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By C. F. Davan, C. T. Houseman

The news pages of MINING ENGINEERING and other trade publications have for the past two years carried a great many items about new developments in phosphate and potash, reflecting the surge in world consumption of these products as fertilizer. Today the question often arises concerning how much growth can be further anticipated by the phosphate and potash industries. To answer this question, a 15-year projection of world fertilizer consumption in terms of the three basic plant food nutrients-nitrogen, phosphate and potash-has been prepared. Two of these, phosphate and potash, are basic products of the mining industry. Nitrogen, once an important product of mining, is now mainly a chemical product. Another mineral, sulfur, although not a primary nutrient, depends on the fertilizer manufacturing industry for the bulk of its market. In crop year 1962-63, there began a startling in- crease in world fertilizer consumption. In that year, consumption increased by about 10% and in the following year by 10-12%.

Jan 12, 1965

By J. H. Anderson, G. A. Parks, B. K. Jindal

Both temperature and humidity are important variables in electrical separations. By independent control of temperature and water vapor pressure, it is shown that charge depends primarily upon relative humidity, not on temperature or water pressure alone. All the effects of temperature changes other than modification of humidity are apparently small. However, humidity control can be achieved through manipulation of the more tractable variable, temperature. Both temperature and humidity are important variables in electrical separations. Some of their effects have been described in general by Fraas1,2 and by Ralston.3 The influence of temperature and humidity may be considered a problem in industrial separations because humidity, especially, is not normally controlled, hence leads to unpredicted quality control problems. The problem is significant whether the separation is based on conductivity differences or on contact electrification. There is no doubt that water adsorbs from humid atmospheres onto mineral surfaces resulting in conductivity changes.'-8 An empirical relationship between conductivity and humidity is1.4-6,8 where a and b are constants peculiar to the substrate, and s and h are the conductivity and relative humidity respectively. Some authors have taken advantage of differences in a and b among minerals to make or propose electrodynamic separations in which h is the key control variable. Fraasl,2 reported that the charge developed on quartz and feldspar through contact with aluminum is sensitive to humidity, as illustrated schematically in Fig. 1. Lawver9 found that the charge developed by quartz on contact with several materials was tem-

Jan 1, 1967

By Robert L. Voss, Richard D. Hagni

Sparry dolomite from all of the operating mines in the Viburnum Trend of Southeast Missouri have been found by cathodoluminescence microscopy to reveal a systematic pattern of banding resulting from a growth zoning within individual dolomite rhombs. Four principal bands have been recognized throughout the entire Trend and each of the major bands contain even finer internal banding. Minor bands a few microns in width can be correlated in specimens collected ten's of kilometers apart along the trend. The first three principal dolomite bands decrease from south to north. This feature, together with the fact that the white sparry dolomite crystals decrease in abundance from south to north in the Trend, suggests that a major source for the fluids was from the south. The application of cathodoluminescence microscopy to crystalline dolomite demonstrates a strong correlation between ore grade and the intensity of internal banding and dissolution textures.

Jan 1, 1985

By T. N. Singh, B. Singh

SUMMARY. The supports account for over 501 of the total expenditure for a longwall face. The success and economics of a face depend upon the optimum selection of type and density of the supports. Empirical solutions involving uncertain safety factor are replaced by a geo-mining approach developed at OMRS in which the support resistance is defined by the stability index of the roof rock mass and the failure pattern of the immediate roof. The paper gives the methodology adopted to define the support resistance for Alkusha colliery longwall face of Jharia coalfield (India). The stability index of the roof mass varied from 218 to 520 for the individual beds and 1100 to 1374 for the immediate roof mass. The exact support resistance for the condition was found to be 42 t/m2.

