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By R. A. Deju, R. B. Bhappu

The basic structural unit of all silicate minerals is a tetrahedron with a silicon atom at the center and four oxygen atoms at the corners. The oxygen-silicon distance is about 1.6 & and the oxygen-oxygen distance about 2.6 &. The different types of oxygen-silicon frameworks in the various silicates are based entirely on the combinations of the tetra-hedral oxygen-silicon groups through sharing of oxygen atoms. In recent years, infrared spectroscopy has permitted estimation of the ratio of the ionic character of the oxygen-silicon bond to be a few times that of the oxygen-carbon bond and the ratio of electro-negativity of the two bonds has also substantiated this finding. On this basis, it is generally accepted that the oxygen-silicon bond is the strongest one occurring in silicate minerals. As the oxygen-silicon ratio increases from quartz to the olivines, a greater percentage of the oxygen bonding power is available for bonding to cations other than silicon. Hence, with an increasing oxygen-silicon ratio, there is increasing oxygen-to-metal bonding. Upon the fracturing of a silicate mineral crystal, the oxygen-metal bond, which is almost entirely ionic in character, should break more easily than the stronger oxygen-silicon bond, resulting in a greater number of unsatisfied negative forces on the surface. If, then the mineral is immersed in a liquid containing hydrogen ions, these negative forces should tend to be neutralized by hydrogen ions from solution, resulting in a change of the pH of the solution. An increase in the degree of adsorption of hydrogen ions is to be expected as the oxygen-silicon ratio in the crystal structure increases. This study attempted to correlate the oxygen-silicon ratio for various representative silicate minerals to the adsorption of hydrogen ions. Experiments to determine the effect of surface area on this adsorption and to investigate the effect of surface iron were also conducted. It is believed that such studies of the surface properties of silicate minerals will supply pertinent information about their behavior in froth flotation systems. EXPERIMENTAL PROCEDURE Ion Exchange: Carefully selected, hand-picked samples of the minerals investigated were dry-crushed in a ceramic ball mill and sieved to obtain a minus 100 plus 200-mesh sample. The sized samples were then run through the electro-magnetic separator to remove any iron-bearing particles. A 10-g sample of each mineral was placed in 100 ml of freshly deionized water previously adjusted to a pH of 3.50 with HCl. The beaker containing the sample and the water was placed under a bell jar from which the air was displaced at once by nitrogen gas from a tank. All experiments were carried out in a nitrogen atmosphere. The sample and solution were stirred gently but continuously during the entire experiment, the stirring speed being kept about the same for all runs. Changes in pH were followed with a Beckman Zeromatic pH meter and recorded on a

Jan 1, 1967

Aamot, Olav Crone, (M'29) Chem. Engr., Elektro¬kemisk, Raadhusgt, 23; Oslo, Norway. Abadilla. Quirico A., (M'33) Min. Engr., Dir., Bureau of Mines, Manila, P. I. Abbott, Agatin T., ( J'40) Asst. Geol., Trench Mine, Patagonia, Ariz. Abbott, Clarence E., (M'04) Civil Engr., V.P., Tennessee Coal Iron & R. R. Co.. 159'3 Brown Marx Bldg.. Birmingham, Ala. Abel, Raymond L., (M'28) Chem. Engr., Chief of Inspection Div., Pittsburgh Chem. Warfare Pro¬curement Dist., American Batik Bldg., Pitts¬burgh. Pa. Abel, Walter D., (M'32) Min. Engr.. Div. of Cor¬porations, State of Calif.. 403 California State Bldg., Los Angeles, Calif. Abele. Louis T., (M'31) 4800 Patterson Ave.. Richmond, Va. Abell, Leo M., (M'311 Research Met., Mount Mor¬gan Ltd., Mount Morgan, Queensland, Australia. Abenius, Hakan V., (M'37) c/o Falu Gruva, Falun, Sweden. Abernathy. G. E., (M '33S) Geol., Kansas State Geol. Survey. Pittsburg, Kan. Abernathy, Jack. H.. (M'40) Chief Engr., Sunray Oil Co.. Philtower B1dg., Tulsa. Okla. Ahorn, Robert H., (M'19) Asst. Met., Research Lab., U. S. Steel Corp., Lincoln Highway, Kearny, N. J. Abraham, A. W., (M'30) Petr. Engr., Richfield Oil Corp., 555 S. Flower St., Los Angeles. Calif. Abramowitz, William L., (J'40) Chem., National Oil Products Co., Harrison, N. J. Abrams, Charles Jackson, (M'36) Gen'l Supt., Climax Molybdenum Co.; Climax, Colo. Abstein, Henry T., (M'27) Yellow Pine, Idaho. Ackerman, D. E., (M'35) McKinsey & Co., 2 Wall St., New York, N. Y. Ackerman. E. Dumont, (A'3S) Petr. Geol.. Dist. Geol., Quiriquire' Dist., Standard Oil Co. of Venezuela, Caripito, Venezuela.

Jan 1, 1941

New York Meets first Wednesday after first Tuesday of each month. DAVID H.-BROWNE, Chairman, JOHN H. JANEWAY, Vice-Chairman. F. E. PIERCE, Secretary, 35 Nassau St., New York, N. Y. P. A. MOSMAN, Treasurer. LEWIS W. FRANCIS. Boston Meets first Monday of each winter month. HENRY L. SMYTH, Chairman. . ALFRED C. LANE, Vice-Chairman. HENRY A. WENTWORTH, Secretary-Treasurer, 60 India St., Boston, Mass. ROBERT H. RICHARDS, ALBERT SAUVEUR. Columbia Holds four sessions during year. Annual meeting in September or October. FRANK A. ROSS, Chairman. RUSH J. WHITE, Vice-Chairman. LYNDON K. ARMSTRONG, Secretary-Treasurer, P O. Drawer 2154, Spokane, Wash. FREDERIC KEFFER, FRANCIS A. THOMSON.

