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By Alfred Fisher

CONSERVATION of mine timber is becoming in-creasingly important, and the consumer is en-couraged to use treated wood to permit longer life of mine timbers, and attempts are also made to substitute other material for wood. The great diffi-culty in substituting metal and concrete props for wood is the inability of these to give yielding resistance to roof pressure as wood supports do. In Europe, where mine timber costs are somewhat more important than in America, many designs of steel props have been tried, but have been unsuccessful, chiefly on account of inability to give yielding resistances. A metal pit prop that gives the desired effect has been extensively used in European mines and has caused a considerable reduction in accidents from falls of roof. Where mining operations have been sus-pended on account of strikes, conditions were found to be much better where such props were used instead of wood props, and machinery, which would have been destroyed by roof falls had wood props been used, was protected by the use of these yielding metal props. As this prop is adjustable, all the work of adjusting and transferring long props through narrow ways is done away with. It can also be drawn with greater ease and safety than wooden props; when properly used it is practically indestructible. European users have reported savings as against wooden props as high as 80 per cent. It gives audible warning of its working because the sliding action takes place in minute jerks. As the prop yields gradually to pressure its force is taken up by friction between the H sections, and this movement progressively increases the resistance of the prop to the increasing roof pressure. In the early development of the prop, it was designed with two steel members a and b of standard H steel sec-tions of equal dimensions provided with guide claws a' and b', held in frictional contact against each other by two differential wedges, f and g, and a floating link, e. In setting up the prop its two members are drawn out to the required length, the loose wedge, g, is then fitted into the space between the left-hand roller of the link d and the lower member of the prop b, and tapped suf-ficiently tight to prevent any relative movement of the two members from taking place prematurely. The prop is then raised to its intended position and secured in the usual way.

Jan 8, 1927

By A. Mitchell, T. Bagshaw

A recent paper by Thomas1 has presented new data on the solubility of hydrogen in solid silver at 1 atm pressure in the temperature range 600° to 963°C. However, no data is reported in the literature on hydrogen solubility in liquid silver. The Sieverts technique which has been described previously2,3 was used in the present work. Charges of approximately 160 g were melted in Morgan "purox" recrystallized alumina crucibles and purified helium was used for the determination of the "hot volume" during each experiment. A chemical analysis of the silver indicates that the impurity content (Cu + Al) is less than 0.02 wt pct. Hydrogen solubility in the temperature range 963° to 1200°C was investigated. The results of three experiments are shown in Table I. Fig. 1 shows an Arrhenius plot of the present work together with the solid-state data of Thomas, Steacie, and johnson,4 Eichenauer et al.,5 and Siegelin et al.6 The following expression has been derived from the Arrhenius plot of the present data: log (solubility of hydrogen, cm3 per 100 g) = 2.154-3512.0/ToK The heat of solution derived from Fig. 1 is 31,150 cal per g mole H2 compared with the value of 33,020 cal per g mole H2 obtained by Thomas and 12,000 cal per g mole H2 obtained from the data of Steacie. It was observed that hydrogen evolution took place when the silver melts were solidified under 1 atm of hydrogen, which would not be expected from an extrapolation of the results of Steacie. Schenck and Lange7 have observed that, for several transition metals at their melting points, the ratio of the hydrogen solubility in the liquid to that in the solid lies in the range 2.1 to 3.1. The present results and those of Thomas are in accord in this respect having a ratio of 2.8. 'C. L. Thomas: Trans. TMS-AIME, 1967 vol. 239, pp. 485-96. 2T. Bagshaw and A. Mitchell: I. Iron Steel Inst., 1966, vol. 204, p. 87. 'M. Weinstein and J. F. Elliott: Trans. TWS-AIME, 1963, vol. 227, p. 382. 'E. W. R. Steacie and F. M. G. Johnson: Proc. Roy. Soc. (London), Ser. A, 1928, vol. 117, pp. 662-79. 'W. Eichenauer et al.: Z. Metallk., 1958, vol. 49, pp. 220-25. 6W. Siegelin et al.: Z. Elektrochem., 1957, vol. 61, pp. 359-66. 'H. Schenck and K. W. Lange: Arch Eisenhuettenw., 1966, vol. 37, no. 9, pp. 739-48.

Jan 1, 1969

By L. C. Brown, J. S. Kirkaldy

Measurements have been made of carbon diffuswn in the five ternary austenites Fe-C-Si, Fe-C-Ni, Fe-C-Co, Fe-C-Mn, and Fe-C-Cr in which the carbon (component 1) diffuses through interstitial sites and the ternary addition (component 2) diffuses substitutionally. Values of the diffusion-coefficient ratio, D12/D11 were determined for each system with finite couples using the transient equilibrium method. The effect of temperature and of concentrations of both the carbon and substitutional component upon D12/D was examined and was found to agree with the theoretical predictions. It is concluded that within an experimental uncertainty of 10 to 15 pct, it is possible to calculate the ratio D12/D11 from purely thermody-namic data. Difficulties of measuring the other off-diagonal coefficient, 4,, are discussed. Any quantitative attack on the fundamentals of the hardenability problem in steel must begin with the multicomponent diffusion formalism and with the accumulation of data pertaining thereto. In a recent paper Kirkaldy and purdy 1 employed the formalism derived from irreversible thermodynamics to treat the problem of diffusion in ternary austenites. In the latter solutions, carbon diffuses through interstitial sites and the substitutional component diffuses through the lattice. Examples were given of diffusion in the systems Fe-Mn-C and Fe-Si-C. In the present paper, we present new results on and discuss their agreement with the thermody-namic theory. Since the theory has been slightly modified from the original presentation of Kirkaldy and Purdy, their results on Fe-Si-C and Fe-Mn-C have been recalculated and are presented here for completeness. The flux of the interstitial component with respect to a fixed lattice framework can be written as a linear expansion in the independent concentration gradients, where X1 and X2 are the independent thermody-namic forces in the lattice fixed frame of reference. These forces can be obtained from the general statement for forces in a volume fixed frame2 if the partial molar volume of carbon atoms is set equal to zero and that of the substitutional component 2 is set equal to unity, viz where the are the chemical potentials and the N's are mole fractions. Introducing into [3] and [4] the function If, as suggested by statistical arguments, the off-diagonal interaction L12 is sufficiently small, [6] reduces to i.e., the coefficient ratio becomes purely thermo-dynamic. The activity of components 1 and 2 in a dilute ternary system (standard state at infinite dilution) may be represented by the expansion3

