely will be followed underground to mine the Mahogany Ledge. The aim has been toward complete mechanization of all mining operations. A mining unit would comprise a square mile containing 100,000,000 tons of oil shale with allowance for mining losses. An investment of $1,000,000 would be $0.01 a ton; such an expenditure, therefore, could be made to save, say, $0.015 per ton daily operating cost. A goal of a mining cost of $0.50 per ton was set up in 1945. Open-cut mining costs then were about $0.25 per ton of material handled; it was hoped that a cost double this amount could be obtained in mining the Mahogany Ledge. Costs of labor and supplies have increased since 1945 and so has the selling price of petroleum products. To those unacquainted with the character of the Green River deposits, the name "shale" suggested high mining costs. Others assumed that coalmining costs of $2 to $5 per ton would apply. To many, the expected mining costs appeared the principal handicap to the establishment of an oil-shale industry. The purpose of the Bureau of Mines is to demonstrate methods and to establish costs for mining the oil shale on a large scale. It is hoped this work will lead to the establishment of a large-scale, commercial oil-shale enterprise.

Jan 1, 1950

By R. A. Swalin, L. A. Neimark

The research work presented in this paper had initially a two-fold goal. First, further data concerning the low-temperature recovery of cold work was desired. Recovery phenomena have been extensively studied in face-centered-cubic metals but at the time of initiation of this research, no investigation concerning the low-temperature recovery in body-centered-cubic metals had been made. During the course of the investigation a paper by Martin on the recovery of point defects in molybdenum appeared.&apos; Comparison of our results on tungsten with Martin&apos;s results on molybdenum will be made. Secondly, knowledge concerning the influence of a particular type of impurity addition on the recovery kinetics was desired. It has been known for a long time that extremely small amounts of certain impurity additions exert a profound influence on the recrystallization behavior and the resulting microstructure of tungsten. Small amounts of potassium silicate and aluminum chloride added prior to the reduction of tungsten oxide to the metal have been found by Smithells to raise the recrystallization temperature markedly,2 and yield an ultimate microstructure in which grains several millimeters long are produced in fine wires of say 10 mil diam. If the impurities are added singly, ordinary secondary recrystallization results with none of the spectacular properties of the wire to which special additions were made. Swalin and Geisler3 and Rieck4 have studied the recrystallization behavior of such doped wire in some detail. The former workers found that small amounts of these impurities raised the recrystallization temperature over 400°C and electron microscopic examination revealed no obvious inclusions in the microstructures. In fact. chemical analysis showed that there was <0.001 pct K, <0.002 pct Al, trace of Si, and <0.0003 pct 0 in the wire studied. The possibility that the role of the special impurities is to keep the structure open by void formation and that submicroscopic porosity acts as the inhibiting agent has been discussed.2&apos;3 Meijering and Rieck5 have suggested that the impurities are strung out as second-phase particles in a direction parallel to the drawing direction. It was thought that a kinetic study of recovery could perhaps elucidate the role of the impurities to some extent. When a metal is deformed by cold work three basic types of defects are thought to be introduced into the crystal lattice, namely, interstitials, vacancies, and dislocations. Van Bueren6 has proposed that recovery of cold-worked metal is a four-stage process, each step being the result of the annealing of a primary defect or a combination of defects and having a unique activation energy. The steps in order of increasing activation energy are attributed to a) the diffusion of interstitials recombining with vacancies, b) diffusion of vacancy pairs, c) the diffusion of single vacancies, and d) climb of dislocations. In metals with relatively low- or medium-range melting points the temperatures for recovery are low enough so that the first three steps may occur during room-temperature deformation. For tungsten, because of the high melting point and subsequently high recovery temperature, it was calculated, using Nowick&apos;s approach7 that this recovery would occur in the temperature range 200" to 600°C. It is also known that recovery of X-ray line broadening, presumably due to dislocation climb, occurs at about 600°C.8 EXPERIMENTAL METHOD Two types of cold-rolled 10-mil-diam tungsten wire were used in the investigation; a) pure tungsten, (called undoped) and b) G. E. No. 218 wire (called

Jan 1, 1961

By R. T. DeHoff

Saltykov&apos;s meihod for the determination of the size distribution of spherical particles from measurements made on random plane sections is extended to particle shapes which are not equiaxed. The analysis permits the deterrrzination of the size distribution of aggregates of ellipsoidol particles provided all particles have tlze same shape. V ARIOUS solutions to the problem of the determination of the size distribution of spherical particles from measurements made on random plane sections have appeared in the literature since the original solution was first published by Scheill in 1934. Solutions have been offered utilizing measurements of the diameter1y2 or area3&apos;4 of circular sections that result when a test plane is passed through an aggregate of spherical particles, and the length of intercept5y6 that results when a test line is passed through the aggregate. To the best of the knowledge of the author, no method has been proposed which permits the determination of the size distribution of particles that are not equiaxed. The purpose of this paper is to develop a method which permits the determination of the size distribution for a specific class of particle shapes which cover awide range of axial ratios; namely, ellipsoids of revolution. In the interests of simplicity, it is necessary to limit consideration to aggregates of particles which are all similar in shape; that is, the ellipses which, by rotation about one of their axes, generate the particles, all have the same axial ratio. The size distribution, which is to be determined by the analysis, is arbitrary. It is also assumed that the section, or sections, upon which the measurements are made represent the average of all possible sections through the structure. This ideal condition can be approached as nearly as may be desired by observing a sufficient area of sections taken at random positions in a randomly oriented aggregate, and in random positions and orientations in an aggregate that has one or more axes of orientation. SIZE DISTRIBUTION FOR PROLATE ELLIPSOIDS Consider an aggregate of cigar shaped, geometrically similar particles (prolate ellipsoids), dispersed in an opaque matrix. Let the size of each particle be specified by the length of its minor axis, By Fig. 1, and the shape, q, be defined by the ratio of its minor to its major axis, B/A. Let the index, j, refer to dimensions of ellipsoids in a particular size class, and the index, i, to dimensions of an ellipse resulting from the intersection of a test plane and a particle. The size of such a section is specified by the length of its minor axis, b. Let the particles be arbitrarily divided into k size classes, and let the increment of size between each class be A, where A = &,$, B,,,being the minor axis of the ellipsoids in the largest size class. Since all sections are represented on the test plane, the minor axis of the largest of the sections observed, results from the intersection of the test plane with an ellipsoid in the largest size class at its center, and is therefore equal to Bmax Thus the increment, A = The final result will consist of the k numbers which represent the number of particles in each size class per unit volume of aggregate:

Jan 1, 1962