Jan 11, 1915

By M. Bevis, A. F. Acton, P. C. Rowlands

Defor~nation twinning and transformation twinning modes most likely to be operative in Fe-Ni and Fe-Ni-C martensites have been determined using a new theory of the crystallography of deformation t~inning.~ This analysis shows that potentially important conventional and nonconventional twinning modes1 have been omitted in previous analyses. Discussion is given on the relevance of the predicted twinning modes to the lattice invariant shear associated with the martensite transformation in steels and to anomalous deformation twinning in Fe-Ni-C martensites. THE two most important criteria which appear to govern operative twinning modes in metallic structures1 are that the magnitude of the twinning shear should be small and that the twinning shear should restore the lattice or a multiple lattice in a twin orientation. The latter criterion ensures that the shuffle mechanism required to restore the structure in a twin orientation is simple. These criteria have been adhered to in the prediction of twinning modes2"6 in bcc and bct single-lattice structures with axial ratios in the range y = 1 to 1.09 as, for example, encountered in martensite occurring in steels. Refs. 2 and 3 in particular consider the martensite transformation in steels and the twinning modes in these cases relate to transformation twinning, and hence the lattice invariant shear associated with the martensite transformation. The list of twinning modes which can be compiled from these sources is incomplete and the ranges of magnitude of shear considered could be unrealistically small, particularly in the case of deformation twinning. The latter consideration is supported by the fact that twinning modes with magnitudes of shear large compared with the smallest shear consistent with a simple shuffle mechanism have been established in, for example, the single-lattice structure mercury7 and the multiple-lattice structure zirconium.&apos; In addition the anomalous deformation twins reported by Ftichrnan4 to occur in a range of Fe-Ni-C martensites still remain unexplained. It is clear that a comprehensive analysis of twinning modes likely to be operative in martensite In steels is required. The results of the application of a new theory of the crystallography of deformation twinningg to these structures are presented in this paper. The theory has been used to determine all shears which restore the lattice or a multiple lattice in a new orientation with magnitude of shear up to a required maximum. The orientation relationships between parent and twinned lattices are not restricted to the classical orientation relationships of reflection in the twin plane or a rotation of 180 deg about the shear direction. PREDICTED TWINNING MODES Twinning modes which restore all or one half of lattice points to their correct twin positions will be referred to as m = 1 and m = 2 modes, respectively. These modes are the most likely to describe operative modes in single lattice structures. The bcc m = 1 and m = 2 modes which have magnitudes of shear s in the range s < 2 and s < 1, respectively, have been given10 and are reproduced here in Tables I and 11. Detailed discussion of the crystallography of these modes and cubic modes in general will be discussed elsewhere (~evis and rocker, to be published). The four twinning elements Kl, &,ql,7)2 as well as the magnitude of shear s are given for each twinning mode, and the twinning modes are given in order of increasing shear. Two twinning modes are given in each row of the tables, the twinning mode Kl, Kz, ql, q2 and the reciprocal twinning mode with elements Kl = K,, Ki = Kl, q: = q2, and 17; = ql. The m = 1 and m = 2 twinning modes which describe twinning shears with small magnitudes of shear and simple shuffle mechanisms in bct crystals with -y = 1 to 1.09 are given in Tables I11 and IV, respectively. On increasing the symmetry of the tetragonal lattice to cubic, that is making y = 1, all modes listed in Tables 111 and IV must reduce to crystallographically equivalent variants of the modes given in Tables I and 11, respectively, or become twinning modes with both shear planes as symmetry planes in the cubic lattice and hence not considered in Tables I and 11. With the exception of this last type of mode only those tetragonal twinning modes which reduce to modes 1.1, 1.2, 2.1, and 2.2 of Tables I and I1 are considered in Tables 111 and IV. For values of y in the range -y = 1 to 1.09 the tetragonal modes and the corresponding cubic twinning modes have approximately the same magnitude of shear. The twinning modes listed in Tables 111 and IV are therefore by the criteria given above the most

Jan 1, 1969

By Leo H. Glanville

Until 1934, natural ventilation was depended upon in the mine of the Climax Molybdenum Co. at Climax, Colorado. In that year a 7-ft. axial-flow, low-pressure fan was installed as an exhausting unit. In 1936, three more fans of the same kind were installed, all as exhausting units, with a total capacity of 115 000 cu, ft. per min., and since then fans and sprays have been added as required. Atmospheric Conditions Adverse atmospheric conditions at this elevation of 11,500 ft. account in part for difficulty in maintaining adequate ventilation throughout the mine. Barometric pressures range from 18.99 to 20.01 in. of mercury; the norma1 average being 19.70 in. Air weight is 0.051 lb. per cu. ft., and humidity is low—about a 30 per cent yearly average. This makes the use of mechanical humidity aids mandatory the Year around to prevent excessive dryness of the mine workings and the resultant dust hazard. The yearly temperature range is from minus 24" to 75°F.; typically, in February 1942 the mean low was minus 3.25°F. and the mean high, 21.3°F. In August the mean low was 34.8°F.; the mean high, 64.26°F. Even during the summer month air filtration through the openings of the cave area is 32°F., owing to accumulation of snow in the glory hole and in Part to glacial ice, which, combined with a rock temperature of 39°F. on the upper levels (elevation 11,945 ft.) and 42°F. on the main haulage level (elevation 11,470 ft.], makes it difficult to maintain a comfortable working temperature. The one advantage in ventilation of mine workings at the altitude of the Climax mine is that the power required to circulate a given air volume is 32 per cent less than would be required at sea level. Problems since 1936 the mine management has studied intensively plans for providing adequate ventilation for the entire mine for its expected life. As the ore breaks into large pieces, much secondary blasting is necessary, therefore there is a considerable amount of smoke, gas and dust, which requires circulation of a large amount of air to remove the contamination, It is undesirable to use haulage drifts and manways as air passages because some would be passageways for contaminated air also, and there would be undesirable high velocities in some drifts. High velocities and large volumes of subfreezing air dry out the passageways through which they pass, and thus increase the amount of dust. Regulating doors in haulage drifts are difficult of upkeep and interfere with production. It was decided as a general principle to distribute fresh air to each working place at low velocities and low pressures and to remove contaminated air as soon as possible with a minimum of travel through working places.