Jan 1, 1964

Dr. Robert Bell died on June 18, 1917, at Rathwell, Manitoba, in the seventy-seventh year of his age. He was born in Toronto on June 3, 1841, and was a son of the Reverend Andrew Bell of the Free Church of Scotland. He was educated at the Grammar School of the County of Prescott, Ontario, and subsequently at McGill University and the University of Edinburgh. While still a boy of 15 years of age, he joined the Geological Survey of Canada, under Sir William Logan, in the capacity of Junior Assistant, and was rapidly promoted in the service, where lie remained-with but one short interval-for over fifty years, retiring as Chief Geologist and Acting Director in the year 1908. He married Agnes, daughter of the late Alexander Smith, of Westbourne, Glasgow, and Auchentroig, Stirlingshire, and is survived by one son and three daughters. Practically nothing was known of the geology of Canada, and very little with reference to its geography, when Mr. William E. (afterward Sir William) Logan was called upon to undertake the organization of the Geological Survey of Canada, and as its first Director to carry out the mapping of this vast area and the examination of its mineral resources. Dr. Bell's work as a member of Sir William Logan's staff in these early years consisted, therefore, exclusively of geological reconnaisance and geographical exploration. Even in later years, and until his administrative work confined him to his office, Dr. Bell's work remained essentially of this character. The exploratory traverses and track surveys which lie carried out were, chiefly within the area of the great Laurentian protaxis or Canadian Shield, which forms such a striking feature and which has played and will continue to play so important a role in shaping Canadian history and in influencing the character of the Canadian people. Dr. Bell's lines of exploration crossed and re-crossed this area from the Atlantic Coast to the Great Lakes on its western border, and from Lake Huron and Lake Superior on the south to the Arctic Sea, following the water ways of this great land. He also worked along the coast line when acting as geologist and naturalist to the "Neptune" Expedition in 1884, and to the "Alert" Expedition in 1885, both of which carried out explorations in Hudson's Bay and Hudson's Straits; also on the "Diana" Expedition in 1897, when he surveyed the coast of Baffin Land, and was one of the first white men who penetrated to the great 'lakes in the interior of that immense

Jan 11, 1917

By V. Koump, T. F. Perzak, R. H. Tien

A series of experiments were carried out in which the rates of propagation of the liquidus and the eutectic fronts Mere measured during essentially one-dimensional freezing of Al-Cu alloys. The dimensions of the ingots were 3 by 5 by 6 in. Three different alloys containing 0.1, 4.5, and 17 pct Cu were used in these experitments. For each alloy the rate of heat removal was varied to give a total jreezing time in the range 3 to 30 min. The results of these measurements cowlpared favorably with the theoretical model of freezing of binary alloys with time-dependent surface temperature. IN engineering analysis of solidification of commercia1 steels and nonferrous alloys it is a common practice to assume that an alloy freezes by propagation of an isothermal solidification front, i.e., essentially as a pure metal. In two recent theoretical investigations'j2 the present authors explored the possibility of a more realistic approach to the problem of solidification of alloys. In the proposed model the freezing of an alloy is assumed to take place by propagation of two isothermal fronts, i.e., the liquidus front and the solidus (or eutectic) front. The region between the two fronts contains both liquid and solid and is referred to as the solid-liquid region. The width and the solid content of the solid-liquid region vary with alloy type, solute concentration, and cooling rate. For a given alloy system, initial concentration of solute, and the mode of heat removal, the proposed model yields the temperature distribution within the solid skin, temperature, solid fraction, and concentration distributions with the solid-liquid region, and the rates of propagation of the liquidus and the solidus fronts. This model is obviously of considerable practical importance in engineering analysis of solidification processes, since it gives a more realistic estimate of skin strength during solidification and a better estimate of the total freezing time. Before the new model can be used with confidence, however, it is necessary to test this model experimentally. The experimental testing of the proposed model is a relatively simple matter since the effects to be measured are large and a relatively simple experiment will suffice. The theoretical model predicts, for example, that during freezing of an alloy containing substitutional type solute (negligible diffusion in the solid during freezing) the solid-liquid region occupies an appreciable portion of the ingot, even at low concentration of solute.' Another prediction of the theo- V. KOUMP, formerly with U. S. Steel Corp., is now with Research and Development Center, Systems and Process Division, Westinghouse Electric Corp., Pittsburgh, Pa. R. H. TlEN is Senior Scientist, Fundamental Research Laboratory, U. S. Steel Corp., Research Center, Monroe ville, Pa. T. F. PERZAK, formerly with U.S. Steel Corp., is now with Fiber Industries, Greenville, S. C. Manuscript submitted March 6, 1968. IMD retical model, easily verifiable by experiment, is that the rate of propagation of the solidus (or eutectic) front increases as the solidus front approaches the center of the slab. This prediction is contrary to well-known behavior of the solidification front during freezing of pure metals, where the rate of propagation of the solidification front decreases with time and freezing is completed at the lowest rate. A rather severe test of the proposed model is provided by comparison of theoretical predictions and experimental measurements of the effects of cooling rate and composition on the rates of propagation of the liquidus and the eutectic fronts. In order to test the soundness of the formulation and the method of solution of the problem of solidification of alloys a series of experiments were carried out in which the rates of propagation of the liquidus and the eutectic fronts were measured during essentially one-dimensional solidification of A1-Cu alloys. The A1-Cu system was chosen strictly as a matter of convenience. Three different alloys containing 0.1, 4.5, and 17 pct Cu were used in these experiments. For each alloy the rate of heat removal was varied to give the total freezing time in the range 3 to 30 min. The results of these measurements are compared with the predictions of the theoretical model of solidification of binary alloys, with time-dependent surface temperature.' Before the experiments described in this paper were undertaken, a serious attempt was made to utilize the measurements of previous investigators to test the theoretical model. In the course of this preliminary study a careful review was made of experiments of Pellini and coworkers3 and Doherty and Melf~rd.~ The measurements in Pellini's work were carried out using a steel containing at least four major components. Evaluation of the solid fraction-temperature relation for this steel (required in the theoretical model) is difficult and uncertain. Doherty and Melford, on the other hand, measured the solid fraction-temperature relation experimentally, but did not give sufficient data to explore the effects of composition and the cooling rates on solidification. Hence it was not possible to utilize these measurements to test our theoretical model. EXPERIMENTAL METHOD The experimental technique used in this investigation differs somewhat from the more conventional techniques employed in solidification studies. This technique was developed primarily to eliminate con-vective mixing in the molten metal caused by pouring of molten metal into the mold. In our experiments A1-Cu alloys were melted directly in the mold. The mold assembly used in solidification experiments is shown in Fig. 1. The mold was fabricated from *-in. stainless-steel sheet. The dimensions of

