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By Walter Kauzmann

ALL viscous or plastic flow of incompressible matter is the result of shear strain; the changing shape of any body that is being plastically deformed can be completely described in terms of the shear strain occurring at each point in the body.[t] Furthermore, the relative amounts of shear strain occurring in different parts of a body under stress depend upon the relative rates of shear strain at those different points, so that if the dependence of the shear rate of any material on the temperature, shear stress, previous history, etc., were understood, the principles of plastic deformation would be known, and we could calculate how a body made of a given material, having a given shape, and subject to a specified system of forces, would change its shape with time. It may be said, then, that the problem of plasticity resolves itself into, first, the problem of the rates of pure shear processes, and second, the application of what is known about pure shear to actual cases. It is the purpose of this work to investigate the former problem -i.e., the dependence of shear rates on temperature, stress, etc.-from the standpoint of recent developments in the field of chemical-rate theory and with particular reference to the phenomena occurring in the creep of metals and in the plastic flow of crystalline solids in general. It is left for the mechanical engineer, and perhaps the expert in hydrodynamics, to deal with the problem of applications1 RESOLUTION OF MACROSCOPIC SHEAR INTO MICROSCOPIC MOVEMENTS; RESEMBLANCE TO CHEMICAL REACTIONS Just as any large body is made up of many small units, or atoms, so macroscopically observable shear is the result of many microscopic unit shear processes; just as the understanding of the behavior of large bodies demands the understanding of the atoms of which it is made, so the understanding of macroscopic shear demands the understanding of these fundamental unit processes. The study of shear from this "atomistic" point of view has made considerable progress. There has been fairly complete understanding of shear processes in gases for a long time, at least for nonturbulent flow, as a chapter on gaseous viscosity in any text on the kinetic theory of gases will prove. In recent years Andrade2 and Eyring3 have presented important theories for the flow of liquids and amorphous solids. Becker,4 Orowan,5 Taylor,6 Burgers,7 and Kanter8 have considered the

Jan 1, 1941

By Edward Jeffrey

THE use of coke in metallurgy, to any important degree, dates from the middle of the 18th century. Its utilization came most opportunely for European civilization. The forests of Europe, except in the most remote and inaccessible regions, had been largely fed, in the form of charcoal, into the smelting furnaces. For a hundred years-the middle of the 17th to the middle of the 18th century-there was a stationary condition of population corresponding to the exhaustion of European forests. This situation, which was particularly evident in Great Britain, was due to the fact that the forests had been depleted and the practical utilization of coke had not begun. The coking industry is essential for our metallurgical industries, which in turn are basal to healthy economic progress. But coke is of great importance, not only on its own account, but for its byproducts, which enter fundamentally into all the arts of peace and war. The dyestuff industry and the manufacture of explosives are intimately connected with one another, as was shown by the recent war. The subject of coking coal, therefore, is well worthy the serious attention both of practical industry and the scientific investigator. The most valuable coking coals, from the metallurgical standpoint, are derived from the coals of highest ranks. Coals, for example, that have a carbon ratio of from 70 to 80 per cent. yield the most valuable coke for the blast furnace. The difficulty of investigating these coals, however, is great, for they are rather friable and delicate and possess a high carbon content, which makes them difficult to manipulate. They present, on account of their high carbon content, a considerable degree of opacity when examined, in thin sections, under the microscope. The tenderness of structure and blackness of such high-grade coking coals as those of Connellsville and the Pocahontas region make them extremely difficult to investigate.

Jan 1, 1925

By David W. Brunton

From the old-fashioned " grab-sample " to the modern timing-device, which takes a machine-sample with mathematical precision, there is a wide gap, which was only crossed by many years of toil and unremitting endeavor. Even to-day, notwithstanding the advancement in the art, " grab-sampling " is still practiced—sometimes to afford the unscrupulous mine-promoter a basis for fairy-tales with which to entrap the too-gullible investor, and often by milling and smelting companies to determine the amount of moisture in custom-ores. The latter practice is almost as reprehensible as the former, and it causes more trouble and ill-feeling between seller and buyer than all other factors put together. -NO reputable concern to-day would think of attempting to determine by grab-sampling the amount of gold, silver, lead, or copper contained in an ore, and yet many buyers expect the miner to accept the results of grab-sampling in the determination of the amount of water contained in the ore, forgetting that accurate results are just as necessary here as in the determination of the metals, because the result determines the percentage of weight of the ore which shall be excluded and considered to have no value whatever. Samples for the determination of moisture should be taken with as great care as samples for the determination of metallic content, and in order to avoid the extra expense of a separate operation moisture-samples should be taken from the sample-safe. As the sample reaches the sample-bin in a smaller stream and by a more circuitous route than the " reject" travels in its path to the outgoing car, it loses more moisture en route, and a constant should be added to compensate for this difference. Carefullg ,con ducted experiments have shown that the differ.elice in loss of moisture between the two routes does not exceed 10 per cent. in summer and 7 per cent. in winter. For instance,

