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By R. S. French

The purpose of this paper is to present data that have been obtained during the past two years concerning the effects of prior cold-work and temperature and time of anneal upon the recrystallization and grain growth of 70-30 cartridge brass. It was desirable to study certain of these phases so that an accurate picture of the principles of the subject could be shown. The work is not intended to provide explicit annealing data, but to provide material examples that may help to clarify analogous problems concerning this alloy. Specifications often set limitations upon the grain size of annealed materials because of the importance of grain size upon subsequent manufacturing operations. It was, therefore, worth while to study the variables that affect the recrystallized grain size of this material. C. H. Mathewson and A. Phillips,l W. R, Webster,2 and others have presented annealing characteristic curves of this alloy. A recent typical curve presented by R. S. Pratt3 is shown in Fig. I. The tensile properties and grain sizes are shown as functions of the annealing temperature. Such curves serve as a useful guide in determining the physical properties of annealed material, but as they are made generally under carefully controlled laboratory conditions they do not indicate the performance of metal annealed in a mill muffle, where such conditions as amounts of metal, heating time and temperature may differ. Study of the effect of time and temperature upon grain growth and subscquent recrystallization was made with a coil of metal having the following analysis: 70.04 per cent copper; 0.007 lead; 0.007 iron; 0.00 tin; 0.00 silicon; 0.001 nickel; 0.000 phosphorus; balance zinc. The sample coil was obtained from metal that had been rerolled from hot-rolled mill stock, and was received at 0.228-in. gauge, soft, with a grain size of 0.125 mm. This material was then rolled 43.5 per cent to 0.129-in. gauge and annealed to a 0.053-mm. grain size. In this condition, samples were cut and used in all of the experimental work reported in this paper. Time The first study was of crystal growth at a constant temperature over a moderate length of time. Material was cut from the stock coil at 0.129-in. size and rolled 75 per , cent hard to 0.032-in. gauge. From this piece small samples were cut M by 2 in., suitable for grain-size determina.tions. Twelve samples were placed in an electric furnace uniformly across the width, approximately an inch from the floor. A thermocouple was wired to the center sample, so that the approximate metal temperature could be followed. At various

Jan 1, 1944

By R. S. French

The purpose of this paper is to present data that have been obtained during the past two years concerning the effects of prior cold-work and temperature and time of anneal upon the recrystallization and grain growth of 70-30 cartridge brass. It was desirable to study certain of these phases so that an accurate picture of the principles of the subject could be shown. The work is not intended to provide explicit annealing data, but to provide material examples that may help to clarify analogous problems concerning this alloy. Specifications often set limitations upon the grain size of annealed materials because of the importance of grain size upon subsequent manufacturing operations. It was, therefore, worth while to study the variables that affect the recrystallized grain size of this material. C. H. Mathewson and A. Phillips,l W. R, Webster,2 and others have presented annealing characteristic curves of this alloy. A recent typical curve presented by R. S. Pratt3 is shown in Fig. I. The tensile properties and grain sizes are shown as functions of the annealing temperature. Such curves serve as a useful guide in determining the physical properties of annealed material, but as they are made generally under carefully controlled laboratory conditions they do not indicate the performance of metal annealed in a mill muffle, where such conditions as amounts of metal, heating time and temperature may differ. Study of the effect of time and temperature upon grain growth and subscquent recrystallization was made with a coil of metal having the following analysis: 70.04 per cent copper; 0.007 lead; 0.007 iron; 0.00 tin; 0.00 silicon; 0.001 nickel; 0.000 phosphorus; balance zinc. The sample coil was obtained from metal that had been rerolled from hot-rolled mill stock, and was received at 0.228-in. gauge, soft, with a grain size of 0.125 mm. This material was then rolled 43.5 per cent to 0.129-in. gauge and annealed to a 0.053-mm. grain size. In this condition, samples were cut and used in all of the experimental work reported in this paper. Time The first study was of crystal growth at a constant temperature over a moderate length of time. Material was cut from the stock coil at 0.129-in. size and rolled 75 per , cent hard to 0.032-in. gauge. From this piece small samples were cut M by 2 in., suitable for grain-size determina.tions. Twelve samples were placed in an electric furnace uniformly across the width, approximately an inch from the floor. A thermocouple was wired to the center sample, so that the approximate metal temperature could be followed. At various

