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By Horace C. Porter

Most of the bituminous and semibituminous coals of this country will coke, and all of them yield, on carbonizing, more or less marketable gas and byproducts. We need, however, a finer distinction as between various grades of coking coals and between coals of different degrees of byproduct and gas-making possibilities. There is required by the consumer or the coal producer a dependable test to show whether a certain coal or mixture of coals will make coke of good commercial value for blast-furnace, foundry, water-gas, or domestic use; whether any difficulties in operation may arise from properties inherent in the coal; and whether gas and byproducts may be expected of good quality and in profitable quantity. For determining coke quality, the most dependable test is an actual run in an oven, but for byproducts a coal may better and more accurately be tested in the laboratory or in a miniature oven or retort. As to what are the most desirable qualities in blast-furnace coke, the furnace men themselves are not in complete agreement. Some desire a hard, well-burned, "hot" coke, and others get better results from a llgreener," less hardened product that burns somewhat more readily in the furnace. But certain qualities of cell structure and porosity are commonly agreed upon as desirable. Information as to what kind of coke a certain coal may be made to yield is valuable in advance, whatever may be the consumer's ideas as to the particular kind most suitable to his needs. The question arises, Can we predict coking quality with any degree of satisfaction from a small-scale test? It used to be said that coals could not be tested satisfactorily on a laboratory scale either for the coke they would yield or the byproducts. On account of the mystery with which the coking quality of coal has been shrouded and the large determining influences that many believe are exerted by mass, pressure, and the passage of carbonaceous volatile matter through the coking material, it has seemed difficult to reproduce in the laboratory the exact conditions of commercial practice. Great progress, however, has been made in recent years in elucidating the process of carbonization and many of the factors that make for the formation of high-grade coke and the recovery of the best

Jan 1, 1920

By R. S. Dean

The careful work of Gross and Zimmerleyl has established the fact that the energy actually used in grinding is proportional to the new surface produced. This confirmation of Rittinger's law was made by crushing quartz in a frictionless drop-weight machine and determining the surface of the quartz by its rate of solution in hydrofluoric acid. The details of this procedure have been described adequately elsewhere and need not be repeated here. The resultant data furnish the only available basis for comparing accurately the efficiency of grinding machines. This method is so cumbersome experimentally that it has been little used. As an alternative all sorts of approximations have been proposed. The best of these is complete size analysis by sieving and elutria-tion. Such procedure is very lengthy and difficult to carry out accurately. Furthermore, any sizing method becomes very inaccurate for determining surface with very fine sizes where the ratio of surface to volume becomes very large. To avoid the lengthy and difficult technique of elutriation it has been proposed to estimate the size distribution below 200 mesh from various probability formulas. Such a procedure is at best an engineering approximation; at worst it is a mere guess. Some time ago Dr. V. H. Gottschalk2 found that the coercive forces of magnetite powders were directly proportional to the surface area, regardless of size distribution. It was at once apparent that this furnished a method for determining grinding efficiency quickly and accurately. The only requirement was a single determination of the relation between the work input of the Gross-Zimmerley drop-weight machine and the coercive force of the resultant crushed magnetite. For this purpose Ural Mountain magnetite in definite octahedra was

Jan 1, 1939

By R. S. Dean

The careful work of Gross and Zimmerleyl has established the fact that the energy actually used in grinding is proportional to the new surface produced. This confirmation of Rittinger's law was made by crushing quartz in a frictionless drop-weight machine and determining the surface of the quartz by its rate of solution in hydrofluoric acid. The details of this procedure have been described adequately elsewhere and need not be repeated here. The resultant data furnish the only available basis for comparing accurately the efficiency of grinding machines. This method is so cumbersome experimentally that it has been little used. As an alternative all sorts of approximations have been proposed. The best of these is complete size analysis by sieving and elutria-tion. Such procedure is very lengthy and difficult to carry out accurately. Furthermore, any sizing method becomes very inaccurate for determining surface with very fine sizes where the ratio of surface to volume becomes very large. To avoid the lengthy and difficult technique of elutriation it has been proposed to estimate the size distribution below 200 mesh from various probability formulas. Such a procedure is at best an engineering approximation; at worst it is a mere guess. Some time ago Dr. V. H. Gottschalk2 found that the coercive forces of magnetite powders were directly proportional to the surface area, regardless of size distribution. It was at once apparent that this furnished a method for determining grinding efficiency quickly and accurately. The only requirement was a single determination of the relation between the work input of the Gross-Zimmerley drop-weight machine and the coercive force of the resultant crushed magnetite. For this purpose Ural Mountain magnetite in definite octahedra was

