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By John G. Simmons

A tutorial account of the tunnel effect between metal electrodes separated by a thin insulating film is presented. Energy diagrams of metal-insulator -metal sandwiches are briefly discussed, and the isothermal and thermal J-V characteristics for symmetric and asymmetric tunnel junctions are derived from a generalized expression. Experimental data from tunnel junctions are presented, and it is shown how, correlation between theory and experiment permits a determination of some of the oxide properties. Finally, the barrier heights in AT-Al2O3-A1 junctions determined by various inr3estigators are discussed. The object of this paper is to give a tutorial account of the electric-tunnel effect between metal electrodes separated by a thin insulating film and to illustrate its utility in the study of metal-oxide interfaces. This paper will emphasize the theoretical aspects of the electric-tunnel effect: however, a brief account of the more recent experimental work will be presented. A more comprehensive experimental study of the tunnel effect will be presented in the following paper by Drs. Pollack and Morris, see p. 497. We will open with a discussion of the energy diagrams for metal-insulator-metal junctions and what we mean by the electric-tunnel effect. Following this is an account of the theoretical studies of Sommerfeld and Bethe, and Holm, and the recently reported calculations on symmetric and asymmetric junctions using the generalized formula. The theoretical presentation is concluded with calculations on the temperature dependence of the tunnel J-V characteristic. In the experimental section, it is shown how barrier heights and thicknesses are determined by comparing the experimental data with the theory. Finally, the results of various investigators on the determination of the barrier heights in Al-Al2O,-A1 systems are discussed. I) POTENTIAL BARRIERS BETWEEN CLOSELY SPACED ELECTRODES Since it is necessary to supply energy to a metal in order to observe electron emission from its surface, it is evident that the potential energy of an electron within a metal is lower than that of an electron at rest outside the metal. It follows, then, that the electron must undergo a change in potential as it crosses the metal-vacuum interface. In the Sommerfeld1 free-electron theory of metals it is assumed that the free electrons, the electrons responsible for the electrical characteristics of metals, move in a constant potential environment in the metal, and are contained within the metal by a potential barrier at the metal-vacuum interface. It will be evident that the idea of a constant potential environment is a very idealized model, since the potential energy of an electron is influenced by all of the atoms and the other electrons within the metal; however, its use is justified by the many excellent results it gives.2 Fig. l (a) is the energy diagram of the model envisaged by Sommerfeld; the metal is represented by a potential-energy well of depth V,; the vacuum level represents the energy of an electron at rest outside the metal. At 0°K the electrons, which exist in pairs in discrete energy levels, fill up the well to an energy ?, the Fermi level. The distance, Vo - ?, from the Fermi level to the vacuum level is known as the work function of the metal, and represents the minimum energy required to free electrons from the interior of the metal at 0°K.

Jan 1, 1965

Jan 1, 1969

By J. P. Zannaras

If we assume that testing of the model started at time C, that time t2 was the instant at which the elastic limit of the material was passed at the points of the maximum stress, and that at time t3 the failure of the model was completed as shown in the typical photograph (Fig. 1), then actually the photograph shows the final results of what took place between time t2 and t3. By the principle of similitude all conclusions drawn from the behavior of the model were applicable and valid for actual mine roofs up to the time t, after time t, motions and friction came into play during the destruction of the model. The events between t2 and t3 and the photograph itself are not representative of the events expected in an actual mine roof unless corrections imposed by the principle of similitude are made.

