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By H. Reiss

The zone-melting process in which redistribution of solute in a solid bar is effected by the passage of a molten zone is considered mathematically. Simple approximate techniques are developed for computing the manner in which redistribution occurs as molten zones continue to pass. The introduction of the "zone-melting flux" provides valuable insight into the nature of the phenomenon, as well as a central mathematical theme in terms of which the process can be discussed. Curves are presented for typical and general cases. AN extremely efficient purification technique was described recently by Pfann.1 Known as zone refining, it consisted of the slow passage of a series of molten zones, produced by external heaters, through a long solid ingot of the substance to be purified. Equations were given for the maximum separation attainable, and a numerical computation method was described for obtaining the concentration in the ingot after a given number of zone passes. The present paper offers an interpretation of the physical nature of zone melting in terms of a transport process in which formal diffusive and convec-tive flows occur. This interpretation, in addition to providing insight into the physical nature of the process, also provides a basis for its mathematical treatment. From this basis, useful equations are developed for the solute concentration in the ingot as a function of the number of zone passes. These are applicable particularly where large numbers of passes are necessary and where numerical computational methods might be laborious. All considerations will deal with the limiting form of the process, described by Pfann,' in which: 1—Diffusion in the solid is considered negligible. 2—Mixing in the liquid is supposed, complete. 3—The distribution coefficient, k, measuring the ratio (at equilibrium) of solute concentration in the solid to that in the liquid is supposed, independent of composition. In general, this paper will be concerned with a bar of uniform (actually unit) cross section, ex- tending in the x-direction from x = 0 to x = L, where L may be infinite. Zone melting is a transport process, and as such must admit of interpretation in terms of a flux of transported quantity. However, the progress of operation is not measured in units of time but in terms of the number of completed zone passes. Consequently, the zone-melting flux will be a rate, per unit pass, rather than per unit time. The description of this flux and the examination of its properties is given below. Zone-Melting Flux Fig. 1 represents an intermediate stage of the nth pass. Concentration C is plotted against distance, x. The molten zone with its back at the point x and front at x + I moves in the direction indicated by the arrow. As it moves, it leaves behind the nth

Jan 1, 1955

By D. F. Kaufman, E. D. Levine, L. R. Aronin

The deformation of' impure beryllium crystals by basal glide at room temperature invariably tevminates by basal cleavage after a few percent strain. It is generally accepted that .fracture of this type is caused by the splitting of low) -angle boundaries, or bend planes, by obstacles that restrict the motion of the bed planes in the deforming crystal. The details of such a process have been developed by Stroh, who showed that the high tensile stress norrnal to the basal plane in the region where the bend plane is split results in the propagation of a basal cleavage crack, provided there is no available dejorvrlatzon mode having a shear component normal to the basal plane It has been postulated that puvification of beryllium might lead to increased basal ductility by the vemoval of barviers to bend plane motion and possibly by the activation of nonbasal defor~rlation systems. Large increases in the amount of basal glide that can he sustained prior to fracture have been observed in crystals purified by zone refining. In each case, eventudal fracture was by sharp basal cleavage, suggesting that the split bend plane model still applies to tile fracture of beryllium of rensonably high purity. In the present work, calculations are made to show to what extent basal duetilits can be increased by purification while the split bend plane .fracture process remains applicable. Experimentally observed ductilities are generally somewhat lower than those predicted by calculation because of premature failure due to defects introd~cced during specimen preparation and testing. SEVERAL investigators1-4 have studied the deformation characteristics of beryllium single crystals of commercial purity, and have related the strong anisotropy of plastic deformation in single crystals to the problem of brittleness in polycrystalline beryllium. For most orientations, the principal deformation mode is basal slip, which, at temperatures between 300" and 900°K, begins at a critical resolved shear stress of approximately 1500 g per sq mm and terminates after 3 to 6 pet glide strain by cleavage on the basal plane in the neighborhood of (1120) bend planes that are formed during the deformation. This type of fracture, which is also observed in zinc at low temperatures, has been interpreted by stroh5 to be caused by the splitting of bend planes by obstacles to their motion. In the Stroh model, a (11.20) dislocation wall, or bend plane, moving along the slip direction under the action of the applied stress, encounters obstacles which cause part of the bend plane to be held up, the other part continuing to move. Stress concentrations are built up in the region where the bend plane is split, with a high tensile component normal to the basal plane, resulting in a microcrack at the end of the split wall. Because no deformation mode having a shear component at an angle to the basal plane is available to relieve the stress at the crack tip, the crack can propagate under a sufficiently high applied stress. The Stroh criterion for crack propagation is given by