Jan 1, 1939

By D. G. Westlake, U. F. Kocks

WHILE single crystals of most materials with cph lattice structure show essentially unlimited ductility, polycrystalline specimens of the same materials exhibit the entire range of ductilities. A difference between the ductility of single crystals and polycrystals may be associated with the special stress concentrations to be expected, for example, at the intersections of slip bands or twin lamellae with grain boundaries. Whether such stress concentrations prove catastrophic depends on the cleavage strength of the material, the size of the stress concentrations, and the speed with which they are formed. Thus, the ductility may vary in degree from material to material. Another possible reason for differences in ductility between single crystals and polycrystals is that a sufficient number of independent deformation modes must be available to insure compatibility between the macroscopic strains in neighboring grains.''2 This criterion is often taken to be a necessary condition for any polycrystal ductility whatsoever, not as one that determines different degrees of ductility; thus, a material with an insufficient number of independent deformation modes would have to be brittle as a polycrystal. The "sufficient number" is five if every grain is to accommodate arbitrary shape changes ("von Mises criterion "). We should like to argue that fewer than five independent modes may be sufficient to satisfy compatibility conditions; and that the internal stresses set up when the plastic strains are not compatible reach the theoretical fracture stress only after a significant amount of macroscopic strain has taken place which may vary in magnitude from case to case, allowing an influence on the degree of ductility. Experimental evidence for these statements is taken from the following review of the number of independent deformation modes observed in the various cph

Jan 1, 1968

By G. P. Connell, R. E. Gilmore, J. H. H. Nicolls

The purpose of this paper is to suggest a procedure for indicating the dividing line between noncaking coals and those that have weakly caking properties. A laboratory agglomerating test as an aid in classifying weakly caking coals is outlined and its merits in comparison with the standard agglutinating method advanced by the U. S. Bureau of Mines are discussed. No attempt, however, is made to discuss in detail either the different methods for determining "caking" and "agglutinating" indices or the various systems of classification. Two methods, differing somewhat in procedure, have been employed and recognized as suitable for determining the caking or agglutinating values of coals; namely, those in which an inert material such as sand, electrode carbon, etc., has been mixed with the coal before being heated, and those in which the coal is carbonized alone. In all such methods, the coal with or without the inert material is in the finely divided state and the index or value sought is derived from the examination of the residue after heating in a closed crucible or other container. The procedure outlined by Selvig, Beattie and Clellandl is the most recent representative of the method using sand as inert material, while the agglomerating test described below is representative of the method in which the coal is carbonized alone. The standard volatile-matter determination affords a means for observing the coking properties of a coal, and this has been described by Rose2 as the simplest of all coking tests. According to him, "the resulting coke button will indicate whether the coal is noncoking, feebly coking or strongly coking," despite the fact that "almost every condition in this test is at variance with large-scale carbonizing practice." Lessing,3 the