Jan 1, 1982

By V. Leroy, A. G. Guy

Serious disagreements are often found between experimentally determined intrinsic diffusion coefficients and those calculated employing the usual form of the vacancy theory. In the new theory it is proposed that the total intrinsic flux, Ji, of component i, is the sum of a part, f, due to the usual random exclzanges of component i with the vacancies, and a second part, Ji, due to exchanges with the uacancies composing the net vacancy flux. The present treatment, while less powerful than that of Manning, has the advantage of easy uisualization and of facilitating the application of the vacancy-flux effect to complex systems. IT is becoming increasingly evident that there are serious deficiencies in the version of the vacancy theory of diffusion that has been widely used for the past 20 years. One type of evidence is the frequent lack of agreement between intrinsic diffusion coefficients and tracer diffusion coefficients, even taking account of the thermodynamic factor. A second kind of evidence is the observation of a Kirkendall shift larger than theoretically possible, that is, larger than can be accounted for without assigning a negative value to one of the two intrinsic diffusion coefficient.'- The thermodynamic factor could conceivably make both coefficients negative, but not just one. It is clear that a cause of these anomalies, apart from any inadequacy of the usual vacancy theory, might lie in an oversimplified treatment of the data. Adequate experimental techniques, including the use of moderate pressure during the diffusion anneal, are now available to insure that porosity, lateral expansion, and so forth, can be kept negligibly small in most cases. The effect of differences in atomic volume can be of major importance, and it is essential that one of the available methods4 be used to account for this factor. In the present treatment this is accomplished by the consistent use of moles per cubic centimeter as the unit of concentration. Of the various possible inadequacies of the vacancy theory, attention will be given here only to effects of the net vacancy flux. annin' has previously considered this question, beginning with an analysis of atomic jumping of tracer atoms. When he added the effect of a concentration gradient, new terms arose that could be associated with the flow of vacancies. The present treatment uses quite a different approach. The usual vacancy flux, J,, is introduced explicitly, and a simple analysis predicts major changes in the intrinsic diffusion coefficients from this cause. The usual assumptions are made that only a vacancy mechanism is operative, that the formation of voids can be neglected, and that changes in the partial molal volumes, vl and v2, are negligible. The significant diffusion coefficients for the present topic are Dl and D,, the intrinsic coefficients, which enter in the equations, where the flux Ji, moles per sq cm per sec, is that crossing the Kirkendall interface. The concentration, ci, is in units of moles per cu cm, and the concentration gradient, aci/ax, is evaluated at the Kirkendall interface. It will be recalled' that the calculation of Dl and D2 involves the measurement of areas on the diffusion curve with respect to the positions of the Kirkendall and Matano interfaces. In the case of the anomalies mentioned earlier, the Kirkendall shift is too large to be accounted for by the diiferetzce in fluxes (J2 -J1), given by Eqs. [I] and [2]. The logical inference is that the flux of the solvent atoms, J1, is actually in the same direction as the flux of the solute atoms, Jz. In terms of Eq. [I] this requires that Dl have a negative value. However, it would be somewhat misleading to state that the solvent atoms are diffusing up their own concentration gradient. The explanation that will be advanced here pictures competing processes producing the net flux of solvent atoms: 1) diffusion of the solvent atoms down their own gradient by random exchanges with vacancies; and 2) diffusion of solvent atoms in the opposite direction by exchanges with the net vacancy flux. ACTION OF THE NET VACANCY FLUX Theories of vacancy diffusion can be formulated with varying degrees of refinement, and the present theory has purposely been kept as simple as appeared adequate to explain the phenomenon in question. In particular the following aspects have been neglected: 1) the gradient of vacancy concentration in comparison to the gradient of the atomic species; 2) departure of vacancy concentration from the local equilibrium value; 3) variation of the jump frequency, LO, with the specific surroundings of the atom-vacancy pair being considered; 4) correlation effects. These and other refinements can be considered once the essential mechanism has been established. The essential idea of the present analysis is to calculate the total intrinsic flux, Ji, of component i as the sum, JlJ?±j{ [3] where J; is attributable to the usual random atomic jumping, and J{ is a contribution arising from the net vacancy flux, J,. The latter quantity, of course,