Jan 1, 1944

By P. B. Baxendell

The performance of a water-drive reservoir having a gas cap depends primarily on the movement of the gar-oil and oil-water contacts. The movement of the contacts during production depends in turn on fluid withdrawals and how the reservoir pressure changes as fluids are produced from the reservoir; that is, on how effectively the aquifer maintains pressure by replacing withdrawals. inasmuch as pressure changes, fluid withdrawals, contact positions, and produced gas-oil and oil-water ratios are interdependent, the analysis and prediction of the performance of a reservoir produced in a given way must take into account this interdependence throughout depletion. This paper presents an analysis which, within the limitations of the assumptions made, yields an engineering approach to predicting future performance based on reservoir pressure and production history. The most significant assumption is the method of extrapolation of future gas-oil and water-oil ratios. The extrapolation procedure smoothly increases both ratios to preselected values as the remaining oil column undergoes a specified decrease in thickness. This preselection is made on the busis of previous field experience in depletion of similar reservoirs under similar conditions. For computing future performance a vdumebic balance L combined with the differential equation defining pressure distribution in the aquifer to obtain positions of water-oil and gas-oil contacts. From these positions are extrapolated produced water-oil and gas-oil ratios. Reservoir performance can be investigated when oil production rates are dependent upon various factors including the performance of the reservoir itself. Examples of practical application of the procedure are included. INTRODUCTION To predict performance of water-drive reservoirs with gas caps and thin oil columns, it is necessary to describe the motions of the fluids within the reservoir during the entire production period to depletion. These motions depend on the pressure changes and on the withdrawal of oil, gas and water. Production of oil from the oil zone primarily causes water to move in to take its place; production of gas from the cap tends to cause oil to migrate into its place. In addition, the volumes of oil and gas remaining in the reservoir depend on changes in the pressure, since a decrease in pressure causes fluid expansion, gas liberation and oil shrinkage. A method of relating the future pressure to total withdrawals is used to describe the motions of fluids within the reservoir under conditions arising in possible modes of production. The analysis is based on two relationships and will reduce the problem to one amenable to digital computation. The first of these concerns the dependence of the pressure distribution in the entire aquifer furnishing the water drive upon the total reservoir withdrawals. This dependence is dictated by the permeability distribution and the extent of the aquifer; at present, such information is most readily obtained from the performance history by means of the resistancecapacitance reservoir analyzer. The second relation involves withdrawals, pressure in the reservoir, and movement of oil, gas, and water within the reservoir. The analysis is subject to certain simplifying assumptions that are necessary to permit solution of the problem. A comparison of the methods of this paper with those presently practiced is pertinent. One method of analysis is to use the reservoir analyzer to predict reservoir behavior based on aquifer characteristics determined from production history. Inasmuch as the total withdrawal rate depends upon the gas-oil and water-oil ratios, which depend in turn upon, among other things, the positions of the gas-oil and water-oil contacts, these ratios must be assumed in advance. In this paper these ratios are, instead, related to the computed positions of gas-oil and water-oil contacts. Thus, our method can be applied to problems in which the oil production rate is limited by produced gas-oil ratio, or to problems in which it is desired to determine the variable gas injection rate that will maintain the gas-oil or water-oil contact stationary. These problems cannot be worked satisfactorily on the analyzer. Another method presently used is based on a paper by Hurst.' Since his procedure is dependent upon using the solution of the heat flow equation, which requires constant permeability within the aquifer, and our procedure recognizes variations of permeability in

By E. W. Pehrson, J. W. Furness

NONMETALLIC MINERALS, exclusive of fuels, may be divided into three groups: Building materials, fertilizer minerals, and miscellaneous minerals. Building materials, such as sand, gravel, slone, lime, and the ingredients of cement and clay products, occur widely in nature and are thus available near consuming centers at relatively low prices. Cost of transportation over great distances deters any' substantial movement in world trade. On the other hand, fertilizer minerals, such as phosphate rock, potash, nitrates, sulfur, and pyrite, and the miscellaneous nonmetallic minerals, such as long-fiber asbestos, mica, graphite, fluorspar, and china clay, do not have such widespread occurrence and consequently contribute the major part of the world's commerce in such minerals. The U. S. Bureau of Mines has prepared charts showing the inter-

Jan 1, 1936

By Lyman Taylor, Alexander R. Troiano

STUDIES of the transformation of austenite at constant subcritical temperatures have been numerous since the work of Davenport and Bain.1 Considerable information has been obtained on low-alloy steels and on high-carbon alloys containing undissolved carbide or graphite at the austenitizing temperature. Little is known of the isothermal transformation of austenite containing in solution large amounts of both carbon and a single alloying element. In this investigation four steels containing one per cent carbon and with chromium in the range 3 to 9 per cent have been examined with the view to establishing the fundamental character of the isothermal reactions when all carbon and chromium are initially in solution in austenite. EXPERIMENTAL PROCEDURE Alloys The chemical compositions of the steels investigated are given in Table I. The 4 per cent Cr alloy is a commercial steel. The other steels were made by the Carpenter Steel Co. as 50-lb., induction-furnace heats and rolled to 5/8-in. round bars. Bars were softened at 650° to 700°C. before the specimens were cut. [ ] Metallographic Method Most of the lines on the transformation diagrams presented here have been placed on the basis of the microscopic examination of partially reacted specimens. Thees specimens were approximately ½ by ¼ by 1/8 in. in size. Specimens of the 9 per cent Cr steel were held 10 to 12 hr. at 1200° to I225°C. before quenching to the various subcritical temperatures. The other steels were held for 2 to 2 ½ hr. at 1200°C. before quenching. These treatments, carried out in an atmosphere of purified nitrogen, produced an austenite grain size larger than A.S.T.M. No. I, some grains being 1 to 2 mm. in diameter. There were a few undissolved carbide particles in some specimens of the 9 per cent Cr steel. It is believed, however, that any errors in the results due to incomplete solution of carbon and chromium in austenite are negligible; that is, austenite compositions may be considered as being those listed in Table I. X-ray Methods Constituents were identified and martensite axial ratios determined from Debye

