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By I. Fatt

Relative permeability and relative electrical resistivity curves are obtained for networks of tubes with a tube radius distribution by means of a network of resistors used as an analog model. These curves are similar to those obtained from real porous media. The effects of pore size distribution and network structure on relative permeability and resistivity are demonstrated. INTRODUCTION Study of the dynamic properties of networks of single size tubes in paper IT' of this series has shown that the network model has flow properties similar to those observed on real porous media. The comparison of properties of single size tube networks with those of real porous media cannot be carried far because very few porous media have uniform size pores. The capillary pressure curve from most porous materials such as soil, sandstone, and sintered glass indicate that these materials have pore size distribution similar to those shown in Figs. 5-1, 9-1, and 10-I.† To properly test the network model, it is therefore necessary to compare the dynamic properties of real porous media with those of networks of tubes in which the tube radii are distributed accord- ing to the distributions in the aforementioned figures. A network in which the tube sizes are distributed cannot be treated in the same manner as a network of single size tubes. In the single size tube network, the relation between tube geometry, flow resistance, and tube volume did not have to be known if the assumption was made that whatever relation did exist was the same for all tubes in a particular network. In a network of distributed tube size, the relation between tube geometry and flow resistance must be known or assumed in order to replace the tubes by equivalent electrical resistors. Relation of Tube Geometry to Flow Resistance The interchangeability of tubes and electrical resistors in the network model is possible because of the analogy between Poiseuille's law and Ohm's law. Poiseuille's law for a cylinder is q= pr4/8µl ?P.........(1) where q is the volumetric rate of flow, µ is the viscosity, ?P is the pressure gradient, r is the tube radius, and 1 is the tube length. Ohm's law is I=1/R?E..........(2) where I is the flux and is equivalent to the volumetric rate in Poiseuille's law, R is the resistance, and ?E is the voltage gradient. Both laws give the flux as a function of the potential drop and the resistance of the medium. By analogy then, 1/R=pr4/8µl ?P...........(3)

Jan 1, 1957

By Maurice C. Fetzer, Charles R. Austin

It has long been known that plain high-carbon steels may be susceptible to graphiti-zation below the A1 critical, but no data have been available to indicate what factors cause and tend to inhibit graphite formation. Two recent publicationsl,2 have shown that the factors controlling graphitization below the A1 are different from those operating above the A1 inversion where commercial graphitization of malleable iron begins. Furthermore, for plain high-carbon steels graphitization below the critical point does not appear to be related to ordinary chemical analyses. Many years ago it was recorded3 that the rate of graphitization at subeutectoid temperature is not a maximum just below the A1 critical, but at some lower temperature, which Austin and Norris have shown to be about 670°C. Indeed, work done in our laboratory has demonstrated that it is impossible to spheroidize certain steels in the temperature range of 650° to 710°C. without the formation of considerable amounts of graphite. However, if the temperature is maintained just below the A1 (720°C.) these same steels may be completely sphe-roidized at constant temperature. In previous studiesl,2,4 on I per cent plain carbon steels graphitization was encountered during prolonged tempering. The limited number of steels studied did not provide sufficiellt data to permit adequate study of the factors controlling this graphitization. Accordingly, a limited statistical investigation was undertaken, utilizing 18 steels of similar chemical analyses, furnished by four steel companies, who also supplied information regarding the history of manufacture. An extensive program of research is being carried out on these steels, including the effect of pretreatment and atmosphere on the nature and extent of graphitization, and the possible correlation of graphitization with such characteristic properties as hardenability, grain size and mechanical behavior. In the present paper discussion is restricted to a study of the correlation between graphitizing tendency at 670°C. after quenching from several temperatures above the critical, and (I) the minor variations in the chemistry of these steels of "similar" chemical composition, and (2) the deoxida-tion practice employed. The state of the lead bath, oxidized or protected from oxidation by charcoal, used in the tempering treatments is also considered. Materials Eighteen plain carbon steels of about I per cent carbon, and containing similar amounts of each of the other common elements usually found as impurities, were obtained in the form of rods % in, in diameter from four steel manufacturers. The analyses for ordinary and special elements of all the steels were made on the rod stock as received in the laboratory, and the re-