Jan 1, 1934

By Bruno KERL

THE list of deaths reported during the year 1905 comprises the following names (the figures in parentheses indicating the year in which the persons named were elected to membership:- Honorary Member.-Dr. Bruno Kerl. Members and Associates.-Charles Christy Adams (1903), John Wesley Anderson (1898), William Burton Barber (1901), Thomas A. Bennett (1900), Luke W. Bryan (1901), Edwin S. Daugherty (1905), William Scott de Camp (1875), George H. Eldridge (1889), B. W. Frazier (1871), John Broome Guinn, Jr. (1897), Dana C. Irish (1900), Harry Hugh Lee (1899), William Alfred Lindsay (1902), Roland C. Luther (1884), James MacNaughton (1890), Gordon McLean (1899), Herbert Holmes McNamara (1902), August R. Meyer (1886), William Orr (1897), William J. Parker, Jr. (1898), Joseph Phillips, Jr. (1895), Charles O. Ripley (1902), Emmerich J. Schmitz (1883), Ludwig Philip Seeger (1900), Jacob Johnston Sperry (1900), Gustavus H. Stoiber (1902), William L. Study (1905), Robert Macnair Wilson Swan (1900), Richard Henry Terhune (1886), Joseph Thiry (1892), John N. Tisdale (1903), Alfred Isham Totten (1897), Walter H. Virgoe (1902), Charles H. Wellman (1890), Harvey L. Williams (1903). Of these, Dr. Bruno Kerl and Prof. B. W. Frazier have been made the subjects of special Biographical Notices in the Bi-Monthly Bulletin 1 the former in No. 4, July, 1905, p. 743, and the latter in No. 5, September, 1905, p. 1097. Concerning the remainder of the list, the following paragraphs comprise such information as could be obtained by the Secretary. Charles Christy Adams, who had been a member of the Institute since 1903, died in Johannesburg, South Africa, August 31. 1905. He was born in New York City, July 13, 1849, and received his technical training at the Colorado State School of

May 1, 1906

By P. Chiotti, J. T. Mason

Ther?nal, X-ray, metallographic, and vapor pressure data were obtained to establish the phase diagram and standard free energy, enthalpy, and entropy of formation for the compounds in the Sw-Zn system. Four compounds, SmZn, SmZn2 , SmZn4.s, and SmZn8.5, melt congruently at 960°, 94Z°, 908°, and 940°C, respectively. The cornpounds SlnZns, Sm3Znll, and SnzZn7.3 undergo peritectic decomposition at 855", 870°, and 890C, respectively. Another compound of uncertain stoichiometry, SmZn11, undergoes peritectic decomposition at 760°C. Four entectics were observed with the following compositions in weight percent zinc and eutectic tenzperatures in degrees Centigrade: 12 pct, 680°C; 36 pct, 890°C; 58 pct, 850°C; and 72 pct, 900°C. An allotropic transformation and a composition range were observed for the SmZnz compound. The transfor)nation varies from 905" to 865°C as the zinc content increases from 16.0 to 48.5 wt pct, respectively. The free energy of formation of the compounds at 50PC varies between -15.9 kcal per mole for SmZn to -51.1 kcal per mole for SmZn,.,. Corresponding enthalpies vary between -19.2 to -78.3 kcal per mole. The ther-modynamic properties for the liquid alloys are described by the relations: A search of the literature revealed very little information on the Sm-Zn system. Chao et al.&apos; as well as Iandelli and palenzonai have reported the structure of SmZn to be cubic B2 type and Kuz&apos;ma et al3. have reported the structure of -sm2zn17 to be of the Th2Ni17 type. The purpose of this work was to establish the phase diagram of this system, to determine the zinc vapor pressure over the solid two-phase regions of the SYstem, and to calculate the thermodynamic properties of the compounds. MATERIALS AND EXPERIMENTAL PROCEDURES The metals used in this investigation were Bunker Hill slab zinc 99.99 wt pct pure and Ames Laboratory samarium. Analysis of the samarium by chemical, spectrographic, and vacuum-fusion methods gave the following average impurities in ppm: Nd, <200; Eu, <100; Gd, <100; Y, <50;Ca, 225; Ta, 400; Mg, 10; Cu, ~50; 0, 175; H, 20; and N, 15. The elements Fe, Si, Cr, Ni, Al, and W were not detected. The samarium was received as sponge metal and was kept under argon except when being cut with shears and when being weighed. Tantalum was found to be a suitable container for alloys with zinc contents up to the Sm2Znl, stoichio-metry. At higher zinc contents the grain boundaries of the tantalum containers were penetrated by the alloy and the containers failed during prolonged annealing. About 25 g of massive zinc and samarium sponge were sealed in tantalum crucibles equipped with thermocouple wells. These crucibles were in turn sealed in stainless-steel jackets. All closures were made by arc welding under an argon atmosphere. The samples were equilibrated in an oscillating furnace and in some cases were given various heat treatments in a soaking furnace. After appropriate heat treatment the steel jackets were removed and the alloy subjected to differential thermal analysis. The apparatus was calibrated against pure zinc and pure copper and found to reproduce the accepted melting points within 1°C. Alloys were subsequently subjected to metallographic examination and those of appropriate compositions were used for X-ray diffraction analysis and for zinc vapor pressure determinations. The vapor pressures were determined by the dewpoint method. Both the differential analysis and dewpoint measuring apparatuses have been described in earlier papers.4, 5 All alloy samples were etched with Nital (0.5 to 3 pct nitric acid in alcohol) except the samarium-rich alloys. These more reactive alloys were electro-polished in a 1 to 6 pct HClO4 in methanol solution at -700c at a potential of 50 v. EXPERIMENTAL RESULTS Phase Diagram. The results of thermal analysis are indicated by the points on the phase diagram, Fig. 1. Eight compounds and four eutectics were observed. The composition of the compounds and their melting or peritectic temperatures are given on the phase diagram. The four eutectic compositions in wt pct zinc and eutectic temperatures in % are: 12 pct,- 680°C; 36 pct, 890°C; 58 pct, 850°C; and 72 pct, 900°C. The stoichiometry of the most zinc-rich compound is still uncertain, but is very likely either SmZnll or SmZnlz. However, to simplify the presentation which follows it will be referred to as SmZnll. As shown on the phase diagram the phase regions for some of the samarium-rich alloys have not been unambiguously established. A sample of pure samarium was observed to transform at 924°C and to melt at 1074"C, in good agreement with corresponding val-

