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By HENRY FA

HENRY FAY (communication to the Secretary*).-In reply to the discussion of my paper, I wish to take this opportunity to express my appreciation to the Chairman and the various gentlemen who have taken part. I regret that others have not offered criticism, for honest differences of opinion often lead to the truth, and suggest new lines of work. An experiment has been made which bears on Prof. Sauveur's discussion and which helps to emphasize the conclusion that cementation is not a factor in the hardening of: the surface. Dr. Langenberg, of the Watertown Arsenal, has heated for me, in vacuo at 1,000° C., a piece of the metal containing a hard surface. The microstructure shows uniform distribution of carbon throughout the metal, showing that no carbon has been added to .the surface and heating in vacuo has prevented any oxidation of the surface.

Jan 6, 1917

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 stereo-graphic projection with one pole per orientation.' However, accurate data based on calculations of the positions of all {1001 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 in terms of two angle variables, two sets of which appear in the following equations: Polar Net Wulff Net x = , sin ?p cos Fbp x = r COS ?w y = r sin ?p sin Fp y = r sin ?w cos Fw % = r cos ?p z = r sin ?w, sin +, The three numbers z, y and z determine a length r as well as a direction (0, 4) in an X, Y, Z coordinate system. In the present case, r will be set equal to (h2 + k2 + L2)1/2, where h, k and I 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 {Ioo} 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, A' being one of the four {112} or {III} type* first-order twills of S. The orientation of S—i.e., the positions of poles of (I00)

Jan 1, 1945

By Francis A. Pocock

The writer is continually asked, if this electricity:is all you claim for it, why do not the mines put it in and use it? The best answer was given by Mr. John Fox Tallis, in his paper read before the South Wales Institute of Engineers in 1888, namely, that the reasons are similar to those which have prevented the more general employment of other systems of haulage. Managers, as a rule, are " not experienced mechanical engineers; neither are they all versed in electrical engineering." It may be said that there are a number of " able and practical electrical engineers who could do the work; but those electrical engineers are not conversant with the practical routine of colliery work and are, therefore, placed at a disadvantage by not knowing the actual requirements of mining engineers, and the many little difficulties to be met and contended with in underground workings; and, until mining engineers have acquired the necessary knowledge and a confidence in electricity, it is only natural that they will continue to follow the beaten path." In the above remarks, Mr. Tallis has hit the nail on the head. In the face of the partial failure, financially, of the haulage-plant which the Union Electric Company of Philadelphia had set to work at Lykens Valley, Pa., an electric haulage-plant was installed near Scranton, Pa. The question was not whether electricity could do the work, but whether any electrical company knew enough about the practical difficulties to attack and overcome them. That point being settled, the remainder was easy. The contract for the Erie Colliery haulage-plant was signed in January, 1889. This colliery is owned by the Hillside Coal and Iron Company, Mr. Samuel Hines, President, and Captain W. A. May, Superintendent. The company has been using arc-lamps in its breakers for three years. It is the only company in the Lackawanna Valley which has had enterprise enough to do so. Consequently, it was acquainted

Jan 1, 1890

By E. G. Woodruff

Few authors of treatises and papers on engineering subjects hare given adequate attention to topographic maps. The statement applies especially to mining engineering in all branches. Even those who have discussed such maps have treated the subject only in a general way. Therefore it is proposed to outline in this paper a few of the uncommon yet important relationships which topographic maps and their by-product, structure-contour maps, have to modern methods of mining investigation and development when the facts depicted on such maps are properly interpreted. Topography, as suggested by the etymology of the word, means a detailed description of particular places. Written descriptions have been found less effective than the pictorial representations, therefore attempts have been made in various ways to picture the surface features of places. Lines and shading have been used, hachures drawn, and, finally, the contour topographic map. To a large extent this style of map is the result of the demands of engineers. It is designed to meet their needs far more than those of the man untrained in engineering. In fact,. the average man obtains a better idea of the topography of an area from the hachure system than from contour maps. Since the maps have been made chiefly for the use of the engineer, they ought to meet his demands on the one hand, and, on the other, should be used by him to the fullest extent. Such maps, when properly made, accurately portray a portion of the earth's surface and should present the topography better than a personal examination of the area without a map could present it, because the person making such examination views only a limited portion of the surface at a time, and estimates distances only roughly with his eye. Let the engineer consider carefully the fact that in many instances the topographic map is superior to a personal examination of the surface features of a property because the map is based on careful instrumental measurements, whereas the eye gives imperfect data because it can be used merely for the estimation and

