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By R. W. Heckel, R. A. Tanzilli

Treatment of the finite, diffusion-controlled, two-phase, moving-interface homogenization problem has been carried out by numerical methods for a wide range of input parameters. Solutions have been obtained for planar, cylindrical, and spherical diffusion geometries. The effects of parameters such as the interdiffusion coefficients (concentration-independent) of- both phases, the concentrations (time-independent) of each phase at the interlace, mean composition, initial size of the dissolving- phase, and initial composition of- the two phases are considered. The results are displayed to show both the position of the interjace and the degree of homogenization (expressed in terms of concentration at the matrix phase symmetry boundary) as a function of diffusion time. Typical exaw~ples to which the results may be applied are discussed. A limited number of exact, closed-form solutions to the multiphase, diffusion-controlled, moving-interface problem exists in the literature, e.g., Refs. 1 to 7. The exact, closed-form solutions generally consider the outermost phases to be infinite in extent and also assume an interfacial velocity function. It is through use of such boundary conditions that closed-form solutions are readily obtained. An extensive literature also exists on numerical solutions to the mathematically analogous solidification problem, e.g., Refs. 8 to 12. In addition, a numerical solution involving mass transfer with spherical interfaces and infinite boundaries has recently been carried out.13 A practically important class of diffusion problems exists, however, in which the boundaries of each phase away from the interface are finite. For example the finite boundary condition arises when one sets up a model for analyzing the homogenization behavior of two-component powder compacts in two-phase systems or for studying the solution behavior of precipitates. Although exact, closed-form solutions have as yet not been found to this class of problems, solutions are possible using numerical methods. The purpose of this paper is twofold: 1) to describe a numerical method for treating the two-phase, diffusion-controlled, moving-interface problem involving finite boundaries with planar, cylindrical, and spherical interfaces; 2) to present the results of a parametric study which identifies the role played by each variable appearing in the analytical model. R. A. TANZlLLI,Student MemberAIME,onleaveofabsence from the General Electric Co., Re-entry Systems Department and A. W. HECKEL, Member AIME, are Graduate Student in Materials Engineering, and Professor, Department of Metallurgical Engineering, respectively, Drexel Institute of Technology, Philadelphia, Pa. Manuscript submitted May 6. 1968. IMD MATHEMATICAL MODEL The three geometries analyzed are shown in Fig. 1. For each configuration a symmetry element is shown, across whose boundaries the mass transfer is zero. Mean composition, C, and the characteristic solute-rich phase half-thickness (or radius), 1/2, are the independent variables while the characteristic symmetry element half-thickness, L/2 (measured from solute-rich phase center to the matrix phase plane of zero mass transfer), is a dependent variable. The symmetry element for a planar interface accurately represents a real diffusion situation involving the stacking of symmetry elements of constant size. Because cylindrical and spherical symmetry elements of constant size cannot be stacked to fill space, the meaning of the dimension, L/2, for these situations may be considered in terms of the following approximations: and where NA is the number of parallel cylindrical elements per unit area on a surface normal to the cylinder axes and Nv is the number of spherical elements per unit volume. The model consists of a solute-rich phase matrix phase composite of limited mutual solubility. The concentrations at the interface are assumed constant with time; no assumption of local equilibrium at the interface is necessary except for the case where the

Jan 1, 1969

By Earl Greiner

THE constitution of the iron-silicon alloys containing from 14 to 33.4 weight per cent silicon has been studied by a number of investigators, whose results have been reviewed in a monograph published by the Engineering Foundation1. In these previous researches, the solubility of silicon in iron was determined by thermal, microscopic or magnetic methods and the compound Fe3Si2 was reported to be stable at tempera-tures from 0 to approximately 1030° C. This paper describes the results of an X-ray investigation of the solubility of silicon in iron and gives data which prove that the Fe3Si2 phase is unstable below 825° C. In order to obtain the present results on the solubility of silicon in iron, the authors have utilized the lattice constants of the alpha-phase iron-silicon alloys given in a previous publication2, and also some addi-tional data which will subsequently be described.