Jan 1, 1910

By C. Scala, M. Gondouin

Published laboratory data have established that very significant streaming potentials can exist across mud cakes subjected to pressure differentials such as exist between a mud column and formation fluids. Since shale is similar in kind and in properties to a well-formed mud cake, it appeared possible that streaming potentials might also arise across shales. A practical consequence would be that the streaming potential contribution to the SP would be smaller than might otherwise be assumed since the SP is measured with respect to the "shale bare line". The resultant contribution would be the difference between the streaming potential across the shale and that across the mud cake. In order to investigate this possibility, a laboratory apparatus was devised for measuring streaming potentials under pressure conditions normally encountered in wells. Reported data on streaming potentids across mud cakes were verified. More important, appreciable streaming potentials were found across shale samples. As in the case of mud cakes, the shale potentials varied with the concentration and nature of the impregnating electrolyte. Dependence on pressure was In a different rela-tion than that for mud cakes, possibly because of the lower compressibility of shales. The differences in streaming potentials between the shales md mud cakes were generally small, although they might vary considerably in practice depending on the relative electro-kinetic properties of the particular shale-mud cuke combination. A "poorly eflective" shale with a "very eflec-tive mud cake" would produce the largest negative addition to the electrochemical component of the SP. Results of field experiments with pressurized wells were considered in the light of the laboratory results. INTRODUCTION Field experiments wherein the pressure of the mud column in a borehole was varied have often indicated the presence of a streaming potential, but its magnitude was not easily predictable and its sign sometimes changed from one formation to another in the same well.' In the interpretation of SP logs from standard surveys, nevertheless, the correct value of R,, is very frequently obtained, within the limits of field accuracy, using only the simple electrochemical expression of the SP provided that proper corrections are made for bed thickness, ion activity, etc.' Accordingly, it was apparent that the streaming potential component of the SP in a borehole was considerably more complex than commonly assumed and clarification was indeed necessary The close similarity in nature and constitution of a shale to a well-compacted mud cake suggested that a streaming potential might also exist across shales as pointed out by M. P. Tixier in 1953 and as recently emphasized by Wyllie." e practical consequence would be that the streaming potential across the mud cake would be canceled, at least in part, on electrical logs since the SP is recorded with respect to the shale potential as a base line. This appeared to be a plausible explanation for many of the effects observed but no supporting data were available. In 1955 preliminary experiments at low pressures were conducted in our laboratories which supported the hypothesis of the shale streaming potential and formed the basis for later studies at borehole pressures.* EARLY LOW PRESSURE EXPERIMENTS The early experiments were conducted primarily to determine the possibility of a streaming potential across shales. The shale used was a compact type designated as No. 7 from Reagan County, Tex. (Permian). Cut samples were saturated for over one month in .2 to 2.0-N NaCl solutions. In order to eliminate all electrode polarization effects, a dynamic method was used. A transient pressure of about 1 atm was applied across

By R. K. Hopkins

For a great many years fusion welding has been used in and around petroleum refineries, but it is only within six or seven years that the more important pressure vessels have been constructed by this process, because before that time the properties of fusion welds would not with-stand such rigorous service. Since the adoption of fusion welding for the construction of this equipment, the refiner has required pressure vessels suitable for operation over a very wide range of conditions. On the one hand, vessels must operate at extremely high temperatures, in the range of 950° to 1000° F., and on the other vessels must be suitable for operation at sub-zero temperatures down as low as -75° F. Also, vessels are required suitable for operation at pressures upwards of 1000 lb. per sq. in., and as low as a 29-in. vacuum. In addition, vessels are required to withstand the attack of very corrosive mediums. It has been a rather difficult task for the fabricator to meet all of these require-ments, but as a result of the extensive research carried on by steel manu-facturers and several fabricators of class I vessels, practically all of these demands have been met. In order to meet the refiners' requirements for this wide range of conditions, the fabricator has worked closely with the metallurgist. This has enabled him to choose the proper base metal for each service condition, but it has been the fabricator's problem to develop a welding rod and welding technique, as well as a heat-treatment, that would produce in the welded vessel characteristics in and around the weld comparable to those in the base metal. Where corrosion is not a serious problem, and where the operating temperatures are not too high, ordinary carbon steel has served very well. But when corrosion is serious, and/or when the temperatures are either very high or very low, it is necessary to use some form of alloy steel to give satisfactory service.