Jan 1, 1914

APPLICATIONS for loan contracts for the exploration, development and mining of strategic and critical metals and minerals are now being accepted by the Department of the Interior. The RFC is authorized and directed by Executive Order 10161 to make such loans but the Secretary of the Interior must pass on the necessity for the loan. Applications should be addressed to James Boyd, acting deputy administrator, Defense Minerals Administration, Department of the Interior, Washington, D.C. rather than to the Field Offices of the Bureau of Mines as was first planned. Application forms are not yet available but it has been learned that data accompanying the application should include the known quantity and grade of reserves, the anticipated rate of production, the equipment, supplies, and man power required for the additional production, etc.

Jan 12, 1950

By K. L. Temple, A. R. Colmer

ACID coal mine drainage presents a peculiarly difficult problem for two principal reasons. First is the fact that the amount of acid water discharged from active and abandoned mines constantly increases as coal fields are developed and thereby creates a steadily worsening nuisance of rapidly growing importance to the general public as well as to the coal industry. Second is the even more significant fact that there is no method yet known that will appreciably alleviate the acid water problem except at totally prohibitive cost to the coal operators. The problem is thus seen to be an urgent one. With a growing need for good quality water and a growing public demand for abatemknt of stream pollution, a large portion of the soft coal industry finds itself in the position of year by year dumping more and more acid into the streams and waterways and having no way in sight of improving the situation or even of keeping it from getting worse. While some studies have been made, it is only in the last few years that the problem has been seriously considered, chiefly by the group of workers under the direction of S. A. Braley at Mellon Institute and by the Bituminous Coal Research, Inc. fellowship at West Virginia University. Hinkle and Koehlerl reported the results of the earlier West Virginia work. This work pointed to certain biological aspects which had not been noticed previously. These may be summarized as two separate findings. One was that sulphur oxidizing bacteria were present in acid mine water and that their possible role in contributing to the acidity should be investigated. The other was

Jan 1, 1952

By George M. Schwartz

WHEN reviewing the progress made in mining geology for the year 1953, one might say that not much has been accomplished and, indeed, in a subject such as economic geology not much progress should be expected in the 10 months of the year which elapsed before this article was prepared. This seeming lack of progress, however, disappears when the facts are investigated a bit. There undoubtedly are more economic geologists at work than ever before. It is probably not an exaggeration to say that more geologists are now employed by a single company in the Lake Superior district than were employed in the whole district 20 years ago. In most mining districts geologists are busy with numerous problems of production, development, and exploration and some give an occasional thought to the scientific problems of the science, or rather the art, of mining geology. In fact, this very intense activity of mining geologists is one reason why progress seems slow; they do not have time to write up results of investigations. There is also a great amount of work being done which is not released because of company policy. Conditions have improved very much in recent years but mining corporations, in general, have some distance to go before attaining par with the petroleum industry in this respect.