Jan 1, 1968

By R. F. Davis

The evaluation and selection of coals for producing metallurgical coke is indeed a complex process simply because coal is a complex and variable substance which is sensitive to how it is treated from the time it is mined until it is transformed into coke. A review of some of the more common evaluation tests made on coal and how the test results are applied in commercial practice should be of interest. Parameters used to select coking coal blends for wet and preheated charges should also be of interest.

Jan 1, 1982

By K. G. Colman

This text is intended to provide the operator and turn-key contractor with the basic data for sizing vibrating screens to be used in ore crushing plants. The basic capacities, modifying factors, etc. used in the area requirement calculations were developed empirically and modified to their present values based upon years of practical applications. It must be pointed out that screening is much more of an art than an exact science, however, the information presented here should provide for reasonably accurate screen sizing when applied to metallic ores .

Jan 1, 1978

By AIME AIME

CONVENTION plans for the A.I.M.E. Regional Meeting to be held on the Minnesota Iron Range Aug. 12 to 1.5 are being completed to give the visiting member?s from all parts of the country a wide variety of technical and recreational features. High spots of the social events are the official dinner, dance, luncheon and golf: and of course, special provision is being, made for the entertainment of visiting ladies. The technical sessions will fit in with scheduled trips to view all phases of mining, beneficiation and transportation of iron ore. Men from the West and Southwest will find much of interest in the detail of the mining operations. A trip to the steel plant of the

Jan 1, 1941

By C. J. Bise, E. K. Albert

Mathematical modeling and computer simulation are the two primary techniques used for production analysis of underground coal mine layouts. Oftentimes, however, the selection between these two techniques is not based on an awareness of the level of effort needed for input formulation versus the suitability of the desired output. This paper will review mathematical modeling and two of the more prominent simulators (Virginia Tech&apos;s FACESIM and Penn State&apos;s UGMHS) used in underground coal mine production analysis. A hypothetical section will be analyzed by these programs and, based on the results of the aforementioned study, their advantages and disadvantages will be discussed.

Jan 1, 1985

By M. I. Kabir, R. S. Schechter, L. W. Lake

This paper presents the development and application of a novel scaling technique that, when used with a streamline model, causes a "bundle" of one-dimensional (1-D) problems to reduce to a single 1-D calculation. The 1-D bundle is the streamline representation of a two-dimensional (2-D) problem. The 1-D calculation accounts for chemical-rock interactions and the streamline model for areal sweep. The scaling technique significantly reduces computation time, is readily modified to desktop calculations, and can be applied to both absorbing and reacting species. The work was sponsored by the US Bureau of Mines.

