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By Robert J. De Angelis, James H. Barker

An improved method for solving dynawzical dislocation problems using a digital computer is described in this paper. Interactions between two distinct types of dislocations were studied: attractive screw dislocations; and Lomer lock forming dislocations. One dislocation is positioned in the lattice and is initially at rest, while the other dislocation is moved through the lattice on an intersecting slip plane at a constant velocity in the range 0.5 to 0.999C. (C is the transverse velocity of sound.) The results obtained from these computations indicate that screw dislocations account for a small fraction of the total strain over a wide portion of the range of velocities studied. They further indicate that mixed dislocations mainly repel other dislocations in the neighborhood of the active glide plane. From this a possible explanation for cell formation is put forth. The density of Lomer locks expected to exist after a strain of 0.2 was found to be 1.4 x 106 cm-2 which is in good agreement with indirect experimental estimates. IN the past, predictions of favorable or nonfavorable dislocation reactions were based on the associated changes in elastic strain energy. Such considerations take no account of the probability of the two dislocations coming into contact to react. Venables1 was the first to approach these probabilities by considering the interactions between two moving screw dislocations on perpendicular glide planes. Because of the restrictive types of dislocations and glide plane geometry employed, his results have limited application to metallic crystals. The work to be presented here develops a general approach to solving dynamical dislocation problems; either dislocation-dislocation interactions, presented here in detail, or dislocation interactions with any other suitably defined stress field. Two types of dislocation-dislocation interactions common to face centered cubic (fee) materials are considered: those between pure screw dislocations of opposite sign on intersecting slip planes and those between mixed dislocations on intersecting slip planes, that can react to form a perfect dislocation. This latter reaction, referred to as the Lomer reaction, produces a locked product dislocation that finds it energitical favorable to disassociate into two Shockley partials and a stair-rod dislocation. This partial configuration known as a Lomer-Cottrell (L-C) lock plays a major role in work hardening of fee crystals. seeger2 names the L-C lock as the prime contributor to Stage II hardening while Kuhlmann-wilsdorf3 and Meakin and Wils- dorf4 also state that it is a significant contributor to work hardening. However, with a few notable exceptions,5-7 direct observations of the Lomer lock and the L-C lock by electron transmission microscopy are scanty, and even these are subject to other interpretations.5,6 In a study of partial dislocations present in austenitic stainless steel, whelan8 did not observe any L-C locks at the head of pile-up groups. This result contradicted existing work hardening theories and led him to postulate an alternate theory based on the stress required to break away dislocations intersecting a pile-up group, from their stacking fault nodes. Due to the importance of the Lomer reaction in producing L-C locks which are an essential feature in current work hardening theories and because there exist no data giving direct quantitative values for the density of locks, and because there has even been some doubt expressed as to whether this important reaction occurs at all, a study of the dynamic behavior of the mixed dislocations which form the Lomer lock was undertaken. Due to their ability to cross-slip with relative ease, screw dislocations play an important role in the deformation of fee crystals. For this reason, the second type of reaction considered here is between screw dislocations of opposite sign. In addition, computations in volving screw dislocation interactions are relatively simple, thus providing a convenient check on the cornputational scheme employed. DEFINITION OF PROBLEM The force exerted on a dislocation due to a generalized stress field is given by the Peach and Koehler9 equation: Here t2 and b2 are respectively the tangent and Burgers vectors of the dislocation, and T1 is the stress dyadic defining the local stress field. The stress field may be externally applied or generated internally by the presence of a lattice defect, such as a second dislocation, as is the case in this work. Frank10 has shown that an equivalent momentum, P, of a screw dislocation can be defined by: Here, EST is the total energy of a screw dislocation and ESo is its rest energy. The left side of Eq. [2] is the time derivative of momentum and the right side is the position derivative of the energy due to the dynamical nature of the dislocation. The total energy of a dislocation is the sum of the potential and kinetic energies. Weertman11 has developed the expressions which were used here; these give the potential and kinetic energies of uniformly moving edge and screw dislocations in an isotropic medium.