Jan 1, 1967

By J. Hall Carpenter, James E. Lawver

Shortly after the passage of the Taconite Amendment in Minnesota, several mining companies announced their intention to build new magnetite taconite plants and another announced its intention to augment present facilities. It is clear that Minnesota will enjoy an expanding magnetite taconite industry, but despite the fact that the reserves are large, eventually they will have to be supplemented by oxidized deposits. Furthermore, not all producers have magnetite taconite reserves. Due to the extensive oxidation of most of the western part of the Mesabi Range, there are no large blocks of unaltered magnetite taconite that lend themselves to open pit operations. Unless a commercial process can be developed to concentrate the oxidized, or so- called "nonmagnetic", taconite and semi-taconite, the existing mines operating in the western part of the range will be forced to shut down when the direct shipping, wash and gravity ores are depleted, or are no longer salable, because of their poor quality compared to high-grade pellets. KNOWN PROCESSES COSTLY The enormous reserves of the oxidized iron- bearing formation have offered a tantalizing challenge to metallurgists for many years. In fact, several processes for concentrating certain types of oxidized ore have been successful at both laboratory and pilot plant level, but to date no process for concentrating semitaconite or oxidized taconite has reached commercial fruition. Magnetic roasting, followed by low-intensity magnetic separation1, has shown considerable promise because the high iron recovery makes the ratio of concentration of many of the oxidized ores more favorable than that of magnetite taconite. However, the capital and operating costs are high and, in many cases, a high- grade concentrate cannot be made without resorting to flotation of the magnetic concentrate. Hence, most research groups are investigating alternate methods of concentration with the hopes of reducing the cost.

Jan 9, 1965

By E. Lancaster-Jones

THE gravity magnitudes obtained by means of observations with the Eötvös balance in the field are necessarily resultant or total effects due to all abnormalities of mass distribution, including even the effects due to the ellipticity and rotational motion of the whole earth. Since the object of the survey is to isolate the effects which arise solely from some particular subterranean, feature, and to deduce therefrom the configuration and extent of this feature, the first step is to eliminate from the observed effects all those due to "disturbing" (i. e., unwanted) features, whether above or below the surface of the ground. The disturbing features have different characteristics, according to their situation relative to the center of the balance and to the horizontal plane through the foot of the balance, or station point; this diversity was recognized by Eötvös, who divided the total effects into so-called Normal, Terrain, Topographical, Cartographical and Subterranean effects. This classification has been adhered to by most subsequent investigators, but the writer prefers to employ the term "three-dimensional," which really indicates the essential character of the class of effect known as "Subterranean," at any rate from the standpoint of the computer of effects. Before disturbing effects can be eliminated, the features must be measured up or surveyed, whether by topographical, mining, or boring methods, and then the effects of each feature calculated and subtracted from the total observed effects. After this the problem of interpreting the residual effects will itself necessitate the computation of the assumed feature, or even a series of trial features.