Dec 1, 1956

By Robert Davis Longyear

In diamond-drill work, a true sample consists of all the material cut by the bit—both core and cuttings. As the recovery of this sample is the object of diamond drilling, the utmost care should be taken to secure it. Speed of drilling and low costs are of little value if an inaccurate sample is obtained. The engineer in charge must study his material and lay out the plan of sampling, and then see that the drill runner follows his instructions; for the runner may be more interested in obtaining a large footage than in developing accurate methods of sampling. When the core has been removed from the core barrel, it should be placed in a core box in the exact order in which it is taken from the ground. This box, Fig. 1, is usually a shallow tray 4 or 5 ft. (1.2 or 1.5 m.) long, with partitions running lengthwise between which the core

Jan 1, 1923

By Robert Davis Longyear

In diamond-drill work, a true sample consists of all the material cut by the bit—both core and cuttings. As the recovery of this sample is the object of diamond drilling, the utmost care should be taken to secure it. Speed of drilling and low costs are of little value if an inaccurate sample is obtained. The engineer in charge must study his material and lay out the plan of sampling, and then see that the drill runner follows his instructions; for the runner may be more interested in obtaining a large footage than in developing accurate methods of sampling. When the core has been removed from the core barrel, it should be placed in a core box in the exact order in which it is taken from the ground. This box, Fig. 1, is usually a shallow tray 4 or 5 ft. (1.2 or 1.5 m.) long, with partitions running lengthwise between which the core

Jan 1, 1923

By John V. Beall

Thai means free. Historically accurate, as the country has never been subjugated by foreign occupation, the name "The Land of the Free" also seems to fit the attitude of the people. At the Bangkok airport, without so much as a kopkhun (thank you), travelers are found behind, beside and in front of ticket counters. A pretty Thai face on TV calls flights in English and Thai. Baggage disappears with alarming rapidity and your reporter and spouse despaired of ever being reunited with it. But at the entrance, all the parts came together and there was even a limousine from our hotel, The Oriental. Driving downtown English style, we noted that there were four lanes of traffic occupying the space we would allow for three lanes. Motorcycles and enclosed three-wheel motorcycle taxis were much in evidence, but the occasional water buffalo held up the slow lane. In the city, men wore European-type slacks and shirts but the women were colorful in traditional ankle-length wraparound skirts.

Jan 1, 1970

By A. Hellawell

Specitlrens of the Al-Ge eutectic alloy have been frozen unidivectionally at rates between 2.5 x 10-6 and 2.5 x 10-4 cm per sec and the structure examined by optical and X-ray methods. There is no epitaxial relationship between phases, the aluminum having random orientation and the germanium a preferred (011) fiber textuve. Lamellar colonies which are BINARY eutectic alloys occur between either silicon or germanium with the metals aluminum or silver. common in this alloy are constructed from axial and nonaxial (111) plates of germanium which are related by a variety of twin configurations. Irregular or globular regions of the microstructure are composed of continuous single crystals of each phase, the germanium being heavily twinned. There is limited solid solubility in these systems, and the eutectic phases all involve diamond cubic with fcc crystal structures. In the microstructures of these eutectic mixtures the silicon and germanium crystals exhibit an almost infinite variety of shapes which are notably sensitive to