Jan 1, 1969

By Karl S. Kurtenacker

In attempting to find a rapid and economical means for solving many of the subsurface problems that confront the highway engineer, the author for the past two years has utilized a Megger Ground Tester on resistivity surveys in conjunction with highway construction. Electrical surveys in connection with highway work are largely shallow depth surveys, thus differing from most other types of resistivity work. Consequently, the readings are affected by a great many qualifying factors such as the density and moisture content of the media under observation and the amount of weathering and leaching. In most cases the surface layer is decidedly heterogeneous in character, and, because of the great number of side hill cuts, the second layer, which in most cases is rock overlain by some sort of surface soil, silt, or debris, seldom lies in a horizontal position. Shallow strata, lacking homogeneity and not lying in a horizontal position, do not lend themselves readily to accurate theoretical interpretations, therefore the author has used empirical rules to a large extent in interpreting depth soundings. The following empirical rules of interpretation are surprisingly adequate for highway work, since much of the work is in the nature of reconnaissance surveying and the results are construed to be approximations. The writer is careful not to risk interpretation on some special feature of the curve, since such features are usually due to random errors or lack of homogeneity among the subsurface strata. Effect of Surface Medium A resistivity depth sounding taken to a depth of 200 or 300 ft. is not much affected by superficial conditions, but these conditions have a great effect in depth soundings to 25 or 30 ft. In shallow soundings the character of the surface medium has a very marked effect on the entire resistivity graph. Fig. 1 illustrates a very striking example. Graphs A and B are depth soundings taken in approximately the same place. The surface stratum is a clay loam but at the place where graph B was taken

Jan 1, 1934

By J. H. Nelson

An outline survey of the economic outlook for the United States export trade in petroleum products resolves itself broadly into two general divisions; first, a consideration of our present position in this trade, and second, a discussion of the visible factors which promise to affect appreciable changes in the immediate future in that trade. The United States PetRoleum Exports of majoR Petroleum Products 1925, 1926 and 1927

Jan 1, 1928

By Elbert Rowland

THE widespread interest in the alloys of beryllium with copper is due principally to the fact that certain compositions show very favorable precipitation-hardening characteristics and are, in fact, the strongest nonferrous alloys known at the present time. Investigations have been conducted by Masing and Dahl and others on the physical characteristics of ternary beryllium alloys, in an attempt to produce precipitation-hardening effects with a smaller amount of beryllium than that required in the binary copper-beryllium alloys (2.0 to 2.5 per cent Be). The results of these investigations show that ternary alloys of beryllium with Cu-Sn, Cu-Al and Cu-Zn, among others, exhibit promising improvements in physical properties after precipitation-hardening treatment and, while the increases in properties obtained are not as high as those realized from the binary copper-beryllium alloys, excellent properties are obtained with beryllium contents averaging about one-half the amount required in the binary alloys. This paper presents the results of an investigation of the equilibrium relations of certain alloys containing copper, tin and beryllium. The alpha-phase boundary of the ternary system is given for alloys containing from 0 to 1 per cent beryllium. The equilibrium conditions beyond the alpha-phase boundary are presented for alloys containing up to 32 per cent tin and 1 per cent beryllium. The data were collected by means of

Jan 1, 1935

By David M. Hopstock

The performance of the most common type of low-intensity dry magnetic separator is analyzed on the basis of fundamental physical principles. Expressions are developed for estimating the optimal choice of design and operating parameters for beneficiation of magnetite ores. By proper choice of these parameters either a high-grade concentrate or a low-grade tailing can be produced from an incompletely liberated feed.

Jan 1, 1976

By Alexander Squire

One of the principal factors that have contributed to the hesitancy of design engineers to use metal-powder parts is the difficulty experienced in the determination of the mechanical properties of compacted components. Because standard test methods cannot usually be applied in the inspection of such parts, and because adequate special test methods have not been developed, it has been considered desirable to investigate the methods that are applicable. These may then be included in specifications for metal-powder materials and components in order that the design engineer may be assured that the subject parts possess the desired mechanical properties for satisfactory performance. It is known that direct relationships exist between usually nonmeasurable properties as tensile strength and elongation and shear strength and the angle through which compacts may be plastically deformed before fracturing. These correlations are valuable in the inspection of specific parts, but it is necessary to set up standards before they may be satisfactorily employed. Apart from the use of correlations, the number and character of the inspection methods that are applicable to almost all powder parts is limited to three—chemical analysis, density, and hardness. The last of these may or may not be a pertinent characteristic, since the indentation hardness of many powdeied-metal materials is so low as to have little significance. It is, however, occasionally desirable to use hardness measurements as an indication of the uniformity of the structure of pieces of a given type. Chemical analysis reveals very little about the physical properties of metal-powder compacts, since the unpressed powder is usually of a composition almost identical with that of the finished pieces. Density determinations are simple to perform and have the advantage of being nondestructive in character. If the dimensions of a machine part are known (and usually they are), the average density may be determined by weighing a given number of pieces and dividing by the calculated volume of the parts. More accurate measurements may be made by the water-displacement method. It is recognized that mechanical properties of metal-powder materials are related to their density, but usually these relations are determined for only one type of powder, processed under a given set of conditions. Comparisons of the pioperties of compacts formed from different types of powders are made on the basis of compacting pressures instead of density, and for this reason the results obtained by using powders of different types appear widely variant.