Jan 1, 1941

By Maurice C. Fetzer, Charles R. Austin

It has long been known that plain high-carbon steels may be susceptible to graphiti-zation below the A1 critical, but no data have been available to indicate what factors cause and tend to inhibit graphite formation. Two recent publicationsl,2 have shown that the factors controlling graphitization below the A1 are different from those operating above the A1 inversion where commercial graphitization of malleable iron begins. Furthermore, for plain high-carbon steels graphitization below the critical point does not appear to be related to ordinary chemical analyses. Many years ago it was recorded3 that the rate of graphitization at subeutectoid temperature is not a maximum just below the A1 critical, but at some lower temperature, which Austin and Norris have shown to be about 670°C. Indeed, work done in our laboratory has demonstrated that it is impossible to spheroidize certain steels in the temperature range of 650° to 710°C. without the formation of considerable amounts of graphite. However, if the temperature is maintained just below the A1 (720°C.) these same steels may be completely sphe-roidized at constant temperature. In previous studiesl,2,4 on I per cent plain carbon steels graphitization was encountered during prolonged tempering. The limited number of steels studied did not provide sufficiellt data to permit adequate study of the factors controlling this graphitization. Accordingly, a limited statistical investigation was undertaken, utilizing 18 steels of similar chemical analyses, furnished by four steel companies, who also supplied information regarding the history of manufacture. An extensive program of research is being carried out on these steels, including the effect of pretreatment and atmosphere on the nature and extent of graphitization, and the possible correlation of graphitization with such characteristic properties as hardenability, grain size and mechanical behavior. In the present paper discussion is restricted to a study of the correlation between graphitizing tendency at 670°C. after quenching from several temperatures above the critical, and (I) the minor variations in the chemistry of these steels of "similar" chemical composition, and (2) the deoxida-tion practice employed. The state of the lead bath, oxidized or protected from oxidation by charcoal, used in the tempering treatments is also considered. Materials Eighteen plain carbon steels of about I per cent carbon, and containing similar amounts of each of the other common elements usually found as impurities, were obtained in the form of rods % in, in diameter from four steel manufacturers. The analyses for ordinary and special elements of all the steels were made on the rod stock as received in the laboratory, and the re-

Jan 1, 1941

By C. G. Dunn

Nuclei that are formed during the recrystallization of a grain following plastic deformation generally have orientations that differ from the original. This aspect of recrystallization may be described in terms of orientation changes. It was shown previously, in an investigation on recrystallization in silicon ferrite,&apos; that the observed orientation changes were highly improbable on a chance basis, and that some mechanism must be involved. Analysis showed that the data could be satisfactorily classified into the smaller of two subclasses† of the 36 third-order twin transformations. No attempt was made at that time to classify the data within the special class of 12 third-order twin transformations, although results did indicate a greater probability for some of them to occur. A classification of this type would be more valuable, of course, with more data on orientation changes per old deformed grain. The present work fulfills this condition to some degree and also extends the scope of the investigation to include the effects of original orientation and the amount of plastic deformation. The effect of original orientation is of considerable interest because of the known effects of orientation on plastic deformation, particularly with regard to degree of fragmentation and the formation of deformation bands, and because the orientations produced by deformation should influence the orientations obtained through recrystallization. Barrett and Levenson2 reported that single crystals of iron deformed in the range 82 to 97 per cent could be put into three general classes; namely, crystals in class I maintained a reasonably sharp single orientation, those in class 2 transformed into two distinct orientations, and those in class 3 changed into a large number of major and minor orientations. Something similar would be expected for silicon ferrite crystals, and verification of this for a few cases of types class I and class 2 deformation has been reported elsewhere3 for single crystals of silicon ferrite cold-rolled in the range 10 to 20 per cent. As an example of class 2 deformation, it was shown that a crystal of silicon ferrite cold-rolled in a (110) plane in a <100> direction developed two layers, or deformation bands differing in orientation. When this happens it is possible to etch away one band and leave a single structure for use in studying the orientation changes that occur during recrystallization. when preferred crystal orientations are obtained in recrystallization, it is not particularly necessary to evaluate groups of common orientation, as was done previously (ref. I, Table 6); but an

Jan 1, 1947

By C. G. Dunn

Nuclei that are formed during the recrystallization of a grain following plastic deformation generally have orientations that differ from the original. This aspect of recrystallization may be described in terms of orientation changes. It was shown previously, in an investigation on recrystallization in silicon ferrite,&apos; that the observed orientation changes were highly improbable on a chance basis, and that some mechanism must be involved. Analysis showed that the data could be satisfactorily classified into the smaller of two subclasses† of the 36 third-order twin transformations. No attempt was made at that time to classify the data within the special class of 12 third-order twin transformations, although results did indicate a greater probability for some of them to occur. A classification of this type would be more valuable, of course, with more data on orientation changes per old deformed grain. The present work fulfills this condition to some degree and also extends the scope of the investigation to include the effects of original orientation and the amount of plastic deformation. The effect of original orientation is of considerable interest because of the known effects of orientation on plastic deformation, particularly with regard to degree of fragmentation and the formation of deformation bands, and because the orientations produced by deformation should influence the orientations obtained through recrystallization. Barrett and Levenson2 reported that single crystals of iron deformed in the range 82 to 97 per cent could be put into three general classes; namely, crystals in class I maintained a reasonably sharp single orientation, those in class 2 transformed into two distinct orientations, and those in class 3 changed into a large number of major and minor orientations. Something similar would be expected for silicon ferrite crystals, and verification of this for a few cases of types class I and class 2 deformation has been reported elsewhere3 for single crystals of silicon ferrite cold-rolled in the range 10 to 20 per cent. As an example of class 2 deformation, it was shown that a crystal of silicon ferrite cold-rolled in a (110) plane in a <100> direction developed two layers, or deformation bands differing in orientation. When this happens it is possible to etch away one band and leave a single structure for use in studying the orientation changes that occur during recrystallization. when preferred crystal orientations are obtained in recrystallization, it is not particularly necessary to evaluate groups of common orientation, as was done previously (ref. I, Table 6); but an

