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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 J. Edgar Pew

As MOST of the oil production comes from leased-lands and not fee property, I shall refer to "leases" as covering the producing tracts. To produce oil, leases on land must first be obtained. Well-selected leases are all important. Not many years ago, the location for drilling for oil in wildcat territory was too frequently determined by the nearness, of adequate water and fuel supply, or with a view to cheapness of transportation. To some extent, the "creekology" theory is the result of the number of wildcat tests made near streams, to obtain water for operations. Now, an up-to-date operator will depend on his geologists for his location and, in many cases, will spend thousands of dollars to get water to it. The wisdom of following the geologist rather than the creek has been abundantly demonstrated in the past few years. In vast territories, where dry holes are spotted at intervals of a few miles or less. apart, and by reason of which these territories have been condemned for oil, the geologist is now finding many more spots that are producing large quantities of oil. No better tribute to the work of the geologist can be found than the surface and subsurface work being done in practically all parts of Oklahoma and the development had as a result of this, work. A land department is usually organized by placing in charge a man who is not only acquainted with the oil development, but who is a shrewd buyer, a first requisite for which should be unquestioned integrity. It takes a shrewd buyer to resist the persuasive lease broker, frequently backed by a geological picture from which the oil fairly drips. The geologist can help a lot by being absolutely honest when he makes these pictures; he will also thus strengthen his own cause. A geologist should interpret his own work and put his name behind his interpretation. If he does not he is liable to be misquoted and often discredited, as a result, by some overzealous lease broker giving an interpretation never intended by the geologist.

Jan 8, 1925

By R. W. Raymond

In June, 1906, I delivered to the graduating class of Lehigh Cniversity an address upon this subject, the substance of which, with sundry omissions and additions, was subsequently repeated, in October of the same year, in an extempore address before the Schenectady branch of the American Institute of Electrical Engineers. The latter, as stenographically reported, was published in the Proceedings of that society for November, 1906, and was referred to by President John Hays Hammond in his address at the Chattanooga meeting of October, 1908. Requests have been received from various quarters for the repub-lication of this address by the Institute. This I do not regard as necessary or proper; but I yield to that demand so far as to reproduce in the Transactions a summary of my views, as expressed in the two addresses above mentioned.

Jan 1, 1911

By C. W. Hill, G. P. Luckey

In a previous article1 preliminary experiments were described, indicating the possibilities of a quantitative spectroscopic method for the determination of small amounts of lead in copper, which would be accurate and rapid, and could be carried out in the refining plant by one not skilled in chemical analysis. The present paper deals with the development of the method in the factory, giving the details of apparatus and its standardization, and presenting a comparison of the accuracy of the method with that of the standard electrolytic determination. (For variations and other applications of the method, the reader is referred to the first article.) A carefully weighed sample (0.4 gm.) of the copper to be tested is placed in a cavity in a graphite positive electrode. An arc capable of

Jan 1, 1919

By B. M. Larsen, T. E. Brower

IN two previous papersl,2 dealing with the carbon-oxygen reaction, and the simultaneous content of each, in liquid steel in the furnace, we have made use of the quantity 0[O], defined as the excess oxygen beyond what would be in equilibrium with carbon then present if the pressure of carbon monoxide were I atm,; that is, if [C] X [O] is taken as 0.00222, 0[O] = [O] - 0,00222/[C] where [O] is the percentage of oxygen by weight as measured by the method described earlier.' This quantity 0[O] proves to be substantially independent of carbon content over the range 0.08 to 1.2 per cent, as well as of the basicity of the slag, and is nearly always within the limits 0.015 to 0.025 per cent when the bath is boiling normally and is in what we have termed a steady state. Apparently it must be at least about 0.014 per cent before boiling occurs; but this threshold value seems to depend upon the ease of bubble formation at the metal-hearth interface, hence upon the condition of the surface of the hearth. In any case, 0[O], on the average, changes considerably following any disturbance of the bath, as by addition of ore. The present paper deals with the average changes in ?[O] level following addition of Spiegel or crop ends, or after procedures to promote stirring, or by tapping of the steel from the furnace. The observations were made on a large number of commercial heats, and consequently are subject to the influence of various disturbing factors; the results have the compensating merit of showing the consistency obtainable under the limitations imposed by practical operation. VARIABILITY OF EXCESS OXYGEN IN NORMAL OPEN-HEARTH OPERATION The preceding general statements refer to the average value of ?[O] particularly in heats that are boiling actively; on individual heats, which are less active, there may be a variable time lag between the disturbance and its effect, which complicates the interpretation of what is going on. For instance, if in the normal refining process boiling is sluggish, the slag usually is gaining oxygen from the gas phase above it, or from added ore, faster than it is losing oxygen to the metal; yet when the bath starts to boil vigorously, the opposite condition may prevail for some time. The consequence of this lag is a variation of ?[O], the interpretation of which in a single heat may not be immediately obvious, This condition is illustrated in Figs. I and 2. In Fig, I, ?[O] at the beginning of the test period was near the lower limit of its usual range (dashed lines) in the steady state as a consequence of the lime boil, which had ended about as indicated. The bath is now cold, carbon drop is slow, and the first small ore feed causes only a small rise in 0[O]; as the temperature rises and as lime dissolves in the slag, and the bath becomes more active, the