Jan 2, 1954

By Howard Talbot

THE history of the development of the strip in- dustry, mentioned in this paper, was covered in considerable detail by Stephen Badlam in his paper presented. before the American Iron and Steel Institute at its meeting in New York last October. The description of progress in rolling strip there out-lined will be found good reading by anyone interested in the subject. Quoting from Mr. Badlam's paper, "For practically thirty years, we find no record of the use of the backing-roll principle, until in 1916 the Lukens Steel Co., Coatesville, Pa., put in a 206-in. plate mill of the four-high type. This was a reversing mill with two 32-in. working rolls and two 50-in. backing rolls and is today making the widest and heaviest plate made anywhere in the world." The functioning of this mill, though rolling hot plate, is, on account of the extreme width and thinness of plate rolled, quite comparable to the rolling of wide strip either hot or cold and was a considerable factor in demonstrating the marked advantages available with the four-high or backing-roll mill for thin accurate rolling. As the writer has brought out, a demand for a product, the rolling of which required the character-istics of the backing-roll mill, was broached by the In-ternational Nickel Co. This resulted in an inquiry of March, 1924, for the building of a mill capable of cold-rolling wide nickel and monel metal sheets or strip, as mentioned. It may be of some interest to note, that whereas the .six-roll cluster mill with plain bearings was built for this installation, the mill designed by the United En-gineering and Foundry Co. for this inquiry was of the four-high type with roller bearings on the backing-roll necks, being essentially the same design as the four-high roller-bearing mill built in 1925 for the Rome Brass & Copper Co. This Rome mill, to quote again from Mr. Badlam's paper, "fulfilled every requirement, and was the model on which succeeding mills of this type were built."

Jan 5, 1928

By H. S. Kalish, F. J. Dunkerley

Introduction and Previous Work THE determination of the low temperature tensile properties of tin and tin-lead alloys was initiated as part of an extensive research program on the phasial equilibria of tin binary systems below 13.2°C and the property changes associated therewith. A survey of the literature revealed that, although some room temperature tensile data were available for tin and a few tin-lead alloys, there existed no survey report of the low tcmPerature tensile properties of these alloys. Accordingly, the tensile data for tin and a series of pure tin alloys containing from 0.01 to 50 pet lead were measured at eleven temperatures horn — 196 to +20°C and are presented here in survey form. In addition to the importance of these tensile data as a preliminary to certain fundamental research, this information promises also to be of commercial importance because of the extensive use now being made of tin-lead solders in refrigeration and gas liquefaction equipment. Occasional failures of the solders in low temperature service have been attributed by some metallurgists to low temperature embrittlement, while others hold that failure results from the transformation of the tin-rich phase of the solder from the solid white (beta) to the powdered gray (alpha) form. From the data previously available in the literature, neither of these explanations can be completely corroborated. cohen and van Lieshout have estab-lished the beta to alpha tin transformation at 13,2°C and have shown that strain accelerates the transformation. Further, they showed that although I pct lead retarded the transformation, it was not eliminated. It will be pertinent, then, to note whether the beta to alpha transformation of the tin.rich phase will occur in a short-time tensile 'test. polanyi and schmid2 studied the tensile properties of tin single crystals at — 185°~ and report that tin is britlle at this tem-perature. In 1946, Kostenets3 reported that pure tin was brittle at —Ig6 and — 253°~, while lead remained ductile at both these temperatures. He also studied the tensile properties of tin-lead alloys containing from 10 to 75 pet lead at —253, —196 and + I~OC. The ultimate tensile strength increased more than two times in going from room temperature to — I96°C and about three times that value on further cooling to — 253 C- All the alloys were brittle at — 196'C except those containing more than 75 pct lead. Even at — 253'C, the 75 pct lead alloy retained 36 pet elongation in a 30 mm-ga. length. Creep is also an important phenomenon

