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By H. B. Pulsifer

ABOUT 15 varieties, or modifications, of the best magnesium available were prepared and subjected to etching tests, then examined for microstructure. Of the 30-odd etching reagents that were tried, nearly half, mostly ammonium salts, etched the metal satisfactorily. The surfacing and etching of magnesium is shown to be a very simple and quick operation. The density and hardness of magnesium were determined. The most interesting new observations relate to the finding of the hexagonal etch figures, the crystal laminations, and the fact that the metal is plastic, cold, when restrained or quickly deformed. Under slowly applied pressure cold metal deforms slightly, then shears to fracture without plastic flow. The chief structural features of magnesium are presented in two reduced photographs and 30 photomicrographs. MATERIALS TESTED There are only two sources in the United States from which new metal can be procured: the American Magnesium Corpn. and the Dow Chemical Co. No pronounced structural or property differences in the metals from these two companies were disclosed by the work of this investigation. The following materials were obtained from the manufacturers: 1. Massive crystals of distilled metal (American Magnesium Corpn.). 2. Rods of hot-extruded metal, ½ -in. squares and 5/8-in. rounds (American Magnesium Corpn.). 3. Sheet magnesium, 0.005-in. thick (American Magnesium Corpn.). 4. Cast stick metal, 1 3/8-in. dia. (Dow Chemical Co.). 5. Magnesium-aluminum alloy, hot-rolled plate, ½ in. thick (American Magnesium Corpn.). From these materials, were prepared: 6. Sections from a furnace-cooled ingot made from distilled crystal. 7. Cold-strained pieces from (6), (4) and (2). 8. Pieces cold-squeezed to fracture from (6), (4) and (2). 9. Hammer-struck pieces from (6), (4) and (2). 10. Steam-hammer struck pieces from (6), (4) and (2). 11. Sections from furnace-cooled ingot of the magnesium-aluminum alloy.

Jan 1, 1928

By AIME

THE wind howls almost incessantly over the mining engineers working in the near desert that is the Division of Namaqualand, the upper Atlantic coastal corner of South Africa's Cape of Good Hope Province. But when these men at the U. S.-owned mines called Nababeep South and East O'okiep (pronounced Oh-keep) tell you about their achievements, they can be heard above the wind. For their O'okiep Copper Co. Ltd. now produces over half the Union of South Africa's annual output of 30,000 tons of copper metal. Moreover, it is a very decent sample of U. S. geotechnical imagination. financial daring, and managerial skill, all operating successfully in a

Jan 1, 1947

By D. Grosse

At the beginning of the 1960's, the Hannoversche Portland-Cementfabrik A. G. needed to open a new quarry. The land on which this quarry was to be developed was completely flat and separated from the existing quarry by a navigable canal. The area had been exploration-drilled previously, so that enough reliable data on the chemical properties of the deposit were available. From the geologic point of view, the deposit under a very moist surface belongs to the Turon (Upper Chalk) formation, soft on the surface and medium to very hard farther down. Between the 15% sloping banks of chalk (with a calcium carbonate content of 75 to 90% and running from west to east), there are numerous beds, up to 3 m deep, which are rich in alumina and iron oxide but contain only 50 to 60% CaCO3. In the old quarry-worked conventionally by deep-hole drilling, a 2-cu-m shovel, and 900-mm track with 6-cu-m dump cars-an adequate and modern crushing plant was available. The plant crushed the moist material (11 to 13% H2O content) down to 0 to 50 mm. INSTALLATION OF ORIGINAL MOBILE CRUSHER It was decided to employ a mobile crushing unit in the new quarry; the moist and soft ground did not permit the use of heavy trucks for transporting the material, and a road network would have entailed a large investment. The use of a rail system was eliminated from the beginning, since the ground would be very uneven after the quarry was developed. At that time only one prototype of a crawler-mounted mobile crushing unit existed. This unit was operating in a nearby works as a primary crusher. A similar, slightly improved machine (Fig. 1) was purchased

Jan 1, 1969

By W. P. Frey

THE briquet plant of the Lehigh Coal and Navigation Co., at Lansford, Pa., has previously been referred to.1 It has passed. the stage of experiment and now rests,, on a foundation practically and financially sound. The purpose of this paper is to explain how success has been attained, and to set standards for the development of hard-coal briquetting which may eliminate future failures. All the conclusions are based on actual results, avoiding speculation and theory. Up to three years ago, the L. C. & N. Co. used coal-tar pitch as a binder in making hard-coal briquets. The plant operated with a monthly output of 300 to 600 tons and was unable to meet its own expenses. Naturally, no one was satisfied, especially as the ideals of a smokeless briquet were still unrealized. Then came the Dutch oil process, introduced in this country by the General Briquetting Co. of New York. This process uses as binder a small percentage of heavy residue of petroleum, which, being liquid, permits great economy of handling; it also did away with the most objectionable fumes of the former briquets. This oil2 is not absolutely smokeless; heating the fresh fuel to red heat liberates some low-volatile hydrocarbons, yielding a white smoke which is not objectionable. On the other hand, this oil adds to the briquet about 7 per cent. of volatile matter, giving the product a heating capacity equal to that of the best free-burning anthracite coal. The average silt used in the manufacture of these boulets averages 16.5 per cent. chemical ash, corresponding to 12,000 B.t.u. per pound of coal. The Hydrolene used as binder runs about 17,500 B.t.u. per pound, and approximately 7 per cent. of it enters into the mixture, hence 12,000 X 0.93 11,160 B.t.u. 17,500 X 0.07 1,125 B.t.u. Total 12,355 B.t.u. per pound of briquets