Jan 1, 1969

Discussion of the paper of DORSEY HAGER, to be presented at the Colorado meeting, September, 1918, and printed in Bulletin No. 138, June, 191S, pp. 1109 to 1118. WALLACE E. PRATT, Wichita Falls, Tex. (written discussion*).¬Mr. Hager has touched upon interesting problems related to the broad subject with which he has entitled his paper. As to the existence of the important structural feature in the buried Bend series, which Mr. Hager constructs from well-logs, and designates as the "Bend Arch," there seems to be general agreement among a number of observers. Indeed, M. G. Cheney1 and Robt. T. Hill2 have each published structural maps of the Bend Arch that do not differ essentially from the map shown in Mr. Hager's Fig. 1. The reflection, in the overlying, unconformable Cretaceous, of certain folds in the Pennsylvanian, with which the petroleum accumulations has to do, is an important observation on the part of Mr. Hager, since, as he says, much critical territory is covered by Cretaceous, and it is highly desirable that the underlying Pennsylvanian structure be mapped, if possible. If the folds in the Pennsylvanian are of post-Cretaceous age, then it should be possible, in spite of the intervening unconformity, to determine approximately the position of buried folds beneath the Cretaceous overlap. The idea of post-Cretaceous folding would not be out of accord with the suggestion by Carroll H. Wegemann that the folding of the Permian beds in southern Oklahoma was still in progress as late as the Tertiary.3 But most observers have related the folds in the Pennsylvanian and Permian beds at the surface, both in North Texas and southern Oklahoma, to the process of. emergence of the land area at the end of the Permian. It seems more probable that the reflection of Pennsylvanian folds in the unconformable Cretaceous which Mr. Hager observed is due to long continued persistence of stresses which were largely relieved at the close of the Permian, than that the principal period of folding was post-Cre-taceous; this being the case, it seems likely that only folds of greatest intensity in the Pennsylvanian will, be decipherable in the Cretaceous overburden, and that many promising structural features are so concealed by the Cretaceous as to escape detection except by drilling.

Jan 8, 1918

By J. H. Wernick, J. E. Kunzler

HIGHLY pure metals are needed for low-temperature electron transport studies in progress. Recent improvements in purification techniques, such as zone refining, have made it possible to obtain metals with improved purity. For some metals, the improvement has been to the extent that ordinary analytical techniques are inadequate and special methods are needed.1 For other metals purification is more difficult, so that simple but rapid analytical methods are desirable as an aid in evaluating the effectiveness of purification procedures. Furthermore, it is desirable to be able to determine the impurity level of the sample or ingot with the minimum of physical disturbance of the material. In order to aid in the preparation of purer metals, techniques involving the measurement of electrical resistance at liquid-helium temperatures have been devised for studying impurity distributions in zone-refined ingots and other bulk samples without destroying the ingot or its geometry. The method yields information on the variations in purity along the length of the ingot or sample and provides a measure of the overall purity of the material. Compared with ordinary analytical methods, the resistivity method is rapid, sensitive, and does not require significant physical disturbance of samples with reasonable shapes. It has the disadvantage that resistance measurements are not specific, i.e., they do not identify the impurity. However, this disadvantage is offset by the advantage of being able to establish a measure of the overall purity so far as electrically active" impurities are concerned. METHOD AND ITS BASIS The method is based on the well-known fact that the resistivity, at Liquid helium temperatures, of a reasonably pure metal containing no regions with additional phases decreases with increasing chemical purity or a decrease in the number of physical defects. It is convenient to separate the total resistivity into three parts: where is the resistivity due to the scattering of the conduction electrons by the lattice vibrations or phonons, p is the contribution due to physical defects, and originates from the effect of chemical impurities in the metal. Insofar as Matthiessen's rule is obeyed,2 pphys and pchem are independent of temperature. Except possiblyin the very purest metals, ptherm is negligible at liquid helium temperatures and For zone-refined metals, which normally are well annealed and consist of large grains, at the chemical purity levels thus far attained the available data indicate that pphys is negligibly small or at least constant throughout the ingot. Assuming that the effect of physical defects is negligible for isotropic metals, This assumption appears consistent with most of

Jan 1, 1959

By Keith Leonard Sutherland

THIS paper is a study of the differential flotation of the sulphide minerals in the presence of salts of silver, lead and zinc. In practice, accidental activation due to these salts is more important than their use as reagents to replace copper sulphate. The general method of investigation has been based upon contact tests, the temperature of 35°C. being chosen in conformity with earlier work. Potassium ethyl xanthate and potassium amyl xanthate were selected as collectors and pure sulphide minerals were used. The experimental procedure has been outlined in earlier papers and all solutions were kept carbonate-free.'' Contact, or spreading of an air bubble, at a mineral surface indicates the presence of an adsorbed collector film. PURITY OF REAGENTS The xanthates were purified in the usual manner.1 Neither the cyanide nor the sodium hydroxide solutions contained sufficient carbonate to give a precipitate with barium chloride solution. The silver sulphate was prepared from pure silver nitrate by evaporation with concentrated sulphuric acid until there was no evidence of brown fumes. This solution was diluted and the difficultly soluble sulphate washed with water so that unchanged nitrate was dissolved. The resultant crystal-line powder was pure white. The lead and zinc salts were prepared by dissolving especially pure lead and zinc in C.P. nitric and sulphuric acid solution and the crystals drained. The standard solutions were checked by titration. It was felt desirable to use the sulphate radical wherever possible, but since lead sulphate was insufficiently soluble for the purpose of the experiments, it was necessary to use some other lead salt. A.R. copper sulphate was used without further purification. RESULTS The results are presented in the accompanying figures; the areas of noncontact (nonflotation) are shaded in Figs. 8, 9, 10 and 11; in the remainder they lie to the right of the curve. Zinc Sulphate The curves in Fig. I are to be compared with those for Fig. 2, for which zinc sulphate is absent. This comparison shows that the influence of the zinc ion is usually small. Its influence is more marked, however, for chalcopyrite in the absence of cyanide. The influence of zinc sulphate is also marked for copper-activated sphalerite, for which tests were made only in the absence of cyanide. The results are of importance in the separation of pyrite from copper-activated sphalerite when zinc sulphate is added in the lead flotation section (p. 204 of ref. I). Sphalerite does not adsorb the collector (i.e., become floatable) under the conditions chosen.

