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By J. C. Fisher, J. H. Hollomon, David Turnbull

Understanding of the diffusion problem has recently been furthered by the analysis of Birchenall and Meh1.l They pursued the problem of the variation of the diffusion coefficient with composition for non-ideal solid solutions. Their analysis follows the tradition of Wagner,l Jost, Dehlinger, and Darken & who assumed the net flux of diffusing material to be proportional to the gradient of a quantity related to free energy. The basic assumption in Birchenall and Mehl's formulation of the problem is that the net flux of diffusing material is proportional to a thermodynamic activity gradient. To estimate the applicability of the derived relations, they corrected the diffusion coefficients of carbon in austenite by utilizing Smith's6 activity data for carbon, and the diffusion coefficients for zinc in copper with activity data computed from the vapor pressure measurements of Har-greaves.' The corrected coefficients for carbon were virtually independent of carbon concentration. For the diffusion of zinc in copper a moderate variation of diffusion coefficient with concentration remained after the correction. The problem of diffusion can be formulated in another way than that used by Birchenall and Mehl. The method is that of chemical rate theory and has been used by Eyring and his coworkers8,9 as well as by Eyring and Zwolinskilo in a discussion to Birchenall and Mehl's paper. As yet the method has not been applied to substitu-tional solid solutions. On the basis of their assumptions, Eyring and Zwolinski derived a relation between the diffusion coefficient and activity that is identical with that of Dehlinger and Darken but which does not correct for the variation of the diffusion coefficient with concentration as well as does the relation derived by Birchenall and Mehl. It was thought that the theory of diffusion would be more complete if the inconsistency between the two analyses could be rationalized and if diffusion in substitu-tional alloys were analyzed on the basis of the concepts of the chemical rate theory. Chemical Rate Theory According to the theory of absolute reaction ratess the reaction +..... +X, Eq I is viewed as taking place in two steps. First the reactants A1, A², . . . A; combine to form an activated complex M with which they are in equilibrium: A1 + A1+ . . . + A=M. Eq 2 Second the activated complex decomposes to give the products XI, XZ, . . . Xi: M?X, + X²+ . . . +Xi Eq g It has been showns that the number of activated complexes decomposing per unit volume per unit time is given by the expressiont kT -h CM † The transmission coefficient has been taken as unity.

Jan 1, 1949

By David Turnbull, J. H. Hollomon, J. C. Fisher

Understanding of the diffusion problem has recently been furthered by the analysis of Birchenall and Meh1.l They pursued the problem of the variation of the diffusion coefficient with composition for non-ideal solid solutions. Their analysis follows the tradition of Wagner,l Jost, Dehlinger, and Darken & who assumed the net flux of diffusing material to be proportional to the gradient of a quantity related to free energy. The basic assumption in Birchenall and Mehl's formulation of the problem is that the net flux of diffusing material is proportional to a thermodynamic activity gradient. To estimate the applicability of the derived relations, they corrected the diffusion coefficients of carbon in austenite by utilizing Smith's6 activity data for carbon, and the diffusion coefficients for zinc in copper with activity data computed from the vapor pressure measurements of Har-greaves.' The corrected coefficients for carbon were virtually independent of carbon concentration. For the diffusion of zinc in copper a moderate variation of diffusion coefficient with concentration remained after the correction. The problem of diffusion can be formulated in another way than that used by Birchenall and Mehl. The method is that of chemical rate theory and has been used by Eyring and his coworkers8,9 as well as by Eyring and Zwolinskilo in a discussion to Birchenall and Mehl's paper. As yet the method has not been applied to substitu-tional solid solutions. On the basis of their assumptions, Eyring and Zwolinski derived a relation between the diffusion coefficient and activity that is identical with that of Dehlinger and Darken but which does not correct for the variation of the diffusion coefficient with concentration as well as does the relation derived by Birchenall and Mehl. It was thought that the theory of diffusion would be more complete if the inconsistency between the two analyses could be rationalized and if diffusion in substitu-tional alloys were analyzed on the basis of the concepts of the chemical rate theory. Chemical Rate Theory According to the theory of absolute reaction ratess the reaction +..... +X, Eq I is viewed as taking place in two steps. First the reactants A1, A², . . . A; combine to form an activated complex M with which they are in equilibrium: A1 + A1+ . . . + A=M. Eq 2 Second the activated complex decomposes to give the products XI, XZ, . . . Xi: M?X, + X²+ . . . +Xi Eq g It has been showns that the number of activated complexes decomposing per unit volume per unit time is given by the expressiont kT -h CM † The transmission coefficient has been taken as unity.