Jan 1, 1918

By Regis M. N. Pelloux, N. J. Grant

Five or six alloys each in the systems Ni-C.v, Ni-Mo, and NL-W, spaced to cover the single phase areas as well as a part of the adjacent two-phase field, were prepared as uacuum-melted alloys. Tensile tests at room temperature and stress rupture tests at 1200° and 1500°F we.ve run for time periods to give fracture in 0.1 to 500 hr. Observations mere made of solid-solution and second-phase strengthening or uleakening, coupled with studies of ductility and the role of structure on the noted behavior patterns. THE development of stable creep-resistant alloys while broad and systematic is also highly empirical. A number of simple rules have been suggestedL-" but these are based on scant data. Whereas rules for low-temperature alloy strengthening can be applied with some success in more simple systems, the extension to behavior at high temperatures (greater than about 0.4 of the absolute melting temperature) is very poorly understood and has encountered important exceptions and deviations in terms of atom size or valency effects. In particular, the occurrence of both solid-solution weakening4,5 and second-phase weakening2 at high temperatures is of interest. MATERIALS AND PROCEDURE Nickel was chosen as the base material because of its important role in current high-temperature alloy applications, because of its freedom from a phase transformation, and because of wide solubilities for many elements of interest. The selected alloys were single- and two-phase structures in the Ni-Cr,6 Ni-Mo,7 and Ni-w 8 systems. The alloys were vacuum melted and cast, utilizing high-purity raw materials, in the form of 15 lb ingots. They were readily forged into 1/2-in. bar stock (except the two highest chromium alloys). The alloy compositions are shown in Table I. Typical impurity values are: Carbon: Max 0.03 pct (except for 30 and 35 pct Cr alloys which had 0.07) Nitrogen: Max 0.005 pct (except for two of the Cr alloys which had 0.05) Sulfur: Max 0.004 pct Silicon: Max 0.05 pct Each alloy was solution treated (air quenched) to produce comparable grain size. The two-phase alloys were then overaged in an effort to produce a stable structure for testing at 1200° and 1500°F, The results are summarized in Table 11. Following the heat treatments outlined in Table 11, the bars were machined to a gage section of 1.25-in. long by 0.250-in. diam. In addition to room-temperature tensile tests, stress-rupture tests were run at 1200" and 1500°F for time periods from 0.1 to about 500 hr. RESULTS Room-Temperature Mechanical Properties—The ultimate tensile strength, total elongation, and reduction of area values for all the alloys are plotted vs atomic percent of the solute element in Fig. 1. It can be seen that for the same amount of solute element the ultimate tensile strength increases in the order chromium, molybdenum, tungsten. Elongation increases (reduction of area decreases) with increasing amounts of solute for all the solid solution alloys, the values ranging from 50 to 70 pct. The ultimate tensile strength values for the two-

Jan 1, 1961

By Carle R. Hayward

LEAD ore smelting plants have been operating in general at reduced capacities and secondary lead has assumed relatively more importance during the last year. Present smelting practice results in a large amount of dross, often over 25 per -cent, from blast-furnace lead. This is usually treated at a fairly high temperature in a reverberatory furnace to remove part of the lead and produce a matte-speiss product which is shipped to a copper plant. Few smelters are satisfied with this 'treatment. The fume losses are high and the matte-speiss contains considerable lead. It would seem that a fruitful field for research was open here.

Jan 1, 1934

By E. J. KENNEDY

FEBRUARY 15-18 will be the outstanding dates of the month for members of the A. I. M. E., for then the 141st Meeting of the Institute is to be held in the Engineering Societies Building, at New York. What with 41 technical sessions, the Annual Business Meeting at 4 o'clock Tuesday afternoon,, two sessions of the Section and Division delegates, minor committee meetings, and the many luncheons and dinners, the Dinner-Smoker, Informal Dance, President's Reception and the Dinner-Dance, the opportunity will be limited to do- more-than cast sheep's eyes at New York's other multitudinous attrac¬tions until the meeting is over. The technical program is diverse but well organized. The sessions are almost equally divided among the four days, with ten on Monday, Tuesday, and Wednesday, and 11 on Thursday. The meeting opens Monday morning with registration. Be sure to attend to this detail. Failure to do so may have its repercussions at the meeting and throughout the year.