Jan 1, 1964

By Edgar Stansfield

ONE of the most striking features of the coal series passing from peat through brown coal, lignite, etc., up to anthracite is the gradual reduction of moisture content with the increased coalification of the original plant material. Thus drained peat from a bog may contain 90 per cent water, brown coal contain 50 per cent, lignite 30 per cent, while a bituminous coal may contain only 1 per cent moisture. Moisture, therefore, is one of the important factors to be considered in coal classification, especially with the lower rank coals. With bituminous and higher rank coals the moisture content is less satisfactory for classification; it may even pass a minimum value and then increase with increasing rank to anthracite and superanthracite. Coal in an undisturbed seam contains moisture which is an integral part of the coal, but it may also be wet with free, underground water percolating through the seam. Only the former must be considered in evaluating the moisture content of the coal for classification purposes; this will be called the "true moisture" of the coal. When the seam is mined and sampled the sample taken may show the true moisture; on the contrary, it may contain in addition free mine water or, especially in dry, well ventilated mines, it may contain less than the true moisture. Coal contains unstable organic compounds which may decompose, with the production of moisture, when the coal is exposed to air at ordinary temperatures, or is heated with or without exposure to air. The potential moisture of a coal therefore is higher than its actual moisture. The lower the rank of the coal, the greater its instability, as a rule, and the greater the care necessary to avoid oxidation or decomposition in any investigation of moisture content. The majority of coal workers have preferred, on account of the difficulty in evaluating the true moisture of a coal, and for other reasons, to classify coals by analyses calculated to the dry-coal basis. A number of workers familiar with lower rank coals have recently insisted that the classification of such coals can be satisfactory only if analyses on the moist-coal basis are employed. The moisture-holding capacity of coal is therefore intimately connected with coal classification, and in this paper a procedure is outlined for determining the true moisture of a coal.

Jan 1, 1932

By E. V. Potter, E. T. Hayes, H. C. Lukens

LARGE volumes of hydrogen are liberated at the cathode during electrolytic precipitation of manganese. Most of the gas escapes from the electrolyte, but a considerable amount may be entrapped in the manganese plate. Gas has been observed to escape from manganese melts in puffs that ignite at the surface. It has been reported that castings made with electrolytic manganese tend to rise in the molds; for this reason the manganese is often treated to remove hydrogen before the melt is made or it is premelted and used as cast manganese in making the alloys. The effect of hydrogen on the properties of manganese and its alloys is not known, but its effect on iron and iron alloys has been studied extensively.1.2 The close relationship between iron and man¬ganese suggests that hydrogen may have a similar effect on the properties of manganese and its alloys. The purpose of this investigation was to determine the amount of hydrogen or other gases in typical commercial electrolytic manganese sheet and to investigate ways of removing it most conveniently. APPARATUS The apparatus used is shown schematically in Fig. I. It consists of a chamber A in which the metal sample is placed, a vacuum or pressure gauge B, volume gauge C, vacuum pump D, hydrogen container E, auxiliary gas chamber F, and furnace G. The specimen chamber was made of two concentric quartz tubes. The outer one, a, connects with the closed gas system and is surrounded by the furnace G. A second tube, b, fits closely inside a and has a small end that projects into the space for the specimen and holds the thermocouple for measuring the temperature of the sample. The inner tube is joined to the outer tube outside the furnace, with rubber tape and sealing wax, to prevent gas leakage into or out of the closed system. This type of specimen container is loaded very easily and can be used several times if molten metal does not come in contact with the quartz. An ordinary mercury manometer B is used to measure the pressure in the system. The volume gauge C is essentially another mercury manometer, but the volume of the column is much larger than normal and the height of the mercury can be varied by raising or lowering the well H. In this apparatus the tube had a volume of I00 c.c. for a 60-cm. length. For larger changes in gas volumes; auxiliary containers F were used to increase the volume of the system by known amounts. Valves were arranged so that these auxiliary containers could be filled from the system and evacuated by the pump as often as necessary to accommodate the increases in the volume of gas in the system. The furnace G, used to heat the samples, was equipped with an automatic temperature controller, which maintained the desired temperatures within ± 5°C.

Jan 1, 1945

By Warren B. Davis

Introduction If a subject this broad were to be covered in even moderate detail, it would require a set of books about the size of an encyclopedia. Since an acceptable length for this paper is a small fraction of one book, it will have to consist of a few samples of the subjects that I think are the most pertinent to World Fossil Fuel Economics. I plan to discuss the trends in world energy demand, particularly in the U. S. and Europe; the consumption patterns and cost patterns of oil, gas and coal; the prospects of synthetics; and some of the effects of government regulation of fuel economics. World Energy Demands Fig. 1 shows Free World energy consumption by principal areas for the period from 1950 to 1970 and a forecast for the period from 1970 to 1985. These figures include only the measurable forms of energy. An example of energy consumption that is not measured is the wood a peasant might cut in the forest and bum in a fireplace to heat his home. This omission probably is a very small part of the total. This forecast is not identical with that of Wayne E. Glenn (see Page 22), but the differences in total energy consumption are not significant. The U. S. consumption, which was 55 percent of the world total in 1950, had declined to 45 percent by 1970, and is expected to decline further to 38 percent by 1985. Western Europe has consumed 28 percent of the total from 1950 to 1970 and is expected to lose share slightly between 1970 and 1985. The most spectacular gainer is Japan, which increased consumption from 2.5 percent in 1950 to 7.5 percent in 1970, and is expected to reach nearly 17 percent by 1985. The over-all Free World total has grown from 62 quadrillion Btu (equivalent to 29 million B/D of crude oil) in 1950 to 151 quadrillion by 1970, an average growth rate of 4.5 percent/year. This total is expected to grow at a rate of 5 percent/year between now and 1985, reaching 315 quadrillion Btu (equivalent to nearly 150 million B/D). Fig. 2 shows which fuels supplied this energy between 1950 and 1970, and gives an estimate of how it will be supplied between 1970 and 1985.