Jan 1, 1949

By Willard S. Morse

The ores of the district are treated at this mill by the lixiviation process, consisting of drying, crushing, chloridizing-roasting and lixiviation by hyposulphite and Russell solutions. Gas is used as fuel for both drying and roasting, The gas-plant consists of two- Taylor revolving-bottom gas-producers, one 6 feet in diameter for the ore-dryers, the other 7 feet in diameter for the Stetefeldt furnace. The producers were made by Messrs. R. D. Wood & Co., Philadelphia, who also furnished the

Jan 1, 1893

By Wei-Kao Lu, G. Bitsianes

An improved general rate equation for a one-ditnensional gas-solid system has been derived. Fov the veversihle interfacial chemical reaction, there are concentrations of gaseous reactant and product at the reacting zone to be considered. They have been calculated with the velations fuvnished by the constraints on the system, namely, quasi-steady state and equimolal counterdiffusion of the gases. The results of the diffusiori study of Evans, Watson, and ,Mason based on the "dusty gas" model have been applied here. The interfacial chemical reaction is taken as first-order with respect to the concentration of the gases involved. The equation has proper dependence on gas composition and on solid structure through the relative values of Knudsen and normal diffusivities. The existence of the total pressure gradient inside the specimen has been predicted and confirmed experimentally. In a previous communication' we introduced a general rate equation for gas-solid reactions by considering the contributions of chemical reaction at inter- phase boundaries and diffusion through the solid product layer simultaneously. These equations, for one-dimensional and spherical specimens, take care of the whole range continuously from purely diffusion control to purely chemical reaction control. In this paper we study only the one-dimensional system. The corresponding rate equation is reproduced here: Of the two terms on the right-hand side of Eq. [I], the first represents the contribution of interfacial chemical reaction and the second that of gaseous diffusion. The shortcomings of Eq. [I] are that in its derivation the interfacial chemical reaction was assumed to be irreversible and the diffusion rate of gaseous product was not considered. Any pressure effects building up within the porous media were also neglected. Evidently. these simplifying assumptions will limit the general applicability of these equations. The rate of reduction of iron oxide by hydrogen, for instance, is very sensitive to the concentration of water vapor in the main gas stream, as has been reported by cewan' and by Quets et a1.3 Furthermore, the gaseous phase at the reacting interface will contain an appreciable amount of the gaseous product of reaction. If this were not true, a sufficiently high concentration gradient for the outward diffusion of the gaseous product could not be maintained. With these shortcomings in mind, Eq. [1I cannot be rigorously ap-

Jan 1, 1967

By R. E. Reed-Hill, W. H. Hartt

The second order, {1011}-{1012} twin bands observed in critically deformed magnesium are often accompanied by an unusual form of kinking. These kinks, which lie adjacent to and run more or less parallel to the twin band habit, allow plastic deformation that occurs inside the twins to be accommodated into the matrix. The bend planes of these kinks cannot be explained using slip dislocations with Burgers vectors lying in the basal plane. A mechanism involving a single set of {1012)(1011) dislocations is proposed to account for the kink band habit, in good agreement with the experimental observations. It has been shown that second order, {101l)-{1012} twinning is an important phenomenon for magnesium deformed in the ambient temperature range. A detailed study of these twins has recently led to a better understanding of their irrational habit plane1 and their relation to fracture in magnesium.' This paper is concerned with a third aspect of these twins; this being the kink bands, originally referred to as shear accommodation kinks,3'4 that are often induced in the adjacent matrix. A twin band and its shear accommodation kink usually appear as a single macroscopic deformation, as seen in Fig. 1. The complex nature of these deformed regions is easily revealed, however, with the aid of a suitable microscope. It has been proposed374 that the primary function of these kinks is to accommodate the nonhomogeneous deformation that normally occurs in the second order twins. The twins tend to form as small discrete lamellae lined up approximately one in front of the other.''' Very large plastic deformations varying in magnitude from one twin to the next, may occur inside these lamellae. The kinks serve both to pass this strain into the matrix and to accommodate strain variations between twins. Deformation within the kinks, subsequent to their formation, has also been observed;3,4 and it is thought that this contributes to the strain accommodation process. The bend planes of the kinks have a habit near that of the twin band itself, which lies about 56 deg from the matrix basal plane. This orientation does not bisect the angle formed between the basal plane to either side of the bend plane and therefore differs markedly from the kink structure usually observed in hcp metals.'-' The present paper reports the results of a study of shear accommodation kinks and proposes a possible solution to the problem of the orientation of the bend plane. EXPERIMENTAL PROCEDURE Rectangular cross-section tensile specimens with axes parallel to (1010) and faces to (1210) and (0001) were cut and acid machined from a high-purity magnesium single crystal. After straining on an Instron machine the specimens were examined by both optical and replica electron microscopy. The basic procedures have been previously reported."' EXPERIMENTAL RESULTS AND DISCUSSION Structure of Shear Accommodation Kinks. A typical, large (101l)-{1012) twin band with its associated shear accommodation kink is shown running diagonally from upper left to lower right in Fig. 1. In this optical micrograph the twin band, consisting of a row of small, highly deformed twin lamellae, is visible as a narrow dark band along the left hand edge of the structure in question. The kink lies to the right of the twins, is approximately three times as wide, and is lighter in contrast. The horizontal slip lines visible on the general specimen surface correspond to matrix basal slip and are parallel to the tensile axis. Note that on the right-hand side of the band these slip lines can be followed from the matrix into the kink. At the kink band boundary the slip lines suffer a clockwise rotation of about 25 deg. Rotations of this magnitude are not uncommon. When a surface such as that in Fig. 1 is given an etch1 making it sensitive to polarized light, it has been observed that the slip traces in the kink are parallel to the basal plane trace in this region. This is in excellent agreement with the assumption that these regions are indeed kinks. Fig. 2 is an electron micrograph of this same twin band and kink. Note that a row of small supplimation pits has formed