Jan 1, 1947

R. C. Canby, Wallingford, Conn. (communication to the Secretary*). —Apropos of the experimental reduction of copper from cuprous chloride by fusion with ground limestone and colre, as described by Messrs. Laist and Frick, and also proposed for use at Chuquicamata, it might be of interest to refer bricfly to the experience at Argentine, Kan., in the smelting of the suboxide of copper (as produced in the Hunt and Douglas process) containing appreciable quantities of chlorides. In the Engineering and Mining Journal of June 10, 1911,I gave some account of what had appeared to be crucial difficulties with the Hunt and Douglas process, and how the filter-press difficulty had been so rapidly overcorne after my discovery of the effect of the sodium salts in the leaching solutions. I also described the effect of the cupola-furnace gases upon the lime rock with which I had replaced the coke in the absorption tower, which apparently showed the presence of considerable chlorine, due to the imperfect conversion of the subchloride to suboxide, as well as that due to the difficulties of washing thoroughly the suboxide with the means provided, and also to the presence of chlorides in the cement copper which was smelted with the suboxide. The fumes from the cupola, when issuing direct into the atmosphere, were very dense and white, except when a hot furnace top caused a reddish tinge due to dust. These fumes had a peculiarly suffocating effect, SO that when they were blown over into the town the population suffered the greatest actual distress, not the mere annoyance which would have been due to a disagreeable odor. The absorption tower had been built at the instance of the city authorities to abate this nuisance, and not with the idea of making any additional metal savings. A serious feature in connection with the Argentine experience with the Hunt and Douglas process was, that it had been implicitly assumed that there could be no metal loss in the Hunt and Douglas process itself, and that all attempts to locate the ruinous copper losses which were accumulating in the metallurgical accounts were devoted to the roasting department. It is possibly unfortunate for metallurgical advance along these particular lines that just about the time of this discovery of this previously unsuspected volatilization loss, in the smelting of the suboxide, the Kansas City company made a contract with the Western Union Telegraph Co. for its supply of copper sulphate and the Hunt and Douglas

Jan 1, 1915

E. D. TILLYER,* Southbridge, Mass. (written discussion?).-It is quite generally known that there is very little that is standard about a mercurial thermometer at temperatures above 212° F. (100° C.) because so many precautions must be taken-precautions that are rarely realized in practice-such as depth of immersion, aging, elastic fatigue, separation of mercury column, and accidental deformation from very slight excess temperature. One cannot help wishing that Mr. Brown would dwell at greater length on the practical side of both radiation and optical pyrometey, both of which have great possibilities as commercial instruments. In the radiation pyrometer we have ideal conditions for a permanent instru-ment, no materials being exposed to excessive temperatures or subjected to contamination from the furnace fumes which may raise such havoc with an ordinary pyrometer. The development of a radiation pyrometer requires a thermocouple having a relatively high electromotive force but which need stand temperatures of only 200° F. or 300° F. instead of 1500 to 2000° F., which is required of even a base-metal couple. The galva-nometer, if located near the thermocouple, does not need to have a high resistance as at such low temperatures no changes can occur in the thermocouple that will affect its resistance and, consequently, the in-dicated temperature.

