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By S. G. Epstein

Using the capillary-reservoir technique, electromi-gvation rates of cadmium and indium in liquid bismuth were measured at several temperatures. The electric mobility of cadmium Jrom 305° to 535°C and indium from 310° to 595°C can be expressed as a function of temperature by the equations UIn = 1.52 x 10-3 exp sq caz per v-sec Migraion of both solutes was cathode-divected at a rate rnore than four tiMes tHAt previously found for siluer in liquid bisnmth. The electric mobilities of cadmium and indiulrz in liquid bismuth at 500° C are nearly identical with their respective mobilities in mercury at room temperature. AS part of a systematic study of the variables which are considered to control electromigration in liquid metals, the electromigration rates of cadmium and indium in liquid bismuth have been measured. Mass transport properties of silver in liquid bismuth have been reported previously,&apos; and measurements of tin and antimony in liquid bismuth are forthcoming. Comparisons will be made with literature values for these same solutes in mercury.2&apos;3 This series of solutes was selected to determine the effect of the solute valence on its electromigration. Silver, cadmium, indium, tin, and antimony have nearly equal atomic masses but have chemical valences ranging from +1 to +5. They are all fairly soluble in bismuth above 300°C and all have radioactive isotopes, which are an aid in making analyses. EXPERIMENTAL TECHNIQUE Electromigration of cadmium and indium in liquid bismuth was measured by the modified capillary-reservoir technique previously described.&apos; In this method irradiated cadmium or indium is added to bismuth to form alloys containing about 1 wt pct solute (<2 at. pct solute). Several quartz or Pyrex capillaries: 1 mm ID and 5 cm long, vertically oriented, are simultaneously filled in the reservoir of the liquid alloy. A direct current is passed through two of the capillaries, which contain tungsten electrodes sealed in the upper end. The other capillaries sample the reservoir during the experiment. After a measured time interval the capillaries are removed from the reservoir and rapidly cooled. The glass is then broken away from the solidi- fied alloy, which is then weighed, dissolved in acid, and analyzed for solute content by chemical and radiochem-ical techniques. An electric mobility (velocity per unit field) can be calculated from the amount of solute entering or leaving each capillary by the simplified expression1 in which Ui is the electric mobility of the solute, ?mi the solute weight change, Ci the solute concentration of the reservoir, I the current, p the alloy resistivity, and l the duration of the experiment. This expression is valid as long as the experiment is terminated before a concentration gradient develops across the capillary orifice. Earlier experiments showed that the concentration gradient formed initially at the electrode changes with time and eventually reaches the orifice, due to back-diffusion. This condition produces a solute exchange between capillary and reservoir by diffusion or convection, opposing the electromigration, which results in a lower measured value for the electric mobility. To determine if the concentration gradient had reached the orifice, the capillaries used in some of the experiments were sectioned at 1-cm intervals and the solute content of the alloy from each section was radiochemically determined. A typical concentration profile for an experiment with indium in bismuth is shown in Fig. 1; cadmium in bismuth showed similar behavior. As illustrated in the graph, very little back-diffusion has occurred in the capillary containing the cathode, since the concentration gradient is confined to the upper 1 cm of the capillary. In the capillary containing the anode, however, the concentration gradient is much broader, extending nearly to the orifice, even though the net change in solute concentration is nearlv the same in both capillaries. Since cadmium and indium probably lower the density of bismuth when alloyed, depletion of the solute from the alloy adjacent to the anode would increase the density of the liquid in the uppermost region of the capillary. This would give rise to convective mixing within the capillary, causing the broadened concentration gradient. Conversely, the alloy adjacent to the cathode should have a reduced density as the solute concentration is increased by migration, explaining the "normal" concentration profiles found in these capillaries. This disparity was not found for electromigration of silver in bismuth. Both metals have similar densities at the operating temperatures, and nearly symmetrical concentration profiles were found in the two capillaries of each exueriment. This density effect was also apparently encountered when an attempt was made to measure diffusion coefficients for indium in liquid bismuth by the same technique which was successfully used to measure diffusion of silver in bismuth.&apos; Capillaries 1 mm ID and 2 cm

Jan 1, 1968

By W. L. Fink, R. S. Archer

This paper describes results obtained on aluminum-beryllium alloys and aluminum-beryllium-copper alloys in the preparation of which aluminum of 99.95 per cent. purity was used. The constitution and structure of the high purity binary alloys are given. The aluminum-beryllium eutectic occurs at 0.87 per cent. beryllium and 645° C. The solid solubility of beryllium in aluminum at 631° C. is 0.05 per cent, beryllium, and at room temperature is less than 0.013 per cent. beryllium. The densities of the alloys are substantially the same as the values calculated on the assumption that the densities of the elements are not changed by alloying. All of the alloys age-harden at room temperature after a solution heat treatment, and the chill cast aluminum-beryllium-copper alloys age-harden at room temperature without a prior solution heat treatment. Hardness and tensile properties are given. Salt spray corrosion tests on sheet specimens are described. It is shown that beryllium docs not lower the corrosion resistance of aluminum to salt spray provided the alloy has received a solution heat treatment. Commercial Possibilities of Beryllium Alloys Beryllium has certain properties such as low density, high hardness, good corrosion resistance, low thermal expansion and fairly good electrical conductivity, which would indicate that it is worthy of consideration as an ingredient of light alloys. It was not until recently, however, that beryllium could be produced with sufficient ease to encourage research along this line. The production of beryllium by electrolysis from a fluoride bath has now developed to the stage where it could be used commercially if there were sufficient demand for the element. Claims made in certain newspapers and technical articles in regard to thc strength and corrosion resistance of thc aluminum-beryllium alloys are not justified by experimental results. Moreover, beryllium is an expensive metal ($200 a pound at the time this work was done) and, on account of the nature of its ore and the consequent difficulty of its extraction, it will in all probability continue to be a relatively expensive metal, although the cost would undoubtedly be a great deal less than $200 a

By N. A. Stockett

Southeast Missouri is the largest and oldest lead-producing district in the United States. For the year 1941, the statistical picture of pig-lead production, stated in short tons (partly estimated by the Engineering and Mining Journal) is as follows. Tons World production................. 2,000,000 United States Production .........- 460,000 Southeast Missouri production..... 142,000 The consumption of primary lead in the United States in 1941 was approximately 900,000 tons, or almost double the country&apos;s production. The largest previous year&apos;s in in the United States was 718,000 tons, in 1926. The largest quantities of lead are used for cable sheathing, storage batteries and white lead. During 1941 tetraethyl lead for auto and aviation gasoline consumed 50,000 tons of lead. The entire lead production of Southeast Missouri is now mined by the St. Joseph Lead Co., whose dominant position as the largest producer in the United States of lead directly from ores is best shown by the fact that in 1941 it produced approximately 31 per cent of the lead production of the United States from its mines in southeast Missouri, where 22,000 tons of ore, averaging over 3.00 per cent lead, is mined per working day. It is known that lead was mined at Mine La Motte, Madison County, Missouri, by Renault in 1723. Other white men and Indians probably did some mining prior to that time. Since 1865, the recorded production to Jan. I, 1942, shows that the St. Joseph Lead Co. and the various other companies that have operated in St. Francois County mined lead ore, which, after milling and smelting losses produced 5,980,000 short tons of pig lead. • About 95 per cent of the present lead production of Southeast Missouri is mined in St. Francois County. The northern part of this area is 60 miles south of st. Louis. The remainder of the lead is obtained at Mine La Motte, about 25 miles southeast from the center of the producing area in st.Francois county, Prospecting In this district, most of the ore is discovered by surface and underground diamond drills and by prospect drilling underground with rock drills. Each 2-ft. length of the cuttings from these Jack-hamer prospect holes is assayed for lead. These holes are marked and the records are entered on maps. It has been found that close drilling—100-ft. centers of holes, and sometimes less—is necessary in order to locate most of the smaller commercial ore bodies, many of which previously had been missed by drilling the areas with holes spaced 200-ft. centers or more. To date, geophysical and other methods of prospecting, apart from diamond and Mining Practices of the St. Joseph Lead Company in Southeast Missouri