Jan 1, 1969

By Jean-Jacques Prompsy, J. S. Rinehart

Some time ago a study was initiated at the Colorado School of Mines in an effort to arrive at a better understanding of the stress fields developed within drill bits under dynamic loading and the influence that these stress fields could have on the failure of the bits. Particular emphasis has been given to the influence that bit shape has on the establishment of highly localized, potentially destructive stress inhomogeneities within the bit. The study has been divided into three phases involving three velocity regimes: impacts at very low velocities, 0 to 20 ft/sec, a velocity range in which dynamic effects are just beginning to be found; impacts at velocities ranging from 20 to several hundred ft/sec, a range commonly encountered in practical drilling operations; and impulsive loading through the detonation of explosives, a region in which the dynamic effects are greatly exaggerated and made more identifiable. The ultimate objective is to provide basic data which will enable the mitigation through judicious design of the frequency and severity of these transient concentrations of intense stress, thereby prolonging and increasing drill efficiency. This paper presents results of the third phase of this study — the development of a better understanding of the dynamics and mechanics of failures caused by transient stress-wave interactions. The impulsive loading or transient waves in these experiments were generated by detonating small explosive charges placed on the ends of Plexiglas cylindrical rods terminating in truncated cones. Under such intense loading, dynamic effects are greatly exaggerated and, hence, made more identifiable. The explosion generates a high-intensity transient stress disturbance which moves through the rod, reflects from surfaces which lie in its path, and establishes momentarily narrow regions of high concentrations of stress where failure of fracture may occur. The peregrinations of these waves, their interactions and their effects have already been described in the literature (see, for example, Refs. 1 and 2). The locations and extent of the regions quite apparently are strongly dependent on specimen shape, making it possible through judicious shaping of specimens to relocate the highly stressed regions, minimize their extent, or eliminate them entirely. These experiments were designed, first, to identify more clearly the vulnerable regions in geometries relevant to drill-bit design and, then, to modify these regions in a predictable way by changing specimen shape. Through this latter process, it is anticipated that better bit design might evolve. The specimens used in the experiments were cylindrical rods, 1 1/2 and 1 1/8 in. in diameter, ended by a truncated cone, with the cone angles ranging from 45° to 130°. Upper cone face diameters were 1/2, 3/4, or 1 in. A small plastic-covered electric blasting cap detonated on the axis of the specimen produced the spherical shock wave. The detonators used were Olin Mathieson No. 6, which induced into the rod a transient saw-toothed stress disturbance of about 3-microseconds duration, corresponding to a wave length of 0.3 in. in the Plexiglas. Five distinct systems of fracture were observed: (1) along the axis of the rod, a lower system of fractures, the cracks focusing around one point for specimens having cone angles of 80° and 90° and, as the cone angle was increased, spreading downward; (2) just above these fractures, an upper system of fractures composed of horizontal cracks observable in some specimens but not of any appreciable extent; (3) a third system of axial cracks still above the latter, observable in the small cone-angle specimens; (4) in the upper part of the specimen, a system of radial fractures extending from the blasting point; and (5) circular spalling due to reflection of the wave on the boundary of the cylinder. Only the first three systems, the axial fractures, are examined here. LOWER TENSILE FRACTURE SYSTEM The first, lower system of tensile fractures, shown in the photograph of Fig. 1, was observed in almost all of the specimens. It was due to the reflected tensile wave coming in from the boundary of the cylinder as shown in Fig. 2. The reflected wave was cylindrically convergent and focused

By James Boyd

Scientists and engineers must concern themselves not only with technical problems, but with the socio-economic difficulties of our scciety. The author states that raw materials are basic to the economic process and that mineral raw materials occur naturally in nearly limitless quantities. He feels that the economic pocess will provide sufficient raw materials for man's needs, and discusses in some detail the world economic environment. As our society grows in complexity, it becomes more urgently incumbent upon scientists and engineers to bring their experiences to bear on the solution, not only of technical problems, but also on socio-economic difficulties. It is to this field that I have directed a large part of my energies. RAW MATERIALS BASIC TO THE ECONOMIC PROCESS There are certain premises, frequently overlooked, which bear emphasis. As economics concerns the production, distribution, and consumption of goods, so our whole society is based on raw materials. Without the basic extractive industries of agriculture and mining, there would be no economic problems with which to deal. This principle has been expressed as "All productivity is based on three factors: 1) natural resources, whose form, place, and condition are changed by the expenditure of 2) human energy (both muscular and mental), with the aid of 3) tools.77* It seems strange that such an obvious statement needs to be made. It is forgotten by all of us, however, at one time or another when we get involved in the complicated theories of economics dealing with the financial and fiscal policies of the various governments, in the financing of enterprises, in marketing, and in labor relations. Unless decisions in all of these fields are made with this, and the rest of the "Ten Pillars of Economic Wisdom," consciously in mind, the resultant policies are doomed to eventual failure, whether these are policies of individuals, companies, or governments. The economic process is basic to society. But economics and the social aspects of humanity are inevitably intertwined. If human needs are not provided for within the basic economic structure, conflicts arise to disrupt the most carefully laid social plans. Similarly, it is the failure of society to cope with basic economic prerequisites that leads to discord within the body politic and thus to eventual economic disaster. We who are engaged in the various aspects of the mineral industry, therefore, have a large part to play in society's future development. MINERAL RAW MATERIALS OCCUR NATURALLY IN NEARLY LIMITLESS QUANTITIES Throughout my career in and out of government, I have formed my decisions on two principles: 1) Fundamentally, all mineral raw materials exist within the earth's crust in quantities greatly exceeding man's needs; 2) Any problems of supply of these materials are primarily economic in nature. With respect to my first assumption, analyses by geochemists enable them to estimate the quantities in which each of the known elements exist in the earth's crust. One of the most cautious and famous suggests that the average copper content of the lithosphere to a depth of ten miles is about 55 ppm. If this is valid, then the lithosphere contains about 1.4 quadrillion (1.4 x 10 ") tons of copper metal — an unimaginable quantity. This is 8,500,000-fold that which has been consumed by man in his existence. To illustrate further, consider that the deepest copper mine in history went to about 9000 ft below the surface; the present copper mines of the world now average less than 1500 ft in depth. We can assume that in most continental land areas of the world it is technically feasible to mine to a depth of at least one mile. The land areas of the world to an average depth of one mile, then, contain 343 billion tons (343 x 10') of copper metal, or 2000 times that which has been extracted to date. I don't believe man will ever expend his energies to extract copper from rocks which contain only a few parts per million, but he knows that each element

