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By W. L. Mamme, G. Y. Chin

The problem of selection of the active slip systems for a crystal undergoing an arbitrary strain was analyzed by Taylor and by Bishop and Hill in terms of a minimum (internal) and a maximum (external) work criterion, respectively. These two criteria have now been generalized to include crystallographic slip on several sets of slip systems, twinning mixed with slip, and slip by (noncrystallographic) pencil glide. The generalized treatment also takes into account the possibility of a Bauschinger effect and of unequal hardening among the shear systems, which were considered in the Bishop and Hill work. Optimization techniques of linear and nonlinear programming are shown to be applicable for the numerical calculation of the minimum or maximum work. In the case of crystallographic shear, the constraint functions are linear and hence the optimal work is obtained as the saddle value of the lagrangian function Wi(y) e minimum and W,(u) + (a) for the maximum, where Wi is the (internal) work, We is the (external) work, Y is the crystallographic shear strain, u is the applied stress, and and are constraints. It is shown that the Lagrangians are functionally the same and the saddle value of one problem is identical to the saddle value of the other, proving that the two analyses are completely equivalent. In the case of pencil glide, although the constraint functions are nonlinear and neither convex nor concave, the equivalence of the optimal values to the saddle value of the Lagrangian (which is again identical for both problems) is still valid. WHEN a crystal deforms plastically by crystallographic shear, five independent shears are generally required to accommodate five independent strain components specifying the deformation. Assuming slip as the only shear mechanism, Taylor1 in 1938 analyzed the deformation in terms of a minimum work criterion. He hypothesized that of all combinations of five slip systems which are capable of accommodating the deformation, the active combination is that one for which the internal work C is a minimum, where 1 TI is the critical resolved shear stress for slip on the 1-th slip system and is the corresponding simple shear. By further assuming equal 72 for all equivalent slip systems and no Bauschinger effect, Taylor re- duced the minimum work problem to one of minimum and applied the analysis to the case of axisym- Metric flow by {111}(110) slip in fcc crystals. However, he did not consider the question of whether the resolved shear stress has in fact attained the critical value for slip on the newly found active systems without exceeding it on the inactive systems. In 1951 Bishop and ill' put forth the maximum work analysis in which slip is again assumed as the only deformation mechanism. In this analysis, the work o1 done in a given strain ij by a stress ujj not violating the yield condition is maximized. In addition, the analysis takes into account the possibility that the critical resolved shear stress for slip may not be equal among the slip systems and that the slip behavior may exhibit the Bauschinger effect. As with Taylor, a single set of slip systems—{111)(110) — was analyzed numerically. It thus appears that the Bishop and Hill treatment is on a more sound physical basis than the Taylor treatment. However, Bishop and Hill showed that where there is equal hardening among all slip systems and when there is no Bauschinger effect, Eq. [11 ] of Ref. 2, as assumed by Taylor, the results of their maximum work analysis are the same as those of Taylor's minimum work analysis. Hence at least under those conditions there is an implication that the Taylor analysis does lead to a critical resolved shear stress for slip on the predicted active systems without violating the yield condition on the inactive systems. Recently, the Taylor analysis was applied for numerical solutions of the axisymmetric flow problem, for slip on {110}(111), {112}(111). {123)(111) systems as well as a mixture of all three sets of svstems."1 Computational techniques based on the optimization theories of linear and nonlinear programming4 were employed in these solutions. The same techniques were employed in the solutions of an axisymmetric flow problem of deformation by slip on (111) (110) systems and twinning on (111)(112) systems5 which had been considered theoretically from a modified Taylor approach. The utilization of these techniques has led to the realization that the solutions of Taylor's minimum work problem imply the solutions of Bishop and Hill's maximum work problem. The two problems turn out to be dual problems in the well known sense of mathematical programming. It is thus the purpose of this paper to first generalize the minimum and maximum work analyses to include crystallographic slip on several sets of slip systems, twinning mixed with slip, and slip by (non-crystallographic) pencil glide, as well as the possibility of a Bauschinger effect and of unequal hardening