Jan 11, 1919

By Roy C. Kirkman

Dear Editor: It is with great pleasure that I read Mr. Howard M. Wells article in the December 1978 issue of MINING ENGINEERING entitled: "Optimization of Mining Engineering Design in Mineral Valuation." Mr. Wells very adequately presents the case and point that there are a great number of variables which must be analyzed during an economic evaluation of an FUND RESOURCE, such as copper or uranium. I wish to take this opportunity to suggest that, given today&apos;s economic climate, decision making takes place under conditions of uncertainty and that this uncertainty justifies our need to examine each one of the parameters entered into the evaluation model. It is my contention that the influence of the tonnages and grades as well as their distributions, have the most profound effect upon the results of an evaluation. Everyone concerned with the evaluation of FUND RESOURCES realizes that as metal prices decline or stagnate with sharply rising direct operating costs, cutoff grades (Gc) must increase according to the equation below which Mr. Wells uses: Gc = Total Operating Cost/(Market Price X 20 X Recovery) However, historically, we have seen cutoffs move dramatically lower in both the copper and uranium industries for the past decade. Henceforth, this established the metals industry most important argument for processing greater tonnages of lower grade materials from disseminated deposits (refer to paper by Kirkman, Roy C.). These disseminated deposits, created by either concentration processes (uranium) or dispersion processes (copper, gold, molybdenum), have log-normal grade distributions (Fig 1). Gross profits are rising, but unit profits are falling. The industry has created longevity through economy of scale, i.e., mining vast tonnages of low grade. In order to develop the great tonnages necessary to prove economic viability, we must examine alternatives at the low-end of the tonnage grade relationship. Notice from [Fig. 2] that as we move further to the right away from line A-B drawn tangential to the average grade curve at 45°, total profits will increase (given fixed annual production capacity) and unit profits decrease. The theoretical optimum operating point is where: [ ] At this point my observation is that slight shifts in production capacity bring about greater changes in profitability due to greater grade changes. Therefore, the best financial risk evaluation is obtained by totally revising the mining engineers methods and fixing the financial parameters such as discount and interest rates. A 10% shift in either of these two parameters will not cause near the same variance in economic viability as will a change on the GRADE-TONNAGE curve [(Fig. 2)].

Jan 1, 1980

By Frank R. Milliken, Robert Goodwin

In September 1937, the Ohio Copper Co. inaugurated the treatment of its copper-bearing mill tailings at Lark, Utah. These tailings had been accumulated during the regular operation of the Ohio Copper mine and mill over the period 1907 to 1919. Gravity concentration had been employed except for a comparatively short period in 1919, when flotation was used. The ore milled during that period assayed about I per cent Cu. The chief copper mineral, chalcocite, was disseminated in a shattered quartzite, mainly along fracture or cleavage planes. The quartzite gangue was extremely hard and grinding to liberation resulted in excessive sliming of the "sooty" chalcocite, with consequent high tailings losses. Recovery on the seven million tons treated was probably less than 60 per cent of the total copper content. As early as 1918, attempts had been made to sample the dump. In 1928, a complete sampling program was undertaken. The sampling consisted of seventy-four 5-in. post auger holes drilled to the full depth of the dump at regular intervals of 250 ft. Each 10-ft. portion thereof comprised a sample for analysis. Each sample was screened, rolled, divided into three parts, dried and assayed. The reject was retained for testing purposes. From the depth of the auger holes a contour map of the dump was plotted, Fig. I, which gives percentages of tonnage and copper content. The tonnage within the limit of the drill holes was estimated at about five million tons with an average content of 0.42 per cent Cu, 31 per cent of which (0.13 per cent) was acid-soluble. A screen analysis of the composite dump sample is shown in Table I. Flotation tests by several companies and individuals were then made, the results of which ranged from 62 to 74 per cent recovery. On the basis of these, a 200-ton pilot plant employing straight flotation was built and operated for a few months. Operation of this plant was unsuccessful, as no provision had been made to handle the copper-bearing solutions resulting from the water-soluble copper, a point that was overlooked in the laboratory test work. Attempts to decant the copper-bearing solution for precipitation in the usual manner ahead of flotation were not satisfactory because of low water recovery (owing to poor settling characteristics of the pulp) and contamination of the copper precipitate with unsettled slime. Low copper prices in 1931 necessitated the termination of testing. With the stimulus of higher copper prices in 1937, a review was made of metallurgical