Jan 1, 1936

By George S. Rice

The subject of violent bumps in coal mines has been again brought to attention by a recent succession of such occurrences in the coal mines of the Cumberland field of eastern Kentucky and southern Virginia, which have caused fatalities and injuries to underground employees, a report on which is being issued by the United States Bureau of Mines1. The A.I.M.E. has had two valuable papers on bumps in the No. 2 Mine, Springhill, Nova Scotia, each followed by general discussion on bumps and their causes2. This paper gives a brief review of suggested causes and remedial measures given in English, Canadian and United States reports on blimps in coal mines, and then presents suggestions arising from the writer's recent investigation of the bumps in the Cumberland mines, made at the request of the mine operators, to determine the causes and remedies. These bumps, which occur under the simplest natural conditions, provide better opportunity for analysis of causes and effects than afforded under more complex conditions. The simple conditions in this field consist of relatively thin and level coal beds and uniform roof strata free from folding and faulting. Definition of Bumps Bumps in coal mines, as defined in this paper, are sudden violent bursts of coal that usually occur without warning in the extraction of pillars and may or may not be accompanied incidentally by falls of draw slate, upheaval of bottom and smashing of timbers. They are not known to occur where the advancing longwall method of mining, accompanied by

Jan 1, 1936

By George S. Rice

The subject of violent bumps in coal mines has been again brought to attention by a recent succession of such occurrences in the coal mines of the Cumberland field of eastern Kentucky and southern Virginia, which have caused fatalities and injuries to underground employees, a report on which is being issued by the United States Bureau of Mines1. The A.I.M.E. has had two valuable papers on bumps in the No. 2 Mine, Springhill, Nova Scotia, each followed by general discussion on bumps and their causes2. This paper gives a brief review of suggested causes and remedial measures given in English, Canadian and United States reports on blimps in coal mines, and then presents suggestions arising from the writer's recent investigation of the bumps in the Cumberland mines, made at the request of the mine operators, to determine the causes and remedies. These bumps, which occur under the simplest natural conditions, provide better opportunity for analysis of causes and effects than afforded under more complex conditions. The simple conditions in this field consist of relatively thin and level coal beds and uniform roof strata free from folding and faulting. Definition of Bumps Bumps in coal mines, as defined in this paper, are sudden violent bursts of coal that usually occur without warning in the extraction of pillars and may or may not be accompanied incidentally by falls of draw slate, upheaval of bottom and smashing of timbers. They are not known to occur where the advancing longwall method of mining, accompanied by

Jan 1, 1936

By A. T. Miesch, L. B. Riley

An error occurred in the preparation of Fig. 3, p. 249, of Basic Statistical Measures Used in Geo-chemical Investigations of Colorado Plateau Uranium Deposits. This figure shows the relation of the arithmetic mean: geometric mean ratio to the geometric deviation. Curves for the cases where n, the number of samples, is 100, 10, and 5 are too high with respect to the ordinate. The error is negligible at low geometric deviations, but becomes increasingly greater wi,th higher values of geometric deviation. Arithmetric mean values in Table I1 are not effected by the errors in Fig. 3. The authors will endeavor to supply copies of the revised curves on request; write to: A. T. Miesch, Geologist, Branch of Radioactive Materials, U.S. Geological Survey, Bldg. 25, Federal Center, Denver 25, Colo.