Jan 1, 1935

By J. B. Mackintosh

Some months ago I received a sample of a highly crystalline product occurring in the hearth of the shaft-furnace used in smelting the roasted niccoliferous pyrrhotite at Mr. Joseph Wharton's works near the Gap Mine, Lancaster County, Pa. Mr. Wharton first observed this product in cavities in the concretions in these furnaces about the year 1870, and published a description of it in that year.* Thinking that it might show some analogy to meteoric iron, he sent the present sample to Mr. George a F. Kunz, who turned it over to me, with the request that I should analyze it at my convenience. The results do not show the expected analogy, because the sulphur in meteoric iron is combined as FeS., while in this product there is only one-sixth the necessary amount of sulphur, which, however, seems to be combined with all the metallic elements present, forming a sub-sulphide of definite composition. I am informed by Mr. Wharton that he has had for a long time the sample which I have analyzed, and that it probably is about the same age as that which he first described. It is worthy of note that the material does not show any signs of oxidation, but that the crystals preserve a brilliant metallic lustre. The first two analyses, made by Mr. J. Voigt, are those given by

Jan 1, 1888

By C. W. Goodale

As an appendix to the above-mentioned paper, a drawing of the vertical projection of the Knoxville mine workings is here given. In my paper it was stated that the ore-chimneys are found along a crack or plane of cleavage in the limestone ; and as this crack is not parallel with the strata, it is safe to assume that the manganese was not deposited where it is now found before the tilting-up of the strata, but rather that the crack was caused by the folding, and that tile formation of the ore was entirely subsequent to the change of position of the limestone. There are here four chimneys, which have produced, as far as explored, over 12,000 tons of ore, containing at least 7000 tons of manganese oxides, and it is very difficult to apply Prof. W. P. Blake's theory of segregation from the surrounding limestone in accounting for the origin of this ore, as cross-cuts and drifts in the countryrock, even at short distances from the ore-chimneys, have not shown manganese in appreciable quantities. It is easier to believe that, in the language of .Mr. S. F. Emmons, in speaking of Leadville ore-deposits, there was a metasomatic interchange between the minerals brought in in solution and the limestone, and not a deposition in already existing cavities. This in-

Jan 1, 1890

Cyanidation and Concentration of Gold and Silver Ores. By J. V. N. Dorr and Francis L. Bosqui. Second edition, completely revised. Mc-Graw-Hill Book Co., New York. $8.50.-First issued 13 years ago, this book has become a milestone in the literature of mining and metallurgy. Mr. Dorr, with the assistance of F. L. Bosqui, has completely revised the book. Its comprehensive picture of ore dressing and hydrometallurgical methods are of importance to mining engineers and operators throughout the entire field. Operating data and methods, flowsheets, testing procedures, and many miscellaneous methods of extracting bullion are given. The book is divided into two sections, the first discussing principal unit processes involved in gold and silver recovery, and the second describing with flow diagrams a number of typical treatment plants selected from the more important gold and silver mining areas in various parts of the world. International Conference on Coal Preparation in Paris. English Language edition of transactions.-The transactions of the recent conference in Paris will be presented in the form of 6 issues of the revue de l'Industrie Minerale, and may be purchased for 3000 francs per set. About 60 papers were presented at the meeting, covering a wide range of interesting subjects. Ad- dress subscriptions to: Secretariat de la Societe de l'Industrie Minerale, 19 rue du Grand-Moulin, Saint-Etienne (Loire) France.