Jan 1, 1949

By A. Kenneth Schellinger, O. Cutler Shepard

Overgrinding, Or the breaking of ore particles into sizes smaller than required for liberation, is a first-magnitude problem in grinding for concentration processes. The conventional ball mill-classifier circuit used in commercial grinding produces mineral particles that are all ground to pass an upper size limit, while the proportion of very fine sizes, or slimes, is uncon rolled. Calculations based on measurements made in commercial plants which were grinding ore for flotation concentration indicate that about go pct of the energy used in grinding is consumed in useless overgrinding.1 In addition to accounting for the consumption of a large amount of energy, over-grinding is detrimental to the flotation process. Overground slime coats larger partitles and inhibits selective action by the flotation reagents on particles which by themselves could be separated very well. A further difficulty is that extremely finely ground minerals do not respond satisfactorily to flotation-collecting reagents, and both selection and recovery decrease markedly with particles finer than 5 to 10 microns.2 conventional classifier-ball mill circuits inherently tend to overgrind the valuable minerals more than the gangue minerals because most valuable minerals are of higher density and are softer and more friable than the gangue minerals. The rem- edy to this situation would seem to be a separating mechanism which would separate free valuable mineral particles regardless of size and density considerations and a mechanism which would operate in the grinding mill so that valuable mineral grains would be removed from the grinding machine as soon as they are freed. A consideration of these ideas led the authors to the conception of a simultaneous grinding and flotation mechanism. So far as the authors are aware, such a machine has never been tried, even on a laboratory scale. Development oF Apparatus and Experimental Method Apparatus development went through several stages before a really workable machine was devised. Work was started with a large cast-iron mortar 7½ in. in diameter and 8 in- deep. A cast-iron disk Was mounted on the end of a vertical shaft SO that it fitted loosely into the bottom of the mortar. On top of the disk four radial cleats ¼ in. high were bolted to agitate the ball charge as the disk, or impeller, rotated. The vertical shaft was driven at 100 rpm by a mechanism improvised from an old coffee-mill type of grinder. A hole was drilled into the bottom of the mortar through which compressed air was introduced for frothing. In operation, more charges of Ore which had been crushed to pass an 8-mesh screen were placed in the bowl along with water and suitable reagents. The impeller was then started and the compressed air turned On so that the ore was ground while being exposed to air bubbles. Mineralized froth was

Jan 1, 1949

By Louis A. Panek

The purpose of this paper is to present a method of designing safe and economical arch structures that are to be constructed of concrete or directly of original earth materials. The experimental data used to illustrate the design method are taken from Bucky and Fen tress,1,2 and the application of the ideas presented by them is extended by obtaining an additional set of curves from which arch structures may be designed. This design method is based upon the following principles of similitude: A scalar model made of the same material as that of the full sized structure will behave similarly to its prototype if the density of the model is increased in the same proportion as its linear scale is decreased. Let R represent the scale or model ratio, namely, the ratio of a prototype linear dimension to the corresponding model linear dimension. The effect of increased density may be obtained by rotating the model in a centrifuge at a speed such that the centrifugal held exerts on the model an accelerative force R times the accelerative force of gravity. Under these conditions; (I) model unit stresses are equal to corresponding prototype unit stresses, (2) the ratio of the prototype deformation at a given point to the model deformation at a similar point is equal to the scale ratio, R, and (3) the model and the prototype will behave similarly within and beyond the elastic limits of strain. According to the above relations, such models can be used to solve the following problems: I. The dimensions of the most economical safe arch structure for a given load. 2. The miaximum safe roof span underground for given geologic conditions. The procedure is described briefly as follows. Tests are made by rotating in a centrifuge a number of models that repiesent a variety of prototype loads and dimensions. From the experimental data, curves are plotted to show the relations between these loads and dimensions. The curves are used to solve directly the problems stated above. Structural design is based upon the working (safe) stress of the material of construction, which is established by applying a factor of safety to the experimentally determined ultimate strength of the material. In conformity with this principle, each model is gradually loaded until failure occurs. A safety factor is then applied to the results. If a safety factor of 4 is used, a given model at failure represents a safe prototype, the linear dimensions of which are equal to one-fourth the model ratio at failure times the corresponding model dimensions. The safe model ratio is computed from the following formula: Safe R =(1/4)4p2n2r/g=p2n2r/g [I] in which: n = centrifuge revolutions per second at model failure; r = radius of rotation of the model in feet; g = 32.2 ft/sec2.