Jan 1, 1946

By A. T. Tye

Regarding the results of preferential flotation at Cananea, Weinig has stated that "The concentrating mill of the Cananea Consolidated Copper Company at Cananea, Mexico, furnishes an excellent example of modern flotation practice. The complete figures are given because they present so forcibly the advantages of modern selective flotation."l L. 0. Howard notes that "Perhaps the outstanding example so far published of improverrients in results through the use of selective flotation is that at Cananea, Mexico."" The following notes indicate the conditions under which the results were obtained at Cananea; also the effect of preferential flotation at the concentrator and at the smelter. In the majority of cases the full benefit of selective flotation is not fully realized, as the concentrates are shipped from the mill to smelters owned by other companies. The saving made at a certain concentrator by this method of flotation may be well understood but the saving resulting at the smelter from the results of preferential flotation at the mill is not so apparent, as the data are contained in the smelting records of some other company. Even at the smelter the great gains following preferential flotation may not be noted, as a variety of ores and concentrates from various sources are received and the difference from the changed concentrator operations of a certain mill may be obscured. As noted by Professor Weinig and Professor Howard, the results obtained at Cananea brought about a veritable metallurgical revolution at the smelter. There are probably plants at which a better preferential separation is being made than at Cananea. Many ores contain barren iron pyrite which, when depressed, does not carry copper into the tailing. Some concentrators use clean uncontaminated water for milling and in others the ore is ground much finer than at Cananea. All of these items are concerned in perfect separation. The details of preferential flotation at Cananea, therefore, are not presented on account of the perfection of the

Jan 1, 1928

By Eliot Blackwelder

For the purposes of this paper, the boundaries of China and Siberia will be taken as they stood about 1907. Except in the Caspian region, it is doubtful if all the oil ever produced in these countries would equal one day's flow of a good Texas well. Considering the vastness of the regions and the variety of strata, it seems strange that these two countries should have made so small a showing in the petroleum industry. No doubt the condition is caused partly by lack of prospecting and of modern methods of development; in larger measure, however, it is evidently because of unfavorable geological conditions over nearly all of east-central and northern Asia. CHINA The known oil occurrences in China are very few. For many years, perhaps a barrel a day has been obtained by primitive methods from wells near the city of Yenchang in the northwestern province of Shensi. A like amount was obtained from wells bored for salt water in the vicinity of Kiating in southwestern Szechwan. The little oil was separated from salt water by allowing it to stand in jars. The salt wells yield also considerable natural gas, which is used to evaporate the salt and also for domestic purposes. There is evidence that wells were bored in this part of China before the third century. It is said that more than 1200 wells have been sunk in that district to depths of 1600 to 2000 ft. (485 to 610 m.) in connection with the salt industry. The scarcity of petroleum in China may be ascribed to three general geologic conditions: First, China contains practically no marine sediments of Mesozoic or Cenozoic age; second, the Paleozoic sediments are not for the most part of the types that generally contribute petroleum; third, the rocks of nearly all ages have been strongly folded, faulted, and more or less intruded by igneous rocks in all parts of China except certain areas in the west and northwest.