Jan 1, 1951

By S. Gstalder, J. Raynal

Consideration was given to simple tests which could be performed on rocks to give a measure of rock drillability. Various methods of breaking rocks were considered and the hardness test developed by Schreiner was selected for this study. The test involves application of an increasing load on the rock face through a flat-faced cylindrical punch until rupture occurs. Test results show that hardness is a good measure of the breaking strength of rocks. Useful relationships are shown to exist between hardness and other physical quantities such as specific disintegration, Young's modulus and sonic velocity. Specific disintegration (volume of rock broken per unit of work input) provides a possible means of comparing the effectiveness of other methods of rock breakage. The relationship between hardness and sonic velocity may be very significant for it may be possible to deduce rock drillability from sonic log data. provided that a mineralogical factor is taken into account. TO test further the results of the work, laboratory drilling tests were performed which closely simulated down-hole pressure conditions. Correlations of drilling results with rock hardness measurements were quite good. It was concluded that rock hardness, as measured in the laboratory or as deduced from sonic logs, could be used in relations for predicting rock drilling performance. INTRODUCTION Drillability of rocks cannot be defined in an absolute manner by a single quantity or measured by a single test. Resistance of rock to drilling depends to a large extent upon the means used for rock destruction. This complicates drillability classification of rocks for there may be as many classifications as there are methods of rock breakage without known functional relations between them. The objective of this work was to develop. in terms of rock destruction behavior, means of selecting the best drilling method for a given rock or the conditions for optimum output from a given drilling method. ANALYSIS OF ROCK DESTRUCTION TESTS Gauthier and Baron' have reviewed the many test methods which have been developed for determining the resistance of rocks to breakage. These include drilling tests, punch tests, scratch tests, resistance to shock, wear tests, etc. A standard drilling test might be to determine the time required to drill a standard depth (1/16 in.) in a rock using a bi-cone microbit (1 1/4-in. diameter) when a standard load (417 Ib) is applied at a standard speed of bit rotation (110 rpm). From the standpoint of similarity, the results of microbit drilling tests would seem to be most representative of the several methods suggested above. However, evaluation of drilling performance by this method is only qualitative and cannot be applied directly to actual drilling conditions. Punch tests basically measure rock hardness. Punches of various shapes and sizes, including small cones for Vickers' and Knoop's tests, the wedge for Epstein's test and the right circular cylinder for Schreiner's test, have been used. Results of these tests lead to a quantitative hardness classification which would seem to be related to the resistance of rock to bit-tooth penetration. Scratch tests are related to the resistance of rocks to abrasion such as would be encountered in drilling with diamonds. Either the width of the scratch obtained at a fixed load or the load required to give a scratch of a fixed width may be used to evaluate surface hardness of the rock. This should be related to the resistance of the rock to wear. The above tests, and probably many others. give relative measurements of the breakage or destruction characteristics of rocks. There is no direct relation between results of these tests and the drillability of rocks. Also, the tests each measure different quantities which have different dimensions and they do not permit direct comparison of numerical values. As one step in rectifying the above difficulties. it is proposed that the results of all test methods be expressed in terms of volume of rock destroyed per unit of work required; this is referred to as "specific disintegration". Test results may then be reported in a form which shows both a classification of rocks in regard to each method and a comparison of methods with regard to each rock. The disadvantage in using specific disintegration is the difficulty of measuring this quantity with accuracy. The volume of rock damage is difficult to measure. as is the true value of work input. Rock heterogeneity adds to the

Jan 1, 1967

By J. P. Hirth, C. S. Hartley

A simple graphical technique is presented for rapidly determining the ratio of resolved shear stress on slip systems in single crystals to the applied stress (Schmid factor) for various simple states of stress. Master plots are presented which, when used in conjunction with an appropriate stereo-graphic projection, allow one to determine the Schmid factor for all slip systems in a crystal of given orientation. It is shown that one such plot suffices for simple tension or compression, flex-ural bending, and biaxial compression, while a combination of two different plots must be used for torsion and simple shear. STUDIES of the deformation behavior of single crystals are most valuable when the applied stresses are resolved onto the various slip systems of the crystal. A careful study of the available slip systems and proper selection of the state of stress used and the specimen orientation can then yield quantitative information about the probability of specific dislocation reactions, the strength of barriers to plastic flow, and the mechanisms of yielding and flow in general. It is the purpose of this work to analyze some common states of stress used in deformation studies and to present a simplified way of determining for these cases the ratio of the resolved shear stress on the slip systems to the applied stress (Schmid factor). I) CALCULATIONS We first define two orthogonal coordinate systems: one based on the specimen geometry (a right circular cylinder of radius, R, is considered here) and one based on the particular slip system of interest. The unit vectors and angles specifying the two coordinate systems and the relationship between them are listed in Table I. The relationships among the various angles and unit vectors are shown on a stereographic projection in Fig. 1. The transformation matrix between the (XI X2 X3) and (x'1 x'2 x'3) system is x1 x2 x3 X'1 a11 al2 a13 x'2 a21 a22 a23 x'9 a31 a32 a33 where in this case the direction cosines aij are given by a11 a12 a13 aij = a21 a22 a23 a31 a32 a33 sin 0 cos F cos 0 sin F cos 9 = -cos 0 cos F sin 0 sin F sin 6 [1] 0 -sin F cos (p In terms of Eq. [I.], the stresses sij, referred to the slip system, are determined from oij, referred to the specimen axes, by1,2