Jan 1, 1968

By George B. Lee

DURING The Two Years In Which The New Reduction-Works Of The Copper Queen Consolidated Mining Co. Have Been In Operation At Douglas, Ariz., There Has Developed A Remarkable Condition In Regard To The Corrosive Action Of The Water Used To Cool The Jackets Of The Blast-Furnaces. Were It Not For The Many Contradictory Features, It Might Pass As One Of The Unavoidable Troubles Due To The Composition Of The Water. This Water, Obtained From Wells 600 Ft. Deep, Is Also Used In The Steam-Boilers, And Its Composition, As Shown By The Following Analysis, Does Not Indicate The Presence Of Any Ingredient Which Would Explain The Corrosion Grains Per U. S. Gal. Silica, 0.861 Iron Oxide And Alumina, 0.223 Calcium Carbonate, 0.2111 Calcium Sulphate, Magnesium Carbonate, Sodium And Potassium Sulphates, . 14.850 Sodium And Potassium Chlorides, 9.732 Sodium And Potassium Carbonate, 6.452 32.409 The Jackets Are Made Of Inner Plates 0.5 In. Thick And An Outer Plate I In. Thick, With 3-In. Stiffeners Between The Inner And Outer Plates. In From 10 To 12 Months The Inner Plates Have Been Reduced By Corrosion To A Thickness Of From 1/8 To 1/16 In., While The Outer Plate In The Same Time Is Reduced By Less Than 1/16 In., And The Stiffeners Show Very Little Corrosion. The Plates Are Pitted And Eaten Away In Some Places More Than In Others. There Is Practically No Scale Found On The Jackets, But When Cleaned Considerable Iron Oxide Is Found In The Bottoms. With An Action So Marked, Serious Trouble Would Be Expected In The Boilers, But, On The Contrary, A Recent Inspection By a

Mar 1, 1908

By George Stone

THE stack gases from regenerative furnaces are very seldom utilized for the production of steam. If the temperature of the gases is not higher than 300° C. (572° F.) there is no economy in their use for this purpose, as the amount of available heat is very small and the temperature is so little above that of the steam that the interchange is too slow. With higher temperatures of the waste gases, however, good results can be obtained. At the plant of the New Jersey Zinc Co. (of Pa.) at Palmerton there are a number of return tubular boilers, each 6 ft. in diameter and 20 ft. long, with 96 3.5-in. tubes, which are heated by the waste gases from the spelter furnaces. These furnaces have continuous regenerators heating the air only and the stack gases reach the boilers at a temperature of about 450°. The gas producers for one of these furnaces require 14 tons of anthracite (a mixture of Nos. 2 and 3 buckwheat), and the waste heat from the furnace gives a little more than 42 h.p. in steam. The boilers are not well adapted for the purpose, as they are much too large for the amount of heat going to them and the area of the tubes is not sufficient to take the gas from two furnaces without causing an objectionable amount of back pressure. The plant was built without any idea of using waste-heat boilers, and it was impossible to place the latter as close to the furnaces as they should be. Furnace and boiler are connected by an underground brick flue in which the temperature of the gas drops about 100°, losing 40 per cent. of its available heat. If the .boilers were close to the furnaces the horse power of each would be 70 instead of 42. Even under these unfavorable conditions the boilers have been very advantageous, as one boiler easily supplies the steam necessary for two batteries of producers. With such low gas temperatures the heating surface of the boilers is, of course, not as efficient and the flue areas need to be considerably larger than for coal firing.