Jan 1, 1947

By Alexander Squire

One of the principal factors that have contributed to the hesitancy of design engineers to use metal-powder parts is the difficulty experienced in the determination of the mechanical properties of compacted components. Because standard test methods cannot usually be applied in the inspection of such parts, and because adequate special test methods have not been developed, it has been considered desirable to investigate the methods that are applicable. These may then be included in specifications for metal-powder materials and components in order that the design engineer may be assured that the subject parts possess the desired mechanical properties for satisfactory performance. It is known that direct relationships exist between usually nonmeasurable properties as tensile strength and elongation and shear strength and the angle through which compacts may be plastically deformed before fracturing. These correlations are valuable in the inspection of specific parts, but it is necessary to set up standards before they may be satisfactorily employed. Apart from the use of correlations, the number and character of the inspection methods that are applicable to almost all powder parts is limited to three—chemical analysis, density, and hardness. The last of these may or may not be a pertinent characteristic, since the indentation hardness of many powdeied-metal materials is so low as to have little significance. It is, however, occasionally desirable to use hardness measurements as an indication of the uniformity of the structure of pieces of a given type. Chemical analysis reveals very little about the physical properties of metal-powder compacts, since the unpressed powder is usually of a composition almost identical with that of the finished pieces. Density determinations are simple to perform and have the advantage of being nondestructive in character. If the dimensions of a machine part are known (and usually they are), the average density may be determined by weighing a given number of pieces and dividing by the calculated volume of the parts. More accurate measurements may be made by the water-displacement method. It is recognized that mechanical properties of metal-powder materials are related to their density, but usually these relations are determined for only one type of powder, processed under a given set of conditions. Comparisons of the pioperties of compacts formed from different types of powders are made on the basis of compacting pressures instead of density, and for this reason the results obtained by using powders of different types appear widely variant.

Jan 1, 1947

By R. Schuhmann

D. W. Fuerstenau (Associate Professor of Metallurgy, Dept. of Mineral Technology, University of California, Berkeley, Calif.) In his excellent paper, Dr. Schuhmann has proposed a mechanism for conlrninution which can be utilized to explain a number of phenomena which have been observed in the size reduction of solids. The difference between the product obtained from a ball mill and from a rod mill can readily be explained by Dr. Schuhmann's hypothesis. Consider that the size distribution of the product from each comminution event is given by y; - 100 (x/ki) (1) where Yi is the cumulative percent finer than size x, ki is the size modulus, and is the distribution modulus for the single comminution event. The total product from a cornminution operation will be the summation of the products from all of the individual cornrninution events. If the size moduli from the various comminution events range from kl to kn , the size distribution of the total product will be a straight line on a log-log plot only to a particle size equal to k ,. Considering 100 volurnes of feed, the value of y for x equal to kl is Riven by where y is the cumulative percent finer than size kj, z is the number of comminution events of kind i, and vi is the volume of each particle crushed. y=z1 qv1+z2 qv2 (k1/k2) +.............zn qvn (k1/kn) (3) F or particle sizes greater than k1 7 e. 6. x = k3, the value of y will be given by k3 A y = z1 qv1 + z2bv2 + Z3uV3 + zn zn qvn (k3/kn)(4) Only when x is equal to k, will y equal 100. 'Thus, the total product from a comminution operation will be a straight line on a log-log plot strictly up to a particle size equal to kl and above that size the line will curve so that y will equal 100 for the coarsest particle or k, (see Fig. 1). The actual shape of the size of distribution curve will depend upon the relative number of conmninution events of different kinds. In the case of ball milling, the ratio kn/kl may be pite large and there will be considerable deviation at the coarse sizes in a Schuhmann plot. kIowever, the grinding action in a rod mill is such that fine particles are protected from the rods by the coarse particles. Consequently, kn/kl will be quite small and the product from a rod mill will give a straight line Schuhmann plot almost to y equal 100%. In his paper, Dr. Schuhmann also has presented a very straightforward definition of grindability derived from the basic energy equation E = Ak-a (5) where E is the energy required to comminute a material to a size modulus of k and A is a constant. According to Dr. Schuhmann, the grindability of a material is the volume of material comminuted finer than unit size per unit of energy expended, this being 1/A. For comparison of grindabilities at any size two numbers are required, both = and 1/A, and anyone tabulating grindabilities should give both of these numbers. Concerning the experimental determination of grindabilities, if the material being comminuted possesses distinct cleavage, the energy re quired for comminution is given by E = Ak-(a-y) (6) where y is small number less than = . Because of cleavage, less energy will be required for comminution. To be certain that cleavage does not affect the gindability of the material being tested, it is suggested that the method used by Dr. Charles for determining grindability be used to ascertain if the deviation exponent y is zero or finite. R. Schuhmann, Jr. (Author's Reply) Dr. Fuerstenau's interesting comparison of rod milling and ball milling