Jan 1, 1943

By Leo H. Glanville

Until 1934, natural ventilation was depended upon in the mine of the Climax Molybdenum Co. at Climax, Colorado. In that year a 7-ft. axial-flow, low-pressure fan was installed as an exhausting unit. In 1936, three more fans of the same kind were installed, all as exhausting units, with a total capacity of 115 000 cu, ft. per min., and since then fans and sprays have been added as required. Atmospheric Conditions Adverse atmospheric conditions at this elevation of 11,500 ft. account in part for difficulty in maintaining adequate ventilation throughout the mine. Barometric pressures range from 18.99 to 20.01 in. of mercury; the norma1 average being 19.70 in. Air weight is 0.051 lb. per cu. ft., and humidity is low—about a 30 per cent yearly average. This makes the use of mechanical humidity aids mandatory the Year around to prevent excessive dryness of the mine workings and the resultant dust hazard. The yearly temperature range is from minus 24" to 75°F.; typically, in February 1942 the mean low was minus 3.25°F. and the mean high, 21.3°F. In August the mean low was 34.8°F.; the mean high, 64.26°F. Even during the summer month air filtration through the openings of the cave area is 32°F., owing to accumulation of snow in the glory hole and in Part to glacial ice, which, combined with a rock temperature of 39°F. on the upper levels (elevation 11,945 ft.) and 42°F. on the main haulage level (elevation 11,470 ft.], makes it difficult to maintain a comfortable working temperature. The one advantage in ventilation of mine workings at the altitude of the Climax mine is that the power required to circulate a given air volume is 32 per cent less than would be required at sea level. Problems since 1936 the mine management has studied intensively plans for providing adequate ventilation for the entire mine for its expected life. As the ore breaks into large pieces, much secondary blasting is necessary, therefore there is a considerable amount of smoke, gas and dust, which requires circulation of a large amount of air to remove the contamination, It is undesirable to use haulage drifts and manways as air passages because some would be passageways for contaminated air also, and there would be undesirable high velocities in some drifts. High velocities and large volumes of subfreezing air dry out the passageways through which they pass, and thus increase the amount of dust. Regulating doors in haulage drifts are difficult of upkeep and interfere with production. It was decided as a general principle to distribute fresh air to each working place at low velocities and low pressures and to remove contaminated air as soon as possible with a minimum of travel through working places.

Jan 1, 1943

By R. J. Stevens

The Roan Antelope Smelter commenced operations in October, 1931. As originally designed, its equipment consisted of one reverberatory furnace, 120 X 25 ft, two Peirce-Smith converters 12 X 20 ft, and one straight line casting machine. Since that time the following additions have been made: One reverberatory furnace 120 ft X 28 ft (&apos;934) One reverberatory furnace 95 ft X 28 ft (1943) Two 12 X 20 ft Peirce-Smith converters (1934 and 1938) One 13 X 30 ft holding furnace (1938) One straight line casting machine and 2 ladle tilting quadrants (1934) The metallurgy of the smelting process is comparatively simple. However, there are several features of operation which are uncommon to most copper smelters: (I) The high grade of concentrate treated; this has always been about 50 pct copper. (2) The high flux burden on the charge. This is necessary because of the deficiency of bases in the concentrate and the high alumina content of the concentrate. (3) The frequent necessity of adding coal to the furnace charge to control the matte grade. (4) The high grade of matte produced. This has led to unusual converter problems. From the commencement of operations, the ore mined has come from the Roan Basin orebody. The concentrate produced from this ore consists mainly of chalcocite and shale with small proportions of other copper minerals. As mining operations extend to the Roan Extension orebody, the proportions of bornite and chalcopyrite in the concentrate will increase with a corresponding decrease in the copper content of the concentrate. Because of the concentrate grade the capacity of the reverberatory furnaces in terms of tons of copper produced per ton of coal burned is high. This ratio is usually over 2.2, and on especially favourable runs has reached 2.6. Reference to Table I shows that the iron content of the concentrate is unusually low. Only part of this iron is available for slag formation, the balance going to the matte. To make up this deficiency in bases, limerock is added to the furnace charge. This flux ensures a slag that is of the correct silicate degree, is suficiently fluid, of low specific gravity, and it counteracts the thickening effect of the alumina present. An ample supply of flux is obtainable from Ndola, 22 miles distant by rail. Although the reverberatory slag has a high copper content, the slag fall is low and the copper loss in the slag now rarely exceeds 1.0 pct of the total copper charged. The blister copper shipped is of such purity that only one fire refining operation has been necessary to produce a wirebar with properties comparable to electrolytic copper. Bismuth has always been the most troublesome impurity and consequently the problem of its control in the finished product has been of prime importance. Practically none is removed in the reverberatory furnace. The bulk of the elimina-