Jan 1, 1942

By Keith Leonard Sutherland

THIS paper is a study of the differential flotation of the sulphide minerals in the presence of salts of silver, lead and zinc. In practice, accidental activation due to these salts is more important than their use as reagents to replace copper sulphate. The general method of investigation has been based upon contact tests, the temperature of 35°C. being chosen in conformity with earlier work. Potassium ethyl xanthate and potassium amyl xanthate were selected as collectors and pure sulphide minerals were used. The experimental procedure has been outlined in earlier papers and all solutions were kept carbonate -free.1,4 Contact, or spreading of an air bubble, at a mineral surface indicates the presence of an adsorbed collector film. PURITY OF REAGENTS The xanthates were purified in the usual manner.1 Neither the cyanide nor the sodium hydroxide solutions contained sufficient carbonate to give a precipitate with barium chloride solution. The silver sulphate was prepared from pure silver nitrate by evaporation with concentrated sulphuric acid until there was no evidence of brown fumes. This solution was diluted and the difficultly soluble sulphate washed with water so that unchanged nitrate was dissolved. The resultant crystalline powder was pure white. The lead and zinc salts were prepared by dissolving especially pure lead and zinc in C.P. nitric and sulphuric acid solution and the crystals drained. The standard solutions were checked by titration. It was felt desirable to use the sulphate radical wherever possible, but since lead sulphate was insufficiently soluble for the purpose of the experiments, it was necessary to use some other lead salt. A.R. copper sulphate was used without further purification. RESULTS The results are presented in the accompanying figures; the areas of noncontact (nonflotation) are shaded in Figs. 8, 9, 10 and 11; in the remainder they lie to the right of the curve. Zinc Sulphate The curves in Fig. I are to be compared with those for Fig. 2, for which zinc sulphate is absent. This comparison shows that the influence of the zinc ion is usually small. Its influence is more marked, however, for chalcopyrite in the absence of cyanide. The influence of zinc sulphate is also marked for copper-activated sphalerite, for which tests were made only in the absence of cyanide. The results are of importance in the separation of pyrite from copper-activated sphalerite when, zinc sulphate is added in the lead flotation section (p. 204 of ref. I). Sphalerite does not adsorb the collector (i.e., become floatable) under the conditions chosen.

Jan 1, 1942

By Roy C. Kirkman

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

Jan 1, 1980

By Persifor Frazer

I DESIRE to say that, owing to the number of papers which have been more or less crowded at this session of the Institute, and the fact that, as one of the Local Committee, I have the distinguished honor to feel somewhat like one of the hosts, I should not tax the patience of members at this late hour, but would have my paper read by title were it in any way possible to do this. But the task I have set myself this evening is to present to the eyes of the members of the Institute certain objects which have occupied more or less of my time during the last eighteen months or two years. The objects I allude to are some of the igneous rocks of this country, which, until quite recently, have been less understood than any others. It will be well known to some of the members that some of the cooled lavas of a previous age of our planet, when not directly coarsely crystalline and granular, were considered and spoken of as " natural glasses," or perfectly uncrystalline, vitreous, or hyaline masses of matter. Among the first results of the use of the microscope was the dispersion of this fallacy. Sir David Brewster, Mr. H. C. Sorby, and William Nichol (the discoverer of the celebrated calcite prism, which bears his name), had, with greater or less success, examined sections of various rocks and minerals, both by transmitted and reflected light, and also in the form of powder. But, until the genius of Vogelsang undertook the subject, these investigations had no permanent value, nor did they constitute an independent line of mineralogical and geological research. Since the close of his labors, by Vogelgang's premature and much-lamented death, the subject has been made one of renewed interest by his brother-in-law, Ferdinand Zirkel, as well as by Rosenbusch, Tschermak, and many others abroad, and at home by the commencement of a systematic study of the traps of Connecticut by Messrs. E. D. Dana and G. W. Hawes, of New Haven, and by the splendid set of described sections of the traps of the West which have been furnished by Zirkel to illustrate Clarence King's report. I had the honor of presenting a large number of thin sections of our traps at the Washington meeting, for the inspection of the mem¬bers, with the aid of a table microscope belonging to the Smithsonian Institution. Here I propose to project these sections upon the

Jan 1, 1877

By Keith Leonard Sutherland

This paper is a study of the differential flotation of the sulphide minerals in the presence of salts of silver, lead and zinc. In practice, accidental activation due to these salts is more important than their use as reagents to replace copper sulphate. The general method of investigation has been based upon contact tests, the temperature of 35°C being chosen in conformity with earlier work. Potassium ethyl xanthate and potassium amyl xanthate were selected as collectors and pure sulphide minerals were used. The experimental procedure has been outlined in earlier papers and all solutions were kept carbonate-free.14 Contact, or spreading of an air bubble, at a mineral surface indicates the presence of an adsorbed collector film. Purity of Reagents The xanthates were purified in the usual manner.' Neither the cyanide nor the sodium hydroxide solutions contained sufficient carbonate to give a precipitate with barium chloride solution. The silver sulphate was prepared from pure silver nitrate by evaporation with concentrated sulphuric acid until there was no evidence of brown fumes, This solution was diluted and the difficultly soluble sulphate washed with water so that unchanged nitrate was dissolved. The resultant crystalline powder was pure white. The lead and zinc salts were prepared by dissolving especially pure lead and zinc in C.P. nitric and sulphuric acid solution and the crystals drained. The standard solutions were checked by titration. It was felt desirable to use the sulphate radical wherever possible, but since lead sulphate was insufficiently soluble for the purpose of the experiments, it was necessary to use some other lead salt. A.R. copper sulphate was used without further purification. Results The results are presented in the accompanying figures; the areas of noncontact (nonflotation) are shaded in Figs. 8, 9, 10 and 11; in the remainder they lie to the right of the curve. Zinc Sulphate The curves in Fig. I are to be compared with those for Fig. 2, for which zinc sulphate is absent. This comparison shows that the influence of the zinc ion is usually small. Its influence is more marked, however, for chalcopyrite in the absence of cyanide. The influence of zinc sulphate is also marked for copper-activated sphalerite, for which tests were made only in the "absence of cyanide. The results are of importance in the separation of pyrite from copper-activated sphalerite when zinc sulphate is added in the lead flotation section (p. 204 of ref. I). Sphalerite does not adsorb the collector (i.e., become floatable) under the conditions chosen.