Jan 1, 1932

By Ronald K. Linde

Metastable Ag-Cu solid solutions at two compositions beyond the maximum limits of solubility obtainable by quenching from the solid state were obtained by rapid quenching from the liquid state. The process of transformation of the metastable solid solutions into the equilibrium phases was studied by means of X-ray diffraction intensity measurements and electrical-resistance measurements; metallographic examination was also performed. Results are compared with those for an alloy quenched from the solid state at a composition which exists as a solid solution at elevated temperatures. Activation energies for the trans-formation were computed to be 33,600 * 2500 and 33,100 * 2000 cal per g mole for the 60.1 and 75.0 at. pct Ag;Cu compositions, respectively THE kinetics of precipitation in supersaturated solid solutions obtained by quenching from high temperature has been thoroughly studied in many alloys, and detailed investigations of the early stages of nucleation and subsequent growth of the equilibrium phases have been carried out. All of these studies have been made on alloys quenched from the solid state, however, and it is the purpose of this paper to present some of the results on the kinetics of transformation of metastable solid solutions in Ag-Cu binary alloys whose compositions lie outside of the solid-state limits of solubility. Limits of solubility in the solid state can be increased by rapid quenching from the liquid state. This was first demonstrated by Falkenhagen and Hofmann, who obtained appreciable increases in solubility limits of the elements of the first transition series in aluminum by rapid cooling of liquid alloys through contact with a copper mold maintained at liquid nitrogen temperature.' The same basic idea of cooling a liquid alloy by conduction onto a substrate rather than by convection of a gas or liquid (conventional quenching) has been recently revived and extended to very high rates of cooling by Duwez and his collaborators. The new technique was first applied to Ag-Cu alloys because the existence of a eutectic in this system is not predicted by the Hume-Rothery rules of alloy phase formation. Rapid quenching from the liquid state resulted in metastable solid solutions at all concentrations. The kinetics of decomposition of these metastable solid solutions containing 60.1 at. pct Ag;Cu (eutectic composition) and 75.0 at. pct Ag;Cu is the subject of the present paper. EXPERIMENTAL TECHNIQUES Alloys were made in 10- to 20-g heats using silver of purity 99.99 pet and copper of purity >99.999 pct. Components were weighed accurately to 0.1 mg and melted by induction heating in an alumina crucible under an atmosphere of hydrogen. Weight losses amounted to less than 0.02 ~ct in all cases. Rapid cooling from the liquid state was achieved in an apparatus of the type described by Pietrokowsky. 3 In this technique a freely falling drop of molten alloy is caught between a stationary anvil and a fast moving piston, both anvil and piston being lined with copper. The resulting foils were approximately circular (about 2 cm in diam) and from about 50 to 150 u in thickness, depending on the pressure driving the piston. Metallographic samples were prepared for polishing by edge-mounting foils in Quickmount. The mostef-fective etching procedure was found to be: 10 parts NH4OH (concentrated), 1 part H2O2 (30 pct), 5 parts H2O, swab for 5 to 10 sec. The transformation of the metastable alloys to equilibrium was followed by X-ray diffraction and electrical-resistivity measurements. The peak intensity and the integrated intensity of suitable Bragg reflections of the metastable and stable solid solutions were studied with a Norelco dif-fractometer, using nickel-filtered copper KO radiation. The peaks were step-scanned at intervals of 0.05 deg. Using either a Kelvin bridge or a null circuit with a Leeds and Northrup K-2 potentiometer, the changes in electrical resistance due to phase transformation were measured for specimens cut into strips about 20 mm long and 4 mm wide. All resistivity measurements were carried out at liquid-nitrogen temperature. The isothermal heat treatment was accomplished by sealing the samples in argon-filled aluminum containers with stainless-steel O-rings. Containers were then suspended in wax baths with temperatures in the

Jan 1, 1967

By AIME AIME

THE Coal Division holds its fall meeting in the Pocahontas coal field, at the West Virginian Hotel, Bluefield, W. Va., Oct. 9 and 10. The first day will be a busy one-two sessions for the presentation of papers and a dinner in the evening. Hon. E. Fudge, Assistant Undersecretary, Mines Department, and R. V. Wheeler, head of the Mines Research Board of Great Britain, will be the guests of the Division. Mr. Wheeler will discuss the British Mining Act as relates to the coal industry. George S. Rice, Chief Mining Engineer, U. S. Bureau of Mines, will present an account of the recent meeting at Buxton in England, of representatives of England, Germany, France, Belgium and the United States to formulate a plan and to correlate research work now in progress in the various countries. The second day the members will be the guests of the operators on a trip through the Pocahontas field. The work of preparation for the meeting is being actively pushed by committees headed by T. H. Clagett, R. M. Lambie and H. D. Smith, and a good attendance, both local and from the general membership of the Division, is anticipated. Because many will make the trip by car the principal automobile as well as rail-road connections to Bluefield are given here. The program for Friday, Oct. 9, follows:

Jan 1, 1931

By George R. Mansfield

INTEREST in the reserves of phosphate rock in the United States and their proper conservation has recently been aroused by hearings held in different parts of the country by the "Joint Committee to investigate the adequacy and use of phosphate resources of the United States." This committee was appointed within a few days after a Presidential message to Congress on the same subject, dated May 20, 1938, and began to function almost immediately. Hearings were held in Washington, D. C., Pocatello, Ida., Wilson Dam, Ala., Knoxville, Tenn., and Lakeland, Fla. The resulting testimony, when published, comprised a volume of 1182 pages.1 At the earlier hearings held in Washington and Idaho the seeming disparity between the great reserves of the West and the smaller reserves in the East led to some suggestions as to the desirability of curtailing or even prohibiting the exportation of phosphate rock so that eastern producers, becoming alarmed, cooperated in making available for the use of the committee information hitherto closely guarded. This information has provided an opportunity for new studies by official agencies, for a restatement of the reserves of Florida and Tennessee, and for some modification of figures for the Western States. The writer, representing the Federal Geological Survey, was given free access to the Florida material and has prepared for publication a report,2 some features of which are summarized in this paper. The Tennessee material was studied by Dr. G. I. Whitlatch,3 of the Tennessee Division of Geology. Prof. J. Stewart Williams,4 of the Utah State Agricultural College at Logan, has published a recent study of the phosphate resources of Utah and the writer has given some further study to reserves of western phosphate from the viewpoint of including material of lower grade than that hitherto considered. Technologic advances in the phosphate industry must be credited with a large share in the expansion of reserves by making available for

Jan 1, 1940

By F. E. Jaumot, R. L. Smith

Self-diffusion in zinc at temperatures below 200°C has been studied using both single crystal and polycrystal samples. Anomalous results were obtained for single crystal samples, the data indicating that in some cases grain boundary diffusion predominated. These anomalous results are presumed to be due to low angle lineage boundaries in the single crystals. When volume diffusion occurred in either single or polycrystal samples, the values for the diffusion coefficient were as much as several orders of magnitude larger than would be expected from high temperature data. ONSIDERABLE work has been done on self-^-*diffusion at temperatures in the neighborhood of two thirds of the melting temperature (in OK) and higher, but very little has been done at lower temperatures. This is particularly true of self-diffusion in single crystals. This paper reports work on self-diffusion in zinc at temperatures below 200 °C where both polycrystalline and single crystal samples have been used. The measurements were made using both the sectioning and absorption techniques. The experiments on diffusion at low temperatures were initiated primarily for three reasons: to obtain data from single crystal diffusion covering a wide range of temperatures, to obtain values of the activation energy for grain boundary diffusion, and to obtain, if possible, a lower limit to the temperatures at which the absorption technique may be used. It is possible to determine whether volume or grain boundary diffusion predominates at low temperatures by analyzing the manner in which the concentration of the diffusing atoms varies with the depth of penetration. The analysis is possible only for the sectioning technique. For volume diffusion and for the boundary conditions of the present experiment, the curve of the logarithm of the concentration, C, vs the square of the penetration depth, x, is a straight line with the slope proportional to — 1/D. If grain boundary diffusion predominates, Fisher' has shown that a curve of In C vs the first power of the penetration depth should be a straight line. This linear dependence of concentration on depth has been observed experimentally by several investigators. (See, for example, refs. 3 and 4.) Following Fisher's analysis, the grain boundary diffusion coefficient can be written as where 8 is the grain boundary width, D, is the volume diffusion coefficient at the temperature involved, t is the time of diffusion, C is the concentration of diffusing material, and x is the depth of penetration. A more general analysis employing the same model as Fisher's but with fewer assumptions has been given by Whipple.' In contrast to Fisher's analysis the more general analysis of Whipple does not always yield a straight line relation between In C and x. Recently Turnbull and Hoffman have discussed both analyses and have applied the Fisher-Whipple model to a more refined dislocation model of the grain boundary. They have also discussed the possibility of a large effect of grain boundary direction on diffusion. In the case of the absorption technique, for which results are also given, one simply gets a value for the diffusion coefficient with no indication of the predominating mechanism. Experimental Techniques Single crystals of 99.99+ pct Zn were grown using a modified Bridgman method. Polycrystal samples were prepared in three grain sizes (small, about 4 mm2; medium, about 9 mm'; and large, about 25 mmz) by quenching, air cooling, and furnace cooling. The grains of the polycrystalline samples tended to be columnar, with some preferred texture such that the c-axis was inclined at about 20" to 25" from the normal to the diffusion face, particularly in the medium and large grain size samples. The samples were cut from the rod, polished, and heavily etched, and faces cut accurately parallel using a jeweler's lathe. They were again etched to remove the lathe smear and annealed for 3 hr at 250" to 300°C. After annealing, they were etched, examined, and the orientation determined by Laue back reflection photographs. They were then electroplated with Zn. The plated surfaces were examined for uniformity; nonuniform coatings were removed by etching and the samples replated without additional preparation. For the diffusion anneals, the samples were placed in pairs, with active faces together, in evacuated Pyrex tubes. Constant temperature baths were used, and the variation in temperature did not exceed ±l°C, Diffusion runs were made at l00°,