Jan 1, 1965

By David R. Mitchell, B. M. Bird

DENSE-MEDIA processes utilize the familiar laboratory float-and-sink procedure on a commercial scale. Just as wood chips float on water and sand sinks, so coal floats and refuse sinks when placed in a medium intermediate in specific gravity between the coal and refuse. Liquids intermediate in specific gravity between coal and refuse used in commercial plants are of four types: (1) organic liquids of high specific gravity-halogenated hydrocarbons; (2) dissolved salts in water; (3) pseudo liquids obtained by suspending solids, such as sand or magnetite, in water, and, (4) fluidizing a mass of sand or other solids by air currents. Those most widely used for cleaning coal are solutions of calcium chloride in water and a suspended sand or magnetite pseudo liquid. Laboratory float-and-sink testing is an intermittent operation during which every opportunity is given for particles lighter than the medium to float and particles heavier to sink. Commercial processes are continuous; vertical and horizontal currents of the separating medium occur as either part of the process or unavoidedly produced by the introduction of feed and withdrawal of products, 'so that the exact separation of the laboratory technique is not duplicated by commercial processes. However, separations close to the theoretical are obtained in commercial machines by careful technical control of the process. Most machines in commercial installations are crowded to get as much out of the equipment as possible, so that careful technical control is necessary is get the recoveries and grade of product desired. Sizes usually cleaned are plus ¼ in. or plus 1/8 -in. in the United States and plus 1/16-in. in Great Britain. Coal as small as 1 mm. has been cleaned in some experimental installations. The separation of coal from refuse in sizes finer than about 1/8-in. is made difficult by viscosity effects and hence at the present time cleaning is confined to the coarser sizes. Technical advances in the art of cleaning coal by dense-media processes is progressing rapidly and it is likely that equipment, media, and procedures will be developed to clean sizes down to 0.5 mm. efficiently and at low cost.

Jan 1, 1950

By Paul A. Filteau

Asbestos ranks among the leading minerals produced in Canada. It is also mined in Russia, Rhodesia, South Africa, Cyprus, Italy, the U.S.A., Japan, China and several other countries. The most abundant variety, chrysotile, and also the most valuable form of asbestos produced, makes up 90% of the world's supply. In Canada, chrysotile is found in the provinces of British Columbia, Ontario, Newfoundland as well as in Quebec, the latter accounting for almost 90% of all the fibre produced in this country. A number of developments emerging this year could make 1968 a record production and export year for Canada's asbestos mining industry. Asbestos fibre consumption in increasing in the U.S., Canada, up 10% to date this year, Japan and in Latin America. Demand in Western Europe is again on the upswing, following a cut-back last year. As a result, shipments from Canadian mines for the first eight months of this year reached some 916,968 tons versus 873,402 in 1967, an increase of 43,566 tons or 5%. Indications are that Canadian asbestos production will for the first time ever top 1.5 million tons in 1968.

Jan 1, 1969

By T. D. McKinley

Theory, operational characteristics, and indicated precision and accuracy of analytical methods based on vacuum extraction, equilibrium pressure, and combustion approaches are reviewed. At the present time vacuum extraction at 1400°C and the equilibrium pressure method are recommended for determination of hydrogen in titanium and titanium-rich alloys. UNTIL a few years ago the role of hydrogen in titanium was an unknown factor with regard to its effect on the physical and mechanical properties of the metal. However, following the work of Jaffee and othersa-" it is now generally acknowledged that hydrogen has a degrading effect on titanium and its alloys. The chief manifestations are a decrease in impact strength in -systems and delayed cracking in a-ß systems. Since hydrogen does have a de- grading effect on titanium it is essential to control it within tolerable limits. It then follows that procedures for quantitative estimation of hydrogen are a primary requirement for the industry. For greatest benefit these methods should be simple, rapid, and precise. In addition to having these virtues, methods must be easy to duplicate in both equipment and technique to gain widespread use. After inherent accuracy has been established, the, required precision to make a method acceptable is dependent largely on the nature of the work at hand. Ability to obtain a representative sample has a pro-