Jan 1, 1968

By J. C. Scully, G. Sanderson

The electrolytic formation of y hydride in thin foils of Ti-5Al-Z.5Sn alloy and four Ti-A1 binary alloys has been studied by electron microscopy and electron diffraction. Two orientation relationships have been found: THE adsorption of hydrogen by titanium alloys from aqueous solutions has been widely reported. This can occur, for example, in both alkaline' and acidic2 pickling baths, in chemical polishing374 and electro-polishing Solutions,3,4 during cathodic polarization5" and under certain corrosion conditions,7,8 Etching reagents may also produce visible precipitates, sometimes after an aging period.9 During an investigation into the stress corrosion susceptibility of a titanium alloys by thin foil electron microscopy many observations have been made of hydride precipitation which has been deliberately promoted by techniques that are described below. The characteristics of hydride precipitation are reported and the observed crystallographic orientation relationships are discussed with reference to distortion in the titanium lattice created by the presence of the hydride. EXPERIMENTAL TECHNIQUE One grade of commercial titanium and five alloys were examined. Their composition and hardness values are shown in Table I. All the materials were in the form of thin sheet, 0.05 to 0.065 cm thick, which had been annealed after cold rolling. Foils suitable for transmission electron microscopy were made in two ways: a) by chemical polishing; and b) by elec-tropolishing. The solution used for chemical polishing was a mixture of 44 pct HF and 73 pct HNO3 in the volumetric ratio 2:3. During this polishing specimens were manually moved up and down in the solution. The reaction was veFy rapid, specimens thinning to foil thickness (2000A) in 5 min. Since chemical polishing solutions tend not to cause hydride contamination if they are kept cool3 no attempt was made to prevent the solution from becoming hot during the thinning operation. Electropolishing was performed at -30° C with a mixture3 composed of 295 cu cm methyl alcohol, 175 cu cm n-butyl alcohol, and 30 cu cm perchloric acid with an applied voltage of 40 v after chemically thinning specimens to approximately 0.017 cm thickness in a cool solution of 44 pct HF, 40 vol H2O2, and water in the volumetric ratio 1:6:3. EXPERIMENTAL RESULTS 1) Ti-5A1-2.5Sn Alloy. The Ti-5A1-2.5Sn alloy was severely contaminated by hydrogen during the chemical polishing. Foils obtained in this way contained large amounts of the y hydride phase. A typical micrograph is shown in Fig. l. The laths were identified as the hydride phase by selected-area diffraction of a large number of foils examined in a tilting stage that could be turned through 40 deg. Using the lattice spac-ings of the alloy obtained by X-ray diffraction as a standard the a value of the hydride was determined fromo the electron diffraction patterns to be 4.38 to 4.40A. The accuracy of this figure is only about ±2 pct. Further evidence of the identification was obtained by vacuum annealing chemically polished foils of the alloy at 500°C. This resulted in the dissociation of the hydride with the production of dislocations and possibly vacancy loops as shown in Fig. 2. The hydride

Jan 1, 1968

By F. M. Simonds, E. Z. Burns

The Rawley property is located in the Kerber Creek mining-district, Saguache county, Colorado, at an elevation of 10,600 ft. (See sketch-map, Fig. 1.) Ore was found in this vicinity as early as 1880, and claims covering a large area were located and in many instances patented. The ores, however, being of comparatively low grade, and the nearest railway station, Villa Grove, being some 20 miles away, it is extremely doubtful whether any considerable amount of ore was ever handled at a profit. It is safe to say that several hundred thousand dollars were spent (a large part in building mills) previous to 1902-03. About that time a very capable promoter gathered together a group of these claims and interested some New York people, who had had no previous mining experience, in the purchase of these claims. Following the organization of a company, this promoter became General Manager. As often happens under such conditions, the first step was to erect a mill to treat 100 tons per day. It may not be fair to this enterprise to say that the failure which followed might have been foretold, simply on general principles, but this much is certain—the water supply fluctuates in the course of a season through a wide range and for a considerable portion of the year was inadequate to run this mill at capacity. Further, it is currently reported that some of the mill foundations were placed on ice. However true this statement may be, it is a fact that, when first inspected by us, many of the belts in the mill were held on'their pulleys by means of idlers. A shut-down followed, with a material re-adjustment of interests, at which time we became consulting engineers for the company.