Jan 1, 1928

By W. R. Kanne, P. R. Strutt, R. A. Dodd

A study has been made of the creep behavior of ß-NiAl of stoichiometric composition in the temperature range 475" to 775°C. Single crystal tensile specimens were deformed under a constant applied load. From slip line studies and tensile axis rotations it was concluded that the crystals deformed by pencil-glide on (100) and (110) planes with a (100) slip direction. Electron microscope thin-film studies showed evidence for profuse cross-slip, and the dislocation Burgers vector was determined to be (100). There was no tendency for the dislocations to lie in definite slip planes, although a strong alignment of segments of edge dislocations was frequently seen. The activation energy for creep in the temperature range 475" and 775°C was judged to be much lower than that for creep at temperatures above 775°C. It is possible that the rate-controlling process is the thermally activated cross-slip of screw dislocations. In recent years considerable interest has developed in the possible use of high-melting-point intermediate phases for high-temperature applications necessitating good creep resistance. Ordered alloys such as Ni3A1, modified by alloying additions, have received particular attention, culminating in the recent development by Pratt and Whitney of single crystal turbine blades.' The intermediate phase NiAl has considerable theoretical interest from a creep standpoint because not only is it ordered up to the melting point (-1650°C at stoichiometry) but it contains a high concentration of structural vacancies on the aluminum-rich side of stoichiometry. These vacancies are known to exert a strengthening effect under some conditions,' but in addition they might be expected to affect high-temperature creep rates through dislocation climb. The present paper deals with the slip line and dislocation structures developed during creep of stoichiometric NiAl between 475" and 775C, and with possible attendant creep mechanisms. MATERIALS AND TEST TECHNIQUES NiAl ingots of stoichiometric composition were prepared by induction melting 99.996 pct A1 and 99.98 pct Ni (kindly provided by the Kaiser Aluminum Co. and the International Nickel Co., respectively) in 100 cc pure alumina crucibles in a helium atmosphere. No chemical melting flux was used in order to avoid con- tamination of the alloy. Each ingot was slowly direc-tionally solidified to avoid porosity and to produce very large grains up to 2 in. in length. In this way, ingots were obtained which were suitable for sectioning into single crystal creep specimens. Chemical analysis indicated that all alloys were within the range 49.6 0.3 at. pct Ni. For the present investigation, identical rectangular single crystal blanks were cut vertically from one particularly large crystal in an ingot using a series of three diamond cut-off wheels with appropriate spacers. Thus, all sliced crystals had the same orientation with the tensile axis parallel to the long side of the rectangle; the initial orientation of the tensile axis is shown as S, in Fig. 1. The blanks were homogenized at 1250 to 1300°C for 48 hr and subsequently cooled slowly to room temperature. A gage length of rectangular cross section and about 0.75 in. in length was prepared on each specimen using an electrolytic lathe and a dilute nitric/phosphoric acid electrolyte. The gage length cross section was 0.250 0.0005 in. by 0.040 ± 0.0005 in. Holes to accommodate tensile grips were electrolytically machined using a rotating acid jet. After creep testing, this same technique was used to cut discs for transmission electron microscopy. Thus, all shaping was done electrolytically, the only exception being that (122) sections were spark-machined from some speci-

Jan 1, 1970

By J. H. Rushton, L. H. Mahony

Principles of fluid motion and turbulence which have been found to be of use in mixing and agitation problems are discussed, as well as suggested applications in extractive-metallurgy processes. Various types of impellers are described, together with other conditions that affect flow pattern and turbulence. The choice of equipment for particular requirements is considered, and equations for power input are given. Modern heavy-duty mixing and agitation equipment can take an increasingly important part in such extractive-metallurgy processes as solids handling, crystallizing and leaching, chemical operations, and flotation. Application of mixing and fluid-mechanics principles to extraction methods can lead to greater process rates and a resultant saving in time and money. MIXERS are being applied with increasing frequency to problems in the metallurgical industries. The increase represents in part the modernization of mechanical equipment used through the application of unitized drives, modern electric motors and speed reducers, and recently developed materials of construction. Some applications have resulted from process changes and the use of techniques for operations similar to those that have been demonstrated and proven in the chemical industry. Still more applications are being developed through the use of fluid-dynamics principles not previously recognized as applicable to these operations. It is the purpose of this paper to describe those principles of fluid motion and turbulence which have been found to be of use in mixing and agitation problems, and to suggest applications for them in the extractive-metallurgy processes. Modern mixing equipment has been designed to provide the fluid motion consistent with that best suited to different operations.' When properly applied, these more efficient fluid-handling mixers result in lower process-production costs. Metallurgical operations usually involve large amounts of solids. The characteristics of the ore control the process and only enough liquid is added to provide sufficient fluidity for handling and processing. The reactive part of the ore, the mineral value to be extracted, is likely to be low in percentage, and the quantity of reagent required is similarly low, but excessive dilution makes additional reagent necessary and therefore is undesirable. Thus, the primary problems in minerals processing are to handle as high a concentration of solids as possible and to distribute reagents uniformly. These pulps, or slurries, are in a range of solids concentration where hindered settling rates apply, and care must be taken to agitate and mix sufficiently to maintain suspension and flow throughout the equipment. Such slurries have high densities which are the weighted average of the components and viscosities that are spoken of as "effective viscosities" but are difficult to evaluate. It is convenient to separate metallurgical operations involving mixers and agitators into three categories: solids handling, mechanical or physical operations, and chemical operations. In each of these categories fluid motion is required to maintain suspension, to distribute surface-active agents, to blend components and reactants, and to induce high rates of chemical reaction. After a discussion of some basic principles of mixing and agitation, examples of application to the three categories will follow. Fluid Motion The fundamental problems of mixing and agitation of liquids have to do with the mechanics of fluid streams and the means by which they are