Jan 7, 1922

By L. Zwell, H. A. Wriedt

In describing their procedure for measuring the lattice parameters of solid solutions, Abrahamson and Lopata report (p. 77) the final heat treatment of their alloy specimens as "700°C for 100 hr, followed by a furnace cool". The isothermal part of this treatment may be expected to precipitate solute in excess of the stable a solid-solution limit at 700°C; the subsequent slow cooling is likely to reduce the dissolved solute still further. Fig. 1 (upper) presents the data for titanium alloys so he;rt-treated and shows the lattice parameters of solid solutions containing up to 3.5 at. pct Ti; Fig. 17 (lower) shows 2 at. pct Ti as the solubility limit in a iron at 700°C. Figs. 1 and 17 are thus incompatible. The paper contains comparable incon~patibilities for zirconium alloys, for niobium alloys, and for tantalum alloys. The final heat treatment at 700°C may also be responsible for the anomalous "knee" in the lattice-parameter data for nickel alloys, Fig. 3. The "knee" composition is located near the 700°C limit of the stable a solid-solution field;37 alloys of the experimental composition range with more nickel than the "knee" composition are two-phase at 700 C and prolonged heat treatment of them at 700°C would tend to produce inhomogeneity rather than homogeneity. In Figs. 4 and 7, the composition ranges of the zirconium, hafnium, and niobium alloys examined terminate at alloy concentrations of 0.1 to 0.2 at. pct. These metals form very stable oxides and their partial removal from solid solution in iron by impurity oxygen may be expected. We believe that the authors should have reported the procedure by which they distinguished the amounts of alloying elements in solution and in oxide. The diagrams pertaining to copper in Figs. 3 and 18 (lower) are almost certainly incorrect. Three recent investigations of this system38-40 all substantially agree on the solubility of copper in a iron, finding it to be much larger than that reported by Abrahamson and Lopata. The change of the lattice parameter with composition reported by Abrahamson and Lopata is too large by a factor of three to five, as seen by comparison with the findings of other investigators.41738 Moreover, the authors violate, in Fig. 18, the accepted Fe-Cu constitution diagram37 by ignoring the eutectoid at about 850°C.

Jan 1, 1967

By Ralph H. Sweetser

Carbon in pig iron is not only essential but, ordinarily, it is the most abundant metalloid present; iron without carbon could not be pig iron. Carbon in pig iron has been accepted, but seldom specified. How it gets into the pig iron as it is being smelted in the blast furnace, and why just about so much of it enters into the pig iron in certain blast furnaces, and more of it,; or less of it, enters the pig iron in other blast furnaces, or in the same blast furnace under varying conditions, are problems that have not yet been satisfactorily solved. During my own practical blast-furnace experience, I collected analyses of pig iron, including the graphitic and combined carbon, and recorded them in reference to the percentage of silicon present, having in mind the generally accepted explanation that "silicon drove out the carbon." To this actual experience, I have added some analyses given to me by J. B. Rogers, who was superintendent of the blast furnaces of the Ashland Iron & Mining Co., Ashland, Ky., and was making "silvery iron" at the time. These analyses are shown in Table 1. The analyses do not tell the whole story, but they show that with Pocahontas beehive coke, the total carbon was generally high. The data relating to the composition of the slag are lacking but my own customary practice was to have a rather basic slag. During my experience in making pig iron for the Bessemer and open-hearth departments, there were times when the steel men would complain about some mysterious quality in the pig iron that caused bad steel, in spite of the fact that the percentages of silicon, sulfur, phosphorus and manganese were within the specifications. Many reasons were advanced for this undetermined "poison" in the pig iron, but the favorite one offered by the steel men was that the blast-furnace man had "oxidized" the pig iron at the tuyeres in his eagerness to get big production and low cost. To these complaints of the users of steel-making pig irons were added those of the gray iron-foundry men and the malleable iron men. These groups are unaninlous in their conclusions that the trouble lies with the blast-furnace men; but there is not yet any harmonious conclusion as to the exact cause and remedy.

Jan 1, 1927

By Zay Jeffries

IT is well known that many properties of a given metal vary with the size of grain or cell. For most industrial purposes, where high ultimate strength and high elastic limit are desired, the manufacturer tries to produce a. fine-grained structure. For some purposes, for example in transformer iron, a coarse-grained structure is desirable. The terms fine-grained and coarse-grained are used only in a relative sense. For example, a fine-grained cast copper might have grains 100 times larger than coarse-grained high-speed steel. Similarly, a fine-grained steel rail might have grains or cells 100 times larger than coarse-grained wire, which was made of steel from the same heat. In some metals, the change in grain size is more appreciable than the changes in any of the properties determined by the tensile test. Furthermore, in metals which have been annealed or subjected to high temperatures, grain size may prove to be a better indication of the life of the metal in use than the tensile test. One of the authors was able to supplant the tensile test with grain-size determinations in the control of. metal for a specific use, the latter determination being more indicative of. the life of the metal part than the tensile test. A grain-size determination with a tensile test is, of course, more valuable than either singly. At present there is a decided dearth of data on actual grain-size determinations in metals, and consequently a corresponding lack of ability to interpret the determinations after they are made. It would be desirable to have correlation made between grain size and properties of metals, comparing thousands of determinations. In this way, grain-size determinations might be interpreted in much the same manner that tensile tests are now.