Jan 1, 1943

By Robert Goodwin, Frank R. Milliken

In September 1937, the Ohio Copper Co. inaugurated the treatment of its copper-bearing mill tailings at Lark, Utah. These tailings had been accumulated during the regular operation of the Ohio Copper mine and mill over the period 1907 to 1919. Gravity concentration had been employed except for a comparatively short period in 1919, when flotation was used. The ore milled during that period assayed about I per cent Cu. The chief copper mineral, chalcocite, was disseminated in a shattered quartzite, mainly along fracture or cleavage planes. The quartzite gangue was extremely hard and grinding to liberation resulted in excessive sliming of the "sooty" chalcocite, with consequent high tailings losses. Recovery on the seven million tons treated was probably less than 60 per cent of the total copper content. As early as 1918, attempts had been made to sample the dump. In 1928, a complete sampling program was undertaken. The sampling consisted of seventy-four 5-in. post auger holes drilled to the full depth of the dump at regular intervals of 250 ft. Each 10-ft. portion thereof comprised a sample for analysis. Each sample was screened, rolled, divided into three parts, dried and assayed. The reject was retained for testing purposes. From the depth of the auger holes a contour map of the dump was plotted, Fig. I, which gives percentages of tonnage and copper content. The tonnage within the limit of the drill holes was estimated at about five million tons with an average content of 0.42 per cent Cu, 31 per cent of which (0.13 per cent) was acid-soluble. A screen analysis of the composite dump sample is shown in Table I. Flotation tests by several companies and individuals were then made, the results of which ranged from 62 to 74 per cent recovery. On the basis of these, a 200-ton pilot plant employing straight flotation was built and operated for a few months. Operation of this plant was unsuccessful, as no provision had been made to handle the copper-bearing solutions resulting from the water-soluble copper, a point that was overlooked in the laboratory test work. Attempts to decant the copper-bearing solution for precipitation in the usual manner ahead of flotation were not satisfactory because of low water recovery (owing to poor settling characteristics of the pulp) and contamination of the copper precipitate with unsettled slime. Low copper prices in 1931 necessitated the termination of testing. With the stimulus of higher copper prices in 1937, a review was made of metallurgical

Jan 1, 1943

By K. C. Mills, E. T. Turkdogan

The results on the rates of vaporization of Fe-Ni alloys, levitated by an electromagnetic field in a stagnant atmosphere of helium, are shown to be in close agreement with those predicted theoretically. AS shown in Part I of this series of papers, the rates of vaporization of metals enhanced by convection currents are increased further by the process of condensation of metal vapor when there is a steep temperature gradient in the boundary layer. At the time this theoretical work was completed one of the authors (K. C. Mills) had already carried out some experimental work on the rates of vaporization of molten Fe-Ni alloys. The experimental work was done under conditions which make it possible to compare the experimental rate data with those predicted on theoretical grounds. EXPERIMENTAL The object of the experiments was to evaluate the activities in a number of binary metal systems. The details of the experimental technique are given in another paper by Mills, Kinoshita, and Grieveson,2 and, for the present purpose, a brief mention of the relevant features of the experimental method will be adequate. Using an induction coil, the metal weighing about 1 to 1.5 g was levitated by the electromagnetic field in a stagnant atmosphere of pure helium. The helium was freed from oxygen and water vapor in the usual manner, and its pressure in the vaporization chamber was maintained at 1 atm through a bleeder device. The vaporization chamber consisted of a pyrex tube, 2.8 cm diam, with a side arm connected to the helium bleeder. The bottom of the tube, shaped conical, was surrounded by the induction coil, and the top was sealed with an optical flat for the purpose of measuring the melt temperature with a two-color optical pyrometer. By suitable adjustment of the high-frequency power input, the metal was brought to the desired temperature in about 30 sec of levitation. After a specified vaporization time, e.g., 3 to 4 min, the alloy was quenched by switching off the power. The amount of metal vaporized was determined from the difference between the initial and final weights of the sample. During the vaporization time, temperature fluctuations of about ±10°C were observed. COMPARISON OF EXPERIMENTAL DATA WITH THEORETICAL VALUES The experimental results are given in Table I. As already mentioned, the attainment of the vaporization temperature took about 30 sec from the moment of levitation. Therefore, the times recorded in Table I are 30 sec less than the total time; this is considered to be a reasonable estimate of actual vaporization times.

Jan 1, 1964

By Edward Saibel

The object of this study is to investigate the effect of prior tensile strain on the fracture stress of a metal. This is done in a theoretical manner starting from the point of view developed by the author in his thermodynamic theory of the fracture of metals. The results are compared with experimental findings and a rational interpretation is given to work that shows the variation of fracture stress with prior tensile strain. Theory op Fracture In the thermodynamic theory of the fracture of metals developed earlier,&apos; it was shown that a critical strain energy per unit volume exists. This is characteristic of the material and may be calculated from basic thermodynamic data. When the area under the flow curve reaches this characteristic value, fracture occurs. The general criterion for fracture is expressed in the form « ± u. = JLJW/V [r] where L, is the latent heat of melting of the unit volume, AV/V is the ratio of the change in volume of the unit volume to the original unit volume on passing from the solid to the liquid state, uo is an initial energy density, and J is a conversion factor, which changes energy from heat to mechanical units. As a first approximation, it will he assumed that the stress-strain curve is the straight line that extends from the point of maximum load onward, extrapolated back to the axis of zero strain, for example, line AC of Fig. I. If the point of intersection of the straight line with the axis of zero strain is represented by v., and the slope of the straight line is p, the analytic form of the flow curve is a = (To + pd [2] and the strain energy per unit volume evaluated from Jud6 becomes (u,6 + pa2/2). When this latter term reaches the critical value JLbVIV (designated hereafter by M), it is assumed that fracture occurs. This leads to the following expression for the fracture stress: a; = V«r.2 + iMp [3] The strain at fracture may be calculated from Eqs 2 and 3. It is assumed in this paper that the initial energy density is either zero or that it may be neglected. Furthermore, the complicated states of stress and of strain existing in the necked region of the tensile specimen after "necking" has occurred will also be neglected for the present, so that average conditions will be assumed to prevail. Flow and Fracture Curves LudwigZ attributed to materials two fundamental properties: (I) a resistance to flow and (2) a resistance to fracture. He reasoned that at each instant the