Jan 10, 1913

By William H. Baer, George M. Carlton, Blake M. Loring

IT is a well known fact that age-hardening alloys remain in a supersaturated, or partially supersaturated, condition only for limited periods of time at temperatures below the solvus. In order to develop optimum properties by subjecting the quenched alloy to precipitation or age-hardening treatment at a specified temperature, it is necessary that the cooling rate be sufficiently high to maintain the required degree of supersaturation of the solid solution. In practical applications the size and shape of the specimens obviously have considerable influence on the rate of cooling and there is need for more information on the effects of various rates of cooling. Cooling rates of quenched aluminum alloys generally have been established by the type of quenching medium, the temperature of the medium and the dimensions of the specimen.1,2,3 Except for the work of Roth3 little quantitative information is available on the measurement of cooling rates of aluminum alloys and the significance of the influence of various cooling rates upon the mechanical properties. The purpose of the present investigation was to study the use of the Jominy test for aluminum alloys (Table I). EXPERIMENTAL PROCEDURE The material for this investigation consisted of extruded rods 1 ¼ to 1 ½ in. in diam. The chemical compositions were as follows: [ ] The modified L-type Jominy specimen with dimensions shown in Fig I was selected as the most convenient means for obtaining a wide range of cooling rates. The standard Jominy specimen was not satisfactory because its cooling rate was not sufficiently high. The four flat surfaces machined at right angles along the length of the L-type specimen to a depth of 0-015 in. facilitated the hardness measurements. The specimens were machined from the extruded stock with no intermediate forging. New specimens were used for each aging experiment. The specimens were given solution treatments of 2 hr duration at recommended temperatures in a Hoskins furnace (Table 2). The temperature of the furnace was maintained constant to ±3°C. No protective atmosphere was necessary because the thin film of oxide that formed on the surface of the specimens had no effect on the hardness measurements.

Jan 1, 1948

By M. B. Kahle, A. D. Pernichele

Four types of slope failures in waste dumps are recognized debris flow, foundation failure, edge slump, and blowout. The first three types, although at times causing considerable damage to property and interfering with mine operations, are not usually dangerous to personnel because of their slow rate of movement. The fourth type, the blowout, is the most dangerous because of its explosive mode of failure and lack of forewarning. The December 1969 failure at Verona dump is presented as an example of a blowout. Data from piezometer holes indicate that the blowout was due to perched leach solutions near the face of the dump. The level of water in this zone is very closely related to the rate of leach water application on the dump. A detailed analysis of core samples indicates that the impounded water was perched on a zonal accumulation of jarosite which is associated with a buried dump surface. Drain holes proved successful in controlling perched leach solutions in the critical zone near the face of the dump. Monitoring of the water level in the perched zone is considered essential in preventing blowouts. The use of drain and piezometer holes has allowed an increase in the rate of water application on the dump while preventing additional failure.

Jan 1, 1972

Jan 1, 1923

By Miroslaw Hajdasinski

Estimation of the economic effectiveness of industrial development projects including mining ones is generally made on the basis of the discrete model of the value changes in time, although the character of these changes is similar to the continuous model. In this paper an attempt has been undertaken to investigate the problem of the value equivalence of both models exemplified by a construction of an underground coal mine. An effort has been made to determine the errors which for different estimation criteria appear in result of the application of the discrete model. Theoretical considerations have been supplemented with practical conclusions.

Jan 1, 1977

By Shiou-Chuan Sun, R. F. Wesner, J. D. Morgan

0. C. Ralston and F. Fraas—Dr. Sun and associates have presented an interesting paper not all of which is comprehended by us. The data assembled measure the deflections of particles in an electrostatic field as a function of a number of independent variables and some dependent variables that are not sharply differentiated. These data are all based on a Johnson type machine of definite, well-described geometry, something not often done in electrostatic separation literature. One new fact brought out by this technique is the effect of coal dust on admixed pyrite and quartz. The effects are opposite in character, as should be expected and we do not agree with the authors that these effects are negligible. Fraas' also used a multiple cell "distribution analyzer" and gives in fig. 5 of his paper a straight line plot with no humps or curves. This is not necessarily at variance with Sun's results because Fraas used a larger gap between electrodes and had no evidence of particles adhering to or dropping off the charged electrode. The section of Sun's paper on effect of surface conductivity contains a speculation that the dielectric constant "represents more or less the electrical conductance of the bulk body instead of the surface of the mineral particles." A simple picture of the meaning of the dielectric constant is that it is the specific inductive capacity of a dielectric when used as the dielectric between the plates of a condenser. It is at once evident that the above speculation confuses capacity with conductance—two definitely independent variables. We ask the authors to state in what group or subdivision their garnet belongs; what method and units were used in calculating the data of col. A, table I and their meaning; what was the temperature of the carrier roll and, finally, has any effort been made to investigate the effects of particle shape on distribution in the electrostatic field? S. B. Hudson—I have read this article with great interest. We have been engaged in research work on the principles of electrostatic separation in this laboratory for some time now, and our findings agree with those of the authors in many respects. The article shows evidence of careful and valuable research in the field of electrostatic separation. A "distribution analyser," very similar to that described in an earlier article by one of the authors," was incorporated in an inclined plate-type electrostatic separator designed and built in the Melbourne University laboratory in 1948 for investigation purposes.22 The actual splitting edges were machined from y! in. per-spex, and the paper hoppers were supported on linen thread immediately below the perspex dividers. These dividers fitted into machined slots in a framework to give accurate Yz-in. spacings. The hoppers (staggered) fed directly into a rack of test tubes, which is supported on a vertical pantograph arrangement. The rack was positioned with guides on the horizontal pantograph stand, and this ensured positive alignment when replacing the rack after making weighings. In later work, when much heavier feed rates were used, of the order of 30 to 40 Ib per in. per hr a rack fitted with rectangular metal containers and similarly aligned was used. Some work was done here on comparing the distributions of minerals when passed separately and when passed as a mixture, and it was found that there was quite an appreciable difference in the two results.= However, in our separator the particles do not pass down the plate in a single layer, and this difference is probably caused by collisions of one mineral particles with the other mineral particles. In most of the investigational work here, the change of the center point of the distribution is measured to establish the effect of a variable, such as voltage. Two minerals (zircon and rutile) have been studied rather exhaustively, and it was found that their distributions are very nearly normal. Owing to the sharpness of the distribution curves, the usual method of obtaining the mean or median was inaccurate, and was not used; instead the mean (also the median), calculated on the assumption of a normal distribution, was used to locate the center point of each distribution and proved satisfactory. The effect of polarity becomes very apparent in the plate-type separator where frictional charges play a very important part when using highly resistive minerals such as zircon. With rutile, a comparatively conductive mineral, polarity of the electrode has little effect. On the other hand, the magnitude of the voltage has a far greater effect on conductive than on resistive minerals. Shiou-Chuan Sun (authors' reply)—Thanks are extended to Drs. Ralston and Fraas for their keen interest in this paper. Their questions concerning coal dust,