Jan 1, 1943

By Keith Leonard Sutherland

This paper is a study of the differential flotation of the sulphide minerals in the presence of salts of silver, lead and zinc. In practice, accidental activation due to these salts is more important than their use as reagents to replace copper sulphate. The general method of investigation has been based upon contact tests, the temperature of 35°C being chosen in conformity with earlier work. Potassium ethyl xanthate and potassium amyl xanthate were selected as collectors and pure sulphide minerals were used. The experimental procedure has been outlined in earlier papers and all solutions were kept carbonate-free.14 Contact, or spreading of an air bubble, at a mineral surface indicates the presence of an adsorbed collector film. Purity of Reagents The xanthates were purified in the usual manner.' Neither the cyanide nor the sodium hydroxide solutions contained sufficient carbonate to give a precipitate with barium chloride solution. The silver sulphate was prepared from pure silver nitrate by evaporation with concentrated sulphuric acid until there was no evidence of brown fumes, This solution was diluted and the difficultly soluble sulphate washed with water so that unchanged nitrate was dissolved. The resultant crystalline powder was pure white. The lead and zinc salts were prepared by dissolving especially pure lead and zinc in C.P. nitric and sulphuric acid solution and the crystals drained. The standard solutions were checked by titration. It was felt desirable to use the sulphate radical wherever possible, but since lead sulphate was insufficiently soluble for the purpose of the experiments, it was necessary to use some other lead salt. A.R. copper sulphate was used without further purification. Results The results are presented in the accompanying figures; the areas of noncontact (nonflotation) are shaded in Figs. 8, 9, 10 and 11; in the remainder they lie to the right of the curve. Zinc Sulphate The curves in Fig. I are to be compared with those for Fig. 2, for which zinc sulphate is absent. This comparison shows that the influence of the zinc ion is usually small. Its influence is more marked, however, for chalcopyrite in the absence of cyanide. The influence of zinc sulphate is also marked for copper-activated sphalerite, for which tests were made only in the "absence of cyanide. The results are of importance in the separation of pyrite from copper-activated sphalerite when zinc sulphate is added in the lead flotation section (p. 204 of ref. I). Sphalerite does not adsorb the collector (i.e., become floatable) under the conditions chosen.

Jan 1, 1943

ARTICLE I NAME AND OBJECT SEC. 1. This Institute is incorporated under the Membership Corporations law of the State of New York; its corporate name is American Institute of Mining and Metallurgical Engineers, Inc.; and its objects are such as are stated in its Certificate of Incorporation. ARTICLE II- MEMBERS SEC. 1. The membership of the Institute shall comprise four classes, namely: 1. Members; 2. Honorary Members; 3. Associates; 4. Junior Associates. All members shall be equally entitled to the privileges of membership, excepting that Honorary Members, Junior Associates, and Members and Associates whose residences shall be outside of the United States, Mexico, and Canada shall not e entitled to vote. Members and Associates residing within the United States of America, Mexico, and Canada, and not in arrears for dues, shall be entitled to vote in person at the meetings of the Institute, or, as hereinafter provided for, by letter ballot. SEC. 2. Members shall comprise all those persons who on the third Monday of February, 1918, were members of the Institute, and in addition thereto, all those thereafter elected or transferred into the class of Members. A person to be eligible for election or transfer into the class of Members must be at least 27 years of age and must have had at least six years' employment in the practice of-engineering, mining, geology, metallurgy or chemistry, during at least three years of which he must have held positions of responsibility in one or more of these fields. Graduation from the scientific course of a college, approved by the Committee on Membership, shall be considered equivalent to two years' employment, as required in the previous sentence. Employment as a teacher of engineering, mining, geology, metallurgy or chemistry, if in direct charge, may be considered a position of responsibility as specified in the second paragraph. Persons employed in research or any scientific literary work or in teaching in the scientific departments of colleges, approved by the Committee on Membership, who at the same time are engaged in consulting or in the active practice of mining, geology, or metallurgy, shall be entitled to consider the time so spent in active practice as equivalent to an equal length of time of employment in positions of responsibility, . provided the work done or the positions held seem to the Committee on Membership to warrant the. equivalency. The requirement of three years' employment in positions of responsibility may be waived by the Committee on Membership in the case of persons who have done notable original work in mining,. geology, or metallurgy, or have won distinction by

Jan 1, 1925

By E. T. Turkdogan, L. J. Martonik, R. J. Fruehan

Electrochemical measuretnents of the solid oxide electrolyte galvanic cells CY-Cr2O3 I ZrO2 (CaO) 1 O (in Fe alloy) CY-Cr2O3 I Tho2 (Y2O3)I O en Fe alloy) have been made at 1600°C (2912°F) in order to test the Performance of such cells at liquid steel temperatures. The oxygen pvobe (cell) consists of a disk of ZrO2 (CaO) or Tho2 (Y2O3) electrolyte fused at one end of a silica tube filled with a mixture of Cr-Cr2O3 which is the reference electrode. Upon immersion in liquid steel, the electromotive force readings achieve a steady value within a few seconds, and remain steady for 30 win or more. The perforwzance of the probes has been tested using Fe-O, Fe-Si-O, Fe-Cr-O, Fe-V-O, and Fe-Al-O alloys; the oxygen contents of liquid steel derived from the measured electromotive forces are in satisfactory agreement with those determined by arulysis. Use of the probe in the deoxi-datiorz of steel, in laboratory experiments, is discussed. The results indicate that there is insignificant electronic conductivity in ZrO2(CuO) at oxygen activities down to those corresponding to 10 ppm in steel. At lower oxygen activities, probes tipped with ThOn (Y2O3) disks perform satisfactorily at oxygen activities down to 1 ppm O or less. THE key to the control of deoxidation of steel is a sensing device to measure rapidly the concentration of oxygen in liquid steel in the furnace, ladle or tun-dish at any desired stage of deoxidation. The analysis of the cast steel by the neutron-activation or vacuum-fusion method gives total oxygen as oxide and silicate inclusions. This analysis is important for guidance to steel cleanliness; however, such a postmortem is of little value in the control of deoxidation of liquid steel. At the General Meeting of the American Iron and Steel Institute in New York, 1968, Turkdogan and Fruehan' presented a paper on the preliminary results of the work done in this laboratory on rapid determination of oxygen in steel by an oxygen probe. Details of the work done in this laboratory leading to the development of a galvanic cell for the determination of oxygen in liquid steel, and the results of the tests made are given in this paper. It was through Wagner's contributions, since the early Thirties, to the physical chemistry of semiconductors in general that it ultimately became possible to construct galvanic cells for application at high temperatures. In 1957, Kiukkola and wagner2 successfully demonstrated the use of several solid electrolytes in measuring the free energies of several chemical reactions, in particular, the use of lime-stabilized zir-conia in high-temperature oxidation reactions. Starting 7 years later, a number of papers appeared in the technical literature3-' demonstrating possible applicability of galvanic cells for the determination of oxygen in liquid steel. In the earliest work, Japanese investigators3j4 experimented with various types of reference electrodes, e.g., graphite-saturated liquid iron at 1 atm CO or Ni-NiO mixtures; the results obtained, though promising, were not of sufficient accuracy. Except for the work of Baker and West,6 all other investigators5,7,8 showed that ZrO2(CaO) electrolyte could be used for this purpose. The main part of the galvanic cell used by Fischer and ~ckermann' and by schwerdtfeger7 (the latter work was done in this laboratory), consisted of a ZrO2(CaO) tube, -1 cm ID, closed at one end, with a platinum contact wire fixed mechanically inside the closed end. The tube was flushed with a gas of known oxygen partial pressure, e.g., air, CO-CO2 or H2-CO2 mixtures; gas along with the platinum lead wire served as the reference electrode. The oxygen contents derived from measured electromotive forces agreed reasonably well with the oxygen contents determined by vacuum-fusion analysis. It is evident from recent investigations that the electromotive force technique using a solid oxide electrolyte is fundamentally well suited for the determination of oxygen in liquid steel. However, it is equally clear that the cell arrangement of the type as commonly used is in need of considerable improvement, as it exhibits several shortcomings for industrial and even laboratory use. 1) Because of its size, the zirconia tube, though stabilized, has a poor resistance to thermal shock. 2) Fine pores and microcracks, which are invariably present in zirconia tubes, are detrimental to the satisfactory operation of the cell, particularly when gas reference electrodes are used. 3) Air or carbon dioxide reference electrodes give rise to high electromotive force readings; as a result, the determination of oxygen in steel becomes less accurate. For higher accuracy, the oxygen partial pressure of the reference electrode should be in the range similar to that of oxygen in steel. 4) Even in laboratory experiments, difficulties are experienced when flushing the tube with gases and maintaining the proper gas flow rate. Fischer and Ackermann,' who used air as the reference electrode, reported that when the flow rate was too low, furnace gases would leak into the electrolyte tube, therefore lowering the oxygen potential and measured electromotive force. The required flow rate in order to avoid leakage depended on the tightness of the electrolyte tube which varied with different tubes, thus making it difficult to predict in advance the required flow rate. However, if the flow rate is too high the inside wall of the electrolyte tube would be cooler than the wall