Jan 12, 1915

By H. Kazemi

A pressure fall-off test on the injection well of a forward combustion project may permit us to calculate the distance to the burning front. In the mathematical description and analysis of test data, we have considered the effect of temperature on the thermodynamic properties of reservoir fluids. The temperature distribution predicted by Chu' for a combustion wave has been used in analyzing a field test. Numerical solutions were obtained by simultaneous solution of the flow equation, the continuity quation and the equation of state. Although this analysis conccntrated on isotropic systems, the results can be extended to systems having directional permeability. INTRODUCTION Conventional pressure fall-off tests have been used extensively to determine reservoir characteristics in gas- or water-injection projects.- such tests consist of injecting fluid into the formation at a constant rate until steady state is nearly achieved, then discontinuing injection and measuring the bottom-hole pressure as a function of time. A plot of pressure vs the logarithm of time (measured from the instant of shut-in) yields a smooth curve characterized by three distinct regions (Fig. 1): Region I reflects the permeability alterations in the vicinity of the wellbore; Region II reflects the reservoir characteristics further away from the wellbore; and Region 111, the characteristics in the displaced fluid bank. The curves in Regions II and III are straight lines! the slopes of which are proportional to the reciprocal of the flow capacity of the formation behind and ahead of the interface as shown by Eq. 1, respectively:

Jan 1, 1967

By S. M. Moos, R. E. Dugger

In reviewing available vacuum filtration equipment in this paper, several types of filters have been included which are probably not familiar to operators in the mining industry. However, it was felt that these units might be of interest in the event that an application should arise for the filtration of a product in the future that does not exist today. In addition, exposure of our industry to equipment used in other industries might have a tendency to be thought provoking and perhaps lead to the development of equipment and/or applications in our industry which do not necessarily exist at this time. Most innovations in filtration equipment have been confined to the improvement or design change of components and accessories, particularly reflecting the availability of materials of construction that have been developed. Recent developments in the application of horizontal belt filters have been innovative. The application of this unit as a substitute for or an adjunct to thickeners in a CCD circuit can certainly be innovative and perhaps provide a basis for reduction in capital and operating costs in this area. For example, mill tails are generally pumped at the highest possible density that will adequately flow. Tailings ponds and dams with their attendant design requirements are based upon this estimated water volume.

Jan 10, 1979

Endurance Properties of Non-ferrous Metals Discussion of the paper of D. J. McADAM, JR., presented at the Syracuse Meeting of the Institute of Metals Division and issued, as Paper No. 1506-E, with Mining AND METALLURGY, October, 1925. H. F. MOORE,* Urbana, Ill. (written discussion).-This paper says that the results of tests of some non-ferrous metals made at the University of Illinois and in the testing laboratories at McCook Field are abnormal when they do not agree with results obtained by the author. The writer can see no inherent reason why results of the type uniformly reported in this paper are any more normal. The knee of the stress-cycle, or S-N, diagram comes at different lengths of life for different metals. For steel, the knee occurs after from 1,000,000 to about 4,000,000 cycles, and for some non-ferrous metals not before 20,000,000 of 30,000,000 cycles. The writer can see nothing inherently abnormal in finding certain nonferrous metals for which the knee of the stress-cycle curve occurs at 1,000,000,000 cycles or higher. The writer has had experience with both the cantilever and the rotating-beam testing machine, and thinks that the chance of whipping action in the cantilever machine is a more serious handicap than the action the author has pictured. Furthermore, the writer questions whether the author has shown the existence of a clearly marked and definite endurance limit for all the non-ferrous metals he has tested including the following: Nickel (CT and A-16, Fig. 1), monel (CS-5.5 and BK, Fig. 2), bronze (F and CK, Fig. 4), aluminum bronze ( BJb-1, Fig. 6).