Jan 1, 1971

By L. S. Darken

IT has been known for sometime that in an ionic lattice, such as that of Ag2S or FeO, the migration velocity of the anion may differ markedly from that of the cation, the cation being usually the more mobile. It has been shown, for example, that during the formation of silver sulfide tarnish on silver, the tarnish layer grows principally by the motion of silver cations through an essentially stationary silver sulfide lattice. Similarly, the growth of wüstite scale on iron proceeds principally by motion of iron ions, this being accomplished with the aid of vacant iron lattice sites into which the iron may readily move. Likewise investigations of solid solutions of various salts show that there is usually considerable difference in the mobility of the different cations. Measurements of the mobility of various metals in liquid mercury indicate that the various metals move at different rates relative to the mercury. In view of the foregoing it seems reasonable to suppose that when any single phase solution is acted upon by a field, the atoms of different elements respond in different ways; in particular, that the force arising from a particular concentration gradient in a binary alloy would cause the atoms of one component to move with a drift velocity which is in general different from that of the atoms of the other component. The recent experiments of Smigelskas and Kirkendall1 support this viewpoint, since they found, in essence, that during diffusion in alpha brass zinc moves appreciably faster than copper. This was evidenced by the relative motion of inert molybdenum wires. Such a phenomenon is incompatible with the place interchange theory of diffusion proposed by several authors, most recently by Birchenall and Mehl.2 This theory has, however, also been questioned3.4 for other reasons, principally because of the high energy required for direct atomic interchange. The rather large difference between self-diffusivity, as determined by tracer technique, and mutual diffusivity, as determined with the aid of another element at low concentration, might also be interpreted as favoring the above idea; however, Birchenall and Mehl have pointed out that there is another possible interpretation of this difference; this is discussed later. A rather interesting and pertinent observation was made by Schwartz,5 who noticed that tungsten lamp filaments, heated by direct current, commonly fail by necking down in the region at the temperature gradient near the positive end, with a concomitant swelling at the corresponding position near the negative end. He introduces considerable auxiliary evidence to show that this phenomenon is occasioned by the motion of tungsten cations which migrate in the high temperature region from the positive end toward the negative end. The mechanism of this migration is not clearly understood. If, however, this experimental evidence be accepted, we are forced to conclude that alloying elements in the tungsten may migrate by the same or a similar mechanism, whatever it may be, at a greater or lesser rate, thus giving rise

Jan 1, 1948

By W. B. Coleman

Considerable discussion on the effect of iron and steel scrap in blastfurnace burdens was presented in the January, 1927, issue of Mining and Metallurgy. Therein the question is asked as to what causes the difference in physical properties of pig irons where the chemical analyses are practically the same. This point no doubt has been noticed by a number of furnace operators, but several years ago very little thought was given to it. The foundries purchased pig iron, had it analyzed and found it to be within their specification. The castings made from this iron at times would be satisfactory and at other times hardness and shrinkage would occur. Since the iron was chemically correct the foundries generally were at a loss as to what to do. They changed their method of melting in the cupola and in some cases this corrected the trouble. In some instances the foundry would continue eliminating a brand of iron until the castings produced were satisfactory. Through this process of elimination they would finally arrive at the conclusion that a certain brand of iron was causing the trouble. During the course of this elimination minor changes might have been made in the melting and in the end satisfactory castings were secured without discovering any definite reason for the trouble. Frequently the foundries blamed the manufacturer of the pig iron although the seat of the trouble was in their own method of melting. I have in mind one foundry in particular that was using three brands of pig iron for producing their castings and their losses were rather high. Three entirely new brands of iron were substituted in the charge and still the losses continued. Even after using six brands of pig iron the management felt that the pig iron was the cause. The difficulties encountered in the melting of iron in the cupola, over the past several years, reflect in a great many cases on the operation of the cupola. At different times certain brands of iron were unsuitable for producing a certain class of castings, but at the same time one could see no reason why the iron should be considered abnormal. Irons from furnaces where production and low cost are the main factors that are being used in foundries produce in most cases harder cast-