Jan 1, 1949

By P. Dayal, L. S. Darken

THE migration of carbon in austenite under the influence of an electric current has been observed qualitatively several times.14 Lebedev and Guterman5 recently have reported quantitative measurements; their method consisted of welding a low-carbon to a high-carbon wire, passing current, and later estimating the carbon distribution metal-lographically. We believe the method reported in this paper is superior in principle since electrolytic migration and ordinary diffusion are not necessarily coupled as in the weld method; also for the first time the extent of migration is determined by combustion analysis for carbon. A uniform tubular specimen (S.A.E. 1045 or 1095) was mounted as illustrated in the figures. the whole assembly being in an atmosphere of purified nitrogen. Direct current (129 to 226 amp at 0.65 to 1.0 v) served as source both of heat and of potential gradient for carbon migration. The duration of experiment was 7.5 to 12 hr, during which time the temperature was controlled (±10°C) manually. The experimental conditions are indicated in the first five columns of table I. With this experimental arrangement, the temperature initially has a maximum value at the central plane. Also, in this vicinity (by virtue of the symmetry), the carbon entering any volume element is equal in quantity to that leaving; the loss or accumulation of carbon occurs near the electrodes since the carbon moves uniformly near the center and is "frozen" at the cold ends. Hence, providing the time of experiment is not sufficiently long to seriously influence the conditions at the central plane, carbon crosses this plane only under the influence of the electrical potential gradient and not under the influence of temperature or concentration gradient. The amount of carbon which has crossed this plane was determined by combustion analysis of the two halves of the specimen. The results of these analyses are shown in the sixth and seventh columns of table I. It will be noted that substantial amounts of carbon migrated from the anode portion to the cathode portion (except at 920°C, which temperature was too low to exhibit the effect in the allotted time). In spite of precau-tions taken, considerable decarburization occurred as may be seen by comparing cols. 8 and 5. In three cases (indicated by asterisks in table I) the specimen was ground on one side, polished, and examined metallographically before analysis. One specimen was normalized and re-examined. Micrographs of selected areas in specimens 4 and 6 are shown in figs. 1 and 2, respectively. Evidence of carbon migration from the anode toward the cathode is quite apparent. Fig. 2 shows abundant graphite as well as cementite in a region near the cathode. The temperature of this zone is estimated at about 800°C. In fig. 1, particularly in the micrograph on the extreme right (the right side of which is of unaltered carbon content), there is evidence of slight depletion of carbon in the immediate vicinity of the cathode as contrasted to the general increase in carbon of the cathode half of the specimen. Although this may be attributed in part to decarbur-ization, it is believed that it is occasioned also by thermal diffusion—migration (of carbon) from a cool to a hot zone4—a phenomenon superimposed upon the electrical migration. Evidence of carbon migration was visible particu-larly during the course of the high-temperature,

Jan 1, 1951

By P. Farrar, H. Margolin

The Ti-Pb diagram was investigated in the region 0 to 58 pct Pb and from 500°C to liquidus temperatures. Three reactions were encountered: I—ß?a+Ti Pb at 725 10°C; 2—ß+L?Ti4Pb at 1305+ 10°C; and 3—the possible eutectic L-+Ti,Pb and y between 1200" and 1300°C. LEAD-RICH alloys have been investigated by Nowotny and Pesl,' who used sintered compacts and studied the region from 37.5 to 100 pct Pb by X-ray diffraction analysis. The only phase found in addition to titanium and lead was the hexagonal compound Ti Pb. Alloy systems of lead with metals of the transition group, such as iron, chromium, tungsten, cobalt, nickel, or manganese, generally show little liquid or solid solubility.' Craighead et al.,3 however, indicated that lead is soluble in a and ß titanium to at least 2.1 pct. They also found that approximately 50 pct of the lead added was lost during the arc-melting of Ti-Pb alloys. In the present investigation, are-melting also was used to prepare Ti-Pb alloys and similarly large lead losses were encountered. Experimental Procedure Alloy Preparation: Considerable difficulty was encountered in the melting of the Ti-Pb alloys and a number of experiments were performed before the method described was developed. Alternate layers of lead and titanium were wrapped with titanium sheet and compacted. This "sandwich" was annealed at 300" to 350 °C and was melted according to the procedure described by Cadoff and Nielsen.' Using a low current, 150 amp, and an argon atmosphere, four to eight 10 to 20 sec melts were made on each alloy, with the button being turned over between each melt to insure homogeneity. In the high lead range, the preliminary sintering was found to be of doubtful value and was eliminated. In the region above the nominal composition of 70 wt pct Pb, the alloys prepared in this manner always consolidated into two phases. The outside appeared to be composed entirely of lead and the inside was a Ti-Pb alloy. In order to determine whether this phenomenon was caused by a miscibility gap, master alloys with a nominal composition of 40 wt pct Pb were machined and mixed with various percentages of lead sheet. This mixture was compacted and melted in the same manner as the other alloys. Although these alloys were not homogeneous, they did not show the layering that was observed