Jan 1, 1970

By B. Chalmers

THE practical importance of the phenomena of melting and freezing must have been recognized for a very long time. The difference between ice and water, for example, has had a profound influence on the history of mankind and the evolution of society. The possibility of melting a metal and allowing it to freeze in a mold of chosen shape has been an essential ingredient in our mastery of the art of shaping metals, and therefore in the evolution of the: machine age in which we find ourselves. The importance of melting and freezing, as applied to metals and alloys, has been so great, in fact, that empirical solutions have been found for the multitude of practical problems that have arisen. This approach has been so successful that relatively little attention has been directed to arriving at an understanding of the fundamentals of the processes. But metallurgy has come to a stage at which we may expect that some, at least, of the more complex problems that have not yet been solved (or perhaps even recognized) may be handled more effectively by scientific study, theoretical understanding, and logical experimentation than by trial and error. In this lecture, therefore, I propose to describe in outline what I think really happens when a metal freezes. In doing so I hope to explain many of the phenomena which have been observed, and in particular to account for the structures that are obtained in actual ingots and castings. The basic problem, to which this lecture represents a tentative partial answer, is this: a mass of metal, containing known proportions of various elements, is melted, heated to a given temperature, and then allowed to freeze under specified conditions. What will be the "structure" of the resulting metal? The term structure includes: 1—crystal size, shape, and orientations, 2—distribution of chemical elements, and 3-—shape, including cracks, cavities, pores, etc. The Solid-Liquid Interface We will first consider what takes place if a single crystal of a metal in the form of a rod is heated, not uniformly, but so that one end is hotter than the other. If this heating process is continued long enough, the hotter end will eventually melt; we will suppose that the rod is in a containing vessel so that the molten metal does not run away, Fig. 1. When some of the metal has melted, we have some solid, some liquid, and an interface or surface of contact between them. If the source of heat is now removed, the interface will move so that some of the liquid freezes, and if the supply of heat is suitably adjusted the interface will remain at rest. This very simple arrangement allows us to study the basic processes of melting and freezing, and if we fully understand this simple case, we may be able to account for what takes place under practical conditions where the heat does not all flow in the same direction, and where the heat flow is determined not by a controllable source of heat but by the heat capacity and temperature of metal and mold, and by the heat loss from the mold surface. The solid-liquid interface is evidently the region of the greatest interest to us; on one side of it there is crystalline solid, and on the other, liquid. In the solid, each atom has a well defined position, around which it vibrates as a result of thermal agitation. It only leaves this position in the relatively rare event of a "diffusion jump." The liquid is much less systematically organized. The atoms are about as far from their neighbors as in the solid, but the arrangement is much less systematic and is continuously changing. The solid and the liquid are represented diagrammatically in Fig. 2. The average energy of the atoms in the liquid is greater than in the solid by an amount that corresponds to the latent heat of fusion, i.e., the amount of heat that has to be supplied to convert unit mass of solid into liquid at the same temperature. The Two Processes As has recently been shown by Jackson and Chalmers,3 many of the features of the processes of freezing and melting can be understood if it is assumed that a continuous and rapid interchange of atoms between solid and liquid always takes place at a solid-liquid interface." It is necessary to con- sider two distinct processes, that of melting, in which atoms leave the surface of the solid and become part of the liquid, and the converse process,

Jan 1, 1955

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 by- product materials have introduced competition with the products of nature and are having a growing influence on the economic position of the mined minerals.

Jan 1, 1949

By M. A. Schimmelpfennig, A. D. S. Gillies

Loss of visibility due to the occurrence of atmospheric fogging in underground mine airways can lead to longer travel times and loss of production efficiency, an increase in the frequency of vehicular and foot traffic accidents and difficulty in checking rock surfaces for instability and loose material. Where hot and humid surface air meets colder underground air, conditions for fog formation may be present. Further, suspended particulate matter from diesel exhausts or stoping operations together with slow movement of air along passageways may contribute to formation. This study describes an investigation being undertaken with the cooperation of Kennecott's Ozark Lead Co. to identify causes of the problem.

Jan 1, 1984

By Orson Cutler, Shepard

THE OBJECT of this paper is twofold: (1) To analyze the forces that cause air bubbles to spread on mineral surfaces in the flotation process; and (2) To develop a rational expression that will serve as a criterion of the floatability of minerals, to the end that the efficiencies of various flotation reagents can be accurately compared. Heretofore, the subject of the spreading of air bubbles has been dismissed with the statement that the surfaces of minerals on which bubbles spread are water-repellent. Imperfect understanding of the forces involved has led to the use, hitherto, of various erroneous formulas for the calculation of the comparative effectiveness of flotation reagents.