Jan 1, 1914

By A. Hultgren, G. Phragmén

Page Outline of Progress of Knowledge and Theories about Gas Evolution in Steel Ingots. and Its Influence on Crystallization and Segregation................ 134 Object of Present Investigation........................................... 148 Theoretical Discussion of Process of Solidification........................... 149 Gas Given Off from Rimming Steel during Solidification................... 149 Equilibrium Diagram of the Iron-carbon-oxygen Alloys................... 151 Solidification of Pure Iron-carbon-oxygen Alloys.......................... 157 Solidification when Carbon Monoxide Is Given Off at Constant Pressure... 157 Solidification when Gas Evolution Is Suppressed....................... 158 Schematic Application on Solidification of Rimming-steel Ingots.......... 159 Influence of Manganese, Sulphur and Phosphorus......................... 160 Experimental work..................................................... 162 Liquid Steel and the Mold Gas......................................... 162 Ingots Investigated and Methods Used.................................. 165 Ingot structure....................................................... 174 Structure of Rim Zone.............................................. 174 Structure of Core................................................... 181 Structures Obtained under Special Conditions of Freezing................ 182 Distribution of Metalloids............................................. 187 Other Observations Made............................................. 192 General Discussion of Solidification Process................................. 195 Condition of Liquid Steel before Casting................................. 195 Rimming Period...................................................... 202 Composition of Rim Zone............................................. 225 Freezing after Top Is Closed........................................... 228 Slag Inclusions and Ingot Scum........................................ 234 Reaction between Gas in Blowholes and Surrounding Solid Steel during Cooling 235 Summary.............................................................. 237 Appendix—Preparation and Etching of Ingot Sections....................... 238 References............................................................. 239 In 1934, Jernkontoret (The Swedish Ironmasters' Association) appointed a committee for the study of the structure of rimming-steel ingots and the various phenomena associated with their solidification. The members of the committee, including those who have joined it later, have been: I. Bohm, B. D. Enlund, B. Kalling, M. Tigerschiöld, S. Wohlfahrt and the authors. The present paper‡ is a somewhat

Jan 1, 1939

By G. Phragmén, A. Hultgren

Page Outline of Progress of Knowledge and Theories about Gas Evolution in Steel Ingots. and Its Influence on Crystallization and Segregation................ 134 Object of Present Investigation........................................... 148 Theoretical Discussion of Process of Solidification........................... 149 Gas Given Off from Rimming Steel during Solidification................... 149 Equilibrium Diagram of the Iron-carbon-oxygen Alloys................... 151 Solidification of Pure Iron-carbon-oxygen Alloys.......................... 157 Solidification when Carbon Monoxide Is Given Off at Constant Pressure... 157 Solidification when Gas Evolution Is Suppressed....................... 158 Schematic Application on Solidification of Rimming-steel Ingots.......... 159 Influence of Manganese, Sulphur and Phosphorus......................... 160 Experimental work..................................................... 162 Liquid Steel and the Mold Gas......................................... 162 Ingots Investigated and Methods Used.................................. 165 Ingot structure....................................................... 174 Structure of Rim Zone.............................................. 174 Structure of Core................................................... 181 Structures Obtained under Special Conditions of Freezing................ 182 Distribution of Metalloids............................................. 187 Other Observations Made............................................. 192 General Discussion of Solidification Process................................. 195 Condition of Liquid Steel before Casting................................. 195 Rimming Period...................................................... 202 Composition of Rim Zone............................................. 225 Freezing after Top Is Closed........................................... 228 Slag Inclusions and Ingot Scum........................................ 234 Reaction between Gas in Blowholes and Surrounding Solid Steel during Cooling 235 Summary.............................................................. 237 Appendix—Preparation and Etching of Ingot Sections....................... 238 References............................................................. 239 In 1934, Jernkontoret (The Swedish Ironmasters' Association) appointed a committee for the study of the structure of rimming-steel ingots and the various phenomena associated with their solidification. The members of the committee, including those who have joined it later, have been: I. Bohm, B. D. Enlund, B. Kalling, M. Tigerschiöld, S. Wohlfahrt and the authors. The present paper‡ is a somewhat

Jan 1, 1939

By K. S. Choi, B. S. Shin

The adsorption characteristics of sodium silicate on scheelite, calcite, and fluorite minerals were investigated. Adsorption equilibrium took about 60 minutes. Adsorption data show that the masimum amounts of adsorption of sodium silicate occurs at about pH 9.8. The adsorptivity was in the order of calcite > fluorite > scheelite. The amount of adsorption of sodium silicate increased with the increase in temperature of sodium silicate solutions. The amount of adsorption of sodium silicate decreases in the low concentration range of ferrous sulfate, while in the high concentration range of ferrous sulfate, the adsorption of sodium silicate increases.