Jan 1, 1945

COMPARED with the equipment used in most industrial processes, the open-hearth furnace has a relatively short life. The most important quality of an open-hearth refractory, therefore, is its rate of failure. This discussion of the physics and chemistry of the individual refractory materials will keep upper- most the question "Why, how, and where does it fail?" CAUSES OF FAILURE The principal causes of failure of open-hearth refractories are, in their order of importance: 1.Reaction with iron oxides. 2. Reaction with slag. 3. Flow and failure under load. 4. Melting. 5. Spalling. 6. Mechanical breakage. Reaction with Iron Oxides and Slag. Reaction with iron oxides and slag is by far the most important cause of failure. Liquid iron oxide comes near to being the "universal solvent" sought for by the alchemists. Among the materials commonly used in the open-hearth furnace, magnesia has the greatest resistance to this liquid and fireclay the least. The relations of iron and oxygen at high temperatures are illustrated in Fig 14-18. The liquid iron oxide that forms wherever iron is in contact with air or combustion gases cannot be given a definite formula. The percentage of oxygen at steelmaking temperatures may range from 21 to 28 (iron 79 to 72), depending upon the temperature and the oxygen pressure and also upon whether or not the liquid is in equilibrium with metallic iron. Oxide mixtures exist not only in the solid and liquid phases but also in the vapor phase, for metallic iron and its oxides have

Jan 1, 1951

COMPARED with the equipment used in most industrial processes, the open-hearth furnace has a relatively short life. The most important quality of an open-hearth refractory, therefore, is its rate of failure. This discussion of the physics and chemistry of the individual refractory materials will keep uppermost the question "Why, how, and where does it fail?" CAUSES OF FAILURE The principal causes of failure of open-hearth refractories are, in their order of importance : 1. Reaction with iron oxides. 2. Reaction with slag. 3. Flow and failure under load. 4. Melting. 5. Spalling. 6. Mechanical breakage. Reaction with Iron Oxides and Slag. Reaction with iron oxides and slag is by far the most important cause of failure. Liquid iron oxide comes near to being the "universal solvent" sought for by the alchemists. Among the materials commonly used in the open-hearth furnace, magnesia has the greatest resistance to this liquid and fireclay the least. The relations of iron and oxygen at high temperatures are illustrated in Fig 14-18. The liquid iron oxide that forms wherever iron is in contact with air or combustion gases cannot be given a definite formula. The percentage of oxygen at steelmaking temperatures may range from 21 to 28 (iron 79 to 72), depending upon the temperature and the oxygen pressure and also upon whether or not the liquid is in equilibrium with metallic iron. Oxide mixtures exist not only in the solid and liquid phases but also in the vapor phase, for metallic iron and its oxides have

Jan 1, 1964

By A. B. Tanner

The effects of radon in drillholes on gamma-ray logs have been described by L. S. Hilpert and C. M. Bunker1 Since these effects may cause drastic error in the evaluation of uranium deposits, it is useful to know the conditions under which significant amounts of radon tend to accumulate in drillholes. In the studies described here, atmospheric conditions were found to dominate in the control of the behavior of radon in drillholes in the vicinity of a uranium orebody. The site of the investigation was in McKinley County, New Mexico, about 12 miles north of Grants. Drillholes of 4 1/4-in. diam, on 25-ft and 100-ft centers, penetrate ore in dry rock at a depth of about 100 ft. A geologic log of the drillhole of primary interest is shown in Fig. 1. Gamma-ray logs revealed three zones of ore-grade mineralization in the Todilto limestone. A 6-ft zone, the lowest of the three, assayed 0.20 pct U3O8 by chemical analysis. The limestone ores in this area contain disseminated uraninite and some yellow and orange secondary minerals. Only radon"", a member of the uranium'" series, was measured in this investigation. Radon is one of the chemically inert noble gases and is radioactive by alpha particle emission with a half life of about four days. In this discussion, amounts of radon are expressed in microcuries (1 microcurie equals 37,-000 disintegrations per sec) and concentrations of radon are expressed in microcuries per liter of drillhole air. Samples of air were obtained by lowering a sampling device (Fig. 2) into a drillhole and actuating the device at the desired depth. It was then raised to the surface and the sample was transferred to a storage tube. Within two days the sample was transferred to an ionization chamber, and the activ- ity of radon and its short-lived daughter products was measured at radioactive equilibrium with a vibrating-reed electrometer. The measurements were corrected back to the time of collection and involve errors estimated generally not to exceed + 5 pct to —15 pct. Radon Behavior in a Covered Hole: Fig. 3, a typical log of radon concentration vs depth in the covered drillhole, was made by using values of radon concentration at discrete depths. Continuous logs of alpha-particle radiation in the drillholes showed that such radon logs depict the continuous variation of radon concentration with depth quite accurately. Three features of radon logs were noted: 1) maximum