Jan 1, 1949

By Leo H. Glanville

UNTIL 1934, natural ventilation was depended upon in the mine of the Climax Molybdenum Co. at Climax, Colorado. In that year a 7-ft. axial-flow, low-pressure fan was installed as an exhausting unit. In 1936, three more fans of the same kind were installed, all as exhausting units, with a total capacity of 115,000 cu. ft. per min., and since then fans and sprays have been added as required. ATMOSPHERIC CONDITIONS Adverse atmospheric conditions at this elevation of 11,500 ft. account in part for difficulty in maintaining adequate ventilation throughout the mine. Barometric pressures range from 18.99 to 20.01 in. of mercury; the normal average being 19.70 in. Air weight is 0.051 lb. per cu. ft., and humidity is low-about a 30 per cent yearly average. This makes the use of mechanical humidity aids mandatory the year around to prevent excessive dryness of the mine workings and the resultant dust hazard. The yearly temperature range is from minus 24° to 95°F.; typically, in February 1942 the mean low was minus 3.25°F. and the mean high, 21.3°F. In August the mean low was 34.8°F.; the mean high, 64.26°F. Even during the summer month air filtration through the openings of the cave area is 32°F., owing to accumulation of snow in the glory hole and in part to glacial ice, which, combined with a rock temperature of 39°F. on the upper levels (elevation 11,945 ft.) and 42°F. on the main haulage level (elevation 11,490 ft.), makes it difficult to maintain a comfortable working temperature. The one advantage in ventilation of mine workings at the altitude of the Climax mine is that the power required to circulate a given air volume is 32 per cent less than would be required at sea level. PROBLEMS Since 1936 the mine management has studied intensively plans for providing adequate ventilation for the entire mine for its expected life. As the ore breaks into large pieces, much secondary blasting is necessary, therefore there is a considerable amount of smoke, gas and dust, which requires circulation of a large amount of air to remove the contamination. It is undesirable to use haulage drifts and manways as air passages because some would be passageways for contaminated air also, and there would be undesirable high velocities in some drifts. High velocities and large volumes of subfreezing air dry out the passageways through which they pass, and thus increase the amount of dust. Regulating doors in haulage drifts are difficult of upkeep and interfere with production. It was decided as a general principle to distribute fresh air to each working place at low velocities and low pressures and to remove contaminated air as soon as possible with a minimum of travel through working places.

Jan 1, 1943

By R. J. Stevens

THE Roan Antelope Smelter commenced operations in October, 1931. As originally designed, its equipment consisted of one reverberatory furnace, 120 X 25 ft, two Peirce-Smith converters 12 X 20 ft, and one straight line casting machine. Since that time the following additions have been made: One reverberatory furnace 120 ft X 28 ft (1934) One reverberatory furnace 95 ft X 28 ft (1943) Two 12 X 20 ft Peirce-Smith converters (1934 and 1938) One 13 X 30 ft holding furnace 6 (1938) One straight line casting machine and 2 ladle tilting quadrants (1934) The metallurgy of the smelting process is comparatively simple. However, there are several features of operation which are uncommon to most copper smelters: (1) The high grade of concentrate treated; this has always been about 50 pct copper. (2) The high flux burden on the charge. This is necessary because of the deficiency of bases&apos;in the concentrate and the high alumina content of the concentrate. (3) The frequent necessity of adding coal to the furnace charge to control the matte grade. (4) The high grade of matte produced. This has led&apos; to unusual converter problems. From the commencement of operations, the ore mined has come from the Roan Basin orebody. The concentrate produced from this ore consists mainly of chalcocite and shale with small proportions of other copper minerals. As mining operations extend to the Roan Extension orebody, the proportions of bornite and chalcopyrite in the concentrate will increase with a corresponding decrease in the copper content of the concentrate. Because of the concentrate grade the capacity of the reverberatory . furnaces in terms of tons of copper produced per ton of coal burned is high.. This ratio is usually over 2.2, and on especially favourable runs has reached 2.6. Reference to Table , shows that the iron content of the concentrate is unusually low. Only part of this iron is available for slag formation, the balance going to the matte. To make up this deficiency in bases, limerock is added to the furnace charge. This flux ensures a slag that is of the correct silicate degree, is sufficiently fluid, of low specific gravity, and it counteracts the thickening effect of the alumina present. An ample supply of flux is obtainable from Ndola, 2 2 miles distant by rail. Although the reverberatory slag has a high copper content, the slag fall is low and the copper loss in the slag now rarely exceeds 1.0 pct of the total copper charged. The blister copper shipped is of such purity that only one fire refining operation has been necessary to produce a wirebar with properties comparable to electrolytic copper. Bismuth has always been the most troublesome impurity and consequently the problem of its control in the finished product has been of prime importance. Practically none is removed in the reverberatory furnace. The bulk of the elimina-