Jan 1, 1970

By L. G. Huntley

Discussion of the paper of L. G. HUNTLEY,. presented at the San Francisco meeting, September, 1915, and printed in Bulletin No. 102, June, 1915, pp. 1333 to 1349. E. W. SHAW, Washington, D. C. (communication to the Secretary*). -The comparatively great extent and uniform character of the Dakota sandstone make it of great interest to the student of rock pores and the movements of their fluid contents. However, compared with other sands in areas of carbonaceous rocks facts concerning it do not seem to be of such great direct importance to the producer for it has thus far yielded few important pools of oil or gas. Information concerning the sandstone is extensive but scattered, hence a general treatise regarding it-particularly its pores, the fluids they contain, and the movements of the fluids-has been much needed. I therefore feel that the. chief thing to be ,desired concerning Mr. Huntley's paper is that it were more extended, particularly as to the discussion of the data presented. The general structure map of the Dakota is of especial interest. Slight changes in wording seem to be desirable here and there in the paper. For example, at the beginning of the third paragraph one-wonders if flora instead of fauna were not intended. In Figs. 2, 3, 4, and 5 the vertical scale seems incorrect. Concerning the analyses of oil quoted it is noted that they "are given, as indicating what may be expected in different localities." This seems to need modification for the average analysis of oil from Powder River, which indicates for example that this oil begins to boil at 213°C. The fact is that the samples to which this figure refers were taken from seeps long exposed. to the air :find hence the underground Dakota oil of this district no doubt differs profoundly from that which the analysis indicates. The product of a well here would probably differ more in boiling point and other. respects from the samples analyzed than it would from almost any other petroleum in the world. The use of the word synclinorium does not conform to the original definition, but this may be pardonable because misuse of the term, though a different misuse, has become general. Synclinorium is an orographic term and cannot be correctly applied outside of mountain regions, for it is derived in part from the Greek word for mountain. It has, however, been widely used in a purely structural sense for compound syncline. The broad shallow syncline of the Dakota sandstone falls in neither category. Objection might also be made to the use of

Jan 12, 1915

By C. S. Giggins, F. S. Pettit

The oxidation properties of Ni-Cr alloys with fine grains, coarse grains, and deformed surface layers have been studied at temperatures of 900" and 1100°C in 0.1 atm of oxygen. The oxidation rates of alloys containing between 10 and 30 wt pct Cr have been found to be dependent upon the grain size of the alloy. Finegrained alloys had smaller oxidation rates than coarsegvained alloys because of the selective oxidation of chromium at alloy grain boundaries. In this compositional range alloys with deformed surface layers behaved similar to fine-grained alloys due to recrys-tallization of the deformed surface layer. In the preceding paper1 it was found that during the oxidation of Ni-Cr alloys, the volume fraction of precipitated Cr2O3 could be greater at alloy grain boundaries than at other areas of the alloy surface. In the case of alloys with chromium concentrations equal to or greater than 30 pct,* the volume fraction of Cr2O3 *AIL compositions are given as weight percent unless specified otherwise. precipitated at grain boundaries and within grains on the alloy surface both exceeded the critical amount required for lateral growth of the Cr2O3 particles and the surfaces of these alloys were completely covered with a continuous, external layer of Cr203 during oxidation. However, in the case of alloys with chromium concentrations between approximately 5 to 30 pct, the volume fraction of precipitated Cr2O3 exceeded the critical value required for external scale formation only at grain boundaries.but not within the interior of the grains. Consequently, the surfaces of these alloys had external scales of Cr3O3 over the grain boundaries but internal Cr2O3 subscales with external scales of NiO away from the grain boundaries. Under these latter conditions, it was found that chromium could diffuse laterally in the alloy from those areas covered with an external layer of Cr2O3, i.e., grain boundaries, to areas where the Cr2O3 was present as a subscale. This diffusion of chromium resulted in an increase in the volume fraction of Cr2O3 precipitated in the sub-scale zone and continuous layers of Cr2O3 could be formed at the subscale front in these regions. For the alloys used in the previous studies,' continuous layers of Cr2O3 were formed on Ni-20Cr alloys in the subscale regions after approximately 30 hr of oxidation at 900°C. For shorter periods of oxidation, the Cr2O3 layer was semicontinuous with the continuous portion at the subscale front emanating from points where the Cr2O3 had been formed as an external scale over alloy grain boundaries. Some lateral growth of a Cr2O3 layer in the subscale region was observed on Ni-15Cr and even Ni-10Cr alloys but this layer was never continuous after 30 hr of oxidation. These results indicate that the selective oxidation of chromium in Ni-Cr alloys with chromium contents between 5 to 30 pct may be dependent upon the grain size of the alloy. Fine-grained specimens in this compositional range should have a larger fraction of the surface covered with external Cr2O3 than coarsegrained specimens and the subscale areas required to be sealed via lateral diffusion of chromium should be smaller. It is therefore to be expected that a continuous layer of Cr2O3 can be formed on alloys in this compositional range after short periods of oxidation providing the alloy grain-size is sufficiently small. bo studieS2,3 have established that the oxidation behavior of alloys can be significantly influenced by pretreatments which produce mechanically deformed surfaces. It has been found that deformed surfaces usually promote the selective oxidation of elements in alloys and it is believed that these effects are due to rapid diffusion of elements in the deformed layer. In view of the previous results,' which showed that alloy grain boundaries may play an important role in the selective oxidation of chromium in Ni-Cr alloys, deformed surfaces may promote the selective oxidation of elements in alloys as a result of the numerous grain boundaries formed on the alloy surfaces via recrys-tallization during heating to the oxidation temperature. The purpose of the present studies was to determine the effect of alloy grain size and surface deformation on the selective oxidation of chromium in Ni-Cr alloys at temperatures of 900" and 1100°C in 0.1 atm of oxygen. EXPERIMENTAL The average grain diameter of the alloys used in the previous studies1 was not less than 0.04 mm and alloys with compositions between 5 and 30 pct chromium had average grain diameters between 0.04 and 0.14 mm. Since the oxidation kinetics were already available for these relatively coarse-grained alloys, it was desirable to use these same alloys in the present studies. The surfaces of the alloys listed in Table I of the previous paper were deformed by using a Model F S.S. White Industrial Airbrasive Unit, which delivered a controlled mixture of 25 µ Al2O3 particles in a stream of dry air at high velocity against the surface of a specimen. The amount of surface deformation produced by this treatment was not determined but a re-crystallized layer about 15 µ thick was formed upon annealing deformed specimens. The grain size at the surface of the specimens was reduced to an average grain diameter of 0.01 mm by annealing the deformed specimens, i.e., grit-blasted,