Jan 1, 1927

By Theodore Simons

During the last half century a great amount of ingenuity and energy has been devoted to the invention of appliances for the recovery of valuable minerals from very fine sands and slimes. The reason for this is that in almost every dressing plant the greatest losses of values, considered relatively as well as absolutely, occur in the treatment of slimes. The natural aim of mill operators to minimize these losses has in recent years received another impetus, from the fact that the gradually diminishing occurrence of high-grade ores makes a more intense recovery of values from existing resources absolutely necessary for profitable operation. The results of such attempts are found in the appearance of a great number of machines and appliances which make it profitable to-day to rework old clumps, containing the tailings of older processes. A constantly growing difficulty of obtaining skilled labor and the increase in wages made it prohibitory to employ those types of machines which required much attention, and in the middle of the ninieteenth century the various concentrating tables of the percussion type, which automatically discharge their products, began to take the place of the intermittent tables, on which, when the bed had reached a certain thickness, operation had to be stopped in order to allow the skimming by hand of the separate layers formed on the table. In the course of years, two general types of machines evolved for the treatment of fine sands arid slimes: The so-called concentrators and vanners, on the one hand, and the buddles and round tables on the other.' For the profitable treatment of the very finest slimes, round tables have as a last resort proved more satisfactory and econoillical than other machines. In recent years they have agaiu become the subject of close inves-

Jan 1, 1914

By D. Harrington

WHEN the word gas is mentioned in connection with mining, almost invariably it is inferred that the explosive gas, methane, is in mind and that it must refer to coal mining. While it is true that methane occurs, or is likely to occur, in almost any or all coal mines, it is also a fact that the metal mines of the world have in them by far a greater variety of gases than have the coal mines. In many cases the gases in metal mines are as dangerous to individuals as the gases likely to be found in coal mines; in some instances the metal mine gases are even more deadly. The coal mine is more likely to have methane than the metal mine, in rare instances it may have high percentages of nitrogen or high carbon dioxide, or there may be a deficiency of oxygen where the air is confined in a blind end or in a sealed region; much more rarely there are found in coal mines in relatively small percentages, ethane, or other hydrocarbons with odor of ether, gasoline or kerosene, or there may be minute percentages of hydrogen sulfide. In time of coal mine fire or explosion, there is likely to be high carbon monoxide (4 per cent. or over in some cases) and if the coal contains much sulfur, there may be some sulfur dioxide in the fire fumes. In metal mines there are a number of cases of occurrence of methane and attendant explosions; some metal mines have appreciable percentages of the decidedly explosive hydrogen; in some metal-mining regions carbon dioxide flows into the mine, fills the workings and overflows just like water. In other regions, at many working faces there are high-temperature gases containing a mixture of gases of sulfur (sulfur dioxide, hydrogen sulfide and possibly SO3 in some cases) together with carbon dioxide and nitrogen, and the deadly hydrogen sulfide in lethal proportions is found in some high-sulfide metal mines at blasting time. Carbon monoxide constitutes a decidedly dangerous day by day hazard in connection with metal-mine blasting, because of the heavy charges of dynamite that are used and the use of fuse, which in burning gives off much carbon monoxide. The poisonous gas hazard is accentuated because of the relatively small openings where metal-mine blasting is done and to the inefficient ventilation of the usual metal mine.

Jan 1, 1930

By J. S. Kirkaldy, D. G. Fedak

The extra degree of freedonz introduced by a second independetzt concentration in a tenzary system gives rise to the possibility of unstable planar phase interfaces in semi-infinite diffision layer couples. Diffusion paths which pass continuously in and out of too-phase regions of the phase diagram but which are not coincident with tie-lines give rise to super saturated zones which may be either adjacent to or isolated from planar phase interfaces, with corresponding nonisolated or isolated precipitates. Nonisolated precipitates are equivalent to morphological development of the interface. Selected couples in the ternary systems Fe-Ni-Cr and Cu-Zn-Sn have been examined nzetallographically and ifz the latter case both isolated and uo~zisolated precipitates have been observed. The diffusion path in one of the couples showing interface morphological developtnent has been examitled using electron probe microanalysis. IGNORING the spurious effects of preferential grain boundary diffusion and anisotropic crystal growth7 it can be unequivocally stated that it is impossible for a binary isothermal diffusion couple constructed of two unsaturated phases to sustain a nonplanar phase interface. Consider for demonstrative purposes the schematic phase diagram of Fig. l(a). Given an initial flat phase interface, semi-infinite boundary conditions and the internal boundary condition fixed by the constitution diagram, xB = xB(T), the unique solution of the diffusion equation requires a persistent flat interface. No other solution is possible. If, however, we anticipate the involvement of surface tension, then the internal boundary condition must be written xB = xB (T,Y) where r is the radius of curvature of a hypothetical nonplanar interface. The introduction of a new parameter such as r can be equivalent to the release of an internal constraint, so that a stable nonplanar interface may be possible after all. Consider a perturbation to the interface as indicated in Fig. 1(b). According to the Ostwald-Freundlich equation: which is applicable to a system of this constitution, the solubility of A in the matrix ß ,xB (Y), at a point of curvature r is given by where Va is the molar volume of the a-phase, R is the gas constant, and a is the interfacial tension. Since the right hand side is positive, xB(r) >xB cm, as indicated in Figs. 1(a) and 1(c). Accordingly, the perturbation will carry the interface concentration in a direction which is opposite to that which would sustain local equilibrium. Such a perturbation is necessarily moderated and the system is returned to its initial condition. This result is general for all binary couples since we can regard an interfacial perturbation as an attempt to precipitate within un-