Jan 1, 1943

By Robert Anderson

The diffraction of x-rays by cold-worked and heavily polished surfaces of metals gives, no evidence of an amorphous state and typically perfect crystallographic diffraction&apos; patterns are obtained. Severely cold-worked metals, reduced as much as 98 per cent. in area, give true crystallographic diffraction patterns, and polished surfaces of large single crystals of metal give typical crystallographic patterns. The conclusion is drawn, on basis of x-ray evidence, that metals are fragmented on cold work and polishing and not amorphized. THE purpose of this paper is to report evidence, regarding, metal: structures, that is contradictory to the amorphous-metal, hypothesis of Beilby, and particularly evidence that is opposed to the proposition that a vitreous amorphous layer is produced by polishing a piece of metal. According to the theory of Beilby, which has been developed, by Rosenhain and others, polishing a piece of metal greatly affects the condition of the metal at or near the surface polished, making that surface entirely different in character from the metal beneath. A vitreous amorphous surface film is said to be formed. The polishing process, on the basis of Beilby&apos;s explanation, is well known-and does not&apos; require discussion here, but it is advisable to seek the precise meaning of,., the term "amorphous." According to Beilby, "amorphous means. Non-crystalline in the most intimate sense of the word&apos;; the molecules are not marshalled in crystalline order and orientation." According to Rosenhain, the amorphous condition is that assumed by a metal when, the .crystalline arrangement is completely broken up so that the atoms exist in a state of disorderly arrangement similar to that ;which exists in the liquid state. Thus, from the point of view of the phase rule, the "amorphous phase" is regarded as being identical with the liquid phase. Amorphous metal is often likened to an undercooled liquid. A crystalline substance is one in which the atoms are arranged in space according to some definite repeating geometrical pattern. The existence of amorphous metal has not been definitely proved.

Jan 1, 1925

By Clarence O. Babcock

Model pillars of limestone, marble, sandstone, and granite, with length-to-diameter (LID) ratios of 3, 2, 1, 0.5, and 0.25 (0.286 for granite), were broken in axial compression to determine to what extent an increase in end constraint increased compressive strength. Radial end constraints of 13 to 23% of the average axial stress in the pillar, produced by solid steel rings bonded with epoxy to the ends of dogbone-shaped specimens, increased compressive strength somewhat above that of cylindrical pillars without ring constraint. However, when the results were compared with those obtained by other investigators for straight specimens of several rock types taken collectively, with LID ratios greater than 0.5, the resulting strengths were not significantly different. Thus, the amount of end constraint produced by the solid steel rings was about the same as that produced by the friction from the steel end plates. In other tests, a radial prestress of 3000 or 5000 psi was applied prior to axial loading by adjustable hardened steel rings to increase the constraint above that obtained for the solid rings. The average radial constraint stress, expressed as a percentage of the average axial pillar stress at failure for the 3000 psi prestress, was 54.3% for limestone, 40.3% for marble, 44.7% for sandstone, and 23.4% for granite. The average radial constraint stress, expressed as a percentage of the average axial pillar stress at failure for the 5000 psi prestress, was 74.2% for limestone, 51.2% for marble, 61.6% for sandstone, and 29.7% for granite. These constraints increased the compressive strength significantly above the strength of straight specimens and solid-ring constrained specimens. These results suggest that large horizontal stresses in orebodies mined by the room-and-pillar method should increase the strength of the pillars and allow an increase in ore recovery by a reduction of pillar size when major structural defects are absent. One important objective of the U.S. Bureau of Mines (USBM) mining research program is the rational design of mining systems. In the design of room-and-pillar mining operations, pillar strength is a fundamental variable. It is customary to estimate this strength from uniaxial compression tests of rock samples and to correct this value for the length-to-diameter (LID) ratio of the in-situ pillar. This method of estimating pillar strength corrects for pillar shape but does not consider the effect of a large horizontal in-situ stress field that sometimes exists in underground formations. The purpose of the work covered in this report was to determine to what extent the compressive strengths of model pillars of relatively brittle rock loaded in axial compression were affected by lateral end constraint. In previous work, Obert l used solid steel rings bonded to the ends of dogbone-shaped specimens to study the creep behavior of three quasi-plastic rocks -salt, trona, and potash ore - during a test period of 1000 hr. These rings provided radial constraint during the loading cycle of 20 to 50% of the axial stress for specimens with LID ratios of 2, 0.5, and 0.25. He concluded that (1) "for a quasi-plastic material the end constraint strongly affects the specimen strength, and (2) as D/L increases (length-to-diameter decreases), the specimens lose their brittle characteristics and tend to flow rather than fracture." He also concluded that model pillars constrained by rings were better for use in predicting the strength of mine pillars than either cylindrical or prismatic specimens. This conclusion appears to be valid where mine pillars, roof, and floor are a single structural element. In the present study, 460 specimens of four relatively brittle rocks — limestone, marble, sandstone, and granite - were tested to failure. The study consisted of two parts: (1) the effect on the compressive strength of end constraint produced during the axial loading cycle by solid steel rings bonded with epoxy to the ends of the specimens, and (2) the effect on the compressive strength of increased end constraint produced in part by a prestress applied prior to axial loading and in part by lateral expansion of the specimen during the loading cycle. The first part of this study was reported in some detail earlier.2 EXPERIMENTAL PROCEDURE AND EQUIPMENT Model rock pillars of the sizes and shapes shown in Fig. 1 were broken in axial compression when the ends were constrained as shown in Fig. 2. he straight specimens were broken without ring constraint. The specimens of dogbone shape were broken with (1) solid

Jan 1, 1970

By J. J. Kramer, K. Foster

The orientation distribution of surface-energy -induced secondary recrystallized grains was determined. This work was conducted on thin sheets of a 3 pct Si-Fe alloy annealed under environmental conditions that furor grouth of grains with a (100) plane in the surface of the sheet. The texture was found to be extremely sharp and almost independent of sheet thickness. The distribution varied exponentially with the angular deviation from the {100} plane. It was possible to relate the distribution to the nu-cleation rate of the secondary rains as influenced by the surface-energy difference. THE role of surface energy in the secondary grain growth of cube-oriented grains (grains with a (100) plane in the plane of the sheet) in thin Si-Fe sheets has been previously discussed.1-4 In high-purity sheet material normal grain growth usually occurs until the grains have extended through the sheet. Further grain growth is inhibited by the thermal grooving of the boundaries at the sheet surface. However, additional growth of cube grains can occur by a secondary grain growth process under conditions where the (100) plane has a lower surface energy than other orientations. Apparently for these alloys, cusps exist in the polar plot5 of surface free energy with the lowest cusp energy occurring at the (100) orientations. This has been reported to be the result of preferential adsorption of sulfur on the (100) planes.6 As a result of this process, a distribution of orientations could arise from two possible mechanisms. First, when a cusp is present in the polar plot of surface free energy, there are orientations inside the cusp that have a lower surface energy than elsewhere on the polar plot. Also, at sufficiently high temperatures, flat surfaces whose orientations are inside or just outside the cusp (depending on its shape) can often thermally etch, yielding a microscopically stepped surface of even lower surface energy. As a result, grains oriented close to cube would also have a lower surface free energy, either because of the cusp shape or by thermal etching, and could possibly grow as secondary grains by the surface-energy phenomenon. One should thus observe a distribution in the surface orientation of the cube grains comprising the secondary structure. It is the purpose of this paper to investigate this orientation distribution experimentally and to discuss the factors involved in its formation. For this purpose, the surface orientations of a large number of secondary grains in various sheet thickness were determined by means of the Laue back-reflection X-ray technique. PROCEDURE A vacuum-melted 3 pct Si-Fe alloy containing a nominal impurity content of 0.005 wt pct was processed into strip. A single cold-rolling step of 90 pct reduction was used for each strip regardless of the final sheet thickness. Final strip thicknesses of 0.60, 0.30, 0.15, and 0.075 mm were used. Care was taken to insure that the final strip surface was smooth and flat. All strips of a given thickness were annealed together at 1200°C in dry hydrogen (dew point -70°C) to develop the desired secondary structure and to insure identical environmental annealing conditions. The annealing time was selected to develop a complete secondary structure in the thinner sheets but to permit the thicker sheets (0.60 mm) to have residual primary grains remaining. This was necessary to determine whether growth impingement could lead to one secondary grain consuming another at a greater angular deviation. For the X-ray determination of the surface orientation of the secondary grains, a special specimen holder was used. The camera and holder arrangement could be aligned by X-raying a grain in three positions rotated 180 deg to each other. Thus, with a small beam X-ray focus (1 mm), the surface orientation of any grain could be determined to within one-half a degree. The surface orientations of one hundred cube secondary grains were determined for each sheet thickness. The criteria of a secondary grain were its size relative to the sheet thickness and the number of sides of the grain observed in the sheet surface. (A primary recrystallized grain extending through a sheet will generally have six edges visible in the plane of the sheet, whereas a secondary grain will have many more when growing entirely into primary grains.) Grains were selected as randomly as possible by X-raying every secondary grain found along a line drawn on the strip. No attempt was made to determine the exact orientation of the planes of the surface, as many strips from randomly selected sheets were used. On1y the angular deviation of the surface plane from {100} was measured. In order to assess the volume distribution in the

Jan 1, 1965

By G. Derge, Ling Yang, John Henderson

Self-diffusion coefficients of aluminum have been measured by the capillary reservoir technique in liquids of the CaO-SiO2-Al2O3 system containirg equimolar portions of CaO and SiO2, in the temperature range 1400o to 1520oC. For the melt containing 6.0 mole pct Al2O3 the results can be expressed by the equation D = [(4.3 * 0.3) x 104] exp [(-85,000 * 17,500)/RT]cm~sec-&apos;; for the melt containing 12.5 mole pct Al2O3, by the equation D = (5.4 i 0.2) exp [(-60,000 * 10,00O)/RT] cm2sec-: A concept of the constitution of these melts has been developed which proposes that the ratios O/(Si +Al) and Al2 O3/CaO determine the dominant species present. In recent years considerable work has been done on the system CaO-SiO2-A12O3 with a view to elucidating the structure of liquids of this system. Conductivity,&apos; electromotive force, 3 density,4 and activity5 measurements have all contributed to an understanding of the problem, but as yet there is no entirely satisfactory theory that can account for all the observed experimental results. In principle, measurements of self-diffusion coefficients should give further information which is not obtainable in other ways. Self-diffusion coefficients for calcium, silicon,6 and oxygen7 have been measured. The present investigation extends the series of self-diffusion coefficient measurements to include aluminum and develops a concept of constitution for liquids of this system which is compatible with all the observed experimental results. EXPERIMENTAL The technique used in the measurement of the self-diffusion coefficient of aluminum was the capillary-reservoir method,8 A126 being incorporated in the melt contained in the capillary and inactive aluminum in the reservoir melt. This method was chosen because it minimizes convection currents&apos; in the diffusion zone. It has the further advantage that the boundary conditions are such that a slight modifica- tion of Anderson and saddington&apos;s8 solution of Fick&apos;s Law yields an equation which requires measurements only of the length and the initial and final average specific activities of the solidified melt within the capillary. where t is the diffusion time, Co is the average specific activity of the melt contained in the capillary at t = O, C is the average specific activity of the melt contained in the capillary at t = t, 1is the length of the capillary, and D is the self-diffusion coefficient. The equation is of somewhat different form than those previously applied to high temperature diffusion studies because the specific activity of the melt in the reservoir was negligible both before and after diffusion. The diffusion apparatus is shown schematically in Fig. 1. It consisted of a silicon carbide resistance furnace containing the inactive melt in a graphite crucible, internal dimensions 7/8 by 4 in., enclosed in a 1 1/4- by 1 1/2- by 30-in. McDanel tube. A 3/8-in. McDanel thermocouple sheath to which graphite radiation shields and a graphite protection tube were affixed, was used to hold the capillaries. By moving this sheath through a rubber seal at the top of the McDanel tube the capillaries could be lowered into or raised out of the melt. Temperature was measured with a Pt-Pt 13 pct Rh thermocouple which was calibrated periodically against a standard couple. The furnace temperature was controlled to ± 5°C through the thermocouple immersed in the melt. Temperature variation over the depth of the melt was less than ± 3°C. The inactive melts were prepared from pure native quartz, assaying better than 99.9 pct SiO2, A.R. grade A12O3 and A.R. grade CaCO,. The same quartz and CaCO3 were used in preparing the active melts, the

Jan 1, 1962

By H. D. Hodges, J. K. Godbey

In order to better understand the fracturing process, bottom-hole pressures were measured during a number of typical fracturing operations. A recently developed system was used that allows simultaneous surface recording of both the bottom-hole and wellhead pressures on the same chart. The results from six fracruring treatments are summarized on the basis of the pressure data obtained. Al-though no complete analysis is attempted, the value of accurate pressure measurements is emphasized. Important characteristics of the bottom-hole pressure record do not appear at the wellhead because of the damping effect of the fluid-filled column. In four of the six treatments described, the formations apparently fractured during the initial surge of pressure with only crude oil in the well. The properties of the fluids used during the treatments are given and the fluid friction losses are obtained directly from the pressure records. This technique is also shown to be adequate for determining when various fluids, used during the process, enter the formation. INTRODUCTION Hydraulic fracturing for the purpose of increasing well productivity is now accepted in many areas as a regular completion and workover practice. Numerous articles have appeared in the literature discussing the various techniques and theories of hydraulic fracturing&apos;. In general, three basic types of formation fractures are recognized today. These are the horizontal fracture, the vertical fracture, and fractures along natural planes of weakness in the formation&apos;. Any one or all three of these fracture types may be present in a fracturing operation. However, with only the wellhead pressure record as a guide, it is difficult at best to determine if the formation actually fractured, and is almost impossible to determine the type of fracture induced. These difficulties arise in part because the wellhead pressure record, especially when fracturing through tubing, does not accurately reflect the pressure variations occurring at the formation. Several factors contribute to this effect and preclude the possibility of using the wellhead pressure as a basis for accurately calculating the bottom-hole pressure. These factors are: 1. The compressibilities of the fluids which damp the pressure variations. 2. The changes in the densities of the fluids or apparent densities of the sand-laden fluids. 3. The flowing friction of the various fluids and mixtures, which is dependent on the flow rates and the condition of the tubing, casing, or wellbore. 4. The non-Newtonian characteristics of a sand-oil mixture and its dependence upon the fluid properties, the concentration of sand, and the mesh size used. 5. The unknown and variable temperatures throughout the fluid column. Because of these reasons it was determined that in order to obtain a more accurate knowledge of the nature of fracturing, the bottom-hole pressure must be measured along with the pressure at the surface during a fracturing treatment. Even with accurate pressure data, a reliable estimate of the nature of fracturing is still dependent upon knowledge of the tectonic conditions. However, the hydraulic pressure on the formation is basic to any approach to a complete analysis. In order to accomplish this objective a system was developed to record the wellhead and bottom-hole pressures simultaneously at the surface. By recording both pressures on a dual pen strip-chart recorder, it was possible to greatly expand the time scale so that rapid pressure variations would be faithfully recorded. By such simultaneous recording, time discrepancies inherent in separate records are eliminated, thus overcoming one of the most difficult problems associated with bottom-hole recording systems. This paper illustrates the results obtained by using this system during six typical fracturing operations. All of these tests were taken in wells that were treated through tubing. By a direct comparison of the wellhead and bottom-hole pressures, the importance of obtaining complete pressure information during a fracturing treatment is emphasized. THE INSTRUMENTATION AND PROCEDURES The bottom-hole pressure measuring instrument consisted of a pressure-sensing element, a telemetering section, and a lead-filled weight or sinker bar. The pressure-sensing element used was an isoelastic Amerada pressure-gauge element. By using an isoelastic element, no temperature compensation was necessary in the tests described, since the temperature was believed to be well below the maximum temperature limit of 270°F. The rotary output shaft of this helical Bourdon tube element was coupled to a precision miniature potentiometer. The rotation of the pressure-gauge shaft thus changed the resistance presented by the potentiometer

By H. E. Swanson

A description of the field apparatus has been published by D. G. Brubaker. Data from laboratory model studies of the in-line and broadside methods of operation are detailed. The conductor models include a single sheet conductor at several strike and dip angles and a schistose-type conductor. In addition, data on the effects of the strike length and of the depth of the conductor are presented for the broadside method of operation. All of the data show that the inclintion reverses direction over the top edge of dipping single sheet conductors. Differences between anomalies over conductors dipping between 90" and 30" are subtle,but flat-lying sheets can be readily distinguished from steeply dipping sheets. Schistose conductors are easily distinguished from single sheet conductors, and a procedure is given for determing the direction of schistosity. The depth of penetration under ideal conditions is 0.7 of the coil separation. In 1950, The New Jersey Zinc Co. (of Pa.) developed a lightweight apparatus for electromagnetic prospecting. A description of this apparatus has been published by D. G. Brubaker.1 It consists of a small, battery-powered vertical source coil and a direction-finding receiving coil. Source and receiver are kept a fixed distance apart and move as a unit along the survey lines. At each receiver station the inclination of the magnetic field created by the source is measured. Two methods of operation are used, in each of which measurements are taken with a constant source-to-receiver distance and with the plane of the source oriented to pass through the receiver station. In one procedure, called the in-line method, source and receiver travel in tandem along the same line. In the other procedure, called the broadside method, source and receiver move along adjacent lines, with the source-to-receiver direction oriented parallel to the assumed strike direction. The data recorded in either case are the inclinations, measured in degrees from the horizontal, of the magnetic field created by the source. These data are plotted at the receiver stations on a map. Scale-model studies of both methods of operation have been conducted in the laboratory and are reported in this paper. APPARATUS Small source and receiving coils wound with many turns of fine copper wire were used to produce and measure an alternating magnetic field in the same manner as the field apparatus. The model source coil was mounted in a vertical position and oriented so that the receiving coil was in the plane of the source. The receiving coil was mounted in a frame so it could be rotated to obtain the inclination measurements. The source coil was excited by a 100-kc signal generator. A tuned amplifier and a voltmeter were used to detect the null position of the receiving coil. The coils used in the field apparatus are usually spaced about 400 ft. The coils used in the model work were spaced from 4 in. to 4 ft apart. Thus the scale of the model work ranges between 1/1200 to 1/100 natural size. The model conductors were aluminum-coated building paper supported on wooden frames. The conductivity-thickness product was measured using a four-electrode system and was found to be about 300 ohms-&apos;. CONDUCTIVITY CONSIDERATIONS The electromagnetic response from a thin sheet conductor is a function of the product of the conductivity of the sheet times the thickness of the sheet times the frequency of the alternating electromagnetic field times some linear dimension of the system such as the coil separation which indicates scale. The secondary electromagnetic field produced by the conductor increases in amplitude from zero at zero conductivity to a maximum value for infinite conductivity, while the phase of the secondary field with respect to the primary field shifts from 90" at zero conductivity to 0" at infinite conductivity. Several authors2-&apos; have shown that most of both the increase in amplitude and the change in phase of the secondary field takes place over a three-decade range of the conductivity-thickness-frequency product. Only small changes in the amplitude and

Jan 1, 1961

By William G. Pariseau, H. Douglas Dahl

Recent subsidence legislation indicates that mining engineers would be welt advised to be able to predict and control surface damage caused by mine subsidence. To date, such an ability is practically nonexistent. Model analysis is suggested as one of the alternative paths available which might yield fruitful results. Similitude requirements developed for a self-loaded body in static or quasi-static equilibrium indicate that complete similitude without centrifuging is an impracticability. However, a pilot experimental study which used a simplifying assumption to correctly model mine subsidence has produced results in qualitative agreement with field observations. The purpose of this paper is to present a discussion of the various approaches that can be taken in the study of mine subsidence phenomena. Particular attention is focused upon the rational selection and use of laboratory models. Broadly interpreted, mine subsidence is the deformation of the rock mass enclosing a mine. Depending upon a number of factors, the movement of the subsiding rock mass may disrupt gas and water lines or other buried utilities, damage surface structures such as buildings and bridges, dislocate streams, roads, and rail lines, aggravate acid mine drainage and fire problems, and generally mar the landscape. It is clearly a problem that no mine manager can safely ignore. It is also a problem that will grow with the general population increase. In the following discussion, a summary review of past and present approaches to subsidence studies is given. The possibilities of duplicating subsidence phenomena in laboratory models are examined, and an analysis of a particular type of model is presented. Some preliminary results obtained from a model of the particular type analyzed are then discussed. REVIEW OF PREVIOUS WORK Historically, subsidence investigations have been empirical studies in the field and laboratory or theoretical analyses of mathematically idealized media. Empirical and theoretical work in the United States has generally lagged behind investigations abroad. In the United States, field studies are mostly pre-World War 11. These are summarized in the Mining Engineer&apos;s Handbook. &apos; Field studies in Europe are more recent and more extensive. Those made in Great Britain are summarized in the Subsidence Engineers Handbook2 and represent observations made at 157 different collieries. Such studies by themselves are of limited usefulness as are all empirical studies. One can never be certain that conditions at one mine will be similar enough to those at another to warrant the drawing of like conclusions. European subsidence formulas rely heavily upon the "angle of draw" and "critical area" concepts. The angle of draw is defined as the angle between a vertical line through the face, and another line extending from the face to the surface at the point where movement is zero. The critical area is defined in relation to the least extraction necessary to produce maximum subsidence. Fig. 1 illustrates the angle of draw and critical area concepts. First and second "limits of influence" are also shown. The angle of draw and associated critical area concept are obviously not well defined, being dependent upon the accuracy of the surface survey. In Great Britain, the angle of draw has increased through the years from about 26 to 35°. In the United States, zero and negative angles of draw have been reported. In the authors&apos; opinion, these purely geometrical concepts represent an oversimplification of subsidence phenomena and their use, in the United States at least, should be discouraged. Empirical observations of laboratory models containing layers of earth, sand, clay, and plaster were made by Fayol (cited by Peele) as early as 1885. An outgrowth of his work was the "dome theory," a verbal description of what is assumed to occur in subsiding rock masses. The dome theory has since fallen into disrepute. Theoretical analyses worthy of the name treat a subsiding rock mass as a deformable body. In these analyses, the actual rock mass is replaced by an idealized material that deforms according to a simple stress-strain relationship. The stress equations of equilibrium expressing the Newtonian laws of mechanical action and the geometry of strain furnish additional equations that must be satisfied. A loading criterion-generally understood, and in some cases stated explicitly-completes the theory.

Jan 1, 1969

By J. O. Nelson, C. J. Altstetter

Single crystals of hcp cobalt, 3 mm in diameter and up to 35 cm long, were grown using an electron-beam, zone-melting technique. The martensitic-phase transformation was studied in single-crystalline and polycrystalline specimens by making length-change measurements as a function of temperature under various elastic compressive stresses. Upon thermal cycling, single-crystalline or polycrystalline specimens repeatedly transformed almost entirely on the same variant of close-packed plane provided the maximum temperature did not exceed 600°C. Cycling to 1000°C resulted in transformation on more than one {111} variant. This behavior is termed multivariance. The multivariant transformation occurred very rapidly at an M, temperature 2° to 6°C lower than the M, of a transformation which would result in a single-crystal product. Elastic compressive stresses (up to 253 g per sq mm) tended to lower the A, and raise the M, temperatures, decreasing the width of the temperature vs dilatation hysteresis loop. The transformation habit plane and transformation shear direction of an as-grown single crystal were not grossly affected by elastic compressi?ie stress. This was evidenced by similar dilatations on the temperature us dilatation loops joy specimens with and without compressive stress. A dislocation mechanism is proposed to explain the observed results. IT has been shown that, on heating, cobalt transforms martensitically from the hcp to the fcc phase.&apos; The transformation habit plane is (0001)hcp || (lll)fcc and the transformation shear direction is (1010)hcp || (112)fcc. The transformation involves a shear of 1g°28&apos;, which may be achieved by a shearing of a/6(112) of every two planes with respect to the plane beneath, thus changing the ABABAB stacking of hcp to the ABCABC stacking of fcc. Associated with the phase change is a 0.3 x 10"3 contraction in the habit plane and a 4.2 X 10"3 expansion perpendicular to the habit plane resulting in a 3.6 x X volume increase on heating.&apos; On cooling, an identical volume decrease takes place. The temperature at which the fcc phase begins to form on heating (A,) is reported as 430°C, and the temperature at which the hcp phase begins to form on cooling from an elevated temperature (A&) is reported as 390oC1,3 Consequently, temperature vs dilatation plots have the form of a hysteresis loop. If heating or cooling is reversed during a transformation, a smaller hysteresis loop results. Upon heating, the transformation is always complete; whereas, fcc is often retained at room temperature as a metastable phase entrapped in the polycrystal-line hexagonal matrix.1,4,5 Two obstacles in the theory of the allotropic-phase transformation of cobalt have been: 1) a detailed knowledge of the product nucleus, and 2) a plausible method of propagation of the transformation. Bilby,8 christian, 7 and seeger 8,9 have suggested a "pole mechanism" as a means of propagation of partiai dislocations from plane to plane. A pole dislocation and a Shockley partial come together at a node. The a/6(112) Shockley partial rotates about the pole dislocation effecting the transformation shear. The pole dislocation must have a 2a/3(111) screw component which causes extension of the transformed region by two atomic planes with each full rotation of the Shockley partial. Bollmannl0 suggested, on the other hand, that transformation propagation occurs due to the stress fields of intersecting (111)-type stacking faults. As faults intersect, a stress distribution is set up about their intersection which is in turn reduced by the emergence of another fault on the second nearest plane. This process continues with the final result of a complete phase transformation. In view of the similarities between deformation and transformation in cobalt, the effect of stress on the transformation would, hopefully, yield valuable information concerning nucleation and propagation. In the present work single-crystalline and polycrystalline specimen length changes were measured as a function of temperature at various compressive loads. PROCEDURE Several orientations of single crystals of hcp cobalt in lengths up to 25 cm were grown by electron-beam floating zone melting from 99.95 and 99.999 pct, 3-mm-diam cobalt rod as supplied by Johnson

Jan 1, 1964

By Seymour G. Epstein

Using a modified capillary-reservoir technique, electromigration of dilute solutions of silver in liquid bismuth has been measured with relatively good precision. The effects of experiment duration, temperature. current density, and silver concentration have been investigated. Chemical diffusion coefficients of silver in liquid bismuth were also measured at temperatures ranging from 300°to 600°C. The effective valence of silver in bismuth was calculated as a function of temperature from a comparison of electric mobilities and diffusion coefficients. In an alloy containing 1 wt pct Ag, the electric mobility of silver increased from 1.65 x X sq cm per v-sec at 300°C to 2.38 x 10-4at 600°C; the diffusion coefficient in-creased from 3.0 to 17.5 x 10-5 sq cm per sec over the same temperature range. Calculated values of effective valence decreased from 0.28 at 300°C to 0.10 at 600°c. ALTHOUGH there has been considerable progress in the theoretical treatment of electron-transport properties in liquid metals, the mechanisms of mass-transport phenomena in liquid metals are still not clearly understood. This is especially true for the case of electro migration, alternatively termed elec-trotransport or electrodiffusion, which is mass transport induced by an applied electric field. A thorough knowledge of the mechanisms governing electromigration will considerably aid in understanding the electronic state of an impurity atom in a liquid metal. Electromigration has been long observed and studied in liquid metals and alloys. However, no satisfactory theory to explain the observed effects has been developed. The disparity in the present theoretical treatments, summarized by Verhoeven,1 has been attributed to the difficulty in describing the momentum transfer between electrons and ions and to the lack of precise measurements in liquid metals, especially at elevated temperatures. Prior to the last decade most of the electromigration studies were qualitative, in that only the direction of migration of alloy constituents was determined with any degree of reliability. These results have been summarized by schwarz,2 who was able to measure the electric mobility of several elements in mercury. More recently electromigration in liquid metals has been measured by a variety of techniques, with a varying degree of success. Mangelsdorf3,4 made precise measurements on dilute amalgams at room temperature, using a technique relating changes in composition to changes in alloy resistivity, but was unable to make measurements at elevated temperatures. Using a modification of this technique, Verhoeven and Hucke5 measured electromigration and resistivities in liquid Bi-Sn alloys. However, the resistivity technique is not sensitive to small composition changes and is impractical for very dilute alloys. Verhoeven and Hucke6 also measured electromigration of several solutes in liquid bismuth by adapting the capillary-reservoir method for determining diffusion coefficients in liquids. The reported precision of these measurements was poor, however, primarily due to the large uncertainties in the chemical analyses to determine concentration changes. Belashchenko7 has summarized the recent Russian investigations of electromigration, many of which, however, are of questionable accuracy. The present study was initiated to develop an experimental technique which would be both versatile and sufficiently sensitive to yield precise measurements of electromigration of solutes in dilute metal alloys at elevated temperatures. Using this technique, a comprehensive study of silver in liquid bismuth was made to determine the effects of experimental variables on the apparent electric mobilities. Chemical diffusion coefficients of silver in liquid bismuth were also measured over the same temperature range for comparison with the electromigration data. EXPERIMENTAL TECHNIQUE Electromigration Measurements. Electromigration of silver in liquid bismuth was measured by the capillary-reservoir technique, similar to that used by Verhoeven and Hucke,6 but modified to yield more

Jan 1, 1967

By P. K. Koh

With identical annealing heal treatment the development of major annealed texture component seems to depend primarily upon the degree of cold reduction. Cube texture was evident on annealing- 1/2-, 1,/4- , and 1/8-mil tapes at 760°C, but it dissap-)eared on 927°C annealing of 1/8-mil tape cold reduced 96.9 pct. Some cube texturee remained as tile strongest 927 °C annealed texture component in 1/4- and 1/2-mil tapes cold reduced 93.8 and 87.5 pet, respectively. The switching coefficient increases and the squareness ratio of the hysteresis loop decreases proportionally with increasing cube pole concentration. PREVIOUS studies 1,2 on the 1/8-mil ultra-thin molybdenum permalloy tape established cold rolled and annealed textures and their magnetic performance for switch-core and coincident-current memory applications, The major cold-rolled texture was found to be of {110}<335> which is quite similar to the cold-rolled texture of silver and 70-30 cartridge brass. The major annealed texture components were found to be of {120)-- <001> and {113)<785>. Although the direction for easy magnetization for this type of alloy by the single-crystal technique is not avaliable, knowledge from related studies indicated [Ill] as the easy magnetization direction, similar to that of nickel.&apos; Therefore, a cube orientation, if present in the tape core, would be most detrimental to its magnetic performance.3 In its cold-rolled state the tape had < 111 > directions in the rolling plane 14.5 deg from the rolling direction.&apos; But the coercive force of the tape in such condition will be excessive due to large amounts of internal stresses, and therefore makes its use impossible for memory applications due to long switching time. In lower nickel alloys, suchas 50-50 nickel-iron and 65 pct Ni-Fe sheets, previous investigators4"7 found the presence of cube texture on annealing at 900° to 1000°C. Although no cube texture was found in annealed 1/8-mil tape,"&apos; its presence in some annealed 1,/4-mil tape cores was firmly established a year ago as verified by significant differences in magnetic properties. The present investigation is devoted to the orientation study and related magnetic measurements on three thicknesses of the ultra-thin tape, namely, 1/8 mil, 1/4 mil, and 1/2 mil, cold rolled directly from annealed 4-mil stock in the cold-rolled state as well as after they were annealed at 760°C (1400° F) and 927°C (1700°F). The results obtained might serve to elucidate the development of annealed texture as well as to establish clearly the importance of preferred orientation on the magnetic performance of such memory tape core despite its well-known low magnetic anisotropy exchange energy. EXPERIMENTAL PROCEDURE Samples were taken from one production heat (0.010 wt pct C, 0.004 P. 0.016 S, 0.80 Mn. 0.29 Si. 79.69 Ni. 4.42 Mo. 0.054 Co, 0.002 Ti, 0.12 Al, 0.04 Mg, 14.56 Fe). Annealed 4-mil sheets were cold re-

Jan 1, 1962

By Craig S. Hartley

An approximate expression is obtained for the energy of a closed dislocation loop in equi1ibriu)n with a constant net stress. The result obtained is valid for loops in isotropic or anisotropzc materials provided that they are suJficiently large that the energy per unit length of a segment of the loop can be approximated by that of an infinite straight dislocation tangent to the loop. It is shown that this approximation leads to very close agreement with a more rigorous calculation of the elastic energy of a circular glide loop. The Gibbs-Wulff Form, GWF, of a dislocation is the closed planar loop which has the smallest elastic self-energy of all possible loops having the same Burgers vector and enclosing a fixed area, A.&apos; The energy of such a loop is related to the net resolved shear stress* required to expand the loop and to the stress required to activate a Frank-Read source.223 In the following sectiorls the problem of determining the form of the GWF is discussed and an approximate method for calculating its elastic self-energy is presented. It is demonstrated that the approximations employed lead to no serious errors when applied to a calculation of the elastic energy of a circular glide loop. This method is then used to obtain a closed form expression for the energy of GWFs in isotropic and anisotropic materials. THEORY Burton, Frank, and cabrera4 have proved that the relationship of the equilibrium shape of a two-dimensional array of atoms under the influence of the Gibbs free energy associated with unit length of its boundary, G(O), is that the polar plot of G(0) vs 0 is proportional to the pedal of the GWF.* The angle 0 is measured "The pedal of the polar graph ofG(0) vs0 is the envelope of tangents to the eraph.relative to some crystallographic reference direction. The difficulty in applying this result to a closed dislocation loop arises from the self-interaction of the loop. For a dislocation the energy analogous to G(0) is a function of the total configurati~n.~ Consequently the relation which determines the GWF is an integro-differential equation rather than the simple differen- tial equation which results when G(8) is a function of 0 alone. Mitchell and smialek3 and Brown~ have used the self-stress concept introduced by ~rown&apos; to calculate the shapes of dislocations in equilibrium with an applied stress. In this approach the glide force on an element of the dislocation loop due to the interaction of the element with the rest of the loop is equated to the glide force exerted by the local applied stress. The shape of the loop is then adjusted so that the two forces above are equal at all points on the loop. It is possible to calculate the energies of such loops by noting that, for equilibrium with an applied stress, the energy is equal to pijbiAj (summation convention) where bi is the Burgers vector, p.. is the local net stress tensor, and Ai is a vector directed perpendicular to the plane of thd loop with magnitude equal to the area of the loop. Also Brown&apos; has calculated the energy of a hypothetical polygonal GWF using the above technique and anisotropic elasticity. However, his indicated solution for the energy in the general case of an arbitrary GWF is only slightly less involved than an iterative solution of the integrodifferential equation referred to earlier. In the present work the approximation employed by DeWit and Koehler&apos; is used to calculate the energy of a closed loop in equilibrium with an applied stress. That is, the energy of a loop segment, ds, is approximated by the product of ds and the energy per unit length of an infinite, straight dislocation in a cylinder coaxial with the tangent to the loop at the angular position of the segment. This is known as the "line tension" approximation. The inner cutoff radius of the elastic solution defines the core radius, while the outer cutoff radius is determined by some characteristic dimension of the loop. Actually, both of these radii vary with the edge-screw character of the segment. The effective core radius changes because of the orientation dependence of the Peierls width of a dislocation,8 and the outer radius should be the radial distance from the circumference of the loop to the center of symmetry of the area enclosed by the loop.g However, since the energy varies logarithmically with the ratio of these radii while depending directly on the effective elastic constants, only the effect of the latter is considered. This approximation also neglects the self-interaction of the loop segments. For small loops this will doubtless be extremely important, but for large glide loops produced by plastic deformation the self-interaction is not nearly so important in determining the energy of the loop. This point is illustrated by the following calculation of the energy of a circular loop. Consider a circular loop of radius R which lies in the XI - x, plane of an infinite isotropic continuum and whose Burgers vector makes an angle $ with xs. The first-order solution for the elastic self-energy is:&apos;

Jan 1, 1970

By Warnie Flint

PERSONAL INJURY ACCIDENTS According to statistics compiled by the National Safety Council, US Bureau of Mines, American Medical Association, and other agencies, accidental injuries cause more deaths than all the leading diseases. NO one is immune to an accident. Probably the best way to describe an accident is to say that it is an unexpected happening. The automobile driver is not expecting a terrifying crash, the electrician does not expect to be electrocuted, nor is the coal miner expecting the roof to fall on him. All personal injuries will not result in death. There is a multitude of victims who are living proof of what accidents can mean to an individual-victims who are blind, paralytic, missing arms, legs, etc. In most instances the earning power of these individuals is gone, and they are utterly dependent upon family or welfare. For many years there seemed to be an attitude that prevailed in industrial America that accidents were inevitable, and that so many fatalities and injuries should be expected. This, of course, was utter nonsense. Since the birth of such organizations as The National Safety Council, American Society of Safety Engineers, and the US Bureau of Mines, much progress has been made in reducing accidents. The enactment of compensation laws greatly contributed to the progress that has been made. Does this mean that all accidents can be prevented? Unfortunately, it does not. Human psychology indicates that men will work unsafely or perform unsafe acts for the following reasons : 1) Lack of knowledge or skill. 2) Conflicting motivations, such as: (a) to be more comfortable, (b) to save time or effort, (c) to be accepted by a group. 3) Physical or mental condition. Nearly everyone desires his own safety, but not all individuals are willing to do what they know to do to insure their own safety.

Jan 1, 1981

By L. L. Swift

AT the present time there are four base metals being used for automotive bearing alloys. Of course there are numerous variations in the amounts of alloying elements added to each base metal and nearly all of these alloys have the conventional, if not classical, duplex structure; that is, they are composed of a hard constituent embedded in a soft matrix. The well-known theory is that the former will wear well, while the latter will be plastic enough to allow the bearing to be broken in and conform to the contours of the shaft. The requirements of the modern bearing have been most aptly described by W. M. Corse: In order to meet the engineering demands of today a good bearing metal must be able to carry the weight of the shaft and stand up under steady or suddenly applied loads, or even blows in some types of service. A certain amount of plasticity is desired to compensate for minute irregularities in the shaft or bearing surface, and to permit yielding, thereby avoiding dangerous stresses in bearing and shaft and preventing overheating and rapid wear of parts. Less plasticity is required in a bearing metal if the surfaces of bearings and journals are machined accurately, aligned, and kept in alignment. It is desirable, of course, that a bearing metal have a low coefficient of friction. Under most operating conditions the friction depends on the unit pressure of the bearing, the speed, the temperature, and the properties of the lubricant. A good bearing metal must have a low rate of wear to reduce the necessity for frequent replacements, and adjustment of the bearings. It must wear more rapidly, however, than the journal or shaft running on it, because replacement of the journal or shaft is more difficult and costly than replacement of the hearing., The hardness of, the bearing alloy is a property closely related to several of the foregoing. With a duplex microstructure, the measurement of hardness with any of the usual commercial devices means little. The Bierbaum method of measuring the hardness of the individual constituents was developed to, fill this need. MICROCHARACTER The Bierbaum microcharacter2.3 measures the scratch-hardness of a solid by pulling a weighted diamond point over the surface. The diamond point is ground. so that it is the corner of a cube, and mounted

Jan 1, 1938

By K. T. Aust

It is proposed that the intergranular corrosion of austenitic stainless steels is associated with the presence of continuous grain houndary paths of either second phase, or solute segregate resulting from solute-vacancy interactions. Experimental observations of structural changes and crrosion behavior of different types of austenitic stainless steel provide support for this poposal. On the basis of this model, it is shown that the intergranular -corrosion susceptibility of austenitic stainless steels in nitric-dic hromate solution may be substantially reduced either by suitable heat treatments or by impurity control. AUSTENITIC stainless steels, such as Type 304, generally have excellent corrosion resistant properties when properly solution heat-treated and used at temperatures where carbide precipitation is slow. However, several corrosion environments have been found which produce intergranular corrosion of solu-tion-treated stainless steels, that is, those steels with no detectable carbide precipitation.&apos;&apos;2 Of the various corrosion environments, the most widely used test solution has been the boiling nitric-dichromate solution. In these acid solutions, stainless steels have been found to be susceptible to intergranular attack despite the addition of carbide-forming elements such as titanium or columbium, or despite lowering of the carbon content or use of high-temperature solution treatments. Studies of the electrochemical mechanism of corrosion attack have been made by several worke1s3&apos;4 who found that oxidizing ions such as crt6 depolarize the cathodic reactions and consequently raise the open-circuit potential of stainless steel immersed in nitric acids. As a result of this, the anodic reaction is accelerated. The reason for the localization of anodic activity at the grain boundaries, and resulting intergranular corrosion, has not been conclusively determined. Several workers, e.g., Streicher,3 and Coriou et al.,4 have suggested that the strain energy associated with grain boundaries provides the driving force for the accelerated intergranular corrosion. This argument would predict that alloys of high purity would still be susceptible to intergranular attack. However, work by chaudron5 and by ArmijO,6 has shown that high-purity alloys are immune to attack, in disagreement with this argument. An alternative suggestion is that chemical concentration differences exist between grains and grain boundaries, that is, impurity segregation at boundaries, and that these chemical differences provide the driving force for localized attack. It is this impurity segregation which can lead to accelerated dissolution of grain boundaries when the alloy is exposed to a suitable corrodant. This mechanism would predict the immunity of high-purity alloys to inter-granular attack, which is in agreement with experi-mental observations. In the present paper, some recent studies on inter-granular corrosion of austenitic stainless steels which were conducted by coworkers and myself will be re-tibility A simple model will be described in which it is proposed that the intergranular corrosion of aus-tenitic stainless steel is associated with the presence of continuous grain boundary paths of either second phase or solute-segregated regions.* On the basis of this model, it is suggested that the intergranular corrosion rate can be markedly reduced by the formation of a discontinuous second phase at the grain boundaries if the discontinuous second phase incorporates the major part of the segregating solute, drained from the grain boundary region. Results are presented of corrosion tests and electron microscopic studies of different types of austenitic stainless steel after various heat treatments which provide experimental support for this model. Finally, a solute clustering mechanism, based on a solute-vacancy interaction, is shown to be consistent with the results obtained for inter-granular corrosion of solution-treated austenitic stainless steels. EXPERIMENTAL Corrosion tests using weight loss measurements were made on sheet specimens, which were lightly electropolished, washed, and immersed in boiling (115°C) 5 N HN03 containing 4 g crt+6 per liter added as potassium dichromate. Studies in which the inter-granular penetration depth was measured both by electrical resistance and metallographic methods have shown an empirical correlation between the rate of intergranular penetration and the weight loss per unit time for identically treated specimens of stainless steel." As a result, although all the corrosion data reported here are in terms of simple weight loss measurements, these data are considered to reflect primarily the rate of intergranular dissolution. Fig. 1 shows a typical result of intergranular attack of a solution-treated Type 304 stainless steel after 4 hr in a boiling nitric-dichromate solution. The wide grain boundary grooving at the surface, and the attack at incoherent twin boundaries, are evident; very little corrosion attack is seen at the coherent twin boundaries. INTERGRANULAR CORROSION MODEL

Jan 1, 1970

By C. H. Stewart, R. A. Fagin

A two-dimensional, three-phasereservoir simulator was programmed for a large memory digital computer. It was designed to provide a practical solution to describing the complex physical relation between the natural forces and the physical properties of a heterogeneous reservoir when subjected to a specific set of conditions. A reservoir study is briefly described to illustrate application of the model. A full volumetric account of three phases (oil, gas and water) is performed simultaneously throughout an integration net representing the reservoir. Absence of one or two of the phases is treated as a special case of the more general situation. Expansion (or contraction) of all phases, including rock expansion, is performed so that the pressure calculation is the general unsteady-state case. To account for the large variations of subsurface elevation encountered in some reseruoirs, and to allow for segregation of the various phases, a gravity head term is included in the basic drive potential. Appropriate fluid and rock properties are used in polynominal surface form (functions of pressure and/or depth) or they can be entered as space variables at each position of the integration net. An unsteady-state water influx calculation, based on the method of van Everdingen and Hurst, l was connected to the boundary of the matrix to simulate aquifers of various sizes. In addition to reservoir calculations, three-phase fluid flow from the producing depth to the wellhead, including provisions for gas lift, was incorporated in the simulator. A workover routine was also built which can automatically switch to a different set of production relations when a gas-oil ratio or water fraction reaches a limit; or it can shut-in the well if prescribed. INTRODUCTION This paper describes a reservoir engineering mathematical simulator used to represent the complex interaction of natural forces and physical properties of a reservoir during natural depletion or with various injection schemes. The simulator, which was programmed for a large memory digital computer, is a two-dimensional calculation which handles three mobile fluid phases simultaneously (oil, gas and water). Basic requisites for the method are individual well production and pressure data, hydrocarbon fluid properties, geological data (producing depth and net sand), capillary pressure data, relative permeability data and permeability and porosity information. Matching the past performance of a combination drive reservoir often has yielded information concerning continuity and the validity of basic data. Detailed predictions of future performance can be made for continuation of current depletion methods (natural depletion) as well as for various types of recovery by gas or water injection. Combination injection cases and pattern studies can also be performed. Workover programs, gas lift and different types of artificial lift programs have been investigated using a technique similar to that described by Kern and Nicholson2 except that conditions of pressure and saturation at the block within which the well is located are used rather than average reservoir conditions. Drilling additional wells to optimize profit was explored, both as to number and location, by placing wells at different spots within the reservoir matrix. Special depletion processes can be examined, such as upstructure drainage and lateral (or strike) waterfloods in thin oil columns. In one case the mathematics of the simulator were modified to calculate the displacement in the vertical plane rather than in the horizontal plane. In this manner specific reservoir problems can be studied, such as coning of gas and/or water around production points, fingering along permeable stringers or, more generally, frontal advances in a heterogeneous section.

Jan 1, 1967

By G. Bruggeman, K. G. Kreider

Grain boundary dij]usion coefficienls were measured in tungsten between 1400° and 2200° C and can be expressed by the equation sq cm per sec This activation energy confirms some eavlier estimates made .from tungsten sintering experiments. Grain boundary diffusion was found to occur in sub-bozrndavies having -misorientations of less than 10 deg. The actiuation energy for this subboundavy diffusion is equal to that for dijjusion in incoherent grain boundaries with in the limits of error. This is shown to be consistent with the dislocation model of Low-angle boundaries wheve diffusion occlcvs along- the dislocation &apos;YPipes" comprising -tile boundary. RECENT investigations of the sintering of tungsten powders all report activation energies which are considerably less than the activation energy for tungsten volume diffusion. Kothari&apos; reports a value of 100 * 5 kcal per mole, Hayden and Brophy&apos; obtained 90 kcal per mole, and Vasilos and smith3 found 110.7 kcal per mole from their sintering studies. Since most determinations of the activation energy for volume diffu-sion4-&apos; fall between 120 and 160 kcal per mole (the true value seems most likely to be nearer 150 kcal per mole), the conclusion is drawn that the mass transport leading to densification during sintering is accomplished by grain boundary diffusion. This interpretation is consistent with various diffusion models of the sintering process. 10-12 Vasilos and Smith calculate diffusion coefficients from their data which fit the equation D * 1.36 x 10* exp(-llO,700/HD However, no direct measurements of tungsten grain boundary diffusion have been made. Furthermore, considerable disagreement exists between the directly measured values of tungsten volume diffusion.&apos;-&apos; In order to corroborate the inferred results of the sintering experiments concerning grain boundary diffusion and to provide accurate diffusion data essential to the analysis of the kinetics of creep, oxidation, precipitation, and so forth, the present work was undertaken to measure self-diffusion in single-crystal and polycrystalline tungsten between 1400" and 2200°C. It is within this temperature range that tungsten sintering is done, the re crystallization of tungsten occurs, and the widest application of tungsten as a high-temperature material will probably be made. EXPERIMENTAL PROCEDURE Radioactive WlE5 was produced by irradiating tungstic acid in a neutron flux of 1.2 x 1012 neutrons per sq cm per sec for 36 hr. A 2-week waiting period was allowed for the decay of w"~ also produced by the irradiation. (w"~ has a half-life of 24 hr.) The half-life of the remaining isotope was determined to be 75 days confirming the presence of w lE5 and the absence of any undesired radionuclide. Specimens 4 in. in diam and $ in. thick were cut from polycrystalline swaged tungsten rods (recrystal-lized) and from Linde single-crystal rods. Chemical analyses of these materials appear in Table I. Actually upon closer examination, the single-crystal specimens were found to consist of several subgrains separated primarily by tilt boundaries in which the misor-ientation ranged from 3 to 10 deg. Thus, it was possible to measure boundary diffusion coefficients in these low-angle subboundaries as well as in the incoherent boundaries of the polycrystalline specimens. The two faces of each specimen were ground flat and parallel within 0.0001 in. The radioactive tungstic acid was dissolved in concentrated ammonium hydroxide, placed on the ground flat of the specimen, and evaporated to dryness. The oxide was then reduced in hydrogen at 1000°C resulting in a layer of wlE5 approximately 1 p thick. The diffusion anneals were performed in vacuum in a tantalum resistance furnace. Time at temperature ranged from 10 hr at 1400°C to 2 hr at 2200°C. The penetration profile was determined by measuring the residual activity after successive removal of surface layers by grinding on metallographic polishing paper. Extreme care was exercised to insure that sections were always taken normal to the diffusion direction; this was verified repeatedly by checking that front and back surfaces of the specimen remained parallel. The activity was measured with an end-window Geiger-Mueller counter. The sides and edges of the specimen were well-shielded to eliminate possible effects due to surface diffusion. The weight of the

Jan 1, 1968

By E. H. Jr. Dix

OF all the alloying elements used in commercial aluminum alloys, copper stands out as by far the most important, and it is perhaps for this reason that the constitution of the aluminum-copper system has received the attention of a number of experimenters covering a period of approximately 20 years. It would be expected that during this time the equilibrium relations had been thoroughly and exactly worked out. In a general way this is true, but there is a surprising lack of agreement in the details of the high aluminum end of the diagram, particularly in regard to the solid solubility of copper in aluminum, which has been given variously as 2 per cent. to 5 per cent. at the eutectic temperature. The importance of this is much greater than might at first appear to one unfamiliar with modern commercial aluminum alloys. This is true because, with one exception, the susceptibility of the strong alloys to heat treatment depends, in part at least, upon the solid solubility relations of copper in aluminum. In 1919, Merica, Waltenberg, and Freeman1 published the first detailed information on these solubility relations. They found that the solubility of copper decreases with falling temperature from about 4 per cent. at 5.25° C. to about 1 per cent. at 300° C. and is apparently still diminishing at lower temperatures. In 1921 there was published a brief account of the results obtained in the National Physical Laboratory, Teddington, England.2 This laboratory, however, reported that 5 per cent. of copper is soluble in aluminum at 540° C., and that this amount decreases to about 3 per cent. at 20° C.

Jan 2, 1926