Jan 1, 1957

By Richard E. Chism

The metric system is now in official use in the Republic of Mexico, having been adopted by the Government in the year 1862. Athough it is used to compute all customs and other duties to be paid to the General Government, in the measurement of public and private lands arid in all freight and other transactions on the railroads, and is taught exclusively in the public schools, the system has made but slight head way among the people,and has not succeeded in displacing the old-time weights and measures, which are still used in ordinary commerce. The latter were founded on old Spanish models, but, owing to the inexactness of the first standards and to subsequent changes, differ at present very widely from their originals. As to local modifications, weights are the same all over the Republic, but measures of the same name differ greatly in capacity in different States, and even in neighboring towns. The value in the metric system here assigned to each denomination of the old weights and measures is that fixed by the Mexican Government at the time of the adoption of the metric system. The equivalents in American weights and measures were calculated by me from data found in Trautwine's Pocket-Book as to the comparison between the French and American weights and measures, and are believed to be correct. I shall be thankful for early notice of any error that may be detected, that it may be corrected before the final publication of this paper in the Transactions. Linear Measures. Kilometers. Miles. 1 legua (league) = 5000 varas . = 4.19 2.604375 Meters. Feet. 1 vara (yard) = 3 pies.....= 0.83800 2.749578 1 pie (foot) = 12 pulgadas.....=0.27933 0.916526 Inches. 1 pulgada (inch) = 12 lineas . = 0.02328 0.916526 1 linea (line).......= 0.00194 0.076577 The vara is also divided (for dry-goods-selling) into palms or cuartas (palms or quarters). Meters. Feet. Inches. 1 palmo or cuarta .. .. = 0.209500 =0.687394 = 8.248728

Jan 1, 1887

The materials used for pump construction vary according to the nature of the solution handled. The pump materials in use are the result of extended experiment and are all giving satisfactory results. Research is still in progress, particularly with stainless steel and rubber lining, both of which show considerable promise. Following are the materials used: For tank-room acid, carrying about 100 grams per liter free sulphuric acid, hard lead is used. Stainless steel is under investigation. Duriron is satisfactory, but requires very careful handling to prevent mechanical breakage. For pulps containing low acid (10 grams per liter), abrasive solids, ferric iron, copper, etc. pumps are made of hard lead. Stainless steel is satisfactory. For pulps containing no acid but carrying abrasive materials and copper, bronze is used. Pulps containing acid (10 grams per liter), copper, iron and nonabra-sive solids require lead pumps. Rubber linings are under investigation. Clear neutral solutions containing copper are handled in bronze pumps; neutral solutions free of copper, acid, abrasive material, etc., in iron or bronze. The hard lead used contains 13 per cent antimony. The stainless steel has the following analysis: Cr, 20.0 per cent; Ni, 7.0; C, 0.25; W, 4.0; Cu, 2.0.

Jan 1, 1937

By Lucien Eaton

INCREASED mining activity during the past year has brought to light changes in mining practice and advances in technique, born and incubated in the period of depression from which the mining industry is now emerging. Although the tendency toward large output from individual mines has continued, a salutary trend is evident toward greater efficiency at small mines, in which the gold mines of Canada have led the way. Improvement in excavating machinery and washing plants for small placers has continued, and knowledge of the possibilities and limitations of this kind of equipment has increased. Greater portability through sectionalization has been the keynote. Power, shovels and draglines mounted on caterpillar treads move from one deposit to another under their own power, and floating washing plants mounted on pontoons can be taken down, moved, and set up again by a small crew of men in only a few days.