Jan 1, 1962

By J. H. East, E. R. Maize

INTRODUCTION PROBABLY no other type of equipment is now being introduced into American underground mines about which less is known and about which there is more misinformation than the Diesel mine locomotive. Any equipment installed underground brings with it hazards that were not present before, and it is the purpose of this paper to show that Diesel-powered equipment can be used with safety in underground mining if certain feasible but very important precautions are taken. Diesel locomotives are not new in underground mining, since they have been used successfully in European mines for at least 19 years, but their use in American mines is exceedingly limited; so far as is known, only five Diesel mine locomotives are operating at present in United States mines. Diesel locomotives were permitted underground in Great Britain for the first time in 1939, and the rapid increase in the number in use in those mines, testifies to their safety and efficiency. More than 1300 Diesel mine locomotives are in use in European mines, according to the latest statistics; these locomotives are employed in coal, iron, lead-zinc and mercury mines. So far as is known, the Diesel mine locomotive has not yet caused an explosion or mine fire, and has not been the cause of any fatalities from toxic gases in the mines in which it has been used. ADJUSTMENTS OF DIESEL ENGINES FOR UNDERGROUND USE A Diesel engine adjusted to work in an underground mine should not be confused with the same engine adjusted for use outside the mine. Adjustment of the air:fuel ratio for engines that are used on the surface is intended to give the maximum fuel economy, and little or no attention is given to the chemical composition of the exhaust gas produced. Many such engines are poorly adjusted and perhaps poorly maintained, with the result that the engine emits smoke in quantity as well as the disagreeable odor familiarly associated with Diesel engines. The air:fuel ratio in the case of Diesel engines operated on the surface is generally around 15:1; that is, 15 lb of air to burn 1 lb of fuel. Diesel engines adjusted to work underground usually have an air:fuel ratio of about 20:I, as at this ratio the minimum quantity of toxic gases is given off in the engine exhaust. Diesel engines operated underground must be maintained in better condition than similar engines used on the surface; otherwise, the smoke emitted in the exhaust becomes objectionable if not unendurable. Practically normal air is required for safe operation of Diesel engines underground or in confined places; failure to provide virtually normal air for Diesel engine operation is almost certain to result in trouble. Bureau of Mines engineers have determined that the air in which a Diesel operates in confined places should contain less than 1/2 pct of carbon dioxide and at least 20 pct of

Jan 1, 1947

By W. N. Lacey, R. T. Carter, B. H. Sage

The phase behavior of a number of binary systems consisting of parafin hydro-carbons has been determined in recent years. In addition, the composition of the coexisting phases of mixtures of crude oil and natural gas has been investigated.~ However, the latter study did not include information concerning the influence of the concentration of a component upon its distribution between two coexisting phases. Owing to the paucity of such information it was considered desirable to investigate in some detail the composition of the coexisting phases in the methane-propane-n-pentane system throughout the greater part of the two-phase region at a tempera-ture of 100°F. Information of this nature also permits the establishment of the critical behavior of this ternary system. Method The compositions of the coexisting phases in this ternary system at 100°F. were deter-mined by withdrawing samples from a pres-sure vessel containing a heterogeneous mixture of the three components that had been brought 10 equilibrium by mechanical agitation at the desired pressure and tem-perature. The samples were withdrawn under such conditions that the equilibrium was not disturbed and the composition of each of the phases was ascertained by means of the conventional low-temperature fractionation procedure. The apparatus employed in this investi-gation was nearly the same as that utilized in an earlier study of the methane-pentane system.~ Several minor modifica-tions in the arrangement of the apparatus were made in the interest of simplifying the procedure and avoiding the possibility of condensation in the tubing connecting the equilibrium apparatus with the analyti-cal equipment. The pressures were meas-ured by means of a pressure balance with a precision of 0.5 lb. per sq. in. It is believed that the equilibrium pressure was ascer-tained with an uncertainty of not more than 2 lb. per sq. in., even though small varia-tions in pressure obtained during the withdrawal of the samples. The tempera-ture of the equilibrium equipment was maintained by use of an automatically controlled oil bath. The bath temperature was determined by means of a copper-constantan thermocouple, the electromo-tive force being determined by means of a potentiometric circuit of such a nature as to reduce the uncertainty of the tempera ture to less than O.I f. The fractionating column employed in the determination of the composition of the gas phase had a diameter of 0.12 in. and was approximately 4 ft. long, while the column employed in the analysis of the liquid phase was 0.18 in. in diameter and about 5 ft. long. Each column was equipped with the conventional constant-volume receivers, which were maintained at a constant temperature by means of an automatically controlled oil bath. In nearly every case the distillation in thr neighborhood of the transition between