Jan 1, 1955

By B. L. Averbach

THE rolling process may be considered as a case of a nonhomogeneous plastic flow. In such a heterogeneous deformation there is no direct general solution, and the plastic deformation varies from point to point as a function of the coordinates. It is practicable to determine these plastic strains only at the conclusion of the rolling process, and the local strains can be studied by observing the deformations produced in a suitably placed grid system. Strains at the surface of a bar after rolling have been reported by MacGregor and Coffin,' but the strain distributions within the bar have not been previously observed. Siebel² has investigated the plastic deformations resulting from wire-drawing by splitting the wire along its axis, milling a grid coordinate system on the inner plane surfaces, and binding the .wire together so that it would pull through a die as a single unit. This method was possible because of the rotational symmetry of the die. In the rolling process, however, such a system was not readily applicable. This paper describes another method of including a grid system, and reports some preliminary data on the plastic rolling strains within a square bar. Experimental Procedure 2.1 mm wide (144 network squares per sq in.) was punched from a thin lead sheet with a steel die and supported in a brass mold by thin copper wires. Pure tin was then poured around the grid to form a solid bar, with the network securely imbedded at. a given position. This bar was then machined to a square 15.2 mm (0.60 in.) wide, and then radiographed. The lead grid was quite adherent and sufficiently ductile to follow the deformation of the bar faithfully. The network lines also remained sharp enough to maintain a high radiographic contrast, and the tin bar, with the grid included, could withstand considerable deformation at room temperature without splitting at the interface. In order to fill the mold, it was necessary to cast the tin at 260-280°C and during pouring the lead grid was supported at short intervals to prevent warping. Some shrinkage cavities were encountered, but only bars which were free of shrinkage in the network region were used. This method is similar to the one employed by Steinberg" in an investigation of the strain distribution in a tensile specimen. Before rolling, the machined bars were radiographed in two directions to obtain accurate initial dimensions of each square and to observe whether the grid was straight and correctly positioned. The rolling was performed in a small hand mill with 2 in. diam rolls at room temperature, and a 20 pct reduction based on the original height was employed. The rolls were clean and no lubricant was used. Halfway through the bar, at the center of the network, the rolls were reversed and the bar extracted. These bars were then radiographed again

Jan 1, 1951

By Gerhard Derge, J. Warren Stewart

Extrusion processes are used in the commercial production of a wide variety of products, as indicated by the review presented a few years ago by D. K. Crampton.' Most writers have confined themselves to a general description of the equipment and products and the engineering aspects of the process. The few studies that have dealt with the metallurgical side of extrusion have been concerned primarily with an examination of the mode of flow of the metal during extrusion. This has been accomplished by the use of composite billets, by scribing grids on symmetrical sections of billets and observing the change of dimensions in the gridwork, or by examining microstructures in extruded sections.2"8 Ariotlier limitation of these original studies is that they were confined to the extrusion of very simple shapes, usually rods having a diameter of about one-fourth that of the billet. Tin is particularly well suited to the extrusion of collapsible tubes and similar shapes in which the extruded section is very small in comparison to the diameter of the billet or slug. In modern production, impact extrusion methods are generally employed, therefore the thickness of the slug is small compared to its diameter. Under these conditions the process differs considerably from the processes that have been most fully described in the literature, and it is known that the quality of the product is very sensitive to slight variations in any one of the many variable factors involved, such as coinposition and structure of the alloy, rate of extrusion, temperature, shape of punch and die. An exhaustive examination of all of the above-mentioned problems promises to produce so many data that it seems advisable to initiate the reports at this time, even though all of the factors outlined have not been examined fully, and to confine this paper to a description of the apparatus and method. Only tin and its alloys with small amounts of copper have been considered. These are the alloys most commonly used in this country for the production of the type of articles already described.