Jan 1, 1937

By D. R. de Fontaine

By computing the values of the resolved shear stress for a great many orientations of the tensile axis on all 12 (111) <110> slip systems, Taylor and Elam&apos; were able to map out a stereogram of slip systems, given here, Fig. 1, in Diehl&apos;s notation (see, for example Hauser and Jackson&apos;). The purpose of the present note is to derive such a stereogram by mathematical reasoning and to give a simple method of defining the system with highest resolved shear stress for any direction of the tensile axis, thereby eliminating tedious computation of the Schmid factor. Let the tensile axis, of direction cosines [xyz], make the angles 0 and relative to the slip plane normal [HKL] and the slip direction [hkl] respectively. Fig. 2 shows a simple cubic cell whose edges define a Cartesian coordinate system. Let A be a unit vector of origin 0 supported by the tensile axis. Its end point [xyz] then lies on a sphere of unit radius, on the positive hemisphere of which the planes z = 0, x = y, y = z limit the so called primitive triangle of a standard [loo] stereographic projection. For any point of this triangle, the following hold: 0«2 «y *sx « 1 [l] Now, for given [xpz], the most highly stressed system will be the one for which the following expression of the Schmid factor has the largest possible value: (HKL) belonging to the form (111) and [hkl] to the form <110>, the denominator on the right hand side of Eq. [2] is equal to 1.fi.a. The unknowns H, ... h, . . . can now be determined by correctly distributing +1 and -1 to H, K, L, and +1, -1,O to h,k, 1 giving the numerator of Eq. [2] its greatest positive value (the angles 0 and cpare chosen acute) subject to the condition: Hh+Kk+Ll = 0 [3] since the slip direction must lie in the slip plane. Condition [3] can be satisfied only by having one of its terms vanish and the other two equal to +1 and -1. Taking the case of the tensile axis lying in the primitive triangle, x2y, z and therefore Hh will be chosen equal to +1 with H = h = +1 in order to retain a maximum of + signs. There remain two alternatives: either 1 = 0 or k = 0. 1) take 2 = 0 Then Kk = -1 and the numerator of [2] becomes: Retaining a maximum of + signs gives L = k = +1 and becomes: 2) take k = 0 Then L1 = -1and, likewise, the numerator of [2] becomes: xz - z2 + xy + yz [5] But the difference [5] - [4] can be written: (y - z)(x+y +z) [6] positive or zero by virtue of [I]. If [6] is positive (y > z), then the largest possible value for the numerator of [2] for any xyz inside the primitive triangle is given by [5], i.e., for: That is to say, the active slip system corresponding to an orientat:~on of the tensile axis inside the primitive triangle is:

Jan 1, 1962

By G. Rowan, M. W. Clegg

Approximate analytical solutions for non-Darcy radial gas flow are derived for bounded and infinite reservoirs producing at either constant rate or constant pressure. These analytical solutions are compared with published results for non-Darcy flow obtained on digital and analogue computers, and the agreement is show to be very good. Some observations on the interpretation of gas well tests are made. INTRODUCTION The flow of gases in porous media is a problem that has been the subject of much study in recent years [l - 71 , and many methods have been proposed for solving the non-linear equations associated with it. The assumption that the flow satisfies Darcy&apos;s Law It has been observed, however, that the linear relationship between the flow rate and pressure gradient is only approximately valid even at low flow rates, and that as the flow rate increases the deviations from linearity also increase. It has been suggested by a number of authors that Darcy&apos;s Law should be replaced by a quadratic flow law of the form This form of equation was first suggested by Forchheimer [9] and, later, Katz and Cornell [10], and Irmay [lll, developed a similar equation. Houpeurt [12] derived this form of equation using the concept of an idealised pore system in which each channel consists of sequences of truncated cones giving rise to successive restrictive orifices along the channel. This type of representation leads to a quadratic flow law of type [4], for all fluids, but it is found that the quadratic term is only significant in the case of gas flow. The methods of Houpeurt for solving gas flow problems will be discussed further in another section of this paper. Solutions of the non-linear equation for Darcy gas flow 121 may be classified as either computer (digital and analogue), or approximate analytical ones. The former include the well-known solutions of Bruce et al. [13], and Aronofsky and Jenkins [14] , but the latter solutions, apart from the simple linearisation of equation (2) to yield a diffusion equation in p2 , are not so well-known. Amongst these approximate analytical solutions should be mentioned the work of Barenblatt [IS], who has applied the techniques of dimensional analysis to obtain similarity solution to a large class of non-linear equations; also, a number of Russian authors, including Barenblatt [16] , Kim [17] and others, who have used the method of moments for obtain-

Jan 1, 1965

By H. W. Mead, C. E. Birchenall

SELF-DIFFUSION of iron in austenite is a process which may play a significant role in some of the practically important reactions which occur in solid irons and steels. It also provides a system in which the interaction of vacancies on substitutional sites and atoms in interstitial positions may be investigated. For both purposes, accurate values of the diffusivities are required. Two sets of previous measurements exist, each containing features which require checking. In the course of an investigation to determine the rate of diffusion of iron in certain steels, Garwick and Rosenqvist&apos; measured the self-diffusion coefficient of iron in a 0.10 pct* C steel and obtained a dicated that while at lower temperatures D increased with increasing carbon content, at the higher temperatures it first increased and then decreased. At the same time the activation energy decreased linearly from a value of 69,000 cal per g-atom for pure iron to 33,000 cal per g-atom at 1.06 pct C. This rapid decrease in activation energy implies that iron at higher temperatures within the austenite range would diffuse more slowly in high carbon steels than in steels of lower carbon content. Experimental Procedure The radioactive iron used in this work was obtained from Oak Ridge National Laboratory. The unit consisted of about 1 microcurie each of Fe7 and Fe It was allowed to decay for two years. At the end of this time most of the Fe with a half-life of 46.3 days, had decayed, while most of the original Fe(half-life 2.91 years) still remained. The iron as chloride was extracted into an ether layer, using the method of Ashley and M~rray. After evaporation of the ether the iron chloride was dissolved in 250 ml of aqueous solution containing 2.4 gpl Fe. The compositions of the steels used are listed in Table I. Disks of ¾ in. diam and about ¼ in. thick were machined from these steels for use in diffusion couples. The disks were surface ground on both sides to ensure parallel opposite faces. One face of each disk was polished through 000 emery paper. Half of the prepared disks were plated with radioactive iron. For this, 1 ml of the radioactive iron