Jan 1, 1961

By Edward B. Durham

The refinery at the San Francisco Mint takes the bullion purchased by the receiving department, and carrying Illore than 200 parts of precious metals in 1,000, or, in mint parlance, over 200 fine, and separates and refines the various metals contained therein, using electrolytic processes exclusively. Bullion containing silver is treated in cells charged with a nitric electrolyte. These cells produce fine silver and leave a residue rich in gold. The residue from the silver-cells, together with crude gold-bullion, is treated in cells having a chloride electrolyte. These produce fine gold and leave a residue containing silver chloride. The latter is reduced to the metallic state with zinc and is then treated in the silver-cells. The various waste solutions and the wash-waters, after being freed from the bulk of their precious metals, still contain copper and other metals. These are removed by scrap-iron, and are then treated in the copper-cells, having a sulphate electrolyte. These cells produce pure copper, and collect a residue containing lead, some gold and silver, and all the metals of the platinum gronp that were in the bullion. This residue is relatively small, and is melted into bars and stored until suEcient accumulates to warrant treating it for platinum, etc. The refinery occupies three large and three small rooms. The large ones are, a melting-room, 30 by 34 ft.; a cell-room, 39 by 46 ft.; and a wash-room, 30 by 33 ft. The small rooms are used as foreman's osce, laboratory, and , re- spectively. The methods here described are those in use in December, 1909, when notes for the present paper were taken.

Jan 1, 1912

By R. D. Pehlke, W. M. Small

The effect of added alloying elements on the solubility of nitrogen in a liquid alloy of 74 wt pct Fe. 18 wt pct Cr, and 8 wt pct Ni has been studied. At 1600°C and 1 atm nitrogen pressure, aluminum, chromium, columbium, manganese, molybdenum, tantalum, and vanadium increase the solubility of nitrogen in the liquid 18 Cr-8 Ni alloy, whereas additions of cobalt, copper, nickel, silicon, tin, and tungsten decrease the solubility. Interaction parameters based on a constant ratio of iron, chromium , and nickel have been used to quantitatively define the changes in nitrogen solubility. INVESTIGATIONS on the solubility of nitrogen in liquid iron have usually treated the pure metal, and often the influence of a single added element. Pehlke and Elliott1 carried out a comprehensive study on the influence of alloying elements on nitrogen solubility in liquid iron, and compared their results with previous studies. Turnock and pehlke2 have recently reported a study on the solubility of nitrogen in multicomponent liquid iron alloys. The original interaction parameter proposed by wagner3 was successfully employed in these studies. The need for obtaining information on the gas solubility in more complex alloys is indicated by the increasingly significant role played by dissolved gases in the processing of iron-based materials. The commercial stainless steels, for example, represent an area where data on nitrogen solubilities are required as a function of composition, temperature, and gas pressure. The nitrogen solubility in liquid Fe-Cr-Ni alloys has been studied by Humbert and Elliott.4 Their investigation covered the entire ternary system, and attempted to use data from binary alloys to predict nitrogen contents in liquid ternary alloys. Langenberg,5 using a method developed by Morris and buehl,6 calculated the nitrogen solubilities in multicomponent iron alloys from data available on binary iron alloys at 1600°C. Nelson,7 using a regular-solution model, extended this prediction to include the effect of temperature. Chipman and corrigan8 and Turnock and pehlke2 also employed empirical methods to calculate nitrogen solubilities in liquid multicomponent iron alloys. In order to provide a basis for predicting nitrogen solubility in liquid stainless steels, and to extend the data available for thermochemically modeling systems of this type, the following investigation was carried out. The study involved measupements of nitrogen solubility in a nondilute alloy and examination of the influence of a small addition of an alloying element on the nitrogen solubility. The study was focused on a very narrow range Of composition in the vicinity of 18 wt pct Cr-8 wt pct Ni (herein referred to as 18-8) with special emphasis on the change of.nitrogen solubility with the addition of a fourth metallic element. EXPERIMENTAL PROCEDURE A Sieverts' apparatus, described previously,1,2 was used in this investigation. The charge materials were contained in a recrystallized alumina crucible and inductively melted. Additions were dropped from a glass side-arm. All materials were hydrogen-refined and vacuum-treated to eliminate or minimize the oxygen content. The source and purity of materials is given in Table I. The initial metallic charge was heated to approximately 1000°C and held under vacuum for 30 to 45 min as a means for removing hydrogen and adsorbed gases. Argon was used as the calibrating gas to determine the "hot volume". The average hot volume of the system was approximately 50 cu cm STP and a few experimental runs were made using a reaction bulb with a hot volume of 80 cu cm. The temperature range studied was from 1550° to 1700°C and the temperature was measured optically. THEORETICAL PRINCIPLES General Discussion. Nitrogen dissolves in liquid iron alloys according to the reaction: 1/2N2(g) = N (wt pct in solution) [l] The equilibrium constant, K1, for this reaction is written as:

Jan 1, 1969

By G. L. F. Powell, L. M. Hogan

Samples of silver and Ag-O alloy, 0.12 wl pet, have been undercooled to a maximum of 250°C by melting in a slag of commercial soda-lime glass. Grain refinement occurred in undercooled silver samples whet the degree of undercooling exceeded a critical value which varied from 153° to 175°C, depending on the melting conditions. In under cooled Ag-0 samples, the grain structure was fine and equiaxed at degrees of undercooling larger than 50oC. The grain refinement in both silver and Ag-0 alloy samples was the result of recrystallization during or immediately following freezing. When the oxygen content was increased, the degree of undercooling at which recrys-tallization occurred decreased. INVESTIGATIONS of the grain structure of strongly undercooled melts of nickel and cobalt1-4 have revealed a change in room-temperature grain size as a function of undercooling. At large degrees of undercooling the grain size was fine, but samples undercooled by smaller amounts exhibited a much coarser grain structure. The reported undercooling at which this grain size transition occurred in nickel varied between 140° and 175'C undercooling. Walker1 attributed this grain size change to an enhanced nuclea-tion rate. Cavitation at a melt-solid interface was con sidered to generate a high-pressure wave. This, in turn, produced nucleation in the liquid as a result of an elevated freezing point increasing the undercooling in the melt. A similar grain size transition was observed in undercooled silver between 133° and 153°C undercooling.5 The grain size transition in undercooled silver was found to be dependent on oxygen con tent. More recently, the authors5 showed that a simila transition occurred in an undercooled Cu-O alloy, =0.08 pet, but not in oxygen-free copper undercooled more than 200°C. The transition was attributed to recrystallization of the solidified grains after freezing; the greater the degree of undercooling, the more complete the recrystallization. In view of this effect of oxygen content on grain size transition, additional undercooling experiments were carried out with silver. This paper reports the results of these studies on silver and Ag-O alloys undercooled more than 50°C EXPERIMENTAL 1) Materials. The silver was supplied by Matthey Garrett Pty., Ltd., as fine granulate, silver mini' mum 99.9 pet, and contained the trace impurities shown in Table I. The silver originated from two different refineries resulting in the difference in impurity content shown in Table I. However, the variation in composition had no discernible effect on the undercooling behavior. Samples of the silver were melted in an open-ended, vertical, cylindrical resistance furnace, wound with Kantha] wire, the temperature of which was adjusted by means of a variable transformer, 2) Melting and Undercooling. Bulk samples of silver were undercooled by preoxidation and removal of oxidized impurities in a glass slag, as previously described,5 but special precautions were necessary to allow comparison between oxygen-free silver and a Ag-O alloy. Samples free of oxygen were prepared by first melting weights of granulate varying from 200 to 400 g in clean vitreous silica crucibles in air for approximately 15 min. A sample was frozen and a complete glass cover formed over the top surface by adding granulated glass rod. The sample was then melted and frozen several times until no oxygen bubbles appeared in the glass slag. Subsequent thermal analysis indicated that the oxygen content was negligible. The glass acted as an efficient barrier to absorption of oxygen from the air. Ag-O alloys were prepared by melting silver in silica crucibles with only a partial cover of glass, so that the top surface of the melt was in contact with air. The silver was held molten in air for several hours at 1000° to 1050°C, in the expectation that the oxygen in solution would reach equilibrium with atmospheric oxygen. At T - 1000°C the equilibrium oxygen content was calculated as 0.12 wt pet O, using Sieverts law and Eq, [l], derived by Mizikar et a!.7 from the data of Sieverts and Hagenacker8 for 1 atm of oxygen:

Jan 1, 1970

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 M. C. Chang, J. Dasher

The Crucible mine in Pennsylvania, operating on Pittsburgh seam coal, is rated at 5000 tpd. The washing plant, built in 1943, is rated at about 400 tph, using hydroseparator boxes to wash the coarse coal (4 x 5/16 in.) and hydrotator units for the fine coal (5/16 x 0). It is generally acknowledged that gravity concentration equipment cannot be used efficiently to bene-ficiate coal finer than about 65 mesh. Before the present flotation circuit was installed, Crucible recovered its fine coal slurry, predominantly —24 mesh material, by passing it through a battery of five 14-in. and one hundred and ten 3-in. Hey1 & Patterson cyclones in parallel with a 75-ft Dorr thickener. About two thirds went to the cyclones and one third to the thickener. Underflows from cyclones and thickener were filtered, respectively, in one 12-disk Eimco and two 4-disk Oliver filters fitted with stainless steel cloth. The resulting cakes were added to the coarse metallurgical coal. The filtrates, overflow from the 3-in. cyclones, and thickener overflow were recycled to the coarse coal plant. The three major problems encountered in this system became acute when the mine switched from track-mounted machinery to the more economical off-track equipment. The quality and uniformity of product declined, too much slime accumulated in the circuit, and waste pond disposal became highly impracticable. Lowering of Quality and Uniformity: Since the filter cake was not beneficiated in any way, addition of this material, which contained about 18 pct ash. would certainly lower the quality of metallurgical coal. Difficulties of handling the high-ash, high-moisture cake were compounded by the lack of adequate blending facilities at the mine, making it impossible to maintain uniform feed for the coke ovens. For a two-month test period, to verify the source of trouble, all filter cake was excluded from the metallurgical coal. The excluded filter cake was stocked in the yard. Slime Buildup: The moisture retained in the coarse coal products and the filter cake provided daily the only means of slime bleed from the circuit. As this bleed was not enough to offset the incoming fines in the raw coal feed, there was excessive buildup of slimes. To operate at all, it was necessary to purge the system each weekend by pumping all the solids from the thickener to a waste pond. The slimes built up during the week progressively increased the apparent viscosity and density of the circulating plant water, so that hydroseparators and hydrotator units had to be constantly adjusted. Uniformity, yield, and quality of the metallurgical coal suffered in consequence, and the filter cake ash and moisture contents increased from Monday to Friday. Limited Waste Disposal: Location of the plant does not permit unlimited waste pond area. Maintenance of a waste pond for the purpose of emptying the thickener during weekends became a costly burden that could not be tolerated. HOW THE PROBLEMS WERE SOLVED The flowsheet (Fig. 1) chosen to overcome these difficulties is considered the one most economical to install and operate. In a preliminary change made before the flotation circuit was installed, the cyclones and thickener were first operated in series, the overflow from the 3-in. cyclones, after flocculation, being discharged into the thickener and the thick-

Jan 1, 1960

By E. G. Schempp, W. A. Morgan

The influence of modifications in the molybdenum, vanadium and, to a limited degree, carbon and boron content to a basic composition of 5 pct Cr, 0.75 pct Mo, 1 pct V hot-work tool steel composition, was studied in respect to hardenability, grpain- coarsening temperature, and tempering charactevistics. Tensile, impact, and fatigue pvoperties were studied for the most promising compositions. An alloy with a typical composition of 0.43 pct C, 4.97 pct CI-, 0.33 pct Si, 2.25 pct Mo, and 1.00 pct V uas found to offer the most favorable combination of properties in respect to high-strength applicntions when tempered at 1100°F. MANY 5 pct Cr high-strength steels are at present being manufactured in North America which fit well into the classification of the AISI-SAE system. Much interest has been shown in these materials as ultra-high-strength steels for use at elevated temperatures. The limiting temperature of use lies at the point where the steels begin to soften rapidly. Although a great deal of information has been made available in the past two years on the properties of selected alloys in this series, little information exists on the effect of systematically varying the ccntent of one or more elements in the 5 pct Cr-base alloy. This paper presents the results of an investigation of the effect of variations of the carbon, molybdenum, vanadium, and, to a limited extent, the silicon, manganese, boron, and niobium content of a 5 pct Cr steel to the AISI H-13 base analysis. EXPERIMENTAL PROCEDURE All experimental heats were melted in a 50-lb. induction furnace. The melting stock consisted of