Jan 1, 1948

By Edward Saibel

The object of this study is to investigate the effect of prior tensile strain on the fracture stress of a metal. This is done in a theoretical manner starting from the point of view developed by the author in his thermodynamic theory of the fracture of metals. The results are compared with experimental findings and a rational interpretation is given to work that shows the variation of fracture stress with prior tensile strain. Theory op Fracture In the thermodynamic theory of the fracture of metals developed earlier,&apos; it was shown that a critical strain energy per unit volume exists. This is characteristic of the material and may be calculated from basic thermodynamic data. When the area under the flow curve reaches this characteristic value, fracture occurs. The general criterion for fracture is expressed in the form « ± u. = JLJW/V [r] where L, is the latent heat of melting of the unit volume, AV/V is the ratio of the change in volume of the unit volume to the original unit volume on passing from the solid to the liquid state, uo is an initial energy density, and J is a conversion factor, which changes energy from heat to mechanical units. As a first approximation, it will he assumed that the stress-strain curve is the straight line that extends from the point of maximum load onward, extrapolated back to the axis of zero strain, for example, line AC of Fig. I. If the point of intersection of the straight line with the axis of zero strain is represented by v., and the slope of the straight line is p, the analytic form of the flow curve is a = (To + pd [2] and the strain energy per unit volume evaluated from Jud6 becomes (u,6 + pa2/2). When this latter term reaches the critical value JLbVIV (designated hereafter by M), it is assumed that fracture occurs. This leads to the following expression for the fracture stress: a; = V«r.2 + iMp [3] The strain at fracture may be calculated from Eqs 2 and 3. It is assumed in this paper that the initial energy density is either zero or that it may be neglected. Furthermore, the complicated states of stress and of strain existing in the necked region of the tensile specimen after "necking" has occurred will also be neglected for the present, so that average conditions will be assumed to prevail. Flow and Fracture Curves LudwigZ attributed to materials two fundamental properties: (I) a resistance to flow and (2) a resistance to fracture. He reasoned that at each instant the

Jan 1, 1948

By D. R. Packard, J. D. Verhoeven

The resistivity us atom fraction relationships for dilute solutions of cadmium, mercury, and tin in molten sodium have been determined. With these data and the resistivity capillary-reservoir technique, the electro-transport mobilities, effective valences, and the diflusion coefficients of the three solutes have been determined. The mobilities are found to be higher than in other molten alloys by a factor of around 20. The results are compared to the Mmgelsdorf model for electrotrmtsport. The high values found for the mobility to diffusion coefficient ratio indicate that small quantities of the alkali metals should be susceptible to purification from many solutes by means of electrotransport. PASSAGE of a direct electric current through a liquid metal containing a solute will usually cause a relative motion between the solute and solvent atoms of the alloy. This electrotransport phenomenon may be described experimentally in terms of the mobility of the solute atoms, i.e., the drift velocity of the solute relative to the solvent per unit electric field. In dilute solutions of liquid alloys this relative mobility becomes a measure of the velocity of the solute with respect to the observer since the motion of the solvent is negligible. The mobility is a significant parameter in evaluating the potential usefulness of electrotransport for such things as purification or solute control upon solidification. Prior to around 1958, quantitative data for the mobility of solutes in liquid metals were restricted to some solutes in liquid mercury. Since that time ad- ditional data have been reported for the mobility of solutes in liquid mercury, bismuth, tin, and lead, as shown in Table I. In 1963 Drakin et al.11 reported some values of a transport number for mercury and thallium in molten sodium and potassium. When these values were converted to mobilities, it was found that the mobilities were higher than any of the previously reported values by a factor of around 20, as shown in Table I. Drakin&apos;s experimental technique did not eliminate the presence of back-diffusion and consequently his data were expected to be lower than the true values. The purpose of the present investigation was to determine the mobility of a number of solutes in molten sodium with an experimental technique which eliminates back-diffusion errors. EXPERIMENTAL The technique used to determine the mobility was a resistivity capillary-reservoir technique which had previously been used with a high degree of precision on Sn-Bi alloys.4 This technique consists of dipping the vertical Pyrex capillary cell shown in Fig. 1 into a molten bath of alloy while the bath and capillary are under vacuum. The capillary is then filled by intro-