Jan 1, 1959

By Arvid Anderson

THE weathering of copper-bearing ores with the formation of a water-soluble salt and the recovery of the metal by leaching and evaporation or precipitation, are processes long known, which have at various times been utilized with more or less commercial success. It is commonly assumed that the technical principles involved are quite simple and their application to a particular case easy. If these assumptions were true, we should anticipate a long list of uniformly successful leaching operations, which is not the case, and one would be justified only in calling attention to either unique or peculiar features of any particular enterprise; whereas, in studying the problems of the recovery of copper from the old workings of the Ohio Copper Co. in the light of available descriptions of other leaching projects, we have not found the assistance hoped for to guide us to the best realization of our own opportunities. It appears desirable, therefore, to call attention to these guiding principles, together with a description of the facts of accomplishment. Justification lies in the fact that the leaching and precipitation of copper at the Ohio Copper Co. mine in Bingham Canyon, Utah, is successful. This success is measured by an average monthly production of 600,000 lb. of copper at an average operating cost, to date, of 3.85 cents per pound at the company's workings, or 6.32 cents per pound after paying shipping and smelter charges on the finished copper. A total of 17,076,099 lb. of copper had been shipped to the smelter from the beginning of operations, August, 1922, to April 1, 1925. Probably these results can be bettered with further study and realization of the factors involved and the devising of methods of meeting them. It is now an assured fact that the enterprise will have a relatively long and continuously profitable life and that its reserves will not, nor cannot, be suddenly and permanently depleted.

Jan 9, 1925

By D. C. Sisti

A technical evaluation of actual performance of the preparation facilities at Beaver Consolidated Coal Co.'s Stinson plant is presented, with special emphasis on sulfur reduction in 1-1/2 x 3/8 in., 3/8 in. x 28 mesh, and 28 mesh x 0 size fractions. Evaluation of the heavy medium section of the plant and the treatment of the 28 mesh x 0 coal is included. Design criteria considered for sizing and selection of equipment required to process 1-3/4 million tpy of raw coal on coals of divergent washability characteristics are summarized.

Jan 1, 1976

By Oliver Bowles

EACH year the broad diversified field of industrial minerals offers a panorama of new and interesting developments that not only concern the welfare of the industries themselves but have a more or less direct influence on the lives of citizens at large. Thus, the home life of multirudes may be affected by new building units that transmit light through walls instead of windows, by illuminated processed marble lighting fixtures and decorations, by the vast impetus given to thermal insulation Ly .mineral wool, expanded vermiculite, and related products, and, more remotely, by fireproof rugs and drap-