Jan 1, 1951

By Shiou-Chuan Sun, R. F. Wesner, J. D. Morgan

0. C. Ralston and F. Fraas—Dr. Sun and associates have presented an interesting paper not all of which is comprehended by us. The data assembled measure the deflections of particles in an electrostatic field as a function of a number of independent variables and some dependent variables that are not sharply differentiated. These data are all based on a Johnson type machine of definite, well-described geometry, something not often done in electrostatic separation literature. One new fact brought out by this technique is the effect of coal dust on admixed pyrite and quartz. The effects are opposite in character, as should be expected and we do not agree with the authors that these effects are negligible. Fraas' also used a multiple cell "distribution analyzer" and gives in fig. 5 of his paper a straight line plot with no humps or curves. This is not necessarily at variance with Sun's results because Fraas used a larger gap between electrodes and had no evidence of particles adhering to or dropping off the charged electrode. The section of Sun's paper on effect of surface conductivity contains a speculation that the dielectric constant "represents more or less the electrical conductance of the bulk body instead of the surface of the mineral particles." A simple picture of the meaning of the dielectric constant is that it is the specific inductive capacity of a dielectric when used as the dielectric between the plates of a condenser. It is at once evident that the above speculation confuses capacity with conductance—two definitely independent variables. We ask the authors to state in what group or subdivision their garnet belongs; what method and units were used in calculating the data of col. A, table I and their meaning; what was the temperature of the carrier roll and, finally, has any effort been made to investigate the effects of particle shape on distribution in the electrostatic field? S. B. Hudson—I have read this article with great interest. We have been engaged in research work on the principles of electrostatic separation in this laboratory for some time now, and our findings agree with those of the authors in many respects. The article shows evidence of careful and valuable research in the field of electrostatic separation. A "distribution analyser," very similar to that described in an earlier article by one of the authors," was incorporated in an inclined plate-type electrostatic separator designed and built in the Melbourne University laboratory in 1948 for investigation purposes.22 The actual splitting edges were machined from y! in. per-spex, and the paper hoppers were supported on linen thread immediately below the perspex dividers. These dividers fitted into machined slots in a framework to give accurate Yz-in. spacings. The hoppers (staggered) fed directly into a rack of test tubes, which is supported on a vertical pantograph arrangement. The rack was positioned with guides on the horizontal pantograph stand, and this ensured positive alignment when replacing the rack after making weighings. In later work, when much heavier feed rates were used, of the order of 30 to 40 Ib per in. per hr a rack fitted with rectangular metal containers and similarly aligned was used. Some work was done here on comparing the distributions of minerals when passed separately and when passed as a mixture, and it was found that there was quite an appreciable difference in the two results.= However, in our separator the particles do not pass down the plate in a single layer, and this difference is probably caused by collisions of one mineral particles with the other mineral particles. In most of the investigational work here, the change of the center point of the distribution is measured to establish the effect of a variable, such as voltage. Two minerals (zircon and rutile) have been studied rather exhaustively, and it was found that their distributions are very nearly normal. Owing to the sharpness of the distribution curves, the usual method of obtaining the mean or median was inaccurate, and was not used; instead the mean (also the median), calculated on the assumption of a normal distribution, was used to locate the center point of each distribution and proved satisfactory. The effect of polarity becomes very apparent in the plate-type separator where frictional charges play a very important part when using highly resistive minerals such as zircon. With rutile, a comparatively conductive mineral, polarity of the electrode has little effect. On the other hand, the magnitude of the voltage has a far greater effect on conductive than on resistive minerals. Shiou-Chuan Sun (authors' reply)—Thanks are extended to Drs. Ralston and Fraas for their keen interest in this paper. Their questions concerning coal dust,