Jan 1, 1947

By J. A. Morgan, R. E. Lund, D. E. Warnes

The design, operation, and performance of an integrated pilot plant for recovering zinc and copper from a complex sulfide ore are described. Metallurqical processing comprised selective sulfate roasting in a fluid bed, leaching in a weak sulfuric acid solution, recovering copper by cementation with scrap iron, air oxidation to remove soluble iron, more-or-less conventional Purification for removal of impurities deleterious to zinc electrolysis, recovering zinc by electrolyzing solutions, and recycling spent electrolyte to the sulfating roaster. The effects of several feed preparation and roasting variables on the sulfation response of zinc, copper, and iron are set forth, together with the electrolyzing characteristics of the zinc solutions. SEVERAL years ago, St. Joseph Lead Co. undertook a research program to develop procedures for winning values from a complex ore. The deposit was a massive sulfide ore body containing upwards of 65 pct pyrite. Gangue, composed principally of quartz, calcite, dolomite, and alumina, comprised only 10 to 20 pct of the mineralized zones. Zinc, lead, and copper values were variable, but averaged about 6.7 pct Zn, 2.6 pct Pb, and 0.4 pct Cu. Early in the exploratory test work, it was established that the intimate physical association of the minerals in the ore made beneficiation by conventional flotation procedures difficult. Accordingly, in addition to a comprehensive program to investigate physical methods of ore beneficiation, a research program was established to develop a direct metallurgical method for processing the ore. After surveying a number of potential methods for recovery of both metal and sulfur values, effort was concentrated on the development of a sulfate roasting process. It is the pilot-plant development of the sulfate roasting-solution purification—electrolyzing procedures which forms the subject of the present paper. PREPILOT PLANT INVESTIGATIONS From a thermodynamic viewpoint, it is feasible to sulfate selectively a host of metals, including Zn, Cu, Pb, Cd, Ni, and Co, in an iron sulfide ore without sulfating iron. Of course, a number of conditions such as roasting temperature and gas composition must be controlled. In addition, as first disclosed by Hybinette,&apos; an alkali metal salt is frequently beneficial in promoting the sulfation reactions. The application of fluid bed roasting to the sulfate roasting of nonferrous metals was pioneered by Stephens of Battelle Memorial Institute.&apos; Subsequently, Falconbridge Nickel Mines, Ltd. developed an unique process for selectively sulfating and recovering nickel, copper, and cobalt from their nickeliferous pyrrhotite, which recently has been described in an excellent paper by Thornhill.3 One of the unique features of the Falconbridge process is that the feed is introduced into the fluidized roasting furnace in a manner such that the feed slurry is broken up into droplets and the droplets lose their moisture before contacting the surface of the fluidized bed. The dried droplets do not tend to cake or fuse, but rather remain as discrete agglomerates of concentrate particles and roast without significant degradation. St. Joseph, aware that Battelle Memorial Institute had participated in the development of the Falconbridge process, obtained permission from Falcon-

Jan 1, 1962

By M. R. Tek, K. H. Coats, D. L. Katz

A large number of boundary value problems encountcred in unsteady-state heat transfer, fluid flow through porous media, neutron diffusion and mass transfer involve the solution of a linear, parabolic partial differential equation commonly refcrred to as the diffusivity equation, where U is the dependent potential variable. K is the diffusivity (hydraulic, thermal, neutron, etc.) and 1 is the time variablc. Solutions to Eq. I are available in the literature for a wide variety of initial and houndary conditions. The great majority of these solutions are ohtained for geometric boundaries corresponding to linear. cylindrical or spherical flow models. A typical engineering application where the solution to Eq. 1 is required is the calculation of underground water encroachment across the boundaries of oil or natural gas reservoirs, In this particular area of application, the reservoir boundary is invariably approximated by circular geometry. However. the areal shape of many reservoirs can be better approximated by elliptic rather than circular boundaries. Thus the need for a general method of solving the diffusivity equation in elliptic coordinates arises in this problem as well as in other engineering applications involving elliptic boundaries. The solution to the diffusivity equation usually in volves the Error Function for the linear flow model, Bessel functions for the radial flow model and trigonometric or Legendre functions for the spherical flow model. It is well known that the general solution to the diffusivity equation in elliptic coordinates involves Mathieu functions. The significance of Mathieu functions in the analytical treatment of the diffusivity equation in elliptic coordinates is discussed in the literature However, these references do not providc analytical solutions useful in practical engineering problems. The objectives of this papcr are the development of the equations describing the unsteady-state liquid flow through a porous medium with an elliptic inner boun- dary, the development of a numerical method of solving these equations and, finally, a comparison of the water encroachment quantities calculated from the elliptic flow equation with those calculated from the radial flow equation. While the specific problem treated in this paper relates to unsteady-state liquid flow through a porous medium, the basic equations and computational techniques devcloped will apply equally well to problems occurring in the other areas of engincering interest mentioned previously. The solution given here is limited to a single case in which thc outer boundary encloses an area 100 times that of the inner boundary. DESCRIPTION OF THE FLOW MODEL Fig. 1 shows the flow model upon which the calcu lations presented in this paper are based. The inncr and outer houndaries of the flow model are represented by two confocal ellipses with major and minor axes, respectively, equal to 2a1, 2b1, and 2a, and 26,. The height of the elliptic cylinder flow model is denoted by 17. The following assumptions are employed in the development 01 the equations governing the unsteady-state liquid flow through the described flow model. 1. Uniform porosity and permeability throughout the flow model