Jan 1, 1970

By M. J. Marcinkowski, Gordon E. Lakso

An extensive investigation has been made of the deformation behavior associated with the Fe3Si super-lattice using transmission electron microscopy techniques. Above 243°K the stress-strain curve exhibits three stages. Stage I occurs at a very low stress level and is related to the generation of perfect superlat-tice dislocations. Stage II is characterized by an extremely rapid rate of work hardening and is associated with the Taylor type locking of these superlattice dislocations. Finally Stage III is related to dynamic recovery processes since the work hardening rate is very small. Below 243ºK, only Stage I is observed, but it occurs at a much higher stress level. This latter observation is related to the generation of imperfect dislocations in Stage I with the consequent production of second nearest neighbor antiphase boundaries. The reason for this is that insufficient thermal energy is available at these low temperatures to generate the complete and perfect superlattice dislocations. It has been shown that the fully ordered FeCo alloys, i.e., those possessing the B2 type structure, exhibit three distinct stages of work hardening whereas the corresponding disordered alloys show only one.&apos;" This difference in behavior between the disordered and ordered alloys has been attributed to the fact that dislocations in the former case travel only as ordinary 1/2ao(111) types whereas in the latter case the move through the lattice as coupled 1/2a0(111) dislocations separated by an antiphase boundary (APB), i.e., the so-called superlattice dislocation. Although some preliminary work has been carried out concerning plastic deformation in ordered alloys possessing the DO3 type superlattice,3 no detailed analysis similar to that described in Refs. 1 and 2 has been attempted. Specifically, it has been suggested that the superlattice dislocation in this particular type structure should consist of four ordinary 1/2ao<111> types bound together by first and second nearest-neighbor APB&apos;s. Fe3A1 and Fe3Si are the two classic alloys possessing the DO3 type lattice; however, because of the somewhat higher ordering energies associated with the FesSi alloy, which in turn assures that dislocations will travel through the lattice as perfect superlattice dislocations under at least some conditions, it was chosen for the present investigation. Because of the extreme brittleness of Fe3Si, all deformation was done in compression. Stress-strain curves were obtained using both polycrystalline samples as well as single crystals. In the latter case the crystals were oriented so that deformation could be controlled either by single or double slip. They were then wafered parallel to and at various angles to the operative slip planes. These wafers were in turn examined by transmission electron microscopy (TEM) techniques in order to determine the extent of the interaction from the dislocation configuration contained therein. EXPERIMENTAL PROCEDURE The alloys used in this investigation were arc melted under helium from electrolytic iron of greater than 99.90 wt pct purity and transistor grade silicon of 99.99 wt pct purity. A typical analysis of interstitial impurities showed 120 ppm 0, 15 ppm N, and 65 ppm C Because of the extremely low ductility of the Fe3Si alloys, it was necessary to spark cut 0.230-in. diam polycrystalline cylinders 0.400 in. long from arc-melted fingers using a thin-walled brass tube as a cutting tool. The polycrystalline alloys could not be recrystallized since very little strain was induced in preparation. However they were annealed at 1273°C for 15 min in evacuated vycor capsules to relieve any cooling stresses that may have developed during solidification and then air cooled. The resulting grain size of the alloy was 0.50 mm. According to warlimont4 1273ºC is just within the single phase field where FesSi possesses the DO3 type lattice. In addition because of this high critical ordering tem-ature, air cooling from this temperature was believed sufficient to fully order all of the Fe3Si samples used in the present investigation. For the same reason, no attempt was made to achieve any degree of disorder by quenching. In fact, rapid quenching from 1123°K caused cracking. Such cracking was first suggested by sato5 with respect to the experimental observations of Glaser and Ivanick.6 Single crystal compression specimens were spark cut from single crystal ingots grown in a Bridgman type furnace. The iron and silicon for the crystals was prealloyed by arc-melting two 130-g buttons which were cut into small pieces before remelting in the furnace. This procedure resulted in a long-range inhomogeneity of 0.5 at. pct Si between the top and bottom of the 2-in.-long single crystal ingot, which was assumed to be negligible in the present investigation. The single crystals, after orienting and spark-cutting, were about 0.37 in. by 0.37 in. in cross section and about 0.5 in. long. True stress-strain curves were obtained using an Instron Tensile Testing machine in conjunction with techniques described previously. 1,7 The strain rate was 0.05 in. per in. per min. Prior to testing, the ends of all the compression cylinders were hand polished using a special jig to insure parallelism after which the sides of the samples were electrochemically polished to eliminate stress risers and to facilitate slip line observations. Test temperatures between 77" and 823°K were obtained using various cooling and heating media as described in Ref. 7 while at the upper end of this temperature range, a mixture of equal