Jan 1, 1940

By Pierre de P. E. M. Ricketts

HAVING had occasion while in Europe during the past summer to visit some of the foreign mints and assay offices connected with the same, I thought a brief description of the general process of coining employed, and such items connected with assaying as were new, might prove interesting to the Institute. The principal foreign mints are: the Royal Mint, London; and the mints in Paris, Brussels, Utrecht, Berlin, Vienna, Copenhagen, St. Petersburg, Stockholm, Madrid, Milan, Rome, and Constantinople. My time only permitted my visiting a few of the principal and largest given in the list, and for a description of the remainder I am indebted to the kindness of Mr. James M. Napier, who in company with the deputy master, and chemist of the Royal Mint, made a complete inspection of all the European Mints in 1870.

Jan 1, 1876

By J. D. Miller Discussion by N. P. Finkelstein, M. C. Fuerstenau

The point designating 10 -4 nole/per liter sulfonate addition in Fig. 1 has been presented incorrectly. This figure, with the corrected scale, is shown at right. N. P. Finkelstein (National Institute for Metallurgy, Johannesburg, South Africa) - The qualitative conclusion the authors of this paper have reached in evaluating the influence of hydrocarbon chain length on collector effectiveness agrees with conclusions in several published reports. However, in two other

Jan 1, 1969

By William P. Blake

A recent paper by Prof. George P. Merrill, Curator of the Department of Geology of the U. S. National Museum, Wash-

Jan 1, 1897

By R. E. Collom

VARIOUS chapters already written in the history of development of the North Dome of Kettleman Hills are monotonously identical in the one underlying theme of conservation of oil and gas. Discovered on Oct. 4, 1928, by Milham Exploration Co. with its wildcat Elliot No. 1, the field has been subjected to practically every modern form of produc-tion restraint in the name of conservation. The record thus far developed shows that conservation was had for a time, at a price; and that unitiza-tion must he blessed by single ownership or 100 per cent participation to be effective. In fact, incomplete unitization places a heavy handicap upon its participants in the competitive development that follows.

Jan 1, 1937

By William P. Prof. Blake

THE occurrence of siderite in beds of considerable thickness in the clay formations of Martha's Vineyard, Mass., may have some economical importance, and is at least interesting in a scientific point of view.

Jan 1, 1876

There have been no major field developments during 1935. Operations have proceeded normally on the company's three producing fields, Masjid-i-Sulaiman, Haft Kel and Naft-i-Shah. The refinery at Kermanshah was commissioned in September, 1935, with a rated throughput capacity of 75,000 tons a year of topped crude to meet local requirements. Crude production from the Masjid-i-Sulaiman and Haft Kel fields is tabulated below: Masjid-i-Sulaiman Field.—The flowing lives of wells have been extended by (I) a process of acid treatment, thereby reducing the bottom-hole pressure differentials, and (2) by reducing the back-pressure. Optimum producing conditions for individual wells have been determined as a result of an experimental study of the amount of available energy in the reservoir crude and of energy losses in flowing wells. The return of surplus products to the reservoir has continued to be a satisfactory economic operation and the crude throughput capacity of the topping plant has been increased. The viscosity of residue returned to the reservoir is reduced before injection by regassing at 35 lb. per sq. in. absorption pressure with surplus gas. The pressure in the gas dome is falling at the low rate of one pound per annum. Haft Kel Field.—The delimitation of the main structure has proceeded; the oil-bearing area so far proved being about 50 square miles.

Jan 1, 1936

By H. K. Work, H. T. Clark

The instrument for the rapid determination of carbon in steel, described in this paper, was developed originally to facilitate the operation of the pilot-sized open-hearth furnace in the Jones & Laughlin Research and Eevelopment Laboratory. In this small furnace, with its shallow bath, the drop in carbon is accelerated, and a rapid, reliable test for carbon content is indispensable. This problem becomes rather acute when it is desired to finish heats at a carbon content higher than can be estimated with any degree of accuracy by the fracture test. Several independent methods for determining carbon were investigated, therefore, and it was found that a relatively simple magnetic device could be made to give reproducible results. A laboratory instrument was designed and set up for the use of the furnace operators. It was tested exhaustively in the laboratory and was used with considerable success for following the carbon content in the furnace bath. As soon as sufficient data had been compiled to indicate that the instrument might have a wider application, a more rugged model was constructed and placed in the mill to be tested on commercial heats. Finally, about a year ago, instruments were furnished to the plant open-hearth shops, and these have been in use since that time. As a matter of convenience, the instrument has been named the "Carbanalyzer," and will be referred to by this designation in the following pages. $ Eaklier Investigations While by far the greatest number of magnetic investigations in which the carbon content of ferromagnetic materials was considered have had to do with the evaluation of the magnetic properties of steels of known