Jan 1, 1960

By W. Philippoff

ALTHOUGH Gaudin1 and more recently Sutherland2 have calculated the probability of collision of a falling mineral particle with a rising bubble, there is no published information concerning the details of the mechanism of attachment of a collector-coated particle to a bubble. During the past year the writer has developed a theory for the mechanism of attachment, which has been substantiated experimentally. Funds for the investigation and for some of the equipment used have been supplied by the Mines Experiment Station of the University of Minnesota. Motion picture studies of the phenomena involved in the collision between mineral particles and bubbles, such as those of Spedden and Hannan," show that the contact can be completed within 0.3 millisec. Formulas developed for rigid bodies have hitherto been used' for the calculation of the motion of bubble and particle, but it is obvious that a bubble cannot be regarded as a rigid body. On the contrary, Spedden and Hannan's pictures show a great degree of deformation during the collision. The time of attachment was calculated as the time the particle drifted past the bubble. Time of Collision The theory presented in this paper enables calculation of the time of collision, using the concept that the bubble, or more generally, a liquid-air interface, acts as an elastic body. The elasticity, defined as the restoring force on a mechanical deformation, is caused by the surface tension and is the result of the principle of the minimum of free surface energy. It is well known that an elasticity together with a mass determines a frequency of vibration. The vibrations of jets and drops caused by the elasticity of the interface are known to comply exactly with the classical theory of capillarity.' However, the vibrations of isolated bubbles, as distinct from foams, have not been investigated previously. The following equation, presented elsewhere,' has been deduced for these frequencies: 3_____________________ fB = 9.20.vV.vn. (n-1).(n+2)/8 [I] in which fB is the frequency of a harmonic of the bubble in cycles per second, V the volume of the bubble in cc, n a number determining the order of the harmonic, and n = 2 the basic vibration. The first (basic) harmonic describes a change of the spherical bubble to an ellipsoidal bubble. The higher harmonics are more complicated, for the circumference of the bubble is divided approximately into as many parts as the order of the harmonic. As an example, Spedden and Hannan's published motion picture of a vibrating bubble corresponds to the sixth harmonic. Eq 1 shows that only the first and third harmonics are simple multiples (1 and 3), all the others being irrational fractions of the basic frequency. This means that the shape of the vibration can change with time and is in general unsym-metric in respect to the time axis. Such conditions prevail when there is a distributed elasticity or mass, as in the case of vibrating membranes or rods. The constant 9.20 is valid for water at room temperature, but a general solution involving the physical constants of the liquid has not been found. The case of the floating particle is much easier to treat than that of the bubble. It can be assumed that the elasticity is caused exclusively by the interface and that the mass is concentrated in the particle together with some adhering water. The following expression for the frequency of a system of one degree of freedom can be applied: fP = -1/2-vE/m [2] Here fp is the frequency of the particle vibration in cycles per second, E the elasticity in dynes per cm, and m the mass in grams. The classical theory of impact phenomena gives the time of collision during the striking of a spring (in this case the surface of the bubble) by a mass, as: t, = 2/f = nvm/E [3] It is now possible to develop an expression for the elasticity of a floating cylindrical particle. The force equilibrium of a cylinder floating end on at the air-liquid interface is given by the well-known equation (Poisson7 1831) P = /4 D2-pL-g-h + D.y sin a [4] which accounts for the buoyancy and the action of the surface tension where P is the force acting on the particle in dynes (weight-buoyancy), D the diameter of the cylinder in cm, PL the density of the liquid in grams per cc, g the acceleration of gravity = 981 cm per sec2, h the depression of the cylinder below the surface of the liquid in cm, y the surface tension in dynes per cm and a the supporting angles or the one required to insure equilibrium, a being smaller than the contact angle 0. Although demonstrated by Poisson, it has not

Jan 1, 1953

By W. Philippoff

ALTHOUGH Gaudin1 and more recently Sutherland2 have calculated the probability of collision of a falling mineral particle with a rising bubble, there is no published information concerning the details of the mechanism of attachment of a collector-coated particle to a bubble. During the past year the writer has developed a theory for the mechanism of attachment, which has been substantiated experimentally. Funds for the investigation and for some of the equipment used have been supplied by the Mines Experiment Station of the University of Minnesota. Motion picture studies of the phenomena involved in the collision between mineral particles and bubbles, such as those of Spedden and Hannan," show that the contact can be completed within 0.3 millisec. Formulas developed for rigid bodies have hitherto been used' for the calculation of the motion of bubble and particle, but it is obvious that a bubble cannot be regarded as a rigid body. On the contrary, Spedden and Hannan's pictures show a great degree of deformation during the collision. The time of attachment was calculated as the time the particle drifted past the bubble. Time of Collision The theory presented in this paper enables calculation of the time of collision, using the concept that the bubble, or more generally, a liquid-air interface, acts as an elastic body. The elasticity, defined as the restoring force on a mechanical deformation, is caused by the surface tension and is the result of the principle of the minimum of free surface energy. It is well known that an elasticity together with a mass determines a frequency of vibration. The vibrations of jets and drops caused by the elasticity of the interface are known to comply exactly with the classical theory of capillarity.' However, the vibrations of isolated bubbles, as distinct from foams, have not been investigated previously. The following equation, presented elsewhere,' has been deduced for these frequencies: 3_____________________ fB = 9.20.vV.vn. (n-1).(n+2)/8 [I] in which fB is the frequency of a harmonic of the bubble in cycles per second, V the volume of the bubble in cc, n a number determining the order of the harmonic, and n = 2 the basic vibration. The first (basic) harmonic describes a change of the spherical bubble to an ellipsoidal bubble. The higher harmonics are more complicated, for the circumference of the bubble is divided approximately into as many parts as the order of the harmonic. As an example, Spedden and Hannan's published motion picture of a vibrating bubble corresponds to the sixth harmonic. Eq 1 shows that only the first and third harmonics are simple multiples (1 and 3), all the others being irrational fractions of the basic frequency. This means that the shape of the vibration can change with time and is in general unsym-metric in respect to the time axis. Such conditions prevail when there is a distributed elasticity or mass, as in the case of vibrating membranes or rods. The constant 9.20 is valid for water at room temperature, but a general solution involving the physical constants of the liquid has not been found. The case of the floating particle is much easier to treat than that of the bubble. It can be assumed that the elasticity is caused exclusively by the interface and that the mass is concentrated in the particle together with some adhering water. The following expression for the frequency of a system of one degree of freedom can be applied: fP = -1/2-vE/m [2] Here fp is the frequency of the particle vibration in cycles per second, E the elasticity in dynes per cm, and m the mass in grams. The classical theory of impact phenomena gives the time of collision during the striking of a spring (in this case the surface of the bubble) by a mass, as: t, = 2/f = nvm/E [3] It is now possible to develop an expression for the elasticity of a floating cylindrical particle. The force equilibrium of a cylinder floating end on at the air-liquid interface is given by the well-known equation (Poisson7 1831) P = /4 D2-pL-g-h + D.y sin a [4] which accounts for the buoyancy and the action of the surface tension where P is the force acting on the particle in dynes (weight-buoyancy), D the diameter of the cylinder in cm, PL the density of the liquid in grams per cc, g the acceleration of gravity = 981 cm per sec2, h the depression of the cylinder below the surface of the liquid in cm, y the surface tension in dynes per cm and a the supporting angles or the one required to insure equilibrium, a being smaller than the contact angle 0. Although demonstrated by Poisson, it has not