Jan 12, 1925

By H. C. Spaulding

Every constructing engineer and designer knows how often it is desirable to provide a speed-adjustment between parts of a machine performing different functions, or between a prime mover and the devices to which it furnishes power, and how bulky and unsatisfactory are most of the methods by which the result is usually accomplished. Of course the step-pulley is the most simple and generally used. It requires, (1) parallelism of shafts; (2) a considerable distance between centers; and (3) a cessation of power during the change from one speed to another. Add to this the necessity for careful design in order to obtain equal belt-tension for all positions; the weight and hulk required for a wide range; and the operative's positive conviction that better results could be obtained at a speed intermediate between those furnished by two successive steps, and we begin to realize the mechanical shortcomings of this old and familiar friend. The hundred and one other devices, patented and otherwise, for accomplishing similar results, present other objections of varying importance, which need not be discussed here. Without pretending to overcome these entirely, and indeed without claiming absolute novelty, a recent invention of Mr. E. F. Gordon, of Dover, N. H., has seemed to the writer to offer such advantages in flexibility and range of application as to merit a more extended study and use than can be given in his own work, to which it is being applied as rapidly as opportunity permits. It is placed before the members of the Institute, not only to bring out an expression of opinion as to its limitations, but also with the hope that it will thus find opportunities for applications hitherto untried and outside the scope of operation of those at present interested in its development. Simply stated, the device consists of a narrow pulley with a deep V-groove, split by a plane passing through the bottom of the groove, one of the two symmetrical parts so formed being fixed to the shafts, and the second being capable of adjustment so as to bring the

Jan 1, 1893

By W. H. Emmons

MOST mineral deposits change as they are followed downward on their dips. Some of these changes are due to primary arrangement; different ores were precipitated at different depths when the deposits were formed. Other changes are due to weathering or secondary enrichment. The chief changes resulting from weathering, in the main, are understood and standard changes are recognized. The processes are relatively simple. They take place at ordinary temperatures and pressures and can be duplicated in the laboratories. Moreover, there are thousands of deposits available for study, because the processes take place near the surface where the development of mines is begun. The changes due to primary arrangement of the deposits of the metals are not so well understood. Deposition has taken place at higher temperatures and our knowledge of the chemistry of the processes leaves much to be desired. Very few experimental data are available. The deposits, moreover, offer fewer examples because many mines are not, developed to depths where the changes can be studied and a change to unprofitable material usually results in stopping work. Most, students of ore deposits now accept, as confirmed, the hypothesis that nearly all lodes and related deposits were formed by solutions originating in intrusive igneous masses. Outward from these masses, the deposits at many places are grouped in zones and the arrangement noted from the intrusions outward are commonly the reverse of the changes noted from the surface downward in a single lode. A study of the changes in groups of deposits, from the parent intrusion outward, will throw light on the changes to be expected in a single lode downward. Because the changes in series of deposits from the intrusive outward may all be observed near the surface, where more data are available, it is possible to increase the number of examples many fold and to apply the statistical method of study with greater confidence of avoiding error.

Jan 3, 1924

By J. O. Mack, J. B. Russell

In recent years, solders containing 20 per cent tin with no bismuth or cadmium have been developed by a few companies, and personnel have been properly instructed in their use. In addition, since the tin shortage, a number of solders containing less than 10 per cent Sn, and some with no tin, are being used in special applications; however, a solder of this type has yet to be developed that is satisfactory for general use. Table i.—Composition Ranges Prescribed for a Commercial Substitute Solder Element Per Cent Tin............................ 18.0-20.0 Bismuth (maximum)a............ 0. 80 Silver.......................... O. 10-1. 25 Bismuth plus silver (minimum).... 0. 85 Antimony (maximum)............ o. 50 copper (maximum),,,,,,,,..,,,, 0. I3 Other elements, each (maximum)6 0.03 Lead........................... balance a When silver is present in excess of I per cent, the Bi content shall be 0.50 per cent or over. b Total not to exceed 0.10 per cent. The Purpose of this investigation was to develop an alloy containing a maximum of 15 per cent tin, with no cadmium or bismuth, having solder properties equivalent to or better than those of substitute solders now specified containing 18 to 20 per cent tin (Table I), or even approaching the properties of the standard 40 to 60 tin-lead solder. The wartime restriction of bismuth and cadmium, elements that have beneficial effects on fluidity, solidification range and strength, makes it increasingly difficult to develop a general-purpose solder containing a maximum of 15 per cent tin. In the course of this investigation, 11 elements were used in various combinations with the basic I5-85 tin-lead alloy. These elements were antimony, silver, copper, indium, thallium, lithium, calcium, barium, potassium, sodium and arsenic. In all, 116 low-tin solders were investigated, with the idea of developing a solder that will give satisfactory working properties, specifically in regard to "wetting" of copper, brass and iron, solidification range, capillarity and shear strength of a soldered joint. The relative importance of these various properties plays an important role in the search for substitute solders, since it is almost impossible to retain all of the desired qualities of a high-tin solder and still make drastic changes in the alloy composition. Because of the expected uses of a general-purpose solder, it is necessary that it have properties, especially in regard to wet-tability, that will enable it to be used on the metals in common use. Basic Considerations The maximum liquidus temperature of a solder is determined by the particular application involved and the temperature that can be obtained by the source of heat. If a soldering iron is used, it must not only