Jan 1, 1969

By H. V. Winchell

It seems to me that uniformity of mining law in North America must of necessity start with uniformity in each country. I understand that the Provinces of Canada have the right to make their own individual laws and conditions, to prescribe the terms under which the prospector or the applicant for mineral titles may secure the same. That is not true of the states in the United States. In this country, the Federal Mining Law was made applicable to the public domain, which, at the time of the adoption of this Act in 1872, was chiefly west of the Missouri River; it is impossible to locate a mining claim in most of our eastern states. It is true, however, that there are certain holdover rights, mostly obsolete, arising from the fact that at the time of the formation of the Confederation of States, the land that belonged to each state became the property of the Federal Government. I am not quite correc-t in that, it was sometime after the adoption of our Constitution, I think it was 1778, but those rights were largely, by agreement, surrendered to the Federal Government; but it is a fact that the great acquisitions of territory in the West, with the single exception of Texas, were of domain that came into the possession of the Federal Government and our Federal Mining Law applies to that territory. No state has the right to (by legislative enactment) enlarge upon the rights given by the Federal Mining Law, governing the acquisition of mining claims in its territory, within its boundaries. Each state, however, may, and some of them do, limit somewhat the rights given to the prospector. For instance, the Federal Mining Law provides that a claim may be taken, staked upon the public domain, of 600 ft. in width and 1500 ft. in length. Some of the states, like South Dakota and Colorado, have at times said "that is an excessive amount of land for a single mining claim; we will therefore limit it to 300 ft. or 200 ft. in width." There is, therefore, not any direct and immediate need for uniformity of mining laws in the United States, such as there might possibly be if it were considered at all desirable upon the whole in Canada. The initiation of mining rights under the Federal Mining Act is the act of discovery of valuable mineral in place, referring now to the lode mining claims, but the same is true of the placer claim. It is true that the emphasis has never been laid upon the word valuable and that

Jan 1, 1920

By J. K. Stanley

Iron-cobalt alloys in the range of 35-50 pct cobalt are of interest in the electrical industry because they possess the highest magnetic saturation of any magnetic material known. l1,2The magnetic saturation induction of the 35 pct alloy is 24,200 gausses, compared to 21,600 for pure iron (Fig I). This difference is significant in electrical apparatus, whcre weight or space is at a premium. Saturation values higher than that for iron can be attained up to about 70 pct CO hut economics restrict the use to as low a cobalt content as possible without sacrifice of saturation. Fig 2 shows the iron-cobalt equilibrium diagram. Up to the present time, two factors have retarded the use of iron-cobalt alloys in the electrical industry for magnetic purposes.? One is the high cost of cobalt ($I.50 per pound) and the other ig the inherent brittleness of the binary iron-cobalt alloys. Straight iron-cobalt alloys up to 25 pct cobalt are ductile and easy to process to thin sheet or strip by conventional methods of hot and cold rolling, but the alloys containing higher percentages of cobalt, including those for which the saturation magnetization is a maximum (35 to 40 pct), are increasingly brittle with increasing cobalt, at least up to 50 pct, and are consequently difficult to process, either hot or cold. Work by White and Rah13 indicated that iron-cobalt alloys could be made ductile by alloying with vanadium, and after quenching the alloys (vanadium up to about 4 pct) were found to he colt1 rollable to very thin gauges. With this as a background, we resumed our work on these alloys with the objective of developing methods for economical commercial production of wide strip. For this purpose we have concentrated on the 35 pct alloy in order to obtain the highest possible saturation value. Experiments were carried out on many alloy additions to the iron-cobalt alloys and on the response of these compositions to heat treatments. This work finally culminated in a commercially producible iron-cobalt alloy which has been named Hiperco.* Materials StudIEd and Procedur&apos; Binary alloys of iron and cobalt in the range of 35 pct cobalt are difficult to hot work (by forging or rolling) without such additions as C, Mn, Si, V, Cr, Mo, W Or perhaps others. Another beneficial effect of such additions is that they increase to a greater or less extent the strangely low electrical resistivity of these alloys about 10 microohms per cm3