Jan 1, 1932

By R. J. Woody

Design of the most economic continuous counter-current decantation (CCD) circuit is based on selection of the number of stages and the wash volume that will give the minimum summation of the following items: 1) Capital and operating costs of the CCD circuit. 2) Capital and operating costs of the precipitation circuit. 3) Value of the dissolved product lost.

Jan 1, 1959

By Charles S. Barrett

Metallurgists are making use of the stereographic projection to a steadily increasing extent. In the last five years no less than 20 papers in American metallurgical journals alone have employed the stereographic projection; recent books on physical metallurgy, plastic deformation, X-rays and their applications, and crystal structure use it. Mineralogists have used the stereographic projection for many years in the description of symmetry classes and crystal planes, for it presents an accurate, easily understood plot of any angular relations in crystals with all unessential features eliminated (such as the accidentally determined size and shape of crystal faces). In metallography and physical metallurgy the projection is much used for the analysis of markings appearing on polished grains: slip lines, twins, cracks, structures formed by precipitation, magnetic-powder patterns, etch pits, etc. Data from certain types of X-ray photograms are most conveniently analyzed by its use, particularly those for determining the orientation of single crystals or the preferred orientation of grains in an aggregate. Calculations of how to tilt or cut a crystal parallel to a certain crystallographic plane or to reflect X-rays from a certain plane are rapidly carried out. It has been adopted almost universally to the exclusion of other methods by those studying the deformation of metallic crystals, save where the accuracy required is greater than a few tenths of a degree. Any directional property in a crystal or polycrystalline material can be shown on a stereographic projection; for example, the modulus of elasticity, yield point, etc. It has been repeatedly called to our attention that there is need of an elementary explanation of the principles and methods of stereographic projection, covering all the common applications in the field of metallography and physical metallurgy. The following contribution is an attempt to fill this need. The description of each method is supplemented with references to publications in which the method has been used. For convenience to the reader, these illustrative references are chiefly in American journals, particularly the publications of the American Institute of Mining and

Jan 1, 1937

By CHARLES SIMENSTAD

COAL preparation, or coal washing, is not a new subject to the Pacific Northwest. Most of the coals mined in this state smaller than lump, and nearly all such sizes mined on the Pacific slope of the Cascade mountains, require washing before marketing. A large proportion is being put through some washing process, but coal washing in this state, has not reached the efficiency it is practicable to obtain. In fields where the coal, as mined, contains less impurities, where working conditions make it practicable to eliminate some of these impurities under- ground, or where a large proportion of the run-of-mine coal is lump, coal preparation does not present the problem it does in our local field. Here the coal is associated with considerable impurities and the slack, or steam sizes, aggregate about 80 per cent. of the output. Therefore, approximately 80 per cent. of the coal mined must be washed to become a valuable fuel. Washing then becomes a major operation, as hand picking of the 20 per cent. of lump is a standard and comparatively simple operation. Some coal beds here are so interstratified with bone, of a more or less massive nature, that hand picking of lump is not economically efficient. In such cases the coal must be crushed fine enough for it to be freed from the bone, so that the two may be separated. Coal cleaning in this field, therefore, must receive skilled attention to purify this fuel and raise its stand- ard. Without greater efficiency in cleaning, the importation of coal from outside the state will be even greater than in the past.

Jan 1, 1926

By A. C. Stevenson

THE hoisting equipment selected for use at the Hecla mine in 1907 was one of the first Ilgner type Ward-Leonard controlled hoists put into ser- vice. Development of the Hecla below the 2000-ft. level, which is the ultimate depth of the old equipment, and the additional service required by the "Star," necessitated additional hoisting capacity. It will be our endeavor to give j70u a brief summary of the engineering which determined the selection of the new equipment. The engineer in making his decision as to size, speed, etc., must .make a duty study approximating as closely &s possible the actual opePating conditions which will eventually result. Primarily, it is necessary to know what work must be done. The amount of material which must be hoisted under the maximum condition, as well as its distribution from the various levels of the mine was carefully studied by the mining engineering department, as the ore reserves, their relative-position and the probable method of working them had to be considered. The final figures reached, taking into consideration four different operating conditions, were, in tons per day, as follows:

Jan 1, 1930

By Richard W. Smith

THERE are three distinct varieties of phosphate rock, in Tennessee, known commercially as: (a) the "brown" rock, which is the residual pro- duct of the weathering and natural concentration of certain phosphatic Ordovician limestones; (b) the "blue " rock, which is an unaltered phosphatic stratum of Mississippian or Devonian age; and (c) the "white" rock, which is the result of chemical replacement and deposition. Before 1894, South Carolina and Florida had supplied most of the phosphate of the United States, South Carolina leading until that date and Florida from then until the present time. In December, 1893, the blue phosphate of Tennessee was discovered almost simultaneously on Swan Creek, in Lewis County, by two independent parties-by one as the result of a careful and systematic search for a workable deposit of the long known kidney phosphate, and by the other through mistaking it for a "bloom" of coal. Leases were taken and, with further prospecting disclosing other deposits in the region, the development progressed as rapidly as 'could be expected without railroad transportation

Jan 1, 1924

By G. S. Anderson

PRIOR to 1912 the only rail outlets for a large part of the coal regions of Carbon and Emery Counties. Utah, were over single-track lines of the Southern Utah R.R. and Castle Valley Ry. Companies, forming a route extending from Mohrland and Hiawatha, Utah, to a point of connection at Price, Utah, with what is now The Denver and Rio Grande Western R.R. Co. These two tap lines were poorly and inadequately constructed, with impracticable grades, lacking in equipment, and incapable of being put into condition to serve this region and handle the output of the mines, to say nothing of making possible increased production and new development. Any plans for the new development and increased output necessarily involved new and adequate railroad service. It was essential, not only that additional facilities be provided but that these facilities be in the form of an efficient and up-to-date railroad providing an independent through operation from the coal mines to a point of direct connection with the lines over which the product would be distributed to consumers. For this purpose, the Utah Railway Co. was incorporated in

Jan 1, 1948

By Henry M. Howe

The brilliant and very original matter in Professor Jeffries' discussion† should rank not only as an independent paper, but as a most important one. In particular, the explanation which it gives of the remarkable Sauveur phenomenon, over which so many of us have puzzled long and hard, is so clear, complete, and cogent as to go far toward establishing Professor Jeffries' hypothesis. The very leatures of Professor Sauveur's photographs which fit this hypothesis so exactly are reproduced in Chap-pell's photographs of steel coarsened under somewhat different conditions.' The ideas developed by these discoveries are so novel that convenicnce of language seems to call for new conventional terms for expressing them. In what follows here I propose certain terms for this end, for criticism and improvement, and I attempt to generalize from Professor Jeffries' hypotheses. Generally speaking, a given set of grains which undergo no growth in the cold will, when the temperature is raised progrcssively, start to grow on reaching a certain temperature, and will continue growing at all higher temperatures. The "germinative" temperature is that at which growth begins, quite as the conditions which cause a seed to grow are "germinative." We have then an inert temperature range below the germinative temperature, and a growth range above it, the germinative temperature being the limit between these two ranges. So, too, a germinant grain is one which is at its germinative temperature, and hence beginning to grow, while inert grains are those below their own germinative temperature, and the term "growing grains" includes those which are germinant and those which are above their germinative temperature. These last could be called " supergerminant" if the distinction should be needed. "Germinative temperature" seems better than "critical temperature

Jan 1, 1917

CONTENTS PAGE Simons, Theodore.-Basic Principles of Gravity Concentration-A Mathematical Study : :.. 1 Taggart, Arthur F. and Gaudin, A. M.-Surface Tension and Adsorption Phenomena in Flotation 11 Hersam, Ernest A.-Factors Controlling the Capacity of Rock Crushers 12 Shaw, S. F.-The Ore Deposits of Sierra Mojada, Coahuila, Mexico 12 Wilson, Philip D.-The British Columbia Batholith and Related Ore Deposits 26 Greensfelder, N. S.-Shot-firing by Electricity 27 Mitke, Chas. A.-Metal Mine Ventilation in the Southwest 28 Foley, F. B. and Howell, S. P.-Neumann Bands as Evidence of Action of Explosives upon Metals 30 Schwartz, H. A., Payne, H. R., Gorton, A. F., and Austin, M. M.-Conditions of Stable Equilibrium in Iron-carbon Alloys 30