Jan 1, 1945

By P. Somasundaran

Flotation of minerals has usually been discussed in terms of solid-liquid interfacial phenomena. This paper discusses the relative importance of phenomena such as collector adsorption at other interfaces formed between the bubble, liquid and solid. Adsorption of collector ions of various chain lengths at liquid-gas and solid-gas interfaces has been obtained. The data have been analyzed under conditions corresponding to those of flotation to show the significant role of collector adsorbed on the bubble surface in determining the bubble-mineral attachment required for flotation, and consequently to suggest consideration of this role in the development of better flotation conditions. Vacuum flotation of quartz with alkyl ammonium acetate reported in the foregoing paper1 showed that the collector chain length has an effect on flotation even at concentrations below those necessary for hemi-micelle association of the hydrocarbon chains at a solid-liquid interface. This chain length effect might be explained by the following arguments: Hydrocarbon chains find it energetically favorable to be in a medium of low dielectric constant. Considering the possibility of an iceberg structure at the solid-liquid interface, such a structure would produce a region of lower dielectric constant at the solid-liquid interface than in the liquid phase, because the dielectric constant of ice is 2 to 3,2 while that of water is 80. Depending on chain length, this difference will certainly cause even individual ions to adsorb in higher quantities at the solid-liquid interface. Another mechanism to consider is the possible formation of dimers, trimers, etc and chain length would influence this formation. But, above all, the chain length effect on flotation at concentrations of low adsorption at the solid-liquid interface could be due to the significant but often-neglected role of the collector adsorption at the bub- ble surface. Collector ions or molecules are adsorbed both at the solid-liquid interface and the liquid-gas interface. Below the concentration for hemi-micelle association at the Stern plane adjacent to the surface, the bulk of the collector ions adsorbed at the solid-liquid interface are in the diffuse part of the double layer. If such systems, where there is a gas bubble coming in contact with the solid surface, are to achieve some degree of electroneutrality, those collector ions would have to migrate from the diffuse part of the double layer to the region directly adjacent to the surface during the induction period when the bubble is making contact with the solid. The time necessary for this migration would contribute to the induction period required for creation of the solid-gas interface. It seems reasonable that the induction period could be reduced sufficiently for flotation to occur if these collector ions were carried to the surface by the bubble. In an attempt to ascertain whether or not the bubble could possibly have sufficient collector ions at its surface to meet the requirement mentioned above, the adsorption density of the collector ions at the liquid-air interface was determined. For this purpose, the surface tension of alkyl ammonium acetate solutions was determined as a function of concentration. Adsorption densities of the collector at the liquid-gas interface were calculated using the Gibbs adsorption equation: where y is the interfacial tension and ri and pi are the adsorption density and the chemical potential, respectively, of the chemical species, i. Using the convention that the adsorption density of water at the interface is zero, the following relationship is obtained for the liquid-gas interface where lg refers to liquid-gas interface and RA+ refers to the alkyl ammonium ions. For dilute solutions, rf^-wri^&rfwW [3] where C is the concentration of the collector ions in solution. l?:: can now be evaluated using Eq. 3 and surface tension measurements.