By W. M. Johns

The geological mapping of Lincoln and Flathead Counties was a five-year project undertaken by the Montana Bureau of Mines and Geology. This paper, written by the Project Geologist of the survey, is primarily concerned with the stratigraphy of the Belt rocks encountered in mapping. Lincoln and Flathead Counties of northwestern Montana are underlain by sedimentary rocks of the Belt Series of Precambrian age. In only a very small part of the area, near Libby and Troy, have economic mineral deposits been worked with any success. Most of the area has been inadequately mapped as to geology. The region is crossed by the Great Northern Railway and served by the Pacific Power and Light Co.; officials of these two companies believed that with better geologic maps, prospecting might be stimulated and lead to the discovery of mineral resources that would contribute to new economic development within the area. A cooperative mapping agreement was proposed jointly by the two companies to the Montana Bureau of Mines and Geology in May 1958, and thus was born the Kootenai-Flathead five-year project. The dual objectives of this project are: 1) the possible location of mineral deposits of economic value, and 2) the &apos;&apos;stimulation of prospecting exploration" by others. This was to be achieved by geologic mapping of some 6800 sq miles and by establishing a field office in Kalispell where prospectors could come to have their rocks and minerals identified and receive geological advice on their problems. This writer has finished four field seasons as Project Geologist and thus became familiar with the Belt section in the Libby, Yaak River, Ural, Thompson Lakes, Pleasant Valley, and Stryker quadrangles (see Fig. 1). Progress on the project is given in annual reports issued by the Bureau.* This *Montana Bureau of Mines and Geology, Bulletins 12 (1959), 17 (1960), and 23 (1961). paper is concerned essentially with the stratigraphy of the Belt rocks so far encountered in mapping. PREVIOUS WORK IN THE AREA Willis28 made the first study of the stratigraphy and structure in the Lewis and Livingston Ranges of Glacier Park just east of the project area. In 1904, Daly made a study of the Belt rocks of the 49th parallel, using the names from bottom up, Creston, Kitchener, Moyie, and Gateway, for rocks ranging in age from that of Prichard to that of basal Missoula group. Walcott26 studied the Belt rocks exposed in the Mission Range (see Fig. 1) and other areas to the south of the area under discussion. Calkins and McDonald made a reconnaissance of northern Idaho and northwestern Montana in 1905. Calkins was the first to use Walcott&apos;s term &apos;Ravalli&apos; as a group name for the strata equivalent to the Burke, Revett, and St. Regis formations (see Table I). Clapp worked on the Belt of western Montana (including Lincoln and Flathead Counties) throughout his lifetime. The Fentons9 studied the Belt of Glacier Park and

Jan 1, 1962

By Walter J. Mead

By American tradition, if not by rational decision, publicly owned natural resources have been transferred to private industry for processing. The process of transfer requires specific determination of the price which the patentee, buyer, or lessee must pay to the government in exchange for the right to develop a resource, and selection of the patentee, buyer, or lessee from among several possible contestants. Pricing of natural resources owned by the government presents a set of problems quite different from ordinary commodity pricing. Natural resources in situ are not homogeneous commodities. Within any class of natural resources, specific leasable parcels will differ in value by reason of location and accessibility, as well as quality and quantity. Thus, there is no "going price;" every lease within a specific resource class will have a different value. To complicate further the pricing and buyer selection problems, competition may not be reliable. Natural-resource markets are characterized by oligopsony conditions. In a significant number of cases, as will be shown later, there has been only one bidder for a given lease, and in most lease sales the number of bidders is equal to or less than three. As a further complication, there is great uncertainty regarding the value of specific resources, even among the best-informed buyers, as well as within the leasing agency. In some instances, particularly with regard to oil and gas resources, there may be uncertainty about the presence of resources, as well as the quantity and quality of any resources contained in the tract offered for lease. In other cases, such as oil shale and some deep ocean minerals where new technologies are involved, the presence of the resource is clearly established. There may be a relatively high degree of knowledge about the quantity and quality of the resource, but there is great uncertainty concerning the cost of production. These problems in total make it difficult for the leasing agency to appraise accurately the resource to be leased, as well as for the potential bidder to calculate a bid price that will yield him a normal profit. The pricing goal of the federal government as the seller or lessee may be to capture the economic rent; that is, the price of a resource might equal its discounted present value. A required price substantially above this amount would either generate no bids, or, in the long run, would bankrupt the buyer. A price below this amount is a disguised subsidy to the lessee. A subsidy to mineral lessees, as to any other economic interest group, as a minimum should be justified by a clear showing of net external benefits from the economic activity. In the case of timber sales by the U.S. Forest Service, the Forest Service Handbook asserts that "the aim in national forest stumpage appraisal is to determine market value,"8 and "market value" is equated to "fair market value." Regarding minerals, there is no reference in legislation or regula-

Jan 1, 1976

By William Mikulas

LITTLE work has been done in the field of the nickel-tin binary system. The complete diagram has been investigated on two occasions, but the results are in very poor agreement. The structure of a compound NiSn, and the solubility of tin in nickel have been determined by X-ray methods. Several investigations have been made of the liquidus curve, and the compositions of the eutectics have been determined. A study of the literature, however, shows that there is no satisfactory agreement between the data presented in the various papers. The present investigation was undertaken in an attempt to determine the equilibrium conditions, and to correlate X-ray with metallographic data. The equilibrium diagram was determined by thermal and metallo-graphic means, and the solubility of tin in nickel further investigated with X-rays. Powder diagrams were made of the intermetallic com-pounds, and three of the structures were partly determined. No attempt was made to determine the range of homogeneity of the inter-metallic compounds.