Jan 1, 1957

By A. S. Yue

Small-angle tilt boundaries have been observed in a lamellar eutectic structure. These boundaries are morphologically similar to a theoretical till boundary originally proposed by Burgers. The production of a small-angle tilt boundary in the lamellar eutectic structure is attributed to the formation of an indentation on a planar solid-liquid interface during growth. Constitutional supercooling due to the accumulation of impurity atoms ahead of the interface is primarily responsible for the generation of an indentation. The distance between two faults of like sign, designated as lamellar fault distance, is calculated by the Burgers equation for small-angle boundaries. It was found that the lamellar fault distance decreases exponentially and the tilt angle increases exponentially with freezing rate. SMALL-ANGLE tilt boundaries have been observed in many crystals in the as-grown states by etching techniques. However, a detailed substantial proof for revealing the presence of dislocations in the form of etch-pits was recently accomplished by Vogel. These boundaries are described as an array of dislocations of like sign. The angle of tilt associated with a boundary is treated theoretically by Burgers3 and is given by 0 = b/D for small tilt-angle where b is the Burgers vector of the dislocations and D is their average spacing. During the course of experimentation on the solidi fication of the lamellar Mg-32 wt pct Al eutectic a microstructure which was strikingly similar to a dislocation tilt boundary was observed. An example of the type of microstructure is given in Fig. 1, which shows a combination of transverse and top sections of the lamellar eutectic structure. The lamellae of the top section on one side of the apparent tilt angle are not parallel with those on the other side. Consequently, some lamellae must be terminated somewhere. Fig. 1 shows that the termination of lamellae is analogous to a dislocation tilt boundary in a crystal lattice originally proposed by Burgers. This work represents a closer look at such structures. The factors governing the production of the small-angle tilt boundary are discussed in terms of the freezing condition and impurity distribution in the melt. The effect of freezing rate on the distance between two faults, designated as lamellar fault distance, and the tilt angle is also described. In addition, the lamellar fault distance is determined by means of the Burgers equation for small-angle tilt boundary. EXPERIMENTAL PROCEDURE The slightly impure Mg-32 wt pct Al eutectic rods, 5/8 in. in diam and 12 in. long, were made from 99.99 wt pct Al and 99.98 wt pct Mg and were cast in a high-purity graphite mold. Some of these rods were purified by zone-refining the eutectic using direct-radiation helical-coil furnaces5 A molten zone about 2 in. long was passed through the cast rods at a speed of 5.3 x 104 cm per sec for ten passes of the molten zone. Before the freezing experiment was begun, 2-1/2 in. of the material from the head and tail ends of the zone-refined eutectic were removed from the rod to eliminate any impurity. The freezing experiments were carried out under controlled conditions,8 using a protective atmosphere of purified argon. At the end of each run, observation of the tilt boundary was made throughout the entire length of the rod with a light microscope on the top, longitudinal, and transverse sections (three mutually perpendicular sections) of the lamellar eutectic solid. The experimental data used for the determination of interlamellar spacing and tilt angle were taken from the middle portion of