Jan 1, 1956

By Ernest Lilley

THE tin deposits of Cornwall appear to have been worked for at least 3000 years. Prior to the sixteenth century, the tin came exclusively from alluvial deposits. At that time, shallow pits or mines were started in the hill sections. Mining of copper seems to have begun at the same time, but does not appear to have been especially important until about 1700. From that time until the close of the nineteenth century, copper was of major importance. Lead, and to a lesser extent, other metals, such as antimony, iron and manganese, were produced in commercial quantities during the same period. With the opening of the eighteenth century carne increasing difficulties with water because of the increasing depth of the mines. Among the efforts made to overcome this difficulty was the construction of the "Great County Adit," begun in 1748, taking 20 years to complete, and with its branches having a length of 20 miles. Adits proved capable of handling-only a few of the water problems, and led to rapid adoption of the steam pumping engine in the latter part of the eighteenth century and the early part of the nineteenth. It was in this period that the Cornish pumping engine, still considered by Cornishmen to be the most satis-factory unit for handling large quantities of water, carne into existence. The development of a means of controlling the water made possible the opening up of a number of rich deposits where profitable work-ing was further assisted by numerous improvements in mining and milling machinery. During the middle of the past century, Cornwall, with an average yearly production of 10,000 tons of tin metal and an even slightly larger tonnage of copper, enjoyed a period of unprecedented prosperity. How-ever, the relatively high prices of both copper and tin served not only to encourage prospecting (and much speculation) in Cornwall, but also in other countries. The rapid development of copper mines in the United States, together with sudden impoverishment of the lodes with increasing depth in the greatest of the Cornish copper mines, brought the copper boom to an abrupt end, the production of copper at the close of the cen-tury being negligible in importance and being secured in large measure

Jan 1, 1932

Jan 1, 1931

Ask any mineral industry executive what he considers one of the most expensive aspects of getting a product to the ultimate consumer and invariably the answer will be transportation. Some company officials say that transportation charges alone account for over half of the total cost of most products. If these judgments are correct and a recent invention turns out to be the long-awaited breakthrough that shippers have been looking for, then many producers can look forward to slashing their delivery costs by 90%.

Jan 9, 1969

By Ray Arms

This paper includes a brief classification of dry-cleaning devices, with a theoretical discussion of the principles involved. It outlines the methods of handling dust and screening difficulties at the McComas plant, as well as other plants that are being constructed and other dry-cleaning devices being developed. It describes the American Pneumatic Separator and discusses the sizing required, the effect of moisture in the raw coal, disposition of the middlings, and other aspects of the process. It gives s results of tests on various coals, and results of operation at Raton and McComas. DRY CLEANING, or pneumatic separation, is not, strictly speaking, a recent discovery. Among the archives of the Patent Office may be found many patents dating back as far as 1850 which cover early attempts to separate materials of varying specific gravity or of different shape by means of air. Hundreds of patents covering this art have been issued, which may be roughly classified into four general groups, as follows: 1. Stationary devices with pulsating air currents. The separating surface is usually riffled and air is supplied by bellows or compressors. This group' also includes air jigs, which have been used rather extensively. 2. Stationary devices with continuous air currents. These submitted the material to a continuous current of air, either horizontal or vertical. Chaff is blown from wheat by such a device. 3. Reciprocating or vibrating devices with pulsating air. A small group in which the pulsating air is supplied by bellows and some motion provided in the separating surface to move the stratified material to various discharge points. 4. Reciprocating or vibrating devices with continuous air supply. This is by far the most important group and all recent developments have been along this line. All of the above groups involve the stratification of material by air and include none of the dry methods that use other principles, such as coefficient of friction, magnetism, etc.