Jan 1, 1962

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By H. W. Hockin, D. r. Brandt, R. H. Walsh, P. L. Dietz, P. R. Girardot

New Jersey, Florida, and Canadian ilmenites were reduced with hydrogen or coke under various experimental conditions and the phase changes occurring in the ilmenite upon reduction have been studied by microscopic examination of polished sections and by X-ray diffraction. The products formed were dependent upon the type of ilmenite, temperature, time and reducing agent. Of the reducing agents, hydrogen was the more effective at lower temperatures. 1 HE possible utilization of ilmenite as a source of both iron and titanium has resulted in the development of a number of methods for the separation of the iron and titanium content. Slagging processes as currently used in Canada are typical of such methods. Somewhat less attention has been given industrially to the reduction of the iron content at less than the slagging temperature. Although references maybe found to such work, in general only one type of ilmenite, either natural or synthetic, has been studied by each author. We have attempted to draw some relationship between the results of experimental reduction and the type of deposit from which the ilmenite was derived, as evidenced by phases occurring in the ores and in the reduction products. Ilmenite ores having from 27 to 61 pct titanium dioxide were included in this study and in each case reduction was carried out at such temperatures that only limited coalescence of the particulate iron product occurred within the ilmenite grains. The history of the individual ilmenite samples and the temperature of reduction were found to determine the occurrence of various phases and the mode of distribution of the iron. REVIEW OF EARLIER WORK ON REDUCTION One of the earliest references to the reduction of ilmenite at less than the slagging temperature was made in 1917.' The metallic iron produced was_____ leached out by the action of dilute sulfuric or hydrochloric acid, to leave a product high in titanium dioxide. Subsequent to this, numerous patents2-'? and other references13"21 have appeared concerning reduction of ilmenite by carbon, hydrogen, carbon monoxide, methane, coal gas, water gas, or the like in the absence of fluxing agents. Mineragraphic examinations were not reported, and in the main, the only examinations made were chemical analyses. However, in two cases3,13, titanium suboxides were reported in the products and in one case2' rutile was reported, in addition to metallic iron. Both were identified by X-ray diffraction. While reductions in the absence of fluxing agents were generally followed by either a wet or dry chemical process for removal of the metallic iron, a Canadian source17 reported removal of the metallic iron by magnetic separation. By the addition of fluxing agents during reduction, the metallic iron has been coalesced into "pearls." Each reference to such a process23-28 has shown that the coalesced iron could be removed by magnetic or gravity means after the product was crushed. In the absence of fluxes, the coalescence did not generally occur. The major part of the present study has been limited to reductions without fluxing agents in order to determine the primary reactions of naturally occurring ilmenites. Titaniferous iron ores have also been studied,29-33 17, l9 their reduction having been used as the basis of a commercial process for beneficiation of such ores in Norway29 and more recently considered in the United States34,35. The ease of reduction of titaniferous iron ores relative to that of hematite or magnetite has been referred to,33 with the conclusion that the more

Jan 1, 1961

By C. A. Siebert, G. Sandoz

Oil quenching of steel, in good commercial practice, is carried out using a great deal of agitation in the quenching bath. Many of the tests reported in the literature represent the results obtained on steels quenched into still oil. Scott1 describes three stages of cooling in liquid quenching baths, namely: "State 'A'— Vapor Blanket Cooling—In this, the first stage, a thin stable vapor film surrounds the hot metal. Cooling is by conduction and radiation through the gaseous film and is therefore relatively slow. "Stage 'B'—Vapor Transport Cooling— Termination of the 'A' stage is marked by wetting of the metal surface. Vapor forms copiously in bubbles and is carried away by gravity and convection currents to condense in cooler surrounding liquid. This is the fastest stage of cooling. "Stage 'C'—Liquid Cooling—The 'B' stage ends as the surface temperature of the metal approaches the boiling point of the quenching liquid. Vapor no longer forms, so cooling is by conduction and convection and the temperature difference is greatly decreased. This mode of cooling is slower than that of the 'B' stage." Mechanical agitation of the quenching medium will accelerate all three stages of cooling. The greatest effect, however, will be noted on stage ' B' because the removal of the bubbles from the surface of the steel will not be entirely dependent upon gravity and natural convection currents. The method employed in this investigation for evaluating the oils was the end quench test. The various oils were substituted for water as the quenching liquid and hardness determinations were made at various distances from the quenched end. Most of the tests were run using a 3/8-in. orifice with a 21/2-in. stream height. However, to check the effect of other velocities two additional conditions were used, namely: (I) A 3/8-in. orifice and I-in. stream height, and (2) a 1/2-in. orifice and a 31/2-in. stream height. In all cases the samples were suspended so that the quenched end was 1/2-in. above the orifice. Some tests were run on an NE 8740, .3,312, and a 4340 steel. The results obtained on these steels confirmed those obtained on the NE 9450 and have therefore been Omitted from this paper. The test bars were machined from 1/8-in. stock to I-in. diam by 4 in. long.