Jan 1, 1970

By H. B. Huntington

Some of the basic problems in understanding elec-tromigration in metals are discussed, along with the attempts that are being made to handle them. One such problem is the effect of the electrostatic forces. It is now acknowledged that the momentum exchange with charge carriers plays generally a dominant role in the driving force but the question remains to what extent the electrostatic force may still be effective. The electromigration of interstitial impurities is also an area which presents some intriguing questions. For the substitutional impurity, moving by the vacancy mechanism under the influence of an electric field, the correlation considerations are somewhat more complex than have been previously recognized. Another problem of basic importance in the calculution from first principles is the strength of the "electron friction" force, say for a simple one-band metal. A related problem growing out of the preceding is the prediction of the direction of the "electron wind" force for metals with band structure involving both holes and electrons. THE term electromigration has come to be used to describe the flow of matter in condensed phases carrying high electronic currents such as metals and alloys, whereas one usually reserves the term electrolysis for situations where the current is largely ionic, particularly in the liquid state such as molten salts. It follows that the mass transport number in electromigration is always very small, of the order of 10-7. Studies of electromigration date back some 30 years but the modern period would appear to date from the work of Seith and Wever1 who in the mid 1950&apos;s first incorporated markers to display mass motion relative to the lattice and first suggested that the direction of the mass flow was primarily determined by the sign of the charge carriers. Since that time interest in the field has grown steadily and more rapidly recently as certain technological applications became apparent. Chief of these is certainly the deleterious effects that electromigration can cause, even at relatively low temperature, to current-carrying elements in integrated circuitry.2 These phenomena have been the subject of intense study and considerable ingenuity. On the constructive side electromigration has proved a useful tool in the purification of certain metals.3 The interest of this paper is, however, centered more on the basic aspects of the subject than on its technological applications. That high electric currents should give rise to mass flow in metals and that the driving force should be more directly associated with momentum exchange with the charge carriers than with the electrostatic field are ideas that no longer cause surprise or particular interest. The field has matured to the point where the general concepts are widely accepted and continued progress in basic understanding rests on more detailed and quantitative exploration. It is the purpose of this paper to point out what are some of the current problems. As a result, we expect to raise more questions than we answer. The first of these will be the role of electrostatic forces, if any, in electromigration. A second section will deal with the electromigration of interstitials. A third and final section treats with electromigration of substitutional impurities or of the matrix atoms themselves. ELECTROSTATIC DRIVING FORCE In the conceptual treatments of electromigration it has been customary to write the driving force in terms of an effective charge number Z* and to divide it into two terms F = e£Z* = e£[Zel- z(pd/Nd)(N/p)(m*\m*\)] [1] The first of these represents the electrostatic force under immediate consideration in this section and the second and usually dominating term for metals arises from momentum exchange with charge carriers, commonly called the "electron drag" term. As can be seen it is set proportional to the electrons per atom, z, and the ratio of the specific resistivity of the moving entity to the corresponding resistivity per matrix atom. The (m*/Im*I) factor takes into account the fact that the sign of the charge carrier determines the sign of the driving force. The specific resistivity of the moving entity is averaged over its path. In the case of motion of the matrix atoms by vacancies this gives rise to approximately one-half the resistivity at the saddle point since the scattering power of the atom at its equilibrium position bordering the vacancy differs only slightly from that of a normal matrix atom. Although the formulation of the "electron drag" term in Eq. [I] is based on a highly simplified model for electron defect scattering, the essential features implicit in the expression are common to all the theoretical approaches that have so far appeared in the literature.4-6 As for Zel, most treatments of electromigration have included the quantity as the parameter which measures the direct interaction of the electrostatic field with the ion and equated it to the nominal valence of the latter. However, there has been considerable discussion whether this interaction may not be 0 in many cases.6 If the moving ion is always enveloped by the same distribution of shielding charge, then clearly its motion will not involve any work done by the electric field and one can expect there will be no electrostatic force exerted on such a neutral composite. From this point of view the shielding charge around the ion would be said to be complete and hence the entity within the Debye shielding sphere would be unaffected by the electrostatic field per se. There is, however, the prospect that, as the moving ion progresses, new charge comes in to participate in the shielding action

Jan 1, 1970

By C. G. Dunn

IDENTIFICATION Of the kinds of orientation relationships that may exist among crystals is an important problem in the metallurgical field. As an aid to its solution standard orientations of several orders of twins would be very useful for rapid analyses to discover high-order as well as low-order twin relationships. Although data have been published that give orientations for three generations of twins, these data are not readily useful in the form presented; i.e., in a stereographic projection with one pole per orientation.1 However, accurate data based on calculations of the positions of all {100} planes for such groups would be very useful when presented in tabular form. Therefore, calculations have been made for a group of four orders of twins and the data are listed in Table 3. Illustrative applications are considered briefly, with the idea of pointing out what may be done with large groups of orientations. METHOD OF COMPUTING ORIENTATION OF A TWIN It is common practice to describe the orientation of a crystal in terms of the positions on a stereographic net of the poles of certain planes of the crystal. A single position on a net may be given it terms of two angle variables, two sets of which appear in the following equations: [Polar NetWalff Net x=rsinOocos4pyx=rcos0. y=rsinB,sin4,ny-rsin0.cos¢,, z=rcos0,,z=rsin0.sin4,,] The three numbers x, y and z determine a length r as well as a direction [(0, 0)] in an X, Y, Z coordinate system. In the present case, r will be set equal to (h2 + k2 +12)1/3, where h, k and 1 are the usual Miller indices for a crystallographic plane, a restriction that facilitates determination of the positions of poles of new planes from those of old or known ones,2 as will become evident later. Furthermore, since twinned lattices have certain planes in common, it is an easy matter to determine the orientation of a twin of a crystal if the orientation of the crystal itself is known. We start therefore with a crystal of known orientation (positions of three {100} poles given) and determine where the cube poles occur in first, second, third and fourth-order twins. Methods for identifying twinned lattices and for making the calculations to find the orientation of a twin have been published.3 4 Reference 4 will be illustrated in the calculation of the orientation of a twin, even though this method differs from the one used by the writer in obtaining the following data on four orders of twins. Consider a crystal S and its twin A1, A1 being one of the four {112} or {III}

Jan 1, 1945