Jan 1, 1986

By F. M. Perkins, R. H. Jamison

Publications concerning scaling laws for laboratory flow models of oil reservoirs indicate that the relative permeability and capillary pressure relations must be the same functions of saturation in the model and its prototype. In this paper, the relative permeabilities and saturations are redefined in a way which permits one to have diflerent relative permeability and capillary pressure relations in the model and prototype. The development of the new scaling criteria is demonstrated by deriving scaling laws for one simple flow problem. INTRODUCTION The successful application of information gathered through bench-scale model studies to the prediction of multi-phase fluid flow behavior in petroleum reservoirs requires careful consideration of the scaling criteria. The requirements which must be met for a small-scale model to duplicate the behavior of a much larger reservoir prototype have been discussed by Leverett, et al,&apos; Rapoport,2 and Geertsma, et al.3 According to these authors, the relative permeabilities to water, oil and gas and the dimensionless capillary pressures must be the must have the same values in the model and prototype. Furthermore, they point out that the viscosity ratios must have the same values in the model and prototype. In addition to these requirements, other scaling criteria are given which, when considered, usually dictate a much higher permeability in the model than exists in the reservoir. Since the more permeable model sands may have connate-water and residual oil saturations quite different from those in the prototype, the scaling requirements pertaining to the dependence of relative permeabilities and dimension l ess capillary pressures on saturation usually are not met. Also, if the model fluids are selected to give equal viscosity ratios in the model and prototype, one may find greatly different mobility ratios* in the two cases and, therefore, may expect grossly different flow patterns. For this reason, Craig, et al,&apos; correlated the results of their model studies with mo- bility ratio rather than with viscosity ratio. As yet, however, no satisfactory method has been advanced which permits use of anything other than the scaling requirements outlined in the previously mentioned papers. The purpose of this paper is to present a method of developing a set of scaling criteria which permits different relationships between saturation and relative permeability or capillary pressure in the model and prototype. Rather than attempt to report scaling criteria for a variety of practical situations, this paper demonstrates by use of one simple example how the modified scaling criteria are derived.

By D. Torrey

CONSIDERING the two great interests of to-day, in iron upon the one hand and steel upon the other, and recognizing with measurable distinctness the peculiar fitness of each for special services to which they are applied, the proposition to unite the two metals in combination, to bring into simultaneous use the peculiar advantages which each offers, has great attractions. The limited success which has been attained by trying to bring about such combinations of the two metals through the use of fluxes in welding, has led to the general adoption of the opinion that an effective union of the two metals is impracticable, or to the view that if practicable it would have but limited commercial value. Such opinions are, I think, premature and erroneous, and having gained some knowledge of the character and value of the "Wheeler process" for welding iron and steel without the use of fluxes, I submit the following observations and opinions of the matter for your information, with the hope of eliciting such a discussion of the subject as it may require. The principle of the invention is to bring the two metals simultaneously to a welding heat in one pile, and then to manipulate it.

Jan 1, 1879

By Gen-Hua Shi, Richard E. Goodman

In hard, discontinuous rocks, failure modes and stability are controlled to a great extent by the intersection of discontinuities with the excavated surface. We have solved the general problem of finding the shape and size of all blocks formed through the inter- section of any number of joints and excavation surfaces and will demonstrate a simple graphical method for determining which of these is the "keyblock." An example will explain this methodology applied to a simple open pit. The effects of slope curvature in plan or section, will be demonstrated. Finally, we will show how to determine the optimum orientations for the cut slopes. The methodology is based upon a powerful topologic theorem concerning the finiteness of spatial intersections. This paper is a companion to another dealing with underground openings in the Proceedings of the 22nd Symposium on Rock Mechanics (MIT) , July 1981. This paper discusses the rock blocks created by the intersection of discontinuities and excavation surfaces in a rock mass. It establishes principles and procedures by means of which those blocks that are finite and critically located can be identified and described. The main assumptions are the following: 1. The rock itself is assumed to be strong so that the only concern for stability is the movement of rock blocks them- selves.