Jan 1, 1969

By E. Topanelian

In recent years considerable progress has been made in the development and application of mathematical techniques for the solution of certain problems involving economic "strategies". Such a problem might involve, for example, the scheduling of shipments of a commodity from a number of sources to a number of destinations. The object would be to schedule the shipments in a manner so as to satisfy the destination requirements and at the same time minimize the transportation costs. The solution to such a problem is not necessarily intuitively obvious. The "obvious" solution is frequently far from optimum. If the shipments are to be made from, for example, only two sources to four destinations, the optimum schedule is readily found. However, if shipments are to be made from, say, 10 sources to several hundred destinations, even a competent and experienced scheduler may spend considerable time in finding a reasonable answer. Even then he is not sure that he has the optimum solution. Furthermore, he has no way of knowing how far from optimum the answer is. Consequently, he does not know whether he should accept this solution or seek a better one. Prior to the advent of large high-speed digital computers, little more could be done with such problems because of their great size and multiplicity of possible solutions. A problem involving 20 sources and 50 destinations would require choosing, from a very large number of possible combinations, the optimum combination of 1,000 variables. The best one could do was to utilize intuition, extrapolation from past experience, and other non-exact approaches. With a high-speed computer, however, such problems can be solved providing a reasonable computational procedure (or algorithm) can be utilized. The purpose of this paper is to describe such a procedure (linear programming) and to apply this procedure to a production scheduling problem. THE RESERVOIR PROBLEM A simple reservoir model is used throughout this analysis to illustrate the use of linear programming. Even the simplest reservoir behavior problem is nonlinear in both space and time, but if the geometry is fixed for a particular study and the time variable is quantized, the resultant system may be described by linear constraints on the variable production rates. Crude oil is available from five separate sources and is delivered to a pipeline. Sources 1, 2, 3 and 4 are ideal reservoirs and therefore are subjected to reservoir flow restrictions. Source 5 is labeled "Outside Source" and crude oil from this source is assumed to be available in unlimited quantities without considering reservoir conditions. The general problem is to determine the schedule of crude oil production from five sources which, over an eight-year period and subject to certain restrictions, will result in maximum profit. "Profit" is defined to encompass all economic factors and expenses involved in producing and selling crude oil to a pipeline facility. Such economic factors are lumped to the extent that the term represents the dollars profit from one barrel of crude oil from any of the five sources entering the pipeline system. Table 1 presents the assumed profit per barrel for oil from any of the five sources over each of the four time periods. In this chart the eight years is broken into four equal intervals of two years. The selection of four time periods of two years each and the values representing the potential profit are completely arbitrary selections for the purpose of illustrating this idealized reservoir problem. In any practical application of this work a careful economic study would have to be made in order to estimate potential unit profits for time periods as far in the future as eight years. In this particular study it is assumed that all of the potential unit profits (C) are known and fixed before the production schedule is attempted. For each reservoir arbitrary values are assigned for

By E. L. Kamen, H. D. Kessler, M. Hansen, D. J. McPherson

The highly reactive Ti-Mo and Ti-Cb alloys were prepared and heat treated under protective conditions. Phase diagrams were established based on micrographic and X-ray diffraction analysis and detection of incipient melting. ß titanium forms a continuous series of solid solutions with both molybdenum and columbium, whereas these metals are only slightly soluble in the a titanium modification. PREVIOUS work on the Ti-Mo and Ti-Cb systems was very limited and is discussed in succeeding sections of this paper relating to the respective phase diagrams. The diagrams in the present work were determined principally by micrographic analysis, because other methods such as thermal analysis and dilatometry are not suitable, due to the low diffusion rates of these alloys in the transformation range. X-ray analysis was believed less useful than micrographic analysis because: 1—On quenching certain high titanium alloys from above their transformation range, the body-centered cubic ß phase decomposes into acicular a (hexagonal close-packed) which room temperature X-ray diffraction techniques cannot differentiate from isothermal a. 2— High temperature X-ray techniques might be used, but are difficult to apply and are subject to error because of the high reactivity of titanium with gases such as oxygen and nitrogen. Although metallo-graphic study was the basic method used, X-ray diffraction analysis was applied to a limited extent, to further substantiate the findings. The transformation ranges on the titanium side of the Ti-Cb and Ti-Mo systems were studied both with DuPont Process A (magnesium-reduced) titanium alloys and with iodide titanium alloys. The Process A metal was used chiefly to bracket the transformation range in order to reduce the number of alloys given a particular treatment for the more accurate final study with iodide titanium alloys. Experimental Procedure The analyses of the metals used in the preparation of alloys for this study are presented in Table I. Melting Practice: Early in the work, a consumable electrode, arc melting furnace was used in the preparation of the Process A Ti-base Mo and Cb alloys. This type of furnace has been described by other investigators.', ' One of the major difficulties of the consumable electrode melting process was the prep- aration of homogeneous electrodes (with the mixture of coarse titanium sponge and fine powder alloying addition) which would give homogeneous ingots. Composition gradients encountered may have been due to a tendency for powdered alloying metals to drop away from the electrode in handling. This difficulty in the preparation of homogeneous alloys was overcome by the use of a nonconsumable electrode furnace for later work. This furnace is similar to the one used by Mc-Pherson and Fontana a Ohio State University. A diagram of the nonconsumable electrode arc furnace is given elsewhere.' The source of power was a 400 amp dc welding generator. Electrode tips of tungsten (% in. in diam) were used for all columbium melts and for a limited number of molybdenum melts. Molybdenum tips were used for the majority of molybdenum alloy melts. Columbium tipped electrodes were tried, but disintegrated rapidly at currents above 300 amp. In the Process A titanium melting practice the metals were charged into the water-cooled spun copper crucible in the following forms: l—titanium: sponge (—4 + 16 mesh); 2—molybdenum: sections of 0.003 in. sheet (approximately ½ in. sq); and 3— columbium: powder compacts (? in. lumps broken from large section). After alternately evacuating and purging the furnace several times with argon or helium, the arc was struck against the metal charge,