Jan 1, 1986

Just three years after researchers announced its development, Dravo is putting the finishing touches on a new $60-million Thiosorhic lime mine/kiln complex near Maysville, Ky. Electric utilities in western Pennsylvania and Ohio have already signed long-term contracts for over three-quarters of the projected 907 000-t/v (1-million-stpy) production. Thiosorbic lime, a flue gas desulfurizing agent, proved in industrial testing that at high emission levels (greater than 3000ppm SO2) it could be twice as effective in SO2 capture as conventional lime, while eliminating the major problem of scaling and plugging of scrubber equipment.

Jan 4, 1977

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 Robert E. Thurmond

DISCOVERY of a commercial ore deposit has resulted from a program emphasizing geophysical techniques and concentrating upon exploration of alluvial-covered areas. United Geophysical Co. selected these areas as offering the best possibility of success, for here the surface evidence of ore deposits has been hidden from the eyes of prospector and geologist alike. Pima mining district, Pima County, Arizona, was selected for initial exploration. The project was successful in that a commercial ore deposit was discovered and proved through drilling and extensive underground development. A limited region of activity was chosen and library research was begun on available economic and regional geological publications relating to the mining districts. Field reconnaissance of those districts which seemed to hold exploration possibilities provided a general picture and ascertained the existence of alluvial-covered areas of interest. At the conclusion of the reconnaissance trips all data obtained were compiled, and the district which seemed to present the best exploration possibilities was selected by statistical methods. The statistical summary was based on the following considerations: Geological Factors: 1—type of intrusive, P—presence of favorable host rocks, 3—apparent intensity of mineralization, and 4—presence of favorable structure in covered or unexplored areas. Economic Factors: 1—past production from district or mine; 2—size, shape, grade, and type of ore deposit in the district; 3—ease of acquiring mineral rights; and 4—general development facility. Exploration Favorability Factors: 1—results to be anticipated from geological methods alone; 2—application of geophysical methods, namely, topographic conditions, surface interference, depth-size relation, physical property contrasts as related to ores or controlling structural features; and 3—drilling factors. Admittedly, many of these, factors do not lend themselves to absolute evaluation, but relative evaluation, subject to inaccuracies of personal judgment, is always possible. A relative scale from 1 to 10 was established for every factor, representing varying degrees of favorability. For each district a numerical evaluation of each factor was established and a numerical total determined. The obvious advantage of this scheme is that a more concise summation can be presented by numerical means than can be achieved by descriptive means. After a district had been selected as favorable, the first step was to carry out more detailed geological and economic studies to narrow down the areas of interest. The second step was to compile all available geological data from publications and add to these data by mapping where necessary. Geological interpretation and projection of structural or other control into covered or unexplored areas was made whenever logical. To determine the possibilities of geophysical application and to select a geophysical method, physical property contrasts were related to mineral assemblages and/or structural control. If geophysics seemed applicable, trial profiles were run crossing the area normal to the strike and spaced

Jan 1, 1955

By Graham MacFarlane

The largest area of high-grade cannel coals known in America is doubtless found in eastern Kentucky. Notwithstanding the popular belief to the contrary, there is no reason to doubt that these eastern Kentucky cannel-fields, following the general rule, will be uncertain and treacherous. But, taken in the aggregate, their extent is very great. The principal service to which cannel coal can be put is enriching illuminating-gas. The electric light has, to a certain extent, created a demand for better gas, and has increased the market for gas-enrichers. Before the discovery of rock-oil, coal-oil was distilled from cannel coal and cannel shale. This business was getting fairly started when the cheaper rock-oil, or petroleum, overcame it, and the great distilleries went into disuse and ruin. Now, again, the chief competitor with cannel coal is oil, namely, the cheap oil of Lima, Ohio. Under proper treatment the vile odor of this oil can be removed.