Jan 1, 1948

By J. K. Stanley

Iron-cobalt alloys in the range of 35-50 pct cobalt are of interest in the electrical industry because they possess the highest magnetic saturation of any magnetic material known. l1,2The magnetic saturation induction of the 35 pct alloy is 24,200 gausses, compared to 21,600 for pure iron (Fig I). This difference is significant in electrical apparatus, whcre weight or space is at a premium. Saturation values higher than that for iron can be attained up to about 70 pct CO hut economics restrict the use to as low a cobalt content as possible without sacrifice of saturation. Fig 2 shows the iron-cobalt equilibrium diagram. Up to the present time, two factors have retarded the use of iron-cobalt alloys in the electrical industry for magnetic purposes.? One is the high cost of cobalt ($I.50 per pound) and the other ig the inherent brittleness of the binary iron-cobalt alloys. Straight iron-cobalt alloys up to 25 pct cobalt are ductile and easy to process to thin sheet or strip by conventional methods of hot and cold rolling, but the alloys containing higher percentages of cobalt, including those for which the saturation magnetization is a maximum (35 to 40 pct), are increasingly brittle with increasing cobalt, at least up to 50 pct, and are consequently difficult to process, either hot or cold. Work by White and Rah13 indicated that iron-cobalt alloys could be made ductile by alloying with vanadium, and after quenching the alloys (vanadium up to about 4 pct) were found to he colt1 rollable to very thin gauges. With this as a background, we resumed our work on these alloys with the objective of developing methods for economical commercial production of wide strip. For this purpose we have concentrated on the 35 pct alloy in order to obtain the highest possible saturation value. Experiments were carried out on many alloy additions to the iron-cobalt alloys and on the response of these compositions to heat treatments. This work finally culminated in a commercially producible iron-cobalt alloy which has been named Hiperco.* Materials StudIEd and Procedur&apos; Binary alloys of iron and cobalt in the range of 35 pct cobalt are difficult to hot work (by forging or rolling) without such additions as C, Mn, Si, V, Cr, Mo, W Or perhaps others. Another beneficial effect of such additions is that they increase to a greater or less extent the strangely low electrical resistivity of these alloys about 10 microohms per cm3

Jan 1, 1948

Illustrated guidebooks treating in a popular descriptive way of the geology and other features of the Western United States have been issued by the U. S. Geological Survey. They will be of much interest to mem¬bers in connection with the Arizona Meeting of the Institute and espe¬cially the guidebook of the Santa Fe Route, with side trips to the Grand Canyon, containing as it does relief maps, topographical and geological maps, covering the entire route of the railroad, illustrations from photo¬graphs and other interesting descriptions of this great country. The method of treatment is adapted to the lay-reader, although it includes much valuable and interesting technical information concerning the geographical and other features. The books are well indexed. These volumes sell for 50 c. each and may be obtained from the Superintendent of Documents, Washington, D. C. These guidebooks originally sold for $1 each, but the reprint edition has been reduced to 50 c. A list of the different guidebooks follows: Bulletin 611. Guidebook of the Western United States, Part A, The Northern Pacific Route, with a Side Trip to Yellowstone Park, by M. R. Campbell, and others. 1915. 212 pages, 27 route maps, 27 plates, 39 text figures.

Jan 6, 1916

By W. B. Mather

R. G. Wuerker (University of Illinois, Urbana)—Mr. Mather is to be congratulated for stressing the most urgent need for a program of testing the physical properties of rocks, as they are encountered by the petroleum engineers on their drilling jobs and by the miners on their excavating, roof control and mineral preparation tasks. Another valuable source of information is the Handbook of Physical Constants.22 It stresses the physicist&apos;s approach rather than the engineer&apos;s procedure. The study of hardness, and rock hardness in particular, is beset with many difficulties. There is no satisfactory definition of hardness yet, and the term hardness is used to describe a number of quite dif- ferent properties. Hardness tests are grouped into static and dynamic determinations. They should be expressed with reference to the mechanical action of the applied force, like indentation hardness, scratch hardness, abrasion hardness, rebound hardness. A discussion of all these various hardness tests and of the special difficulties encountered in hardness testing of such heterogeneous material as rocks is given in the U. S. Bureau of Mines&apos; standard proposal. The more critical student may be referred to the book by D. Landau: Hardness, which is in my opinion the best existing treatise on this subject.

Jan 1, 1952

By H. H. Pentz

This paper gives the derivation of a practical formula for the calculation of slopes in seismic reflection prospecting. The derived formula is an approximation and can be used where the slope of the reflecting horizon is less than 250 ft. per 1000 and the depth to the reflecting horizon is greater than 2500 ft. The slope of sediments in oil regions is generally considerably less than 250 ft. per 1000. This is particularly true of the Gulf Coast, with the exception of the salt domes, which usually have the sediments at a greater slope than 260 ft. per 1000. Derivation In Fig. 1, o represents the image of the shot point a. Then the length of the path acb is equal to ob and ae&apos;d is equal to od. In the triangle aob, p is equal to ob, x is equal to , and c is equal to ao. The angle u is the apparent dip of the reflecting horizon. Angle oab is equal to (90" - u). The quantity m is the slope of a line tangent to the curve, defined by equation 1, at the point (p, x). The quantity m&apos; is the slope of the line tangent to the curve at the point (p&apos;, 2&apos;).

Jan 1, 1940