Jan 1, 1949

By G. Sandoz, C. A. Siebert

Oil quenching of steel, in good commercial practice, is carried out using a great deal of agitation in the quenching bath. Many of the tests reported in the literature represent the results obtained on steels quenched into still oil. Scott1 describes three stages of cooling in liquid quenching baths, namely: "State 'A'— Vapor Blanket Cooling—In this, the first stage, a thin stable vapor film surrounds the hot metal. Cooling is by conduction and radiation through the gaseous film and is therefore relatively slow. "Stage 'B'—Vapor Transport Cooling— Termination of the 'A' stage is marked by wetting of the metal surface. Vapor forms copiously in bubbles and is carried away by gravity and convection currents to condense in cooler surrounding liquid. This is the fastest stage of cooling. "Stage 'C'—Liquid Cooling—The 'B' stage ends as the surface temperature of the metal approaches the boiling point of the quenching liquid. Vapor no longer forms, so cooling is by conduction and convection and the temperature difference is greatly decreased. This mode of cooling is slower than that of the 'B' stage." Mechanical agitation of the quenching medium will accelerate all three stages of cooling. The greatest effect, however, will be noted on stage ' B' because the removal of the bubbles from the surface of the steel will not be entirely dependent upon gravity and natural convection currents. The method employed in this investigation for evaluating the oils was the end quench test. The various oils were substituted for water as the quenching liquid and hardness determinations were made at various distances from the quenched end. Most of the tests were run using a 3/8-in. orifice with a 21/2-in. stream height. However, to check the effect of other velocities two additional conditions were used, namely: (I) A 3/8-in. orifice and I-in. stream height, and (2) a 1/2-in. orifice and a 31/2-in. stream height. In all cases the samples were suspended so that the quenched end was 1/2-in. above the orifice. Some tests were run on an NE 8740, .3,312, and a 4340 steel. The results obtained on these steels confirmed those obtained on the NE 9450 and have therefore been Omitted from this paper. The test bars were machined from 1/8-in. stock to I-in. diam by 4 in. long.

Jan 1, 1949

By H. M. Chance

In recent years an important function of the mining engineer has been the appraisal of the value of mining-properties required by those planning consolidations of a number of' individual operations. In no field of productive industry have the economic results attainable by consolidation been more clearly shown than in the mining-regions of the United States. In many important mining-centers unification of ownership of the most valuable properties has already partially or completely been attained, and, in other districts, projected absorptions and consolidations await only favorable financial conditions for their consummation. The iron-ore districts of the Lake Superior region, the coal-mines of Colorado, of Wyoming and of Utah, the anthracite mines of Pennsylvania, the Connellsville coking-coal mines, and large areas of bituminous coal-land in Pennsylvania, in Ohio, in the Indian Territory and in other portions of the United States, are now largely controlled by a few corporations operating on a large scale, or by a number of corporations working in harmony because of an affiliation and interleaving of interests. The tact of keen financiers and the diplomacy of men of great administrative ability are the chief operative forces in conceiving and accomplishing such consolidations, but in formulating and maturing them, the services of the mining engineer are often required to supply the facts upon which they must be based. For this purpose the expert is expected to furnish full and complete reports covering the quantity of ore, coal or other mineral available, its value per ton, cost of mining and treatment, etc. In reporