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By Frank Foote, Eric J. Jette

The unusual physical, electrical and magnetic properties of the iron-nickel alloys has given rise to a voluminous literature. This work will be reviewed critically in "The Alloys of Iron and Nickel," a monograph of the Alloys of Iron Research Series, soon to be published. In what follows we shall therefore confine ourselves to those of the earlier investigations that involved the use of X-ray crystal-structure methods. The earliest X-ray work on the iron-nickel system was by Miss Andrewsl. Using the powder method of X-ray analysis purely as a means of identifying the phases present, she located a region between 20 and 30 weight per cent nickel in which body-centered and face-centered phases coexisted. No lattice constants nor details of heat-treatment were reported. Bain2 also reported some qualitative observations. McKeehan3 made a systematic investigation over the whole of the system, giving many of his alloys four and some five different heat-treatments. In alloys furnace-cooled from 900' to 950' C. he found two coexisting phases between 0.15 and 30 per cent nickel. The precision of the lattice-constant measurements was low in comparison with what can be obtained today. Even for alloys of the same heat-treatment, differences in the constants were often between two and ten parts per thousand. In regions where no change of lattice constant with heat-treatment should occur, differences of the same order of magnitude were found. Since the maximum change in the lattice constant of nickel with change of composition is only about 2 per cent of the constant for pure nickel, these variations in the constants for a given alloy cause the points to "scatter" badly about any curve that may be drawn to represent them and it is difficult to interpret such results. In spite of this, McKeehan shows that the lattice constant of nickel increased as the iron content increased. His results for the alpha-iron phase are less conclusive. Osawa4 also investigated the entire system. For alloys slowly cooled from 1150' C. and then filed into samples for X-ray analysis, he found

Jan 1, 1936

By Daniel N. Beshers, Ralph H. Condit

An expression for the diffusion coefficient of inlerstitial atoms in the bcc lattice is derived which takes account of jumps between tetrahedral and octahedral interstices. The results are applied to the case of carbon diffusion in iron to find values for jump frequencies of the types, octahedral-tetrahedral, tetra-hedral-tetrahedral, and tetrahedral-octahedral. ThERE has been renewed discussion1-5 concerning the mechanism of diffusion of interstitial atoms in the bcc lattice. This lattice has both octahedral and tetrahedral interstices, and it has been pointed out that the interstitial atoms may make jumps of the octahedral-octahedral type, hereafter called o-o, octahedral-tetrahedral, o-t, and tetrahedral-tetrahedral, t-t. Doubt has been cast on the applicability of snoek's8 model for internal friction to some interstitial migrations in bcc lattices wherein he proposed 0-0 jumps as the principal mechanism of migration. Also, the anomalous excess diffusion of carbon in iron at high temperatures4 has been ascribed to t-t jumps,2,3 even though the sites normally occupied are octahedral. In this paper an expression is derived for the diffusion coefficient, taking account of the three types of jump mentioned. The relationship of the coefficient to the corresponding internal friction relaxation time is found for the limiting case corresponding to Snoek's model. These results are applied to the case of carbon in iron. In Fig. 1, the structure is shown with the locations of the interstices. Each o site has four t site neighbors coplanar with it, and each t site lies halfway between two o sites. There are four t site first neighbors of a t site lying at the vertices of a tetrahedron. Let the average fraction of atoms occupying o sites and t sites be No and Nt, respectively. Since there are six o and twelve t interstices per unit cell having a lattice parameter, a, the concentration of interstitial atoms will It will be assumed that three types of jumps may be distinguished, t — t, t — o, o — t,for which the jump

Jan 1, 1968

By John A. Church

When, in 1879,I examined the mines of the Tombstone Mill and Mining Company, at Tombstone, Arizona, I found a bed of tailings containing 12,000 tons, which had a value of 9 to 12 ounces of silver per ton and some gold. The ore had been amalgamated in pans, in which each charge had been ground for four hours, having been pre viously stamped through rough-punched screens, which gave a pro duct varying from 1-100th to 1-20th of an inch, according to the state of wear of the screen. It was certain that a large proportion of the tailings must be in fine slimes, and the question of recovering their value was difficult. Even now the concentration of slimes is . an unwelcome task, and at that day very little was known about it. Nevertheless, after considering the results of a test by repanning the tailings, I advised the company to concentrate and smelt, although they had to face the difficulty of making a smelting-product from slimes containing only 3 per cent. of lead. Limestone was abundant enough, but no iron suitable for flux was to be had for hundreds of miles. One of the company's claims con tained an argeutiferous manganese-ore, which gave but poor results by amalgamation. This was one reason for recommending smelt ing ; for if manganese would play the part of a precipitant, as iron does, the company could smelt by combining two of its silver ores, without other flux than the small amount of lime that might be needed. At that time no smelter had ventured to trust manga nese as a precipitant, though large quantities of this ore containing silver were bought and used by custom-smelters, who looked upon the manganese solely as a basic flux for silica. I believe that no other furnace has been obliged to trust this metal, and that the man ganese practice of Tombstone remains unique among the records of smelting lead-ores in the shaft-furnace. The bright side of the problem was given by the fact that the mines were shallow and that the enterprise would at least begin with oxidized ores. The tailings contained about 85 per cent. of silica,

Jan 1, 1895

By Derek J. Fray, John Chipman

THE solubility of graphite in y-iron has been determined by several workers'12 with reasonable agreement. With the increasing use of more complex steels, it is necessary to understand more fully the thermodynamics of the austenite phase. The activity of carbon in a number of alloys is known but the maximum solu- bility of graphite has only been measured by Sohnchen and piwowarsky3 for Fe-Ni and Fe-Si alloys. Recently, Chipman and Brush reviewed the published data on the activity of carbon in binary and ternary austenite and also obtained expressions for calculating the solubility of graphite in Fe-Ni, Fe-Co, and Fe-Si alloys. On comparing the theoretically derived solubilities with the limited results of Sahnchen and Piwowarsky, it was found that the agreement for Fe-C-Si was excellent but there was considerable discrepancy for Fe-C-Ni and no data for Fe-C-Co. It was therefore decided to measure the solubility of graphite in a series of Fe-Ni and Fe-Co alloys. The alloy samples were made up by induction melting a high-purity master alloy under an inert atmosphere in an alumina crucible and drawing the molten metal into four-bore alumina tubes. Using this technique, it was possible to form alloy rods approximately 2 in. long and 1/18 in. in diam. Sixteen lengths of fine rod could be made without solidifying the master alloy. These were then allowed to cool under the inert atmosphere before being sectioned. The samples were packed in a graphite crucible with spectroscopic graphite powder, together with a piece of pure iron foil. Dry hydrogen, which had been saturated with isopropyl alcohol at room temperature, was passed over the crucible at 1000°C for 72 hr. At the end of the 72 hr argon displaced hydrogen in the reaction tube and the crucible was quickly pushed to the water-cooled end. The samples were thoroughly cleaned of the adhering graphite and analyzed. The pure iron samples always contained 1.5 0.02 pct C, which compares favorably with the data of smith2 and

Jan 1, 1970

By R. M. Brick, M. A. Williamson

Certain features of the response of copper and brass to deformation and recrystallization remain obscure. The textures obtained on rolled sheet are listed by Schmid and Boas1 as: No adequate explanation has been advanced for the presence of the secondary deformation texture of copper and its absence in brass or for the origin of the cubic recrystallization texture of copper.2 A recent publication3 attempted to rationalize the above empirically described annealing texture of brass on the basis of retention of the (110) [112] rolling orientation plus twinning about the central octahedral poles of the usual secondary (110) [115] orientation. The difierence in the textures of annealed copper as compared to 70-30 brass is also shown by the difference in the position of ears for drawn copper, at o° and go", as compared with drawn brasses, at 45o, for all compositions between oo-10 and 70-30.4 Data on indi- vidual crystals are as yet too few to permit of an analysis of these textures comparable to that of mild steel as made by Barrett and Levenson.5 Experimental Methods The materials studied included copper specimens cut from the central, equiaxed crystal portion of a tough-pitch wirebar; brass made from this copper and high-purity (99.99 per cent) zinc including alloys of 7 per cent, 15 per cent, 24 per cent, 29 per cent and 36 per cent Zn and large single crystals of 70-30 bras. Sections 1/4 in. thick of the cast polycrystalline copper and brasses were reduced 40 per cent by rolling, recrystallized to a common grain size of 0.045 mm. and then rolled directly to foil 0.002 in. thick. Hardness readings employing both the Vickers and Rockwell machines were taken at intervals during the reduction. For comparison, similar specimens were cross-rolled—i.e., turned through 90° for each pass—and comparable hardness data were secured. Finally sections from the single crystals of brass were cut to obtain the following initial orientations; these sections were rolled, hardness data secured and a complete micrographic record of structural changes obtained.

Jan 1, 1941

By R. M. Brick, M. A. Williamson

Certain features of the response of copper and brass to deformation and recrystallization remain obscure. The textures obtained on rolled sheet are listed by Schmid and Boas1 as: No adequate explanation has been advanced for the presence of the secondary deformation texture of copper and its absence in brass or for the origin of the cubic recrystallization texture of copper.2 A recent publication3 attempted to rationalize the above empirically described annealing texture of brass on the basis of retention of the (110) [112] rolling orientation plus twinning about the central octahedral poles of the usual secondary (110) [115] orientation. The difierence in the textures of annealed copper as compared to 70-30 brass is also shown by the difference in the position of ears for drawn copper, at o° and go", as compared with drawn brasses, at 45o, for all compositions between oo-10 and 70-30.4 Data on indi- vidual crystals are as yet too few to permit of an analysis of these textures comparable to that of mild steel as made by Barrett and Levenson.5 Experimental Methods The materials studied included copper specimens cut from the central, equiaxed crystal portion of a tough-pitch wirebar; brass made from this copper and high-purity (99.99 per cent) zinc including alloys of 7 per cent, 15 per cent, 24 per cent, 29 per cent and 36 per cent Zn and large single crystals of 70-30 bras. Sections 1/4 in. thick of the cast polycrystalline copper and brasses were reduced 40 per cent by rolling, recrystallized to a common grain size of 0.045 mm. and then rolled directly to foil 0.002 in. thick. Hardness readings employing both the Vickers and Rockwell machines were taken at intervals during the reduction. For comparison, similar specimens were cross-rolled—i.e., turned through 90° for each pass—and comparable hardness data were secured. Finally sections from the single crystals of brass were cut to obtain the following initial orientations; these sections were rolled, hardness data secured and a complete micrographic record of structural changes obtained.

Jan 1, 1941

By Dr. O’Neil Thomas J., Donald W. Gentry

Money is like an arm or leg-use it or lose it." -Henry Ford INTRODUCTION If it were not for the existence of interest, the analysis of investment opportunities would be greatly simplified. In the absence of interest, investors would be indifferent as to when cash outlays are made or cash benefits are received. It would, in fact, be irrelevant whether the outlays preceded or followed inflows as long as both amounts are known with certainty. Of course, it does make a considerable difference whether, for example, a firm receives $1 million now or five years from now. The reason is that money does, indeed, have a value which is a function of time. Interest is how this time value is measured. Interest is generally defined as money paid for the use of borrowed money. In other words, interest is the rental charge for using an asset over some specific time period. The rate of interest is the ratio of the interest chargeable at the end of a specific period of time to the money owed, or borrowed, at the beginning of that period. In order to understand why interest exists, it is necessary to take the lender's viewpoint. The lender can justify charging interest for several reasons: 1) Risk: The lender is faced with the possibility that the borrower will be unable to repay the loan. 2) Inflation: Money repaid in the future will be in units of lower value due to inflation. 3) Transactions Cost: There will be expense incurred in preparing the loan agreement, recording payments, collecting the loan, and other administrative tasks. 4) Opportunity Cost: By committing limited funds to one borrower, a lender is unable to take advantage of other available opportunities. 5) Postponement of Pleasure: By lending money, an individual (or organization) is postponing the pleasure which that money could purchase. Each of these is a valid reason for a lender demanding interest from a borrower. The level of interest is, like the price of other assets, determined by supply and demand. Nonetheless, from time to time various analysts have taken a then current average interest rate and broken it down into the components described previously.

Jan 1, 1984

By L. H. Cadoff, L. M. Adelsberg

The layer growth method has been used to investigate the reaction kinetics of liquid titanium and hafnium with carbon and the [liq] - [liq + TiC] and [liq] - [liq + HfC] phase boundaries at temperatures above 1800°C. The equipment and experimental procedures used in this investigation are basically identical to those described in an earlier paper' on the Zr-C reaction. Temperature control, however, was improved significantly by connecting a Latronics Colo-Ratio automatic pyrometer and a controller to the power source. The subsequent temperature variations were ±10°C; previously ±20°C was obtained using manual controls. The absolute accuracy of the pyrometer, however, must be considered to be only ±40°C.* The spectrographic analyses of the materials used in this study are listed in Table I. The isothermal reactions of titanium (1800° to 2700°C) and hafnium (2300" to 3000°C) with carbon (graphite crucibles) resulted in the formation of carbon-saturated liquid metal and layers of Tic and HfC, respectively. The thicknesses of the carbide layers, determined from metallographic measurements at 100 times, as a function of carburization time and temperature are given in Figs. 1 and 2. At each temperature, parabolic growth behavior for these reactions was observed and could be expressed as x2 =Kpt, where X is scale thickness (corrected for heating and coolingL), Kp the parabolic growth constant, and t the isothermal carburization time. Values of Kp as a function of temperature for the carbides are shown in Fig. 3 and listed in Table 11. The growth constants are expressible as: kpTiC = 0.2 exp(-61,800/RT) sq cm per sec for Tic and Kp HfC = 2.62 exp(-95,300/RT) sq cm per sec for HfC. The liquidus phase boundaries were determined from metal samples treated in graphite crucibles for different times ranging from 4 to 100 min at each of the temperatures indicated in Table 11. Metallographic examination revealed that the carbide precipitates were distributed uniformly throughout the frozen metal matrices. This is attributed to the rapid cooling rates (800°C per min) and the small difference in density between the precipitated carbide and the liquid metal.

Jan 1, 1968

By Robert Franke

In view of the prominence which the conical mill has attained in the fine-crushing field within the few years since its introduction, the following comparison with its more mature forerunner, the Chilean mill, based on extensive tests, is submitted in the interest of the milling profession. Soon after designing the concentrating plant of the Miami Copper Co. in 1909, the Hardinge conical mill made its appearance in the milling forum. Its possibility as a suitable crushing device for the plant was well recognized, but in view of the lack of commercial demonstration, at the time, as to capacity, efficiency for desired product, and the still more uncertain factors of cost of maintenance and power consumption, it was deemed that the immediate adoption of this machine throughout the plant would be a hazardous undertaking. For these reasons it was decided to equip the majority of the immediately required units of the plant with Chilean mills, the fine-crushing proficiencies of which were better known, and one section with Hardinge mills, to serve as a test unit for the guidance of future installations and replacements. Thereby, after 1.5 years' operation with both types of mills, a thorough test as to metallurgical efficiency and cost economy has been obtained. The conical mill used in these tests is the 8-ft. Hardinge pebble mill, having a cylinder 22 in. in length. The cylindrical portion of this mill is lined with cast-iron liner plates, and the conical extensions with silex bricks bound together by cement. Each liner plate carries a projecting lifter, the function of which is to increase the height of drop of the lifted material. Danish No. 5 pebbles, obtained from the coast deposits of Denmark, are used for the grinding charge. The Chilean mill used is a fast-running, 3-roller, 6-ft. Saturn mill, with screens of 0.037-in. opening. The feed to these mills is the oversize of Callow screens having 0.029-in. openings, which follow rolls crushing to 0.5 in. For the ore of this mine, a moderately hard but very fissile schist,

Jan 1, 1914

By Harold H. Goe, Louis V. Bender

The recovery of arsenic was started at the Washoe Reduction Works (later called the Anaconda Reduction Works) in 1904, when an arsenic plant was constructed adjacent to the lower end of the 60-ft. main flue.' This plant originally consisted of a Brunton roasting furnace for treatment of flue dust and a small reverberatory furnace for treating the crude arsenic produced in the roasting operations, together with the necessary kitchens for condensation of the fumes and grinding and barreling apparatus for preparing the refined white arsenic for market. The Brunton furnace was fired with wood. It was 14 ft. 6 in. in diameter with two outside fireboxes. The hearth revolved upon a central shaft. The charge was fed through a dust-tight hopper on to the center of the hearth and slowly moved to the outer edge of three rows of stationary rabbles fastened in the roof of the furnace. There was a 3-ft. space between the hearth and roof. A crude arsenic was condensed from this furnace. The hot flame from the fireboxes passed directly over the charge, vaporizing the As203 that was carried through brick flues to the condensing chamber. This chamber was 8 ft. high, 16 ft. wide and 240 ft. long, divided into small kitchens by partitions spaced every 7 ft. It was connected with the main flue system to provide draft and to receive any losses from the chamber. The small kitchens were connected by openings in such a way that the fumes took a zigzag course, causing them to come in contact with the cold walls and ceiling and condense the arsenic. There was an opening from the outside into each kitchen, for the removal of the deposited arsenic, which was closed by a wooden door. The refining furnace was a small coke-fired reverberatory having a hearth 10 by 20 ft. in dimensions. It had three hoppers through which the crude charge was introduced, and one firebox placed at one end. The hot gas from the burning coke passed over the charge, volatilizing the arsenic and carrying it to the kitchens.

Jan 1, 1934

By K. G. Davis, P. Fryzuk

VALUES for the equilibrium distribution coefficient, ko, are required for solidification studies. The procedure generally adopted1-3 is to progressively solidify alloy rods over a range of growth rates, under conditions where a high degree of convective mixing is present in the melt. The measured effective distribution coefficients are plotted as a function of growth rate, and the extrapolated value at zero growth rate is taken to be the equilibrium ko. The method is limited by the experimental difficulty in obtaining steady growth rates less than approximately 10-4 cm per sec. Extrapolation from rates greater than this can lead to inaccuracy. In the present investigation, an alternative method for determining ko, previously used by the authors for the Ag-Sn system,' was applied to alloy of thallium in tin. Specimens were grown under conditions where convective mixing was absent, and experimental concentration-distance curves in the region of the initial transient were compared with curves calculated for trial values of ko. The ko which gave the best fit was taken as the correct value. To obtain the calculated curves, a value for the diffusion constant in the liquid near to the melting point was needed. This was determined by the capillary-reservoir method. Diffusion Constants. Details of the experimental procedure used by the authors in the capillary-reservoir technique have been described in previous papers,5'6 the only variation being in the use of Tl204, a ß emitter, as tracer, in contrast to previous work where ? emitters were used. The activity of a ß-emitting sample, as measured in a Geiger counter, is proportional to the surface area. To measure the concentration of thallium along the capillary after diffusion had taken place, the solidified capillary (1 mm diam) was cut into 2.5-mm lengths and each length compressed between parallel steel plates to form a disc approximately 5 mm in diam. The discs were placed in a flat-bottomed dish, covered by a thin lead shield with a central aperture, and counted in a 0 counter with fixed geometry. Each disc was etched lightly in a dilute solution of nitric and hydrochloric acids a short time before counting, to eliminate sur-

Jan 1, 1968

By GEORGE D. RAMSAY

ABOUT three miles west of Fontana San Bernardino County, California, and fifty miles east of Los Angeles, the Kaiser Co., Inc., has built an integrated steel plant. By integrated, I mean that from its wholly owned iron ore and coal supply, the Kaiser Co. is producing in its own mills iron and steel products. Pig iron to meet the West Coast needs has been produced at Fontana since Jan. 1, 1943; steel ingots were first poured there May 14, 1943; and steel plate for ships was first rolled Aug. 15, just sixteen months after ground was broken. Briefly, the plant consists of: (I) Two batteries of by-product coke ovens, totalling ninety ovens, carbonizing about 1740 tons of coal per day at capacity; with by-product facilities for the production of tar, ammonia, and ammonium suIphate, light oil distillates, and tar distillates. (2) One blast furnace producing at

Jan 1, 1944

By Clyde E. Williams

MORE has been said about the iron and steel situation on the Pacific Coast than has been done .about it; but perhaps as much has been done as conditions have warranted. The production of finished steel in an amount sufficient to take care of the local demand for certain sizes and shapes is an established industry on the .coast. The amount .and the variety of products, so made, changes with the demand or them which is largely dependent upon the growth in population. An increasing demand will not always increase the quantity of steel produced locally because the cost of production may rise so -high as to let in steel from the outside. The reason for this is that all of the steel made in the West comes from steel scrap, the supply of which is .limited. From the standpoint of the metallurgist, it would. be desirable to subititute pig iron for some of ' the steel scrap, but this cannot be done profitably because the pig iron now available is too expensive. In other words, the large future demand for steel and pig iron on the Pacific Coast must be supplied by reduction of ores in the West, unless we are to be content with paying high transportation costs for material produced elsewhere. ."

Jan 1, 1924

By W. Rostoker

IN the course of the development of the phase equilibrium diagram for the system Zr-Cr,' the structure of an as-cast allov having the composition ZrCr2 was analyzed and established to be isomorphous with MgZn2 (C14, hexagonal lattice, 12 atoms per unit cell). In a recent paper on the same system, Hayes, Roberson, and Davies' report for the ZrCr2 phase an isomorphy with MgCu2 (C15, cubic lattice, 24 atoms per unit cell). It appeared that this conflict might be resolved by assuming a high and low temperature modification for ZrCr2. That this was the case with the phase TiCr2 has recently been demonstrated by Levinger." Specimens of ZrCr2 annealed at 1200°, 1100°, 994", 900°, 834", 800°, and 700°C, respectively, and subsequently quenched were examined by X-ray diffraction analysis. It was successfully demonstrated that a transition from the MgZn, structure at lower temperatures to the MgCu, structure did occur at some temperature between 900" and 994°C. Table I lists the observed structures at the various annealing temperatures. In Table II, a summary of line spacings and intensities is given for each of the allotropic modifications. The first six lines of the MgCu2 structures have been located in the table to illustrate the close similarity between the patterns. Lattice parameters of the two modifications were calculated by a least squares solution of equations for interplanar spacings for a series of high angle lines. The results are as follows: MgZn2 type - c = 8.262 kX, A = 5.079 kX. MgCu2 type — a = 7.195 kX. It is interesting to note that TiCr2 behaves in reverse fashion yn that the MgCu, structure is the low temperature modification and the MgZn2 structure is the high temperature modification. References lR. F. Domagala, D. J. McPherson, and M. Hansen: This issue p. 279. 'E. T. Hayes, A. H. Roberson, M. H. Davies: Trans. AIME (1952) 194, p. 304; Journal of Metals (March 1952). 3B. W. Levinger: Trans. AIME (1953) 197, pp. 195-196; Journal of Metals (February 1953).

Jan 1, 1954

By R. M. Brick, M. A. Williamson

CERTAIN features of the response of copper and brass to deformation and recrystallization remain obscure. The textures obtained on rolled sheet are listed by Schmid and Boas1 as: No adequate explanation has been advanced for the presence of the secondary deformation texture of copper and its absence in brass or for the origin of the cubic recrystallization texture of copper.2 A recent publication3 attempted to rationalize the above empirically described annealing texture of brass on the basis of retention of the (110) [112] rolling orientation plus twinning about the central octahedral poles of the usual secondary (110) [115] orientation. The difference in the textures of annealed copper as compared to 70-30 brass is also shown by the difference in the position of ears for drawn copper, at o° and 90°, as compared with drawn brasses, at 45°, for all compositions between 90-10 and 70-30.4 Data on individual crystals are as yet too few to permit of an analysis of these textures comparable to that of mild steel as made by Barrett and Levenson.5 EXPERITMENTAL METHODS The materials studied included copper specimens cut from the central, equiaxed crystal portion of a tough-pitch wirebar; brass made from this copper and high-purity (99.99 per cent) zinc including alloys of 7 per. cent, 15 per cent, 24 per cent, 29 per cent and 36 per cent Zn and large single crystals of 70-30 brass. Sections ¼ in. thick of the cast polycrystalline copper and brasses were reduced 40 per cent by rolling, recrystallized to a common grain size of 0.045 mm. and then rolled directly to foil 0.002 in. thick. Hardness readings employing both the Vickers and Rockwell machines were taken at intervals during the reduction. For comparison, similar specimens were cross-rolled-i.e., turned through 90 for each pass-and comparable hardness data were secured. Finally sections from the single crystals of brass were cut to obtain the following initial orientations; these sections were rolled, hardness data secured and a complete micrographic record of structural changes obtained:

Jan 1, 1941

By L. W. Holm

This study shows that in the presence of foam, gas and liquid flow separately through porous media representative of reservoir rock. These results were obtained by using tracer techniques to measure the flow of the gas and liquid comprising the foam. Foam does not flow through the porous medium as a body even when the liquid and gas are combined outside the system and injected as foam. Instead, the liquid and gas forming the foam separate as the foam films break and then re-form in the porous system. Liquid moves through the porous medium via the film network of the bubbles and gas moves progressively through the system by breaking and re-forming bubbles throughout the length of the flow path. The flow rates of the gas and liquid are a function of the number and strength of the films in the porous medium. There is no free flow of gas; i.e., no continuous gas phase. On the basis of these results, foam can be expected to improve a water flood or gas drive by decreasing the permeability of the reseruoir rock to a displacing liquid or gas. This improves the mobility ratio and thus the conformance of the flood. INTRODUCTION Foam is formed when gas and a solution of a surface active agent are injected into a porous medium either simultaneously or intermittently. During the past few years, several papers have been published on the subject of foam flow in Dorous media. Foam has been used successfully in the removal of capillary water blocks from producing formations.''2 The use of foam in gas storage reservoirs to reduce gas leaks and to increase storage capacity has been considered in recent years. Foam has also been investigated as an oil displacing agent,3-5 and as an agent to improve the mobility ratio in a waterflood.6-10 However, the mechanism by which the gas and liquid phases comprising the foam flow through a porous medium has nor been described adequately. Normally, when two immiscible phases (gas and liquid) flow concurrently through a porous medium, each phase follows separate paths or channels. At given saturations of the two phases, a certain number of channels are available to each phase, and as saturations change, the number and configuration of the channels available for each phase also change. The effective permeability of each phase is a function of the saturation of that phase only, and the flow of each phase can be described by Darcy's law. When foam is present, the effective permeability of the porous medium to each phase is greatly reduced compaced with permeabilities measured in the absence of foam.6,11-13 Based upon the observed flow of surfactant solutions and gas in capillaries, it has been concluded that the gas and liquid may flow separately or they may flow combined as foam. At least four mechanisms have been postulated to explain how fluids flow with foam present: 1. A large portion of the gas is trapped in the porous medium and a small fraction flows as free gas, following Darcy's law.9 2. The foam structure moves as a body; the rate of gas flow is the same as the rate of liquid flow. 6,13 3. Gas flows as a discontinuous phase by breaking and re-forming films. Liquid flows as a free phase.12 4. A portion of the liquid and gas move as a foam body while excess surfactant solution moves as a free phase.14 It also has been suggested that different flow mechanisms exist for high quality (dry) foams made from dilute surfactant solutions and for foams made from more concentrated solutions. Studies conducted on the flow of foam through capillaries have shown that a plug-type flow occurs and that foam flows as a body.6,15 Fried also has described the flow of foam through porous media as

Jan 1, 1969

By R. A. Swalin

IN this paper, the results of an investigation concerning the diffusion of three elements, magnesium, silicon, and molybdenum, in nickel are presented. The work represents a continuation of a diffusion program relating to solute diffusion in nickel. The program has the dual aim of obtaining useful diffusion data and of yielding insight into the factors governing solute diffusion in close-packed metals. The first paper of this series has been published earlier? In both investigations, in agreement with recent results from other laboratories, the activation energies for solute diffusion were found to be close but not identical to that of self-diffusion in the pure solvent in question. In order to obtain valid diffusion data, certain experimental pitfalls recognized only in recent years had to be avoided. Chief among these were the necessity for minimizing short-circuiting diffusion paths such as grain boundaries and the necessity for using low solute concentration gradients. In this series of investigations the following precautions were taken in an attempt to minimize such errors. 1) Samples with large grain sizes, 0.5 to 10 mm, were prepared. 2) The diffusion coefficients were measured at relatively high temperatures, since imperfections such as dislocations play a less important role at such temperatures than at lower temperatures. 3) Alloys containing less than 1 atomic pct were chosen for study. Experimental Work Materials—A diffusion couple technique was employed in the experimental investigation. Briefly, this technique consisted of the following. A diffusion couple was fabricated by placing a flat face of a cylindrically shaped alloy disk against a similar face of a pure nickel disk, and a bond was formed at an intermediate temperature under pressure. The diffusion couple thus fabricated was subjected to a diffusion anneal at higher temperatures for a measured period of time and then sectioned perpendicular to the direction of diffusion. After analyzing the sections for solute concentration the diffusion coefficient was determined from a probability, plot of concentration vs distance from the diffusion interface. Vacuum melted Mond nickel was used in the experimental program. The chemical analysis of this nickel is listed in Table I. Alloys used were prepared

Jan 1, 1958

By Maxwell Adams

CONSIDERABLE interest has recently been developed in sage-brush oil because of its possible utilization as a flotation agent in the mining industry. A list of some of its physical properties, together with the method used in its extraction, may prove of interest at this time. Something over a year ago, a study of the essential oils in desert plants was begun in the Chemical Laboratory of the University of Nevada. None of the oils so far studied possess properties of special interest to engineers, except the oil of sage, Artemesia tridentate, which has exceptional power as a flotation agent. This plant, known as common sage brush, also called black sage, is widely distributed over the semi-arid West, being found quite generally on most of the dry plains and mountains west of Missouri. The method of extracting the oil followed in these experiments is very simple. The leaves, twigs and small branches are placed in an airtight drum, having a capacity of about 27 cu. ft. Steam is admitted through a number of small openings at the bottom of the retort, and the pressure maintained at 20 to 25 lb. per sq. in. for 3 hr. The escape of the steam from the retort is regulated by allowing it to pass through a stop-cock into a condenser. The water in the receiver is drawn off from time to time and the oil, which is insoluble and floats upon the water, is thus collected. At the end of 2 hr. most of the oil has been driven out, though traces continue to come over for a much longer time. By raising the pressure, the time required could probably be shortened and the yield increased, but the lack of laboratory equipment has prevented the carrying out of this experiment.

Jan 9, 1916

By Jei Y. Choi, Paul G. Shewmon

The surface self-diffusion coefficient of copper (D,) has been measured between 847° and 1069 "C for six different orientations. These were the(111), (110, (100, and three higher index surfaces. The activation energy for Ds (designated Q s) was found to be about 49 kcal per mol for all six surfaces, and Do about 2 x 104 sq cm per sec. At any temperature Ds varied by no more than a factor of three over these orientations. It is shown that, if the free energy of a surface atom is uniquely determined by its number of nearest neighbors, it follows from the Principle of microscopic reversibility that Qs should have the same value for all surface orientations, and Ds should vary little with orientation. This model also suggests that for clean fee metals Qs ~ 2/3 AH, (heat of vaporization). This is true for copper. ALTHOUGH it has been appreciated for several decades that atoms can diffuse more rapidly on a surface than through the bulk of a crystal, it has only been in the last few years that reliable values of the surface self-diffusion coefficient (Ds) have become available. Tracer studies of Ds had been attempted prior to this period, but when a tracer is placed on a surface, an ever increasing fraction of it is drained off into the lattice. The correction for this loss involves a very difficult, and as yet unperformed calculation. Those who have worked with tracers have not corrected for this loss.1, 2 Thus their results indicate that Ds is greater than the self-diffusion coefficient in the lattice (Dl), but it has not been established that they give quantitative data on Ds. A procedure which avoids the problem of tracer loss is to study the rate of mass-transfer under the effect of surface tension. If the surface asperity being studied is very small, the mass transfer occurs entirely by surface diffusion. The kinetics at which a grain boundary groove forms on an initially plane surface is a well-studied case of this type. The smoothing of a slight scratch in an otherwise flat surface is another procedure that has been studied. If these grooves are up to 20 to 30 µ in width, the dominant mechanism for mass transfer is surface diffusion (at least in the case of metals with low vapor pressures), and the widths can easily be measured with an interference microscope. Of these two, mass-transfer techniques only in the case of grain boundary grooving has a rigorous mathematical treatment been given. This was done by Mullins.3,4 His analysis predicted that in the case of copper in an atmosphere of an inert gas, surface diffusion should be the dominant transport mechanism. This analysis gave an equation for the groove profile and predicted that the width of the groove would increase as (time)1/4. Mullins and Shewmon showed that both of these predictions agreed with experiments.5 Thus the validity of the values of Ds given by this procedure seems to be well established. Gjostein has used copper bicrystals and the grain boundary grooving technique to determine Ds and the activation energy for surface selfdiffusion (9,) in the [001] direction on surfaces ranging between the (100) and (110) planes.= He reported that Qs = 41 kcal per mole and Do = 6.5 x 102 sq cm per sec for all orientations studied. Since the results did not change with the dew-point of the dry hydrogen atmosphere or the type of refractory tube used, he concluded that the surfaces were clean, or at least that the results were not influenced by any impurities chemisorbed from the atmosphere. The work reported here reproduces and extends Gjostein's study in that D s and Q s were determined for copper over a wider range of orientations. To study the effects of impurities, two purities of copper were used as well as cathodic etching to remove any possible electropolishing film. Gjostein postulated that the diffusing atoms on a surface near a low index plane are the few atoms which are adsorbed on the smooth region between ledges or steps in the surface. A more rigorous derivation of the equation relating Ds to the concentration and jump frequency of these adsorbed atoms is given here. Using this treatment, our empirical observation that Q s and D s are essentially the same for all surface orientations can be shown to follow from the assumption that the free energy of a surface atom is uniquely determined by its number of nearest neighbors. The studies of D s using the scratch technique have been carried out by Blakely and Mukura on nickel,' and by Geguzin and Oveharenko on copper. The latter study using copper gives values of D s roughly