Jan 1, 1951

By W. M. Myers

Certain minerals possess inherent color and other properties that make them suitable for the pigmentation of paints, mortar, plaster, concrete, face brick, and other materials. Their production is one of the most ancient of mineral industries and their use by primitive man is well known. These natural pigments have some economic factors in their favor, particularly wide geographic distribution, low cost of production, ease of preparation, chemical stability, and permanence in use so that they continue to form the basis of a small but useful industry. When used in paints such pigments act as a filler and supply body and opacity in addition to color. Natural mineral pigments are prepared for the market by the comparatively simple operations of washing, grinding, blending, and calcining. Any one, or all of these processes may be applied to a single pigment. The development of synthetic pigments and the use of byproduct materials have introduced competition with the products of nature and are having a growing influence on the economic position of the mined minerals. Development of the Industry The industry developed to commercial stature in Pennsylvania largely because of the presence of beds of ocher extending from Easton in a southwesterly direction toward Reading, and a variety of small iron mines in the region. The mining of paint ores in the Lehigh Valley was active as early as 1850 and shortly after the Civil War the establishment of mills expanded production and led to the development of new products and eventually the manufacture of synthetic pigments. Pennsylvania continues to maintain it.s leadership as a producer of mineral colors. Production is recorded also in New Jersey, Illinois, Virginia, Ohio, and Georgia. Iron as a Pigment Iron in various compounds is the most important pigment in nature. The iron pigments are characterized by stability, light fastness, good covering power, high index of refraction, and economy in production. Ferrous compounds display a typical green coloration. This has not been employed as a commercial pigment to any great extent except incidentally in such greenstones as have been used in construction, or crushed and sized for application as a granule to roofing. Ferric oxides are characteristically red and form an important group of industrial pignents. Hydrated ferric oxides exhibit various shades of yellow and are present in such familiar pigments as ocher and sienna. The addition of small amounts of manganese oxide or carbon as organic matter to the yellows produces the brown umbers. Magnetite is one of the few black minerals that grinds to a black powder. The mineral pigments vary from earth colors of low intensity and great dilution of iron content to almost pure iron compounds with high tinting strength and correspondingly greater value. There has been some relationship between the mining of iron ores and the production of mineral pigments; although the production of colors is not carried on appreciably as a byproduct of iron mining. A number of mineral pigment producers, particularly in the eastern states, have operated mines which in the past were small producers of hematite, bog ore, or carbonate ore. The knowledge of the location of the deposit and its possibilities as a producer of pigment are due to its past history as a producer of metallic ore. Many iron compounds may be changed in color by calcination, the end product being Fe2O3, a stable red oxide. The yellow hydrated oxides may be changed to red. The gray carbonate, found in Carbon County, Pa., calcines to a fine red product. Ferrous sulphate (copperas) often available in tonnage as a byproduct of the steel industry, breaks down under heat or chemical action leaving a residual red oxide. Pigments produced by calcination or dissassociation of compounds possess the advantage of fine particle size and ease of grinding. Mineral Pigments MINERAL BLACKS Many black minerals grind to a light colored powder. This characteristic is familiar to the mineralogist as the white streak produced by a black

Jan 1, 1950

Jan 1, 1924

By ERLE VICTOR DAVELER

ERLE VICTOR DAVELER, who in his application for membership in the Institute in 1909 modestly described himself as "millman," was born at Denver in 1885 and graduated from the University of California in 1907. After a few months' work at gold mills in California he went to Tonopah, where for the next two years he had a varied experience working on pumps, convey- ors, tube-mills and filters. For the following two years he was experimental foreman and metallurgical engineer for the Utah Copper Co. at Garfield. He was sent in 1911 to be assistant superintendent of mills at the Ray. From 1913 to 1917 he was mill superintendent at the striking but unsuccessful experiment in large-scale low-grade gold mining of the Alaska Gold Mines Co.

Jan 1, 1929

By L. T. Larson, M. L. Picklesimer

The relationship between the apparent angle of rotation of monochromatic plane polarized light and the tilt of the basal pole from the surface normal has been experimentally determined for zirconium over the wavelength range of 500 to 655 mp. This relationship allows the determination of the spatial orientation of the basal pole of an individual grain in a polycvystal-ling zivrconium specimen to within ±3 deg by three simple tneasurements with a polarized-light metallurgical microscope. The method of measurement is discussed in detail. THE optical anisotropy of materials having noncubic crystal structures has long been used to reveal features by polarized-light microscopy. Petrographers have used measurements of certain optical properties to identify and classify transparent or translucent minerals. More recent work (i.e., Cameron1) has extended such measurements to opaque minerals in reflected light. Few attempts have been made to make similar measurements on noncubic metals. Couling and pearsall2 have reported that a sensitive tint plate can be used in a polarized-light metallurgical microscope to determine the position of the basal-plane trace in a grain of polycrystalline magnesium. Reed-Hill3 has reported that the same technique can be used for zirconium. We have found that the precision of measurement can be increased to about ±0.5 deg by using a Nakamura plate4,5 to determine the exact extinction position after the sensitive tint plate has been used to locate approximately the basal-plane trace. This report describes a method for measurement of another optical property, the apparent angle of rotation. This measurement permits determination of the angle between the basal pole of a grain of a hcp metal and the normal to the surface of the specimen. When the two measurements are combined, the orientation of the basal pole in space can be determined from three simple measurements on a single surface. One to two hundred such determinations will permit plotting of a basal-pole figure for the polycrystalline material with reasonable accuracy. When normally incident, monochromatic, plane-polarized light is reflected from the surface of an optically anisotropic material, the light may be converted to elliptically polarized light, the plane of vibration may be rotated, or both may occur. The el- lipticity, the angle of rotation, and the reflectivity can be related to the indices of refraction and the absorption coefficients of the material.6,7 Ellipticity values can be determined with an elliptical compensator, but not with the ease and precision desirable for the present purposes. Measurement of the angle of rotation requires only the determination of the angle from the crossed position (90 deg to the polarizer) that the analyzer must be rotated to obtain extinction when the trace of the optical axis in the surface is at 45 deg to the vibration direction of the polarizer. The angle of rotation of the analyzer is approximately 6/5 that of the true angle of rotation of the light as reflected from the specimen because there is a small amount of additional rotation produced during the passage of the reflected light through the mirror of the microscope. Since we are presently interested only in determining the tilt of the basal pole, the angle of rotation of the analyzer (the apparent angle of rotation of the light, i.e., uncorrected) can be used. Precision of the measurement can be increased substantially by the use of a Nakamura plate4,5 in determining the extinction position. In an optically uniaxial material (hcp or tetragonal crystal structure) the angle of rotation depends only on the optical properties of the material and the orientation of the optical axis of the grain relative to the plane of incidence of the plane-polarized light.7,8 Thus, in a metal such as zirconium, the apparent angle of rotation at the 45-deg position in any given wavelength of light is a direct measure of the tilt of the basal pole from the normal to the surface. If the optical properties vary with wavelength, the apparent angle of rotation for any given tilt of the basal pole will vary. None of the required information exists in the literature for zirconium nor for any other non-cubic metal. MEASUREMENTS ON SINGLE-CRYSTAL ZIRCONIUM A single-crystal sphere of zirconium 9/16 in. in diam was spark-cut from a single-crystal rod grown from iodide bar by an electron-beam zone-melting process.9 The damaged surface was removed by chemical polishing in a 45/45/10 mixture (by vol) of water, concentrated HNO3, and HF (48 pct) and then electropolishing at 50 v in a bath1' of methyl alcohol and perchloric acid (95/5 by vol) at -70-C. The single-crystal sphere was mounted in a five-axis goniometer stage having a removable eucentric X-ray diffraction goniometer head for the two inner orientation axes. The basal pole of the single-crysta sphere was aligned parallel to a third axis of the goniometer stage by using the sensitive tint method to determine the basal-plane trace at several rotational positions of the sphere. The alignment was then checked by removing the sphere and eucentric gonio-