Jan 1, 1953

By W. Philippoff

ALTHOUGH Gaudin1 and more recently Sutherland2 have calculated the probability of collision of a falling mineral particle with a rising bubble, there is no published information concerning the details of the mechanism of attachment of a collector-coated particle to a bubble. During the past year the writer has developed a theory for the mechanism of attachment, which has been substantiated experimentally.' Funds for the investigation and for some of the equipment used have been supplied by the Mines Experiment Station of the University of Minnesota. Motion picture studies of the phenomena involved in the collision between mineral particles and bubbles, such as those of Spedden and Hannan,3 show that the contact can be completed within 0.3 millisec. Formulas developed for rigid bodies have hitherto been used' for the calculation of the motion of bubble and particle, but it is obvious that a bubble cannot be regarded as a rigid body. On the contrary, Spedden and Hannan's pictures show a great degree of deformation during the collision. The time of attachment was calculated as the time the particle drifted past the bubble. Time of Collision The theory presented in this paper enables calculation of the time of collision; using the concept that the bubble, or more generally, a liquid-air interface, acts as an elastic body. The elasticity, defined as the restoring force on a mechanical deformation, is caused by, the surface tension and is the result of the principle of the minimum of free surface energy. It is well known that an elasticity together with a mass determines a frequency of vibration. The vibrations of jets and drops caused by the elasticity of the interface are known to comply exactly with the classical theory of capillarity.5 However, the vibrations of isolated bubbles, as distinct from foams, have not been investigated previously. The following equation, presented elsewhere,' has been deduced for these frequencies: [3fB = 9.20•'./V•Vn- (n-1) • (n+2) /8[1]] in which fB is the frequency of a harmonic of the bubble in cycles per second, V the volume of the bubble in cc, n a number determining the order of the harmonic, and n = 2 the basic vibration. The first (basic) harmonic describes a change of the spherical bubble to an ellipsoidal bubble. The higher harmonics are more complicated, for the circumference of the bubble is divided approximately into as many parts' as the order of the harmonic. As an example, Spedden and Hannan's published motion picture of, a vibrating bubble corresponds to the sixth harmonic. Eq 1 shows that only the first and third harmonics are simple multiples (1 and 3), all the others being irrational fractions of the basic frequency. This means that the shape of the vibration can change with time and is in general unsymmetric in respect to the time axis. Such conditions prevail when there is a distributed elasticity or mass, as in the case of vibrating membranes or rods. The constant 9.20 is valid for water at room temperature, but a general solution involving the physical constants of the liquid has not been found. The case of the floating particle is much easier to treat I than that of the bubble. It can be assumed that the elasticity is caused exclusively by the interface and that the mass is concentrated in the particle together with some adhering water. The following expression for the frequency of a system, of one degree of freedom can be applied: [1E/m[2] fP = 27] Here f, is the frequency of the particle vibration in cycles per second, E the elasticity in dynes per cm, and m the mass in grams. The classical theory of impact phenomena gives the time of collision during the striking of a spring (in this case the surface of the bubble) by a mass, as: [t~ = 2/f = 7r\/m/E[3]] It is now possible to develop an expression for the elasticity of a floating cylindrical particle. The force equilibrium of a cylinder floating end on at the air-liquid interface is given by the well-known equation (Poisson' 1831) [aP = 4 D2.pL•g•h +7rD•y sin a[4]] which accounts for the buoyancy and the action of the surface tension where P is the force acting on the particle in dynes (weight-buoyancy), D the diameter of the cylinder in cm, pL the density of the liquid in grams per cc, g the acceleration of gravity = 981 cm per sec2, h the depression of the cylinder below the surface of-the liquid in cm, y the surface tension in dynes per cm and a the supporting angle' or the one required to insure equilibrium, a being smaller than the contact angle ?. Although demonstrated by Poisson, it has not

Jan 1, 1952

By Tracy Jarrett

In 14-karat gold alloys, as in 10-karat gold alloys,3 the addition of such metals as zinc, nickel, copper and silver produces a wide range of physical and chemical proper-ties such as color, hardness, corrosion resist-ance and melting points. These important factors made gold alloys desirable in the optical work and for jewelry. In 14-karat gold alloys, as well as in 10-karat or 12-karat, it is possible to have two golds of the same color, one of which will corrode more than the other, although it may be harder. Some of these alloys have been investigated by F. E. Carter,1 E. M. Wise,5 and L. Sterner Rainer.4 In this group of alloys the gold content of 58.3 per cent (14-karat) was held constant, while the copper varied from 36 to 24 per cent. The balance of the alloy consisted of one, two, or three of the metals silver, zinc, and nickel. All the alloys were melted in an induction furnace and cast into an ingot that meas-ured 3 by 1/4 by 3/4 in. The method of determining the melting points, color deter-minations and acid test have been discussed in previous papers by the author.2,3 It is necessary to use small test bars (Fig. r). The tensile bars were annealed at 1300°F. for 20 min. and then air-cooled. There being a very marked drop when the yield point was reached, "the drop of the beam" method was used in determining the yield point.