Jan 1, 1952

By E. S. Bumps, M. Baeyert, W. F. Craig

SOME time ago during a study of impact properties of tempered martensite,1 it was postulated that the consistently good ductility of tempered martensite might be caused by its relatively small and peculiarly shaped ferrite grains. The fer-rite grains of tempered martensite have approximately the same size and shape as the martensite "needles." Thus they form an interlocking mass of needle-shaped grains quite different from equiaxed or lamellar ferrite grain structures. When the common mechanical test methods are applied to steel, variations are often observed in the ductility of specimens that have closely similar hardness and tensile strength values. The ductility so measured appears to be structure dependent. When steel from the same heat has been heat treated to produce different structures with the same hardness, the elongation and reduction of area values from the tensile test and the transition temperature determined by the notched-bar impact test vary according to whether pearlite, tempered martensite, or other structural constituents were produced by the heat treatment. It has been widely recognized that tempered martensite gives a consistently good performance, when tempered to the same hardness as many other structures with which it has been compared. In recent years the isothermal transformation of austenite to specific structural products and the quantitative evaluation of the character of these products with respect to their nature and response to deformation has received considerable attention. The objective of the present study was to pursue somewhat further the dependence of ductility upon structure; specifically, it was desired to ascertain whether ferrite grain structure, including both shape and size of the grains, can account for the consistently good performance of tempered martensite in the notched-bar impact test. It was thought that a simple experiment would indicate whether the ferrite grain structure plays any part in the good ductility exhibited by tempered martensite in contrast to other steel structures with different types of ferrite grains. By determining the impact transition temperature, it was proposed to compare spheroidites having similar carbide particle size and spacing but obtained in such a manner that their ferrite grain structures would be very different. Spheroidite obtained by tempering martensite, with its small, needle-shaped grains, was to be compared with spheroidite from pearlite. If the latter is produced by sub-critical annealing, the ferrite grains correspond to the pearlite colonies. Thus, if the pearlite was not too coarse, the ferrite grains of spheroidite from pearlite are equiaxed in contrast to the needle-shaped grains of spheroidite from martensite. It was thought that the ferrite grain structure of spheroidite from martensite might depend to some extent upon the grain size of the prior austenite. The austenite grain boundaries limit the maximum attainable size of the martensite needles and thus of the ferrite grains in the derived spheroidite. In order to evaluate any possible influence of prior austehite grain size, spheroidites were to be prepared from martensites that had been formed from fine-grain austenite and also from coarsened austenite. As the carbide particle size and distribution were to be essentially alike in the various spheroidites, the difference would be in the ferrite grain size and shape. Thus any marked difference in transition temperature could be attributable to the character of the ferrite grain structure. There are certain considerations in assuming that these spheroidites would be equivalent in all respects except ferrite grain structure, and an attempt was made to take them into account. One of the considerations was the choice of the carbon content of the steel. An approximately eutectoid steel was selected for two reasons. First, the pearlitic structure would contain no proeutectoid ferrite which might complicate the picture by producing a non-uniform ferrite grain structure in the resulting spheroidite. Then, too, the high-carbon content would inhibit ferrite grain growth during the sub-critical treatment. Another factor to be taken into account was the choice of an alloying element to assure a martensitic structure throughout on quenching the impact specimens. Nickel was chosen, because it is a common alloying element and resides in the ferrite both upon its formation from austenite and throughout tempering. The formation of alloy carbides, or even a large solubility of the alloying element in cementite, would have complicated the interpretation by changing the composition of the ferrite .during spheroid-ization. The possibility of temper brittleness was minimized insofar as possible by using a tempering temperature as high as consistent with the 1 pct of nickel in the steel, namely, 1150°F. While it certainly is not claimed that no difference other than ferrite grain structure could exist between the spheroidites, nevertheless, reasonable precaution has been exercised within the limits of steel metallurgy. It is believed that any large difference in transition temperatures would reflect the difference in ferrite grain structure and that relatively good ductility in the spheroidites from mar-

Jan 1, 1951