Jan 1, 1890

BLOCK CAVING HAS BEEN DEVELOPED to a high degree of efficiency in the last two decades and more particularly since World War II. At the Jeffrey mine of Canadian Johns-Manville Co., in the Eastern Townships of Quebec, several innovations have increased production and decreased costs. Asbestos ore is produced at the rate of 10,000 tpd from an underground operation supplemented by a large open pit that has been mined since 1881. The orebody consists of asbestos veins in a fractured and serpentinized peridotite. Hardness and structural strength of rock vary from soft shear zones at one extreme to a small amount of hard granitic inclusions at the other. In general the ore is weak and deteriorates on exposure to air, so that it is difficult to maintain underground openings for any period of time. Permanent workings are lined with concrete and temporary ones are driven mini- mum size and supported with steel sets as required.

Jan 5, 1954

By N. M. Levine, W. M. Fassell

In this laboratory study the problem of aerative conditioning to separate chalcopyrite and pyrite from cobaltite was simply effected with a sulfy-drate collector and pH by proper choice of mixing variables. It was shown that for a given impeller type and geometry, selectivity is governed by a relation between the Froude number and a modified power number multiplied by impeller tank-diameter ratio wherein the power factor is expressed as power intensity or horsepower per unit volume of contained pulp. In applying this approach to other systems, other criteria would be used in place of selectivity. The purpose of this paper is to show how solutions to problems of aerative conditioning of pulps may be enhanced by development of mixing parameters in a given system through application of a fundamental approach to agitation. The term aerative conditioning refers to a combination of processes which include mechanical gas dispersion, gas solution in the liquid phase, transport of dissolved gases and other reactants to the reaction zone, physico-chemico interaction within the liquid phase and/or at the solid surface, and, finally transport of products away from the reaction zone. Important elements of these processes are: 1) Air-Liquid Contact Area: This area limits the rate at which a given gas may dissolve in a given liquid. Thus, an aerative conditioning system should be designed for optimum gas dispersion. 2) Diffusional Factors: Such factors as concentration gradient, diffusion film thickness, and diffusivity may govern the rate at which dissolved constituents are transferred to the zone of interaction at a particle surface and the rate at which reaction products are transported therefrom. Thus, such systems would be designed for maximum turbulence to effect good mixing and to minimize diffusion film thickness. 3) Solids-Turbulent Liquid Contact Time: Sufficient time should be provided for interactions to take place at solid-liquid interfaces. The region of maximum turbulence for mechanical systems being in the impeller zone, it is important that the number of passes through this zone be optimized. This means that a proper balance should be struck be- tween flow and turbulent power to achieve optimum conditioning time. Too high a flow rate and insufficient turbulence may be improper if the reactions are diffusion limited. On the other hand, too much turbulent power and too little time in the reaction zone due to insufficient flow power may also be limiting. 4) Geometry and Impeller Design: The design of the conditioning vessel and the type of impeller employed are important factors in determining the relative distribution between flow and turbulent power and the degree of gas dispersion. Maximization of power input would be to no avail if the distribution between flow and turbulent power were improper or gas dispersion insufficient. 5. Physical Chemistry: The reactions between dissolved gases and solid surfaces may be limiting if gas solubility, activation energies and/or free energies are not favorable. J. H. Rushton, E. W. Costich, and H. J. Everett' have summarized the mechanical elements of the combination of processes listed in a fundamental mixing equation. This equation was derived by dimensional analysis and relates the physical variables for a single impeller, centered in a cylindrical, vertical axis, flat-bottomed tank. It is, where T is tank diameter in feet; H is liquid depth in feet; C is height of impeller off tank bottom in feet; S is pitch of impeller; L is length of impeller blades; W is width of impeller blades; R is number of baffles; D is impeller diameter in feet; Np is the power number, pg/dN3D5; P is power in foot-pounds per second; g is the gravitational constant, feet per second; J is width of baffles; B is number of im-

Jan 1, 1961