Jan 1, 1967

By L. R. Raymond, G. G. Binder

One primary purpose of hydraulic fracturing as a well stimulation technique is to overcome formation damage. The literature provides ways of designing fracture treatments and evaluating their results but not of incorporating formation damage in vertically fractured wells. Results of an investigation of this problem are presented in this paper. Prediction of stimulation ratios in vertically fractured, damaged wells is accomplished with a mathematical model relating stimulation ratio to relative conductivity of fractures whose lengths are not more than about half the drainage radius of the well. Comparison of results from the new model to results in published predictions verify its utility; these results also show that the range of stimulation ratios that can be predicted for undamaged wells is extended to include relative conductivities of less than 300. This extension is important when using fracturing to stimulate wells with high production rates and high native formation permeabilities. For example, large increases in daily oil production rate can be obtained with stimulation ratio increases as low as 1.25. The importance of complete fracture fill-up (uniform proppant packing) is shown through use of the mathematical model. If, at the mouth of a fracture, only a small fraction (1/2 percent) of the total fracture length is not packed with proppant, nearly all the polential stimulation increase is lost. Proppant crushing, compaction and embedment have been shown in laboratory studies to be responsible for low fracture conductivities in wells producing from highly stressed formations. Equipment and methods for testing the effect of stress (overburden) on conductivity of fructures in consolidated and unconsolidated sands are discussed in this paper. Laboratory tests with simlilated fractures in cores from both types of formations showed that crushing, compaction and embedment seriously affect conductivity. Results indicate that similar laboratory tests should be made when accurate knowledge of fracture conductivity is needed to assure good stimulation results for important wells. The chief factor in stimulation ratio reduction was found to be overburden pressure, but the size and type of proppant and the hardness of the formation have significant effects. Fracture conductivity reductions of up to 50 percent were observed with sand propping fractures in consolidated cores; a reduction of 83 percent was measured for an unconsolidated core. The range of effective overburden pressures for which conductivities were measured was from 100 to 5,000 psi. An example fracture design and evaluation problem indicates the usefulness of considering formation damage in planning well stimulation jobs. When damage exists, but its extent and the degree of permeability reduction are not estimated from diagnostic tests, the formation permeability used in planning the job may lead to under-designing. As the example shows, too low a target stimulation ratio can lead to much lower production rates (by half) than could be attained otherwise. Solutions of equations representing several special cases of the mathematical model are presented in graphical form and details of the derivations of the equations are given in the Appendix. INTRODUCTION Since its inception in 1947, hydraulic fracturing has proven to be an effective and widely accepted stimulation technique. In the past 18 years the ability to execute a successful hydraulic fracturing treatment has been substantially increased. The development of design and evaluation procedures1,2 has been one of the major contributions to this increased skill. However, as the art of hydraulic fracturing has moved closer to a science, new problems concerning the design and evaluation of the optimal hydraulic fracturing treatment have arisen. Three questions are pertinent to these problems. I. How is a fracturing job evaluated in a damaged well? 2. What is the effect on the stimulation ratio of not filling the fracture in the vicinity of the wellbore? 3. What is the effect of overburden pressure on fracture conductivity and, consequently, the stimulation ratio? A primary objective of fracturing a well is to stimulate production by overcoming wellbore damage. Presently. however, there is no rational basis for designing or evaluating the optimal fracturing treatment in a damaged well. All present fracture design and evaluation techniques assume that proppants can be uniformly placed in fractures. This assumption may be in serious error, particularly for the portion of a fracture directly adjacent to the wellbore. In this area, turbulence of the injected fluid can cause the proppant to be swept farther into the fracture. Also, loss of fluid from the fracture to the