Jan 1, 1937

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 E. W. Dewing

The nature of solid solutions of sodium in non-paphitic carbon at temperatures near 1000°C has been investigated by an electrolytic technique. The activity coefficient is found to vary strongly with the heat-treatment temperature of the carbon, and an analysis of the energy terms involved suggests that this is due to variations in the Fermi level. The diffusion coefficient for sodium is in the range implying that the sodium atoms (or ions) are not bound to specific sites on the carbon, in agreement with lack of evidence for specific compounds in the activity -composition curves. In the light of These results phenomena occurring in aluminum reduction cell linings are dis-cussed. It is concluded that sodium migrates by diffusion through the carbon lallice and not the pores, and that A14C9 is formed within the lining hy The excess of NaF invariably found in used linings is formed by this reaction and by air oxidation: There has recently been much interest in the swelling of carbon which occurs when it is made cathodic in an aluminum electrolysis cell, and there is general agreement that the phenomenon is due to the penetration of sodium atoms, derived from the reaction on the carbon lattice. (NaF and AlF3 are constituents of the fused-salt electrolyte.) The low-temperature lamellar compounds of potassium with graphite are well-known, and one compound between sodium and graphite has been reported.4 There is, however, virtually no information on the basic chemistry of the interaction of sodium with nongraphitic carbon at high temperatures, although Dell3 has made some fundamental studies of rates of penetration. At the time the present work was carried out these were not available. Rapoport and samoilenkol had measured rates of physical expansion in a dilatometer, using the fractional increase in length of a carbon specimen after electrolysis in a cryolite bath for 2 hr as an index of susceptibility to cathodic swelling. Work here with a similar apparatus showed that expansion (of a 1.5-in.-diam cylindrical specimen) ceased in less than 20 hr, and that the final expansion was much more reproducible than the value at some intermediate time. This suggested that an equilibrium was being set up, and that a thermodynamic approach was required. The results obtained are not as accurate as had been hoped, but they are the only ones of their type available and have enabled useful conclusions to be drawn. The experimental work was divided into two parts: an investigation of the activity-concentration diagram for sodium in carbon, and a rough determination of the diffusion rate. For the former, most of the experiments were made with petroleum coke even though this is not a form of carbon used in cell linings. It has the advantages, however, that it is a homogeneous material, that it is low in ash, and that its structure is reasonably well understood. Anthracites and coal cokes gave results of the same type as obtained with petroleum coke, but the reprodu-cibility from specimen to specimen was extremely poor. EXPERIMENTAL 1) The Activity-Composition Diagram for Sodium in Carbon. The petroleum coke was ground, pressed at 40,000 psi into plates 19 by 9 by 2 mm without added binder, and heat-treated. The sodium activities were established by an electrolytic technique. The carbon was made anodic in a cryolite bath with an aluminum cathode, and a controlled potential, E, applied so that the sodium activity at the anode was given by ln Na = 1n asa - EF/RT [21 where as, is the sodium activity generated by Reaction [I]. The relative activity is sufficient for many purposes and is simply given by The value of Na not at present known, but when the thermodynamics of the Na-A1 system have been worked out it can be derived from the equilibrium

Jan 1, 1963

By R. B. Sudderth

The recovery of copper by various combinations of processes centered around liquid ion exchange has certainly been accepted as a technically superior entity when compared to the widely applied classical method of cementation. While the technical aspect of liquid ion exchange processes has received much attention and acclaim through actual operating data, in particular the ease of handling solutions, percentage recovery, reduction of pollution, etc., the corresponding economic data has either gone unpublished or has been held confidential. Much of this economic data has now been made available for publication; and with this data, we at General Mills Chemicals, Inc., will attempt to present an accurate economic analysis of some liquid ion exchange plants and an economic comparison between these plants and the typical cementation facility.

Jan 1, 1974

By R. A. Grange, H. M. Stewart

Man.; steel parts may crack if quenched directly into a bath near room temperature, but not if quenched at a temperature just above the range where martensite forms and then allowed to cool slowly to room temperature. This latter procedure, which is the basis for such modern hardening techniques as "martempering" and "isothermal quenching," may entail some sacrifice in depth of hardening but very little, if any, in intensity of hardening. In planning such treatments, it is necessary to know the upper limit of the martensite range, and often desirable to know the proportion of martensite that would form on cooling to any lower temperature; furthermore, the tendency of a particular steel to crack when quenched is unquestionably associated with the temperature range of martensite formation, and consequently knowledge of this range aids in selecting the optimum composition for a given application. Certain puzzling phenomena associated with the properties of quenched and tempered steel may be at least partly clarified as the manner in which martensite forms is more fully understood. Information on the temperature range of martensite formation, particularly with respect to how much martensite results from quenching to a given temperature, is lacking for most commercial types of carbon and low-alloy steel. These considerations led us to study martensite formation in 14 carbon and low-alloy steels. The resultant data may be directly used in the following ways: (I) for selecting the lowest quenching temperature at which no martensite will form; (2) for selecting the highest quenching temperature at which virtually all marten . site will form, thereby avoiding quenching to an unnecessarily lower temperature with attendant danger of cracking; and (3) in producing a mixture of tempered martensite and bainite, which in high-carbon steels has been found to possess somewhat better ductility than tempered martensite, yet does not require the full transformation time necessary for a completely bainitic (austempered) structure. PART I. OBSERVATIONS OF MARTENSITE FORMATION IN FOURTEEN CARBON AND LOW-ALLOY STEELS Transformation of austenite to pearlite or bainite can be conveniently studied by observing the change that occurs over a period of time at constant temperature; such studies are the basis of the isothermal transformation diagram (S-curve). This isothermal technique is not applicable to martensite formation, which occurs within a time interval too small to measure, at least by any ordinary means. For all practical purposes, therefore, martensite may be regarded as forming only during cooling and not during a period of time at constant temperature. As austenite is cooled below

Jan 1, 1947