Jan 1, 1962

The problem of surface support in coal mining is naturally divided into three branches: 1. Surface covered with improvements of such value as compared with the value of the underlying coal, or with such elements of danger to mining, that absolute support is essential. 2. Surface with improvements of less value than the underlying coal such that moderate settlement may be permitted, but destructive settlement must be avoided, either by reason of danger to human life or unwarranted property damage. 3. Surface of relatively small value as compared with the underlying coal where destructive settlement may be permitted. First Problem In the first case it is evident that the original support must be maintained either (a) by leaving ample pillars and confining the coal recovery to a very conservative first mining, (b) by so supporting less conservative first mining by filling or flushing that the gradual deterioration of the pillars may be prevented and subsidence avoided, or (c) by incompressible support as masonry either as an adjunct to insufficient pillars or in place of the original coal support. a. From tests made by the Scranton Engineers Club, it appears safe to figure on 2000 Ib. per sq, in. as the safe squeezing strength of coal pillars in place, provided that these are, as usual, not higher than their least horizontal dimension; and from this figure the percentage of pillar to be left for various depths may be easily calculated. For safety in this

Jan 1, 1930

By E. V. Crane

A tremendous volume of the metal rolled annually into sheets strips and coil stock finds its way to a host of stamping and manufacturing plants which are the quantity production units of the country. Considerable in volume, too, are the rolled and extruded rods which go into forging and manufacturing plants for conversion into the same general line: those widely sold metallic necessities and luxuries of the household, the office, transportation, farming and building construction. Yet, in spite of its age and its importance, the stamping trade has been doing its "engineering" largely by trial and error. Its distinctive method is shearing out and plastically working metal to finished shape in a few quick strokes with high loads and expensive tools which are warranted only by large quantities to be produced. The principal operations have many features In common with rolling and wire-drawing methods. Combinations of stresses are diffcrent, however, and details of operations are infinite in variety. An engineering study of the subject begins with stress analysis, but must go back to metallurgy for its foundation. A grouping of pressed-metal working operations according to whether the metal is (1) sheared, (2) bent, (3) drawn or (4) squeezed has proved useful. All of these groups include instances of both hot and cold operations. For discussions of metal working properties, the division between hot and cold working is taken as the recrystallization range of temperature. This, of course, brings tin, lead and often zinc into the hot-work range at or near room temperature. The outstanding hot-working press field is in forging: particularly of brass; all of which is included in the squeezing group. Shearing Operations The shearing group of operations, including blanking, piercing, trimming, shaving, slitting, shearing, notching, parting and numerous variations and combinations of these enters once or more into the production schedule of practically every stamped or forged article. The transverse stress, set up in shearing, as shown in Fig. 1A, is a combination of an angular compressive thrust and a tensile stress which is also at an

Jan 1, 1931

By Joseph W. Roe

MaNY questions arising in the work of the mining engineer may be solved quickly and with suffcient accuracy by the methods of descriptive geometry; but, unfortunately, this subject is more often considered from a mathematical view-point than as an effective tool for solving practical problems. Some of the principles involved are merged into the ordinary operations of mechanical drawing, and are used unconsciously by the engineer in his every-day work. The rest are stowed away on the book-shelf with his forgotten or rarely-used college text-books. One reason for this condition of " innocuous desuctude " may lie in the uifortunate and often cumbersome notation which it has been found necessary to introduce. If some of these principles can be recalled to the engineer's attenti011 in terms of' every-day use they may prove of practical hearing. Recently, in talking with several mining engineers, I used some of the drawing-room methods of a machine-designer, to the evident surprise of those around me. These men were perfectly familiar with the methods, but their application to mining-work had not occurred to them. At their suggestion the present paper is offered, not in ally way as a treatise, but merely to suggest a certain point of view, in hope that it may lead others far more familiar with mining-problems to pursue the subject further. I. To Find the Strike. As the simplest and most fundamental problem, let it be required to find the strike of a vein when the location and elevation of three points on the outcrop are known. It mill be assumed for the present that the rein is a plane.