Jan 1, 1940

By C. P. Sandberg

Having been occupied in inspecting and testing iron and steel these twenty years in England, and previous to that having served on the Board of Iron Masters in Sweden, I have naturally been very much interested in the subject of the use of steel for structures. I regret that I can offer but comparatively small experience on that had, having had principally to do with steel for railway plant and rails, but granting these to be a kind of "structure," and also that steel for rails has similar duties to perform in many respects, and is generally manufactured in the same way and at the same works as steel for stuctures, properly speaking, I may be entitled to offer an opinion on the use of steel in construction. In a paper recently presented to the Institution of Civil Engineers in London, Mr. Ewing Matheson has recommended that the Board of Trade rules should be amended so as to allow of a maximum straining of 8 tolls per square inch instead of 6 1/2 tons. But it is equally necessary to fix the amount of ductility or elongation of the metal for such a strain as 8 tons. Strength and ductility should always be spoken of together. Mr. Matheson says that steel can be manipulated in the factory in the same way and with the same tools as are used for iron. This can only be granted for mild steel; for hard steel would be spoilt by the rough mechanical treatment which iron can stand, such as punch ing, for instance; and the remedy for regaining the strength lost by punching hard steel, viz., annealing, cannot always be applied. Noth ing proves this fact better than the punching of steel rails of consid erable hardness, which caused fractures at an early period of steelunaking, and which resulted in the stipulation for drilling instead of punching the bolt-holes, which had been formerly applied to iron rails without any damage. In fact commissions to establish standard tests are now working on the Continent, principally in Germany, where

Jan 1, 1882

By Robert E. Green, T. Hinton

Expressions are derived for tke orientation factors appearing in the Grana to -Lucke theory of dislocation damping, for fcc crystals. The factors are given as functions of the elastic constants, the direction cosines of the specimen axis, atld the direction cosines of the particle displacemeizts, for darnping due to dislocation motion on each of the twelve possible slip systems as ixell as lor simultaneous dislocation rnotion on all twelve systems. RECENTLY Green' has outlined the general procedure for calculation of the modes of wave propagation in a single crystal possessing a given crystallo-graphic orientation. In addition he has suggested how the results of such calculations along with calculations of the resolved shear-stress factors for slip enable the orientation-dependent factors (orientation factors) appearing in the Granato-Lucke theory of dislocation damping to be calculated. However, reen' assumed that the maximum stress on dislocations was in the direction of the particle displacement of the elastic wave giving rise to the dislocation damping. The present cal'culations show that this is an oversimplified approach appropriate only to special cases of high crystallographic symmetry. The exact calculation of stress on the dislocations can only be obtained by resolving the nine components of stress associated with the elastic wave into the appropriate slip direction and then summing. In this paper the general expressions for orientation factors are derived for fcc crystals in terms of the elastic constants, the direction cosines of the particle displacements, and the direction cosines of the specimen axis, bearing in mind the point mentioned above. Equations are presented which give the orientation factors for damping due to dislocation motion on each of the twelve possible slip systems as well as for simultaneous dislocation motion on all twelve systems arising from elastic-wave propagation. These orientation factors are appropriate to attenuation measurements made by the pulse-echo technique, where the elastic wave is a traveling wave. They will be compared with those for the case of a standing wave as derived by Granato and Lucke which are appropriate to measurements of internal friction by the resonance technique. The expressions for the orientation factors are compared with the five values given by insruch,' based on unpublished work of Granato and Liicke, for positions of highest symmetry in the stereographic triangle. The various equations derived for modes of wave propagation and orientation factors have been evaluated for the case of aluminum crystals at 1-deg intervals throughout the stereographic triangle. These results will be presented in the form of contour diagrams in a subsequent paper3 and their relevance to ultrasonic measurements discussed. ORIENTATION FACTORS The coordinate system used for the calculations is shown in Fig. 1 and all specimen axes are taken to lie in the shaded standard triangle. The twelve slip systems are indexed according to Table I. Following the suggestion of lers, we may define the orientation factor Ok in the Granato-Liicke theory5 by the equation

Jan 1, 1967

By AIME AIME

ON the afternoon of Feb. 20 of this year a new volcano was born in the center of the State of Michoacan, Mexico, about 100 miles inland from the Pacific Coast. Creation of this new mountain - forming crater began on an almost flat cultivated field at the south margin of a small basin about a mile in diameter and having an altitude of approximately 6800 ft. above sea level. This basin is connected to a gently inclined plain that forms the Parangaricutiro valley, the chief town of this municipality, bearing the same name as the valley, being situated three miles from the site of the new crater. The village of Paracutin, from which the new volcano received its name, is about one mile to the northwest of the crater. From the City of Mexico to the volcano is a distance of 330 miles. The paved highway running from Mexico City to Guadalajara, by way of Toluca and Morelia, is left at Carapan; from here another paved branch highway goes to Uruapan. The town of Paracutin is reached by a narrow dirt road 18 miles from Uruapan and connects with a road leading to Parangaricutiro where horses may be hired for a 40-minute trip to a place where visitors can enjoy a magnificent view of the volcano. It is possible to get within half a mile of the point of eruption in this manner.