Jan 1, 1941

By B. D. Cullity, S. S. Hsu

The stress distribution at the surface of a twisted cylinder is analyzed along the boundary of a slip plane of arbitrary orientation and this analysis is applied to the torsion of cylindrical crystals of magnesium. A criterion for slip is developed and the critical resolved shear stress of magnesium in torsion is found to be 0.038 kg per sq mm. The mechanism of torsional deformation in magnesium and aluminum is described, as well as the relaxation of a twisted crystal at elevated temperatures. THERE has been considerable fundamental study A of the mechanism of slip occurring during deformation in tension and compression but comparatively little attention has been paid to the mechanism of torsional deformation. This paper is concerned with the way in which a single crystal deforms in static torsion and with the phenomenon of untwisting which a twisted crystal undergoes during annealing. Particular attention is paid to the application of the critical resolved shear stress law to torsional deformation. Probably the most likely mode of torsional deformation that can be imagined consists of rotation of one part of the crystal relative to another on the active slip plane. Here the most interesting feature is the slip direction. If a cylindrical single crystal is twisted about its axis and if, to consider the simplest case, the active slip plane is normal to the specimen axis, then the direction of gross slip at any point must always be at right angles to the radius drawn to that point. It follows that the crystallographic direction of slip must be continually changing, in sharp contrast to slip in tension which occurs in a crystallographically constant direction. Extensive investigations of slip in torsion have been made by Gough and his associates.' They made torsional fatigue tests on metal single crystals belonging to a number of different crystal systems and observed, with a microscope, the appearance of slip lines on the surface and of strain markings on the transverse cross section of cylindrical specimens. They concluded that the critical resolved shear stress law was just as valid in torsion as in tension, in the sense that slip occurred on that plane and in that direction in which the resolved shear stress was a maximum. They also established that the operative slip planes and directions were the same as in tension. They did not, however, measure the critical resolved shear stress in torsion nor, in fact, did they establish that a critical value of the resolved shear stress was necessary for the initiation of slip. Their investigations were, moreover, restricted to torsional fatigue tests which necessarily involve small strain amplitudes. Wilman,' studying crystal growth and the abraded surfaces of crystals, observed crystal fragments

Jan 1, 1955

By L. D. Godshall

A great deal has been written of late regarding the loss of silver in assaying; very discordant results have been published by different writers, and much uncertainty exists concerning even approximate losses in a careful determination of silver, as represented by a fire-assay. In the present paper it has been the aim of the writer to determine as accurately as possible the losses sustained by silver, under certain specified conditions, during the process of cupellation. Such losses are well known to be due to absorption by the cupel and volatilization. The conditions, however, which govern these losses are not believed by the writer to be so well understood. The most important of these are : 1. The effect of variable quantities of silver used. 2. The temperature of cupellation. 3. The character and quantity of impurities in the lead button. 4. The weight of the lead button. 5. The nature of the cupel. The following experiments were made for the purpose of demonstrating, as nearly as possible, the total loss of silver in cupellation under the most favorable conditions to be obtained in commercial assaying. Chemically pure silver and pure lead were taken. The latter was obtained from test-lead, first melted into a bar, from which pieces of the desired weight were cut and accurately weighed. The experiments recorded in this paper were planned by the writer, but executed throughout by Mr. J. N. Walker, whose ability as an accurate, careful and painstaking assayer is too well known and recognized throughout the West to require any further endorsement from me.

Jan 1, 1897

By David B. Brooks

INTRODUCTION Resources are not; they become (Zimmermann 100) . The companion concepts of reserves and resources appear, one way or another, in almost all considerations of mineral supply. Yet, no other concepts in the economics of the mineral industries have occasioned so much confusion. Whereas everyone agrees that in general the terms refer to the amounts of material that-depending upon technology, market conditions, and institutions-will become available for production in the near or more distant future, the apparent agreement disappears when we come to more specific definitions or to application of the definitions. Some definitions emphasize the physical aspects of reserves and resources, while others emphasize the economic. Some treat reserves and resources as fixed quantities, while others regard them as continually varying. Some consider that reserve and resource estimates have validity only for individual deposits, while others insist that they can be measured with sufficient accuracy for regional or national planning. This confusion in concepts that lies at the very heart of mineral economics is both strange and not so strange. It is common in the social sciences to find concepts that have been adopted into scientific jargon from popular usage and given rather special meanings -at the same time that they continue to be widely used without such qualifications. Psychologists have the same trouble with personality and sociologists, with community. Nevertheless, an attempt must be made to straighten out the various meanings of reserves and resources, or at least to clarify the conditions under which different meanings are applicable, before much progress in analysis of mineral problems can be expected. That is the objective of this chapter. Throughout the chapter, an attempt has been made to provide enough references to guide the interested reader to the most pertinent works on the concepts under study. However, even in a review article, it is no longer feasible to provide a comprehensive set of citations; there are simply too many. In many instances the works cited will themselves include the bibliographies needed to complete a literature search; those that are particularly useful in this respect are so noted. Also, because of the limited availability of foreign periodicals, some important works -originating largely in Canada, France, the