Jan 1, 1962

By W. Mitchell, B. H. Bergstorm, C. L. Sollenberger

A unique compression testing machine was constructed to load individual 1/8 to I-in. spheres of glass, etc., at rates from 100 to 100,000 lb per min. During loading the applied load was continuously plotted us the deformation of the sphere-platen system. The load-deformation curve conforms to the theory of elasticity. The spheres were surrounded by steel retaining rings or by gelatin (to prevent secondary fracture). The product size modulus was determined from screen analyses. The data shows: 1) Energy input per unit mass is inversely proportional to the product size modulus (or directly proportional to the surface area per unit mass). 2) Increased loading rates slightly increase the energy input per unit mass required for fracture without affecting the preceding relationship. Theory and experiments show that much of the input strain energy is transformed into kinetic energy of fragments at fracture, this being a reason efficiencies based on "surface energies" are exceedingly small. This large kinetic energy component is usually dissipated as heat but may be partially reclaimed because impact of fragments against the surface of steel retaining rings causes additional comminution. There are currently several theories of crushing, all of which can be derived from the general energy equation of Gillilandl as was pointed out by Mitchellet al in 1954'and more recently by Rose and Sullivan. If the exponent of the equation dE-x-"dx is assigned values of 2,1, or 3/2, one obtains by intergration between suitable limits, the equations of Rittinger, kick,' and Bond,' respectively. Other investigators prefer to let the exponent be a variable parameter. To help resolve the controversy, the Allis-Chal-mers Research Laboratories set up a series of carefully controlled experiments in which the level of energy input required to induce the comminution of a single particle by slow compression loading was very accurately measured. The energy input requirement, in conjunction with the size analysis of the fragments produced at fracture, yielded an accurate energy-product size relationship for the conditions studied. APPARATUS The experimental apparatus was designed to apply a compressive load on opposite sides of an "ideal particle." Spherical shapes were chosen, because point contact loading is typical of the mechanics of conventional crushers. The bulk of the experimental data was obtained with glass spheres because glass is a fairly homogeneous, brittle material for which the properties follow definite statistical distributions. The spheres ranged from 1/8 to 1-in. diam. The compressive load was applied to the specimen at a uniform rate by a loading mechanism (Fig. 1) which acted through a system of levers. The uniform rates, ranging from 100 to 100,000 lb per min, were obtained by metering water into a bucket suspended at the end of the secondary level. Point contact was made with the sphere through tungsten-carbide platens. This latter material is extremely hard and has a high modulus of elasticity, thereby having a minimum of distortion when loaded. The actual load on the sphere was measured independently of the lever system by a load cell, Fig. 2, which was designed so that the voltage output of the load cell would be proportional to load. The deformation of the specimen was indirectly measured by a pair of transformers which were attached to opposite edges of the upper platen. The cores of the transformers, which were attached to the lower platen, moved relative to the transformer so that the voltage output was proportional to the deformation of the sphere-platen system. The load was plotted against the deformation on an X-Y recorder. The area under the curve, as shown on Fig. 3, was proportional to the energy input of the

Jan 1, 1961