Jan 12, 1922

By Charles H. Foreman

IN JUNE 1921, the Sullivan &lining Co., owned jointly by the Bunker Hill and Sullivan Mining & Concentrating Co. and the Hecla Mining Co, started work on the development of the Star Mine. The development work contemplated called for a crosscut from the Hecla workings on the 2000 level to the Star ledge. The length of crosscut necessary to encounter the Star ledge was approximately 8900 ft. from the Hecla shaft. By using workings formerly made by the Hecla Mining Co., only about 8100 ft. of actual crosscutting was necessary. This crosscut has a direction of S 20° W and would have a tendency to crosscut any ledges in the intervening ground.

Jan 1, 1924

"No true conception of the Park City mining district can be obtained without first giving consideration to the part it has played as a consistent producer of mineral wealth. Its position in this regard is almost unique in the annals of a lead silver camp. For over fifty years it has been a continuous producer of lead and silver and for twenty years it has added to the world's supply of zinc. Few camps with its productive history are so little known to the mining fraternity for the reason that its life has never been punctuated by periods of ""boom"" which serve to attract general attention, neither has it been the field of operation for promoters who temporarily focus attention upon their scene of action. Its history is one of legitimate mining operations. These were at first carried on by a number of smaller companies. A period of consolidation followed and at the present time the entire production of the camp is in the hands of two major companies and one smaller company. These are flanked by a number of prospecting properties, which are at this time actively engaged in the search for ores and later events will doubtless put some of them in the producing class.A technical discussion of the ore occurrence and mining operations in the camp will be the subject of a paper to be read before this meeting of the Institute. The mission of this article is to supply a ""Baedeker"" where Baedeker is lacking.The town of Park City is a typical, up-to-date, western mining camp which owes its existence as a town of 4,500 inhabitants solely to the mining industry. The camp is located 7,000 feet above sea level, thirty-two miles east of Salt Lake City. It is situated on the Victory Highway seven miles from its junction with the Lincoln Highway and has the benefit of excellent automobile communication with the metropolis of the state. Both the Denver and Rio Grande and the Union Pacific Railroads give daily train service to the camp and effectively solve the transportation problems of the mining companies."

Jan 1, 1925

By W. S. Landis

In brief, this is the story of an attempt to Americanize a process originally developed in Europe. The story will be recited in two sections, the first dealing with the process as developed by the European engineers; the second containing the improvements and modifications of American origin, together with some details of the operating results of the unit as finally assembled. Developments in other directions in this same field have not, up to the present, pointed out an economic future for the process, therefore our record here is largely a report of development progress. Whether some particularly favorable location will be found at some future time for a commercial installation cannot as yet be foretold. The project is now at a standstill. The peculiar tools of the electrometallurgist should be of great interest to the zinc smelter. The low thermal efficiency of the zinc retort, its comparatively small-scale unit and its intermittent cycle as it stood in 1925, should make this art a particularly fertile field for the electric furnace. Yet in spite of years of work recorded in volumes of literature, and an expenditure of large sums of money, there is not a single electrothermic zinc smelter operating anywhere in the world. In this industry the electric furnace plays only a secondary part today. Historical The first serious proposal to use the electric furnace for the smelting of zinc ores was made by the Cowles Brothers in 1885, but their experimental work did not advance the art to any extent. The next investigator of this field was Dr. Gustav DeLaval, a Swedish engineer well known to the industrial world through his development of the centrifugal and the steam turbine. The DeLaval cream separator is a familiar household appliance in most parts of the world. Although Dr. DeLaval commenced his experiments in the field of electric zinc smelting in 1893, it was not until 1898 that he had a practicable furnace, even then operating but intermittently. His work was done at Trollhättan, Sweden. He continued to improve this early fur-

Jan 1, 1937

Jan 1, 1898

By A. S. McCreath

Jan 1, 1884

Jan 1, 1903

By J. H., R. W. Guard, Westbrook

In 1953 Kornilov and Mints' presented data on thermal expansion and electrical conductivity of the compound Ni3A1 which indicated the possibility of a transformation in Ni3A1 at about 600°C. The present paper gives results of some observations

Jan 1, 1960