Jan 1, 1983

By Richard Moldenke

AmonG the things that will always remain to the credit of the foundry-industry is the circumstance that nearly all the research-work of practical value in daily routine was done by active foundrymen, and the results were freely given by them to the world. Moreover, while consumers felt that to them was due a more systematic and exact method of work, the foundry-men again were the first to act in the establishment of specifications under which their product should be sold. To come to more recent times, the American Foundrymen&apos;s Association has not only made an elaborate series of tests on cast-iron, and adopted tentative specifications based upon them, but, in addition, it has urged the International Association for Testing Materials, through its American representatives, to make the testing and specification of cast-iron a distinct issue. The half-hearted support first granted was greatly augmented by the rapidly-growing recognition accorded to the enormous iron-casting industry; and when the president of the American Society for Testing Materials was instructed to ask for a special commission for this purpose, Europe was ready to cooperate. During the Buda-Pesth congress, at, which America was represented by Prof. Howe, Mr. Wood and myself, it was decided to add five members to the general committee on steel and iron, whose special duty should be to conserve the interests of the cast-iron branch of the industry. America took up the work at once, and enlarged its committee to 67 members, all of whom were actively concerned in the manufacture or study of cast-iron in all of its branches. At the organization-meeting in Philadelphia, April 25, 1903, Mr. Walter Wood was elected chairman, and myself secretary; and, within a week thereafter, the sub-committees were appointed and became active at once. The scope of the work was naturally limited to those branches of the iron-casting in-

Jan 1, 1905

By E. F. Kingsbury

ONE of the well-known and important uses of the noble or precious metals has been for electrical contacts. In fact, the elements of this group, comprising gold, silver and the six platinum metals, have been called "noble" because of their ability to resist heat and corrosion, properties which were early found to be of importance in good contacts. Of these, platinum and its iridium alloys, palladium, and silver, have been extensively used. In recent years the electrical industry has been responsible for about one-eighth of the total consumption of the platinum metals in the United States. Information is not available as to what part of this one-eighth has been used for contacts but it is certainly an important one. SUBSTITUTES FOR PLATINUM During the past 20 years a considerable number of contact alloys have been proposed in the patent literature largely with the aim of more or less replacing platinum by gold or silver, and some of these alloys are finding increasingly widespread application as the reliability of their performance becomes established. From even the partial data-at hand it appears that this substitution by the less precious metals has replaced at least one-half of the amount of platinum that the entire electrical industry would otherwise be consuming at the present time. While the subject is of considerable interest to the metallurgist it is , even more so to the electrical engineer and it is surprising that the literature records no systematic and comprehensive investigation along these lines. Practically all the scattered work on noble metal contacts has centered around platinum as a Standard and has had two more or less distinct aims. One of these has been the replacement of platinum by cheaper materials, and the other, the development of materials of superior electrical performance. The merit of a contact metal has been assumed to be dependent on its infusibility, and since the more precious metals have the higher melting points there has naturally been an association of the two qualities in the sense that the more precious were

Jan 1, 1928

By Harold Earle Cook

The purpose of this paper is to state briefly the inspection requirements of the Bureau of Ordnance, the specifications governing the inspection, and the physical and chemical properties of the steel used in the construction of ordnance for our Navy. It would be of interest to evoke discussion on points in these specifications which do not tend to insure the production of the very best material for the purpose intended. In other words, what requirements of our specifications are useless and also in what manner are our specifications deficient? It might be well at the start to answer the first criticism of this paper which will probably be made, and that is that the title does not agree with the subject matter. Considering metallographic work as covering only the macroscopic and microscopic examination of metals, this paper will have gone beyond the subject; but it is believed that a broader definition of metallography is that it is the study of the relation of the internal structure of metals and alloys to their composition and to their physical and other properties. The internal structure of steel is dependent on its physical and its chemical properties. These physical properties are dependent on the chemical composition and the mechanical and thermal treatment of the steel. So it seems that this subtitle would not be entirely necessary and that the title " Metallography of Steel for Ordnance Purposes" would cover a study, not only of what we can learn of macroscopic and microscopic examination, but broadly of the whole subject of the specifications, the fulfillment of the requirements of which produce the structural conditions revealed by macroscopic and microscopic examination. I will refer but briefly at the beginning to the microscope and its uses in our inspection. It is only very recently that the Bureau of Ordnancc has furnished certain of its inspection offices with a portable Tassin outfit for the microscopic examination of steel. Since that