Jan 1, 1976

By J. T. Mackenzie

HENRY MARION HOWE, in whose memory we are gathered together, was one of the great thinkers who develop from time to time to whom is given the rare gift of synthesis. Analysis is given to few, but synthesis, the ability to show the relation of all parts to each other and thus to give a clear picture of the whole, is reserved for the very few. Analysis can be achieved by honesty, intelligence, and industry, but synthesis is only given to genius Professor Howe's crowning achievement is the picture of the whole iron-carbon series shown in Fig. I, which places steel, malleable, gray iron, mottled and chilled irons in their proper relation to each other and shows the essential unity of the series. Perhaps his best statement of the case is found on page go of the Metallography of Steel and Cast Iron in these words: "Each member of the gray cast-iron series consists of the metallic matrix approximately equivalent to that member of the steel-white-cast-iron series to which it corresponds in percentage of combined carbon with its continuity broken up-by masses of graphite . . . " Apparently he had taken considerable interest in this idea around the turn of the century, for he refers to a discussion at the Franklin Institute in 1900 in which he said: "Though many others had probably conceived this relation between the steels and cast irons, it was here enunciated for the first time, so far as I know. It was received with great incredulity." The concept was explained in some detail in a paper on 'The Constitution of Cast Iron" presented before the A.S.T.M. in 1902 when Professor Howe was retiring president of that young society. In the discussion Dr. Sauveur stated that he was "very well acquainted with Professor Howe's theory of the constitution of cast iron," and went on to say that while he "shared it to the fullest extent, some foundrymen . . . claim cast iron is a metal entirely different from steel . . . that steel and cast iron have very little in common, and that therefore the knowledge gained in the study of steel is of little or no value in the study of cast iron." Dr. Moldenke, in discussing the same paper, said he had been working on the same theory for 12 years but he laid no claim to publication. Discussing the difference in the micro- structure of the metallic matrix, Professor Howe pointed out that "such minor struc- tural differences are indeed to be expected, because of the difference in the conditions under which these constituents are generated. "One difference in these conditions is that the steel of most micrographs has been either forged or at least treated thermally in such a way as to give a new structure radically different from that which formed during the initial solidification, whereas the cast irons have not. Hence what we see in the steels is a transformation structure, but in the cast irons a solidification structure. By giving the cast

Jan 1, 1944

By F. J. Fayers, R. L. Perrine

For many years the problem of increasing ultimate recovery of oil from a reservoir has been a subject of interest to the oil industry. At present, a standard secondary recovery technique is to flood the reservoir with water once natural forces of the system are depleted. The permeability characteristics of the rock, together with interfacial forces which exist between the two fluids and the porous material. allow only part of the oil in the rock formation to be recovered by the water-flooding process. Laboratory experiments have shown that when detergents are added to the flooding water, the flow properties of oil in a porous rock arc improved. This improvement results in greater oil recovery. Even though higher recoveries are obtained using detergents, the extra cost associated with the method may make it economically unsatisfactory. To establish economic feasibility requires experimental laboratory measurement of fluid and rock properties together with a calculational procedure to predict field results. Pilot tests in the field may also be required. This paper presents a mathematical procedure for predicting detergent flood behavior. A number of reasonable simplifying assumptions are made to obtain a tractable system of equations. The resulting method may be regarded as a generalization of Buckley-Lev-crett' theory to solve simultaneously for water saturation and detergent concentration profiles. Consequently this type of calculation can be used in much the same manner as Buckley-Leverett theory is used to evaluate a water flood. The mathematical method employed is the so-called method of characteristics for solving hyperbolic partial differential equations. This application of the method is instructive because several other problems in reservoir analysis may be analyzed in a similar manner. FLUID FLOW EQUATIONS The flow behavior of oil and water without detergent through porous reservoir rock is usually expressed by Darcy's law and a continuity equation for each phase. If gravitational forces are neglected, vrg = kr (s)µr v p rg.........(1) vrg = kr (s)µr v p rg.........(1) ? pa va = F ?/?t (sd) where v is the volumetric flux, k represents permeability, S is saturation, and P the pressure. Fluid viscosity is denoted by 11, p is the density, 4 is porosity, and I the time. The subscripts w and o refer to water and oil. The capillary forces in the system lead to a difference in pressure between phases. This may be expressed by the relation: Pm -P0 =Pc(S).........(5) The capillary pressure? P,, is determined experimentally as a function of saturation. DETERGENT BALANCE EQUATION Addition of detergent to the water phase affects the flow properties of the system. Capillary pressure and relative permeability become functions of detergent concentration, c, as well as fluid saturation. That is: P--P (S,c) and k,,,.- - -- k,,,. At low oil saturation values, the presence of detergent reduces capillary pressure and reduces the relative permeability ratio. Detergents are surface-active and adsorb on rock surfaces. The quantity adsorbed, a, will depend on the concentration c of detergent solution and may also depend on the saturation; thus, a = a(S,c). In this analysis we have assumed that the detergents used are water soluble but not oil soluble, and their movement is therefore restricted to the water phase. The dispersion of detergent in water is neglected by comparison with transfer by flow within the system. Detergent movement is determined by the water flux and adsorption: ? cv m = -F ?/?t (cs + a) We will assume that the quantity of detergent in solution is too small to significantly change water density or viscosity. When the permeability and capillary pres-