Jan 1, 1943

By W. G. Davenport, M. Paneni

Experiments in sheets of mercury and water have confirmed that the dynamics of bubble rise are simi-lur in Liquid metal and aqueous systems. RECOGNITION that bubble/metal interactions are important in pyrometallurgical refining processes (e.g., steelmaking, vacuum degassing, deoxidation of copper) has led to a number of investigations into the dynamic behavior of bubbles rising in liquid metals. Terminal velocities of bubbles rising in mercury (20°C)' and silver (1000" to 1050"c)1,2 have been measured. Good agreement between aqueous and liquid metal systems has been obtained. Shapes of air bubbles rising in mercury have been determined experimentally by Davenport, Bradshaw, and Richardsonl who used a system of electric probes to measure maximum horizontal and vertical dimensions, Fig. 5. In the present work the motion and shape of nitrogen bubbles rising in a thin sheet of mercury (i.e., a "two-dimensional" environment) have been studied with the view of confirming dynamic similarity between aqueous and metallic systems. The use of thin sheets of liquid permitted direct visual and photographic comparisons of bubble behavior in clear liquids and in mercury. EXPERIMENTAL METHOD The thin sheets of mercury or water were held in a clear acrylic plastic container, Fig. 1. The sheets of liquid were 80 cm high by 30 cm wide and 0.47 cm thick. Single bubbles were formed by injecting the desired volume of nitrogen into an inverted semicircular cup (stainless steel). The cup was then rotated into the upright position using an external handle thus releasing a single bubble of measured volume. Nitrogen was injected into the cup from a nitrogen cylinder through the external handle and a hollow rotating axle. The volume of a bubble (volume range 0.01 to 10 cu cm) at any instant was obtained by connecting a soap film meter to a small gas space above the liquid. By this technique any change in the volume of a gas bubble in the liquid (i.e., during cup filling or during rise) produces an equivalent displacement from gas space A into the buret B. This displacement is determined by measuring the movement of a horizontal soap film in the buret. Bubble shapes were determined using single-frame photography. Rising velocities were determined by cinephotography with a 1/100-sec stopwatch in the field of view. In both cases dimensions were referenced to a rule attached to the container surface, also in the field of view. Linear dimensions were measured on projections of the single-frame negatives. Rising velocities were calculated from measured heights of rise (10 to 20 cm) and times of rise. The effects of disturbances caused by cup rotation and by bubble release were minimized by photographing bubbles at a point not less than 25 cm above the cup. MATERIALS Mercury: Technical-grade purified: minimum 99 pct Hg; Johnson Matthey and Mallory Limited, Toronto. Nitrogen: Technical-grade purified nitrogen: 99.99 pct Nz, 0.01 pct 02, trace argon; Air Liquide Canada Limitee, Montreal.

Jan 1, 1970

By P. Somasundaran

INTRODUCTION Large amounts of mineral values are discarded today as fines and ultrafines, because of inadequate technology to process them economically. Most conventional mineral processing techniques fail in the sub-sieve range. Fines respond poorly to processes such as flotation either due to change in mineralogy and surface composition or even simply due to the direct effect of their smallness in size on collision and adhesion rates between them and air bubbles. Indeed if the poor flotation is due to the smallness in size, a solution must rest in aggregating the fines. Inorganic electrolytes as well as polymers have been successfully used as flocculants in the past for obtaining increased flotation of colloidal material from waste water effluents. In mineral beneficiation, this technique can be profitably used if the process of flocculation can be made to take place selectively. The power of the selective flocculation technique has already been proven, with the successful application of it in the case of beneficiation of low grade iron ore by the Cleveland-Cliffs Iron Ore Company and potash ore by Cominco. The process holds tremendous potential when it is followed by flotation, elutriation, etc. Today its application is, however, limited to the above two cases and it has become clear that a full understanding of the process will prove helpful for developing solutions to various problems that exist both at the basic and applied levels. In this paper, principles that are known to govern selective aggregation processes such as selective flocculation, carrier flotation and spherical agglomeration will be examined and areas of uncertainties will be identified.

Jan 1, 1979

By H. D. Merchant

NUMEROUS publications have examined hot hardness of metals and alloys. Some have studied creep in long-time hardness tests, few of which, however, were tested under a spherical indentor. 1-3 The results of Mulhearn and Tabor' indicate a parabolic-type creep for indium and lead, whereas Moore and Tabor2 how a logarithmic-type creep for indium. Similar semilog relationships between hardness and time have been found by Goffard and wheeler3 for magnesium, aluminum, and their alloys. In this note, the elevated-temperature hardness of some complex alloys, shown in Table I, was examined to discover whether any basic information about the deformation behavior of the alloys could be obtained. One of the alloys, H-13 alloy steel, was tested for short-time creep tests to examine the hardness-time relationship at various temperatures. A standard Brinell Hardness Tester, mounted with an appropriate furnace and 99 pct A12O3 poly-crystalline indentor, was employed for the purpose. The alloys were tested at temperatures from room to 1400°F for 30 sec under 1500-kg load. The creep studies were conducted for about 8500 sec at 7l°, 500°, 1000°, and 1200°F. For constants A and B, a relationship of the type H = Aexp(-BT) [ll was obtained for all alloys between hardness, H, and temperature, T. In the semilogarithmic plot, the data points for each alloy were arranged into two groups, each group on a straight line with a specific set of A and B values. These results are in agreement with many such observations on hot hardness, notably those of Westbrook for pure metals,4 The thermal softening coefficient, B, and transition temperature, Tt, for various alloys are shown in Table I. The change in slope around the transition temperature suggests an apparent change in the mechanism of deformation, probably from the shear (below Tt) to the diffusion type of mechanism. At the temperatures above Tt, for constants A' and B, a relationship of the type was obtained between H and T, Fig. 1. The nature of the equation, where R is gas constant, suggests the possibility of a thermally activated mechanism of deformation above Tt. The constant B' may hence be defined as the apparent activation energy of indentation. The B' values of various alloys are shown in Table I. A plot of B vs B' gives a curvilinear relation shown in Fig. 2. The indentation-creep data for H-13 alloy steel is shown in Fig. 3. At 71" and 500°F, the creep initially follows the logarithmic time law. However, the indentation size stabilizes after 7 sec at 71°F, and after 10 sec at 500°F. Further increase in loading time has no effect on indentation size. The creep of 1000° and 1200°F follows the logarithmic time law for the first 1000 sec, after which the