Jan 1, 1937

By John L. Lamont, Walter Crafts

SECONDARY hardening in tempering has long been recognized as a typical characteristic of steels containing large amounts of carbide-forming alloys. These steels, when quenched and tempered, tend to soften somewhat after tempering at low temperatures, and to reharden at intermediate tempering temperatures before finally softening to low hardness. This behavior in tempering has been studied by many investigators, chiefly with respect to the secondary hardening of high-speed steels. The initial softening has usually been ascribed to decomposition of martensite and growth of iron carbide particles. The secondary hardening has been explained by formation of fresh martensite from residual austenite, formation of very fine alloy carbide particles and by precipitation hardening of metallic compounds in the ferritic matrix. However, factors derived for the calculation of tempered hardness in low-alloy steels1 indicated only a tendency toward retarded softening rather than a discontinuous rehardening. A study was, therefore, made to determine whether fresh martensite from residual austenite and precipitation hardening are essential to rehardening and the degree to which tempered martensite could be rehardened by precipitation of alloy carbides. The mechanism of carbide rehardening was also investigated to determine the nature of the process. The causes of secondary hardening in high-speed steel have received serious consideration for about thirty years. Among the earlier workers Bain and Jeffries2 in 1923 recognized residual austenite as a significant factor, but in addition, emphasized the effect of the formation of alloy carbide particles of "critical" size. They conceived that freshly quenched martensite forms low-alloy iron carbide at low tempering temperatures; with further tempering the iron carbide is then modified by alloying elements that can diffuse most readily at intermediate temperatures (850°F); and that the iron carbides grow in size by coalescence so that the steel tends to lose hardness. At higher tempering temperatures carbide stability rather than alloy availability becomes the controlling influence and in high-speed steel "iron-tungsten carbide is the most stable one and forms to the elimination of the earlier formed carbides. . . . The iron-tungsten carbide particles reach approximately the size for critical dispersion after a short reheat at 1100°F." This concept, the formation of alloy carbide nuclei, redissolving of the iron carbide, and diffusion of carbon to the alloy carbide, was restated for vanadium steel in 1932 by Houdremont, Bennek, and Schrader.3 Subsequent studies have confirmed that iron carbide changes to alloy carbide at 1000 to 1100°F, but the mechanism of the process has received little consideration .

Jan 1, 1948

By John M. Campbell, W. E. Portman

A series of correlating charts have been prepared to enable the field engineer to predict the amount of stock tank fluid produced by stabilization of first stage separator fluid. The charts shown are particularly convenient for estimating the relative effect of temperature and pressure in economic studies. Further work is planned to investigate the factors affecting stage separation&apos; yo supplement this preliminary work. The direct correlation of separation variables is dictated as a convenience to eliminate the trial and error calculation necessary when using the standard flash vaporization equations. These are obtained by a material balance using the equilibrium vaporization ratio K, and have appeared in the following, or similar. form many times in the literature. where La = mols of any component n in the separator liquid Ko — equilibrium vaporization ratio for any component at separator pressure and temperature Fa = mols of any component n in the feed Vn = mols of any component n in the vapor V = total mols of separator vapor These equations may of course be effectively and accurately solved by use of digital and analog computers. However, these are not usually readily available in field offices and the need often arises for fast results during routine operational problems. Consequently, many methods have been devised in an attempt to simplify the basic calculation.2-14 The methods proposed are generally satisfactory, but do not eliminate trial and error methods and the necessity of subsequent calculations to obtain the answer in volume terms. The purpose of this work. therefore, was to develop accurate charts that would give the result directly in gallons. When using stage separation the recoveries would be lower than those shown, for stabilization usually gives about 95 + per cent recovery on the potential stock tank components in the separator liquid. The recoveries are shown in terms of a 14 psi Reid Vapor Pressure product which has a true vapor pressure of 14.7 psia at 98°F. Consequently, this product represents a stable stock tank liquid under normal storage conditions. To estimate natural gasoline re- coveries by stabilization the volume shown may be multiplied by 1.20 for 18 Ib RVP natural gasoline and 1.36 for 26 lb RVP natural gasoline. PROCEDURE The five analyses shown in Table 1 were chosen since they were representative of wellstream compositions often found and had almost the same propanes plus liquid content, expressed in gallons per 1,000 std. cu ft of wellstream. The distribution of the components though is widely variant. A temperature range of 0-100°F. and a pressure range of 200 to 1,250 psia was chosen inasmuch as most separations fall within these limits The K values used were modified values of those originally published by Katz and Hachmuth.&apos; In the range chosen these have generally given good results when predicting fluid recoveries. The choice was somewhat arbitrary, for the authors&apos; personal experience has shown that

Jan 1, 1957

By Ivor Jenkins

PROCESSES employing controlled atmospheres in the heat-treatment of metals and alloys are now well established on an industrial scale, and the general principles involved and the advantages to be gained in the use of the technique have received considerable publicity over a period of years. During this time the greatest emphasis has been on the establishment of the process in industry, the main effort being devoted to development work on various types of atmospheres, their useful fields of application and the design of suitable heat-treatment furnaces in which they are to be used. The various types of controlled atmospheres are fairly well standardized, but there still remains a considerable field for the investigation of related problems, in connection with both the gas-generating equipment and the surface chemistry of the heat-treatment of metals, especially in complex controlled atmospheres. This paper describes certain investigations of this nature that were carried out in England up to 1939. The development of processes employing controlled atmospheres has been associated to a very large extent with the heat-treatment of steels, both because of the major importance of steel in industry and the many diverse and difficult problems of surface chemistry involved when steels of such a wide range of composition are heated in the presence of active gases Controlled atmospheres such as dissociated and burnt ammonia or charcoal gas are used in the heat-treatment of low-carbon and high-carbon steels, but from certain points of view a suitable atmosphere generated by the partial combustion of city gas is to be preferred. Both the ammonia derivatives are comparatively expensive, and even if the burnt ammonia is regenerated, thereby reducing operating costs, the capital expenditure of the gas plant may make it prohibitive for the smaller type of furnace installation. Charcoal-gas generators are not without their operating difficulties: especially those associated with the quality of the charcoal, clinker formation and the removal of carbon dust from the generated gas. City gas has the advantage of being comparatively cheap and "on tap" in most if not all industrial centers. The use of raw city gas as a protective atmosphere in the heat-treatment of steels has been described,1 but it presents certain difficulties because of its complex composition and its explosive nature when mixed with air. These factors, together with the tendency toward sooting at elevated temperatures, arising mainly from the hydrocarbon gases present, all militate against its use as a protective atmosphere in industrial furnaces. The following analysis, based on the analyses of city gas in different localities in Great Britain, indicates the wide limits existing