Jan 1, 1940

By R. N. Thurston, E. A. Nesbitt, G. Y. Chin

A general relalionship between the amount of glide shear (due to slip) and the macroscopic shape change has been developed. Since the deformation can be large, finite strain analysis is employed. In this treatnzent, the shape change is expressed by a deformation gradient matrix, F - [axi/aXj1, where X and x refer to the initial and final positions of a particle. This matrix is readily evaluated in terms of the amounl of glide shear, a , and the direction cosines of the slip-plane normal and the slip direction for a single active slip system. In the case of deformation from slip on several systems, the product F(a) of the several deformation gradient matrices is first calculated. Then, by assuming that the final configuration is reached by a long series of small shears of magnitude a, occurring more or less alternately in the several slip sys- IN problems of crystal plasticity, it is often necessary to relate the amount of glide in the operating slip systems to the macroscopic strain components. This relationship is relatively simple when only small strains are considered. In this case the separate strain contributions from several slip systems are additive. Such a procedure is incorrect in the case of large plastic deformation. To the authors' knowledge, no general treatment of the latter problem has appeared in the literature. In specific instances, Mark, Polanyi, and schmid3 have derived the relationship between glide and axial elongation during tensile pulling of a single crystal when only one slip system is active. A similar relationship for duplex slip was worked out by v. Goler and Sachs.4 Taylor and Elam5 have also studied in detail problems of large plastic deformation. Due to uncertainties as to the slip systems at the time, terns, the final deformation gradient matrix can be obtained. Mathematically, the problem is reduced to finding the limit of F(dN as N — m while a — 0 in such a way that the Product Na = 0, a ftnite conslant designatzng the accunzulated amount of shear. It turns out that this limit is simply , where F, is the matrix whose elements are the coefficients of a in the F(a) matix. Application is made of the present treatment to a fcc crystal of Perlrzalloy compressed on the (110) plane and contrained to elongate zn the [112] directzon. In addition, it is shown that one rnay readily obtain from the general analyszs the well-known formulas relating elongation, amount of glide shear, and amount of lattice rotation for crystals deforming by single and double slip under tension. however, they were mainly concerned with proving that slip occurs on {111}(110) systems in fcc metals. The present general treatment arose out of recent investigations of magnetic anisotropy in cold-worked Fe-Ni alloys6 as well as some related problems in strength anisotropy of single crystals.' Detailed application of the general analysis will be provided in the case of a Permalloy single crystal compressed on the (110) plane and constrained to elongate only in the [112] direction. It will be seen that, as expected, the small strain approximation leads to significant errors after moderate straining. It will also be shown that the present general treatment yields the formulas of Mark et al. and of v. Goler and Sachs in those specific cases. GENERAL CONSIDERATIONS Consider a homogeneous deformation in which a material point initially at moves to both positions being referred to the same set of Cartesian axes. Such a deformation can be

Jan 1, 1967

By L. D. Muller, C. P. Sayles

When minerals are mined in arid or semiarid areas where water is at a premium, dry processing is a natural route to take for concentrating or classifying the values. Until recently though, dry processing technique were limited by the lack of suitable equipment. With the advent of the pneumatic pinched sluice at Warren Spring Laboratory, Stevenage, Hertfordshire, England, a new tool emerged to fill this gap and it has the potential of providing industry with a high output concentrator or preconcentrator for dry natural ores and secondary materials. The pneumatic pinched sluice gives every indication of fulfilling these requirements with the added advantage that with homogeneous materials-such as crushed limestone or quartzose sands-it may alternatively operate as a high throughput dry classifier or sizing device. An industrial version of the equipment is now being manufactured by Dryflow Separators Ltd., as sole licensee for the National Re- search Development Corporation.

Jan 1, 1971