Jan 1, 1916

By H. S. Price, J. C. Cavendish, R. S. Varga

A numerical formulation of bigh-order accuracy, based on variational methods, is proposed for the solution of multidimensional diffusion-convection-type equations. Accurate solutions are obtained without the difficulties that standard finite difference approximations present. In addition, tests show that accurate solutions of a one-dimensional problem can be obtained in the neighborhood of a sharp front without the need for a large number of calculations for the entire region of interest. Results using these variational methods are compared with several standard finite difference approximations and with a technique based on the method of characteristics. The variational methods are shown to yield higher accuracies in less computer time. Finally, it is indicated how one can use these attractive features of the variational methods for solving miscible displacement problems in two dimensions. INTRODUCTION The problem of finding suitable numerical approximations for equations describing the transport of heat or mass by diffusion and convection simultaneously has been of interest for some time. Equations of this type, which will be called diffusionconvection equations, arise in describing many diverse physical processes. Of particular interest here is the equation describing the process by which one miscible liquid displaces another liquid in a one-dimensional porous medium. The behavior of such a system is described by the following parabolic partial differential equation:

Jan 1, 1969

By J. C. Scully

In June, 1965, Sanderson and scully5 reported at the Conference on Environment Sensitive Mechanical Properties of Materials at the Research Institute for Advanced Studies at Baltimore that thin foils of titanium could be prepared by chemical polishing in a mixture of 44 pct HF and 73 pct HNO3 in the volumetric ratio 2:3. The technique is simpler than that since reported by Rice and Orava. As-received annealed titanium (containing 0.8 pct Fe and 30 ppm H) in the form of sheet 0.05 cm thick is placed in the solution and moved up and down. The reaction is violent but suitable foils are obtained very easily and consistently. A typical micrograph is shown in Fig. 3. The small precipitates were not identified. Yamane and ueda6 observed many spotlike features which they referred to as small dislocation loops. While their spots may be due to the reaction of the warm foil with the air as suggested by Rice and Orava, the precipitates in Fig. 3 are also found when foils of titanium are prepared by electro-polishing at low temperatures and subsequently examined in the electron microscope without any inter- mediate warming. Furthermore, they are not a surface effect. It is necessary to add that alloys of titanium cannot be so easily thinned by the chemical polishing solution described above since it contaminates the a, phase with hydrogen and produces y hydride. These matters are described at length in a paper7 and their relevance to stress corrosion is considered elsewhere.&apos;-* Author&apos;s Reply The authors are grateful to Dr. Scully for bringing to our attention his hitherto unpublished technique for thinning unalloyed titanium, and deeply regret the unintended apparent duplication. The chemical thinning solution (7 parts HNO3 and 3 parts HF, by volume) reported by us is the same as that with which, for some period in the past, we had experienced success in the preparation of foils from single and polycrystalline niobium. Its subsequent effective application to titanium was a logical step, which, clearly independently of Scully, was conceived by Mr. Rice, to whom full credit is due. A few comments are warranted concerning some of the details of the preceding Discussion. It is evident to the discerning reader that the two thinning techniques under consideration are chemically almost identical, and in that sense are equally "simple". The chemical aspect is, of course, the one of primary importance in both communications. Thereafter, the relative simplicity is dictated by the mechanics of the actual thinning operation selected by the individual investigator. Our standard dimpling, or dishing, procedure was chosen with a view toward providing, for the electron transparent areas of the sample, the maximum protection from extraneous deformation during handling. That the long, straight dislocations visible in Scully&apos;s electron micrograph of a seemingly recovered structure closely resemble handling dislocations would tend to indicate the merit of our adopted technique. Features similar to those which Scully has attributed to precipitates, without any apparent diffraction contrast confirmation, were not observed in any of our clean foils taken from annealed or deformed specimens. This was admittedly somewhat surprising since the 3700 ppm (nominal) Fe in the A-70 commercial-grade titanium examined should have given rise to TiFe precipitates. Presumably these existed but were un-resolvable. Curiously, Scully&apos;s "precipitate1&apos; density is fairly high although the iron content quoted was less than one-fourth of that in our material. One is forced to conclude from the evidence that prior thermal and mechanical treatments are responsible for the two different types of structure observed.

Jan 1, 1968