Jan 1, 1964

By R. F. Shurtz

R. Duval (Mining Engineer, Ancien eleve de PEcole Polytechnique, Paris, France) I do not agree with the Eq. 3, reading: m =1/100- [(0.214x30.4) + (0.7B6 x0.00)] =6.5pct CaO If 0.214 and0.786 were proportions by weight, the equation would represent the well known mixtures law of the conventional arithmetics and 6. 5 pct CaO would be the correct average content. But it is not the case as the author states: "In samples consisting of single grains of mineral, those grains must, as already mentioned, be either of dolomite or magnesite. Since 78.6 pct of the deposit consists of magnesite and 21.4 pct of dolomite (excluding for present purpose the presence of other minerals), for any single grains picked at random the probability will be 0.214 that is it dolomite and0.786 that is it magnesite. In 1000 such samples the expected numbers of dolomite and mapesite grains will be 214 and 786 respectively." 0.214 and 0.786 would be proportions by weigbt under the necessary condition that all grains of dole mite and magnesite should have an identical weight. Obviously it is not the case, as the specific gravities are not the same for mapesite and dolomite and the volumes of the grains are different. Furthermore, because of these differences the conditions for a random sampling are not fulfilled and we are not authorized to state that the probabilities are, respectively, 0.214 and 0.786. The author however makes a simple application of Eq. 1: M = 1/n— ? fi x i . n Should we deduce that this relation is wrohg? Not at all, but when applying Eq. 1 you must not overlook what it actually. means. Eq. 1 gives a definition of the arithmetic mean of a total of n observed values Xi and nothing else. But the average conteht of a deposit has not the same significance. It is the ratio between the weight of concerned mineral in the deposit and the total weight of the deposit. As from 1000 particles the 214 of dolomite and the 786 of magnesite have not the same weight, the two definitions do not concur, and when applying Eq. 1 the result is an arithmetic mean of figures which has no connection with what is named average contentof a deposit. The situation is similar to the calculation of an average velocity. If a car travels a first mile over at 30 miles per hr and a second mile over at 60 miles per hr, when applying formula 1 you find as average velocity for the 2 miles: 30+60 ------- - 45 miles per hour. Many people calculate in this way and they do not realize that a mistake is involved. In fact the definition of he average velocity for the 2 miles is the quotient of the distance of 2 miles by the time (in hours) necessary for 2 miles travel, i.e.: 2 ---------- = 40 miles per hr. 1 + 1 30 60 In other words, the average volocity wanted is not the arithmetic but the harmonic average of the two velocities. The above mentioned bias in the calculation of the average contents of deposits is frequent, even in the assessments made by experienced engineers and is independant of what is named the sampling error. In order to supress the bias and to be able to use Eq. 1, you must apply a correction. An example on the subject can be found in an article by Duval et al. in the January 1955 issue of the ''Annales des Mines" (French), page 19. R. F. Schurtz (Author's Reply) Mr. Duval's position is quite correct. The proportions shown for dolomite and magnesite., respectively, of 0.214 and 0.786 are, in fact, proportions by weight uncorrected for specific gravity. In our day to day operation of producing magnesite from these mines at a very substantial rate, we do not normally make corrections for the difference between the specific gravity of dolomite and that of magnesite. If these corrections are made in Eq. 3 as shown in my article, then the numbers of grains turn out to be in proportions of 0.226 dolomite and 0.774 mapesite instead of the values actually shown in the equation. For the purposes of our work, and in view of the inherently low accuracy of the data, this correction was not deemed worthwhile making.

Jan 1, 1961

By R. C. Croft

Chlorination is frequently employed as a method of chemical attack and separation of the constituents of minerals. Occasionally, bromination has been used similarly. Separation of metal halides resulting from the use of either of these halogens generally entails difficult fractional distillation of the halides. Recovery of the halogens for re-use has often been attempted in the case of chlorine by oxidation of chlorides. Though attractive thermodynamically, this method of recovery fails due to the formation of stable oxychlorides. Although a little less reactive than either chlorine or bromine, iodine offers advantages in the field of mineral treatment. It has been shown, for example, that iron may be removed completely from ilmenite by iodinating the latter in the presence of carbon or hydrogen at temperatures near 800°c where good reaction rates are obtained. Under these conditions titanium does not form an iodide and is not transported in the vapour phase as is the Fe12 formed. Other good separations obtained between zinc and iron in willemite and tin and tungsten in scheelite concentrates confirm that separations of metal iodides by sublimation are more specific than similar separations attempted by distillation of volatile chlorides. Readiness of iodides to form stable vapour-phase complexes appears to contribute to this specificity. The very low stabilities of most metal oxyiodides permit quantitative recovery of iodine by oxidation of metal iodides. In the case of Fe12 derived from iodination of ilmenite, full recovery of iodine can be achieved by air oxidation of this compound at temperatures ranging from 350 to 500° C.

Jan 1, 1973