Jan 3, 1924

By Jim Douglas, H. H. Rachford, D. W. Peaceman

The problem of unsteady-state gas flow through porous media has been solved numerically only for the case of linear or radially symmetric reservoirs. A recently introduced numerical method for solving the unsteady-state heat flow equation in two dimensions is applied to the calculation of the depletion of a square region containing a perfect gas. Solutions are presented in graphical form for various values of dimensionless parameters. The solutions are compared with published .solutions for radial reservoirs. I NTR ODUCTION The problem of unsteady-state flow of gas through porous media gives rise to a second-order non-linear partial differential equation for which no analytical solution has been found. Numerical approximations to solutions of the gas flow problem have been obtained by the stepwise solution of an associated difference equation1,2. However, the methods so far developed have required that the reservoir be either linear or radially symmetric. This restriction in shape has been necessary so that only two independent variables be considered, namely, one distance variable and time. In order to deal with reservoirs having more realistic shapes, it is necessary to develop numerical procedures for the solution of the gas flow problem involving two distance variables. A numerical procedure, denoted as the alternating-direction implicit method, for the solution of the heat-flow problem in two dimensions has recently been introduced" By the use of this procedure, approximate solutions have been obtained for heat-flow problems in a square8, and in regions having various non-rectangular boundariesa. Because of the similarity between the equation for heat conduction in solids and the equation for gas flow in porous media, it is reasonable to expect that the alternating-direction implicit method should also be useful for solving the gas flow problem in various two-dimensional regions. Solutions have been calculated for the simplest two-dimensional region, a square reservoir with a single well in the center. While reservoirs of such simple geometry seldom, if ever, exist, the solution of this problem is of some practical importance because it is also the solution of another problem, that of determining the depletion history about an individual well in an infinite uniform reservoir containing wells spaced throughout on a square lattice and producing equally from each well. Finally, it is of interest to compare solutions for a square reservoir with those for a circular reservoir and to determine the effect of the shape of the boundary for that particular case. METHOD OF CALCULATION Basic Differential Equation By combining the equation of continuity, the perfect gas law,

Jan 1, 1956

By J. W. Spretnak, G. W. Cunningham

Grain growth across the bond region in Pressure bonded copper was found to be mainly dependent upon the presence or absence of microvoids, but it was also found that prior history, bonding pressure, bonding time, and bonding temperature are important variables. An increase in pressure, time, or temperature tends to promote grain growth in the interfacial region. Polygonization is observed after pressure bonding except for specimens previously annealed at temperatures on the order of 1800°F or higher. The dislocation density in bonded specimens was found to be greater in the bond region. THE bonding of metals by the application of gas pressure at elevated temperatures is a relatively new process, having been developed over the past 10 years. The technique, as described by Paprocki, Hodge, and Boyer,l is unique in that assemblies of many parts and complex shapes can be bonded with a negligible amount of deformation. The process thus differs metallurgically from pressure welding, cold welding, and recrystallization welding in that deformation occurs only in a microscopic region whereas, in general, the welding requires severe deformation and may extend the contact surface by a factor of 3 to 10 during the welding. From a practical standpoint, pressure welding is not amenable for bonding large surfaces. During the time in which Paprocki and coworkers were deve1oping the process, West2 established aproc-ess,for bonding aluminum to uranium, and Barnes and Maze? developed a gas-pressure-bonding technique for nickel and copper. Recently, Fugardi and Zambro4 have used equipment similar to that developed by Paprocki and coworkers to establish parameters for bonding stainless steel, aluminum, and zirconium. Most of the investigations on pressure bonding have been empirical in nature and, although methods have been developed for bonding such metals as molybdenum, columbium, titanium, zirconium, and stainless steel, the information concerning the mechanism of bonding is limited. Several workers5"7 have studied the pressure bonding of dissimilar metals in order to gain information on diffusion and formation of inter-metallic phases under application of pressure. Clapson and Robbins8 have shown by a series of annealing studies that voids in the interfacial boundary of roll-bonded copper can prevent movement of the boundary until the voids are spaced far enough apart to prevent pinning. They also indicated that recrystallization and grain growth can eliminate the voids. In this paper it is shown that voids are the major detriment to grain growth across pressure-bonded interfaces, but it is also shown that prior history, bonding pressure, bonding time, and bonding temperature are

Jan 1, 1962