Jan 1, 1911

By P. R. Gage, R. W. Bartlett

At high temperatues and reduced oxygen pressuves, molybdenum silicicles oxidize to form SiO(g) vathev than a passivating SiO2 film. This is a sevious problem for low-pressure applications of sili-cide-coated rejvactory tnetals. As oxiclalion pvoceeds, the higher oxidntion potential of silicon initially suppresses oxidation of molybdenum and silicon is depleted near the surface. Eventually, silicon depletion causes secondary passivation (SiO2) mid an active to passiue transition in oxidntion behavior at moderately low pressures. At very low pressures, silicon depletion continues until steady-state oxidation of both silicon and rnolyhdenum can proceed at rates propovtional to their initial stoicliiorrzetvies. Ohsel-vations of 'oxidatiou-rate belzcriliov at temperatures from 1101° to 1700°C and oxygen pressures from 10-7 to 1 at in were made using thermogravimetn'c, X-ray diffraction, and elect?*on-rtric?ro/,vobe techniqrres. The experimental results are in good agreement with calculated lirnits for the various types of behavior that were based on tlievtnochernicnl atzd dffusion rate data for the Mo-Si system. A protective oxide film normally forms during the oxidation of elemental silicon. However, at elevated temperatures and reduced pressures this film is not present and oxidation is rapid. wagnerl has shown that this behavior occurs because SiO(g) is more stable than SiO2. The behavior of the silicides at high temperatures is similar but more complicated. Molybdenum and several silicide compounds are involved and the chemical activity of silicon, or the equivalent silicon vapor pressure, can vary considerably in these phases. Also, diffusion in the silicides resulting from reactions in which a higher silicide is reduced to a lower silicide, or molybdenum containing dissolved silicon, must be considered. EXPERIMENTAL AND ANALYTICAL METHODS Isothermal oxidation experiments were conducted using hot-pressed MoSi2 and Mo5Si3 wafers. Each experiment was conducted at a fixed oxygen pressure by controlling the flow of oxygen in and out of the furnace chamber. Most of the experiments were conducted in a molybdenum-wound tube furnace. Special construction features, including use of a high-purity dense A12O3 refractory tube, permitted operation in high vacuum to 1500°C. Higher temperatures could be obtained at higher working pressures and with a sacrifice of tube lifetime. Temperature was measured with three Pt 6 pct Rh/Pt 30 pct Rh thermocouples and controlled with a proportional controller. Weight changes were monitored with a quartz spring balance. The few experiments, at higher temperatures and low pressures, were conducted in a cold wall vacuum chamber using induction heating with direct susceptance of the sample. Because of the variable levitation effect of the induction coil on the sample, weight changes could not be monitored continuously in these experiments. All samples representing both experimental methods were weighed before and after oxidiation and examined with a microscope and analyzed by X-ray diffraction. The analytical treatment assumes equilibrium at interfaces and uses existing thermodynamic data. For convenience, equilibria are expressed as chemical potentials or as vapor pressures of the gases involved. The resulting differences in equilibrium vapor pressure between adjacent interfaces and between the surface and external atmosphere drive diffusion processes in the solid and gas boundary film, respectively. These diffusion processes govern the rate of oxidation. A bibliography of the sources of thermochemical data for the reactions pertinent to the Mo-Si-O system is given in Table I. Reactions are listed with the sources of free-energy data referenced. Since all of these reactions involve one or more gas species, usually oxygen, a plot of the product-gas chemical potential, -RT In Pg, vs absolute temperature for each reaction is given in Fig. 1. These curves can be used to determine equilibrium vapor pressures or to compare the stability of different compounds in the various gases: O2, Si, SiO, and Moo3,. The data of Table I and Fig. 1 were used to determine the analytical results presented in this paper. EXPERIMENTAL RESULTS The weight changes for three MoSi, samples oxidized at 1500°C are plotted against time in Fig. 2. The treatments were identical except for the indicated variance of oxygen pressure and each curve represents one of three characteristic types of behavior that were observed. The upper curve is an example of passive oxidation, which is defined as

Jan 1, 1965

By M. E. Gershon

A mixed-integer formulation of the mine scheduling problem is discussed and applied for the purpose of optimizing both the mine production sequencing and the mill blending and processing problem simultaneously. Previous attempts at solving these problem separately, although successful, fail to take into account the interrelationships between these problems. Project structure selves as the outline of this paper Generalized in its organization, this concept is useful for long, intermediate, and short range scheduling. Actual applications that show the concept also is applicable to mining a variety of ore are mentioned.

Jan 1, 1984