By R. G. Hudson, L. Yang

In electrochemical separation of metals, it is necessary to control the potential applied between the electrodes so that only the desired electrode reactions can occur. A knowledge of the minimum potential needed for a given electrode reaction to take place continuously is therefore pertinent to the success of the process. In molten chloride systems at high temperatures, activation polarization is believed to be small,1,2 so the minimum potential needed for the electrolytic decomposition of a molten metal chloride MC1n (n = valence of the metal ion) is therefore essentially the equilibrium electrode potential E of the metal-chlorine galvanic cell in the solution. If the decomposition products are pure M and chlorine at a pressure of p atm, E*Eo-rt/nf in [i] Since EO (the standard electrode potential of MCln) is a constant at a given temperature and R (the gas constant), and F (the Faraday's constant) are all constants, the variation of E with the electrolytic bath conditions is largely determined by the effect of the latter on the activity of the metal chloride amcln (standard state = pure MC1,). Measurement of E and study of how amCin varies with temperature and concentration, the nature of the solvent, and that of the coexisting solutes are therefore pertinent in the selection of optimum operating conditions for the electrochemical separation of metals. Because of its low melting point, high decomposition potentials of its components, and the low solubility of heavier metals in it, the LiC1-KC1 eutectic melt is a useful solvent and has been used in the electrodeposition of Mo,3Ce,4 and u5 metals. Senderoff and Brenner3 measured the potentials of Zn/Zn++, Fe/Fe++, Cu/Cu+, Mo/Mo+++, and Ag/Ag+ against an Ag/AgCl (pure) reference electrode at 600°C and a concentration of 4.1 mole pct of each chloride and came to the conclusion that complex ion formation occurred in some of the melts. Laitinen and LiUe gave an electromotive force series at 450°C for a number of {Metal/Metal ions (unit activity)) electrodes in LiC1-KC1 eutectic melt, the {pt/pt++ (unit activity)) electrode being chosen as the reference. Walker and Danly7 studied the ther-modynamic properties of NiC12 in LiC1-KC1 eutectic melt over a wide range of temperatures and concentrations by measuring the electrode potential between a nickel electrode and a chlorine electrode in the melt. Since potential measurements made by using the chlorine reference electrode are of more direct significance both in the study of electrochemical separation and in the evaluation of the thermodynamic properties of the melt, it is therefore decided to measure the electrode potentials of cells of the type {M/MCin (mole fraction = N) in LiC1-KC1 eutectic melt/Cl2 over a range of N values and temperature for a number of metal chlorides. The results should indicate the order by which the various metals plate out on the cathode and how this order is affected by temperature and the concentration of the metal chloride in the solu-

Jan 1, 1960

By AIME AIME

APOCRYPHAL, no doubt, but widely entertained is the proposition that top-flight mining geologists never agree with each other on anything. Being rugged individualists, they frequently seem intolerant of opinions that conflict with their own. However, one may suspect that controversy is often more apparent than real. For example, at last summer's meeting of the American Mining Congress, Ira B. Joralemon and Reno H. Sales, discussing "Mining Geology, Today and Tomorrow," seemed to be in serious disagreement over various phases of the subject; but much of this arises from the different angles of approach of the two distinguished and successful ore finders.

Jan 1, 1941

By P. S. Rudman

Laves phases, AB2, are considered as Izerrzisub-stitutional solutions m1hich are defined by a one-for-truo replacement scheme. Atomic-size tnisfit is considered in terms of deviations of the ratio 2V°b/V°A from unity, where v° = atomic volume. A simple elastic model has been used to calculated deviations from "Vegard&apos;s law of atomic vol-umes". Comparison has been made between calculated and observed atomic-volume deviations fov 222 Laves phases. Agreement is generally very good although there ave some few exceptions which appear to be excusable in terms of electronic changes that ore beyond the scope of the present model. We can consider the formation of a binary sub-stitutional solution A-B from an A solvent as one-for-one replacements of A atoms by B atoms. As the atomic-size ratio deviates from unity, the solution becomes thermodynamically less stable and hence more restricted because of atomic-misfit strain energy. In accordance with our previously presented conclusion1 that the atomic volume, v, is in general the most appropriate measure of atomic size, the ideal size ratio for a binary sub-stitutional solution is vg/vA = 1. The Laves phases have been described by Berry and Raynor2 in terms of various stacking sequences of hexagonal layers of B atoms for the three structures MgZn2(C14), MgCu2(C15), and MgNi2(C36). To form the Laves phase of ideal composition AB, we start with complete hexagonal layers of B atoms in the appropriate stacking sequence and we remove, according to an appropriate scheme for each structure, two out of every four B atoms and replace the two removed atoms by one A atom. We thus might expect to find that the ideal size ratio for the Laves phases is 2v/B/ VA= 1. From this point of view, then, we call Laves phases hemi-substitutional solutions since we employ one-for-two replacements. By analogy with substitutional solutions we can expect for Laves phases that as the ratio 2VB/Va deviates from unity the phase occurrence will be more restricted. Laves3 has plotted the distribution of Laves phases as a function of the radius ratio, ?A/rB, and found that, while the distribution extended from 1.05 < rA/B < 1.50, the

Jan 1, 1965