Jan 1, 1964

By M. T. Hepworth, T. P. Papazoglou

Hydrogen diffusion in hcp and bcc titanium in the temperature range 610° to 900°C was measured by reacting cylindrical specimens of high-purity titanium at constant temperature with small constant pressures of hydrogen of the order of a few Torr. In the range 0 to 6.7 at. pct H in hcp titanium, the diffusion coefficient D in sq cm per sec is given by: where T is in °K and R in cal per g-atom OK. Only three measurements of diffusivity in bcc titanium were made: at 900&apos; : the diffusivity in ß titanium was found to be 1.8 x 10-4 sq crn per sec. McQUILLAN1 has studied the constitution of the Ti-H system and reported the concentration of hydrogen as a function of pressure of hydrogen and temperature. He found hydrogen absorption was reversible and rapid at temperatures above 500°C in both crystallographic modifications, the a (hcp) phase and the ß (bcc) phase, with the latter phase stabilized by hydrogen additions. Wasilewski and Kehl 2 measured the diffusivity of hydrogen in hcp and bcc Ti-H alloys. For bcc alloys, they reacted cylindrical specimens of titanium with hydrogen gas at 1 atm pressure. They measured the rate of absorption of hydrogen isothermally on specimens ranging from zero hydrogen content when above the transformation temperature to hydrogen contents sufficient to stabilize the bcc phase when below the transformation temperature. By integrating Fick&apos;s second law for a cylindrical geometry, assuming a diffusion coefficient independent of composition, they calculated diffusivities as a function of temperature. In the range 650" to 1000°C their results in bcc titanium yielded the expression: where D is in sq cm per sec, T in OK, and R the gas constant in cal per g-atom-OK. Their studies on the hcp a phase were conducted by exposing long cylindrical titanium specimens to hydrogen at a sufficiently high pressure to establish a surface layer of fl phase 80 to 120 u thick for the duration of an isothermal experiment. Concentration profiles were then determined by hydrogen analysis from chips obtained upon machining quenched specimens. The diffusivity of hydrogen was then calculated yielding the expression: The present investigation was undertaken principally to redetermine the diffusivity data on a titanium by a direct absorption from the gas phase at sufficiently low hydrogen pressures to avoid the presence of a surface bcc phase and also to check the diffusivity data at low hydrogen concentrations in the bcc stmcture. EXPERIMENTAL PROCEDURE High-purity electrolytic sponge titanium (99.9 pct) of BHN 91 was arc-melted, forged, rolled, and machined into cylinders of final hardness, upon annealing, of BHN 92. Cylindrical specimens of two sets of dimensions were used: 1.524 by 2.931 cm and 1.905 by 3.663 cm diam and length, respectively. The experimental apparatus used for annealing specimens and for admitting known amounts of hydrogen at constant pressure is shown in Fig. 1. In a typical experiment, a specimen was lightly abraded with fine-grain silicon carbide, washed with water and detergent, and then thoroughly degreased with reagent-grade tri-chlorethylene and acetone. The specimen was suspended by a Chrome1 wire in the center of a quartz furnace tube, without contact with the tube, and heated to 925°C (as measured by a thermocouple adjacent to the specimen, outside the tube) for a period of at least 4 hr under a vacuum of from 10-6 to -7 Torr as measured by an ionization gage. The furnace temperature was then adjusted to the temperature chosen for the particular diffusion study and the specimen allowed to equilibrate thermally. Hydrogen was then ad-

Jan 1, 1969

By J. Szekely, G. P. Martins

A formulation is given and a general analytical solution is presented for the problem of spherical phase growth in multicomponent systems. The results are valid for describing the rate of bubble growth in the absence of translational motion and, therefore, should be relevant to heterogeneous nucleation processes. Typical worked examples are given, which include bubble growth due to the simultaneous diffusion of hydrogen and nitrogen in molten steel, and the growth of CO bubbles in steel, due to the reaction: C + 0 = CO. The calculations predict that the presence of additional components would enhance the growth rate and also increase the absolute rate at which the individual components are transferred into the bubble. These findings should be relevant to degassing processes. THE problem of spherical bubble growth in the absence of translational motion is appropriate to the description of the heterogeneous nucleation and subsequent growth of gas bubbles while attached to a solid surface. Such problems are of considerable practical relevance to various vacuum degassing and steelmaking processes where bubble nucleation and subsequent growth play an important part in the overall reaction mechanism. A definitive formulation of spherical phase growth has been given in the now classical paper by Scriven1 and the analogous problem for solid phase growth has been discussed by Horvay,2 furthermore a thorough review of the relevant literature has also become available.3 All this previous work was concerned with one component or binary systems. The purpose of this paper is to show that the technique developed by Scriven may be generalized to alow the consideration of multicomponent systems. The results of this generalization would be particularly relevant, as gas bubble nucleation in the metallurgical systems previously mentioned frequently involves the simultaneous diffusion of several components. In the following a general formulation is given and typical worked examples are presented. FORMULATION Consider the growth of a spherical gas bubble due to diffusion in a quiescent liquid of infinite extent, as sketched in Fig. 1. The formulation of such problems requires the statement of the following conservation equations relating to the liquid phase: Equation of continuity Equation of motion Conservation of the diffusing species—Diffusion Equation. The following assumptions are made: a) The fluid is incompressible, quiescent, and of infinite extent b) The bubble is stationary, i.e., it undergoes no translational motion c) Spherical symmetry is observed throughout d) The mass diffusivity is constant e) Chemical equilibrium exists at the surface of the bubble, and any reactions occurring there are fast compared to the diffusion process f) Inertia and surface tension effects are neglected. Equations derived on the basis of these assumptions by previous investigators were found to provide a reasonable representation of bubble growth while attached to a surface in organic and aqueous systems4,5 For gas bubble growth in molten metal systems assumptions a) to d) chould hold reasonably well. The exclusion of chemical kinetics as a possible rate limiting step may not be universally valid, but should hold for many systems operating at high temperatures. The effect of hydrodynamic inertia may be neglected for moderate growth rates; finally, the assumption neglecting the effect of interfacial tension on the bubble growth was made for the sake of mathematical convenience; its inclusion would have required the use of quite cumbersome numerical techniques. While surface tension effects could be appreciable on the initial values of the overall growth rate, especially at low absolute pressures and in case of small bubbles, they are not thought to modify the relative effects present in multicomponent systems, the study of which is the objective of this paper. Within the framework of the above assumptions

Jan 1, 1970