Jan 1, 1947

By Nicholas J. Grant, W. Michael Yim

The creep-rupture properties of nickel, in as-prestrained or prestrain-polygonized condition, were studied at 1300°F and 4000 psi, and also at 700°F and 26,000 psi. An improvement of strength was noted in both the as -prestrained and the prestrain-polygonized tests at each temperature. The as-prestrained tests, however, showed superior creep resistance to the prestrain-polygonized ones. From the results of X-ray and etch-pit studies, the strengthc gain was interpreted in terms of dislocation density and the stability of preformed substructures. COLD work is known to improve the strength properties of metals at low temperatures. At high temperatures, however, the strength improvement is often lost if gross structural changes, such as re-crystallization, take place prior to or during the test. Even in the absence of recrystallization, a prestrained metal may undergo structural changes— polygonization and the formation of well-defined subgrains—which importantly effect the resultant properties. The relationship between substructure and creep properties has received considerable attention in recent years. The work of wood1 indicated that the creep strength of aluminum and its alloys was closely related to the subgrain size. Hazlett and Hansen,2 and Ancker, Hazlett, and parker,3 working with nickel and nickel alloys, had shown that small amounts of prestrain at room temperature followed by a recovery anneal at 800°C (1470°F) improved the strength at both low and high temperatures. The strength gain was attributed to an increase in the number of subgrain boundaries as a result of the prestrain-polygonization treatment. More recently Coldren and Freeman4 studied the effect of substructures on the creep rate of nickel at 1550°F. Their conclusions indicated that the substructure size as measured by the number of boundaries was the factor that controlled the creep rate. In addition, the perfection of the subgrain boundary has been indicated to have an important role on the strength.&apos; On the other hand, there are data which disagree with the above observations. Grant, Chaudhuri, Silver, and Ganow6 found no creep strength improvement by a prestraining treatment. In reviewing the role of subgrains on high-temperature creep, Shepard and Dorn7 concluded that the contribution of the subgrains to high-temperature creep strength was a minor one. Guard,8 in a recent study on poly-gonized nickel, has cast doubt on the validity of the postulate that subgrain size controls the creep rate. In the majority of the previous studies, the subgrain boundaries have been singled out as the most important factor in determining creep strength; however, there is no firm theoretical ground for the postulate that the subgrain boundaries act as effective barriers to dislocation motion.B910 Little effort has been directed toward the study of the relationship between creep strength and other structural variables, such as dislocation density, lattice strain,

Jan 1, 1963

By D. Hanson

Fox most of their practical applications metals are required to with-stand stresses of appreciable magnitude: indeed, it is because they possess the quality of resisting stress without becoming permanently deformed that they find such extensive use in the service of man. Metals and alloys must, in service, usually behave as elastic substances-or nearly so. It is not difficult to satisfy this condition at ordinary temperatures. Iron and its alloys, especially the steels, are at normal temperatures excellent elastic bodies, capable of satisfying most of the mechanical requirements of the engineer: where electrical, chemical or other properties are impor-tant, which cannot be met by steels, it is usually possible to find a non-ferrous alloy such as nickel, copper or aluminum, which will prove satisfactory. When the metals or alloys are not inherently sufficiently elastic, cold-working or heat-treatment may develop elastic properties to a sufficient extent for practical needs. By means of relatively simple, rapid tests we can measure such properties as elastic modulus, limit of proportionality and proof stress, upon which design can be based with confidence. The case of the soft metals, such as lead and tin, is well known to be exceptional. They possess no definite limit of elasticity, and the value of proof stress or tensile strength depends to a great extent on the speed with which the test is carried out. Design here must be based on other considerations than a well-established theory of the proportionality of stress and strain. It is now generally recognized that steels and non-ferrous alloys possess at temperatures not greatly exceeding that of the atmosphere, characteristics quite different from those existing at ordinary temperatures, and that they assume qualities similar to those of the soft metals. Not only have they no limit of elasticity, but the proof stress and the ultimate stress depend on the time of application of the load. Flow under load may persist for long periods of time, possibly indefinitely, and the determination of a true maximum stress becomes a matter of great difficulty.

Jan 1, 1939

By W. P. Haynes

ESTIMATED United States crude-oil production during 1943 established a new annual peak of 1,500,000,000 barrels, a daily average of 4,118,000 barrels. This would be an increase of 315,000 barrels per day, or 8 per cent over 1942 and 7 per cent over 1941, the previous peak. During the first ten months of the year, production jumped from 3,782,000 barrels per day in January to 4,400,000 in October. Available data for the last two months of the year indicate a leveling off of this trend, with daily rates slightly above 4,400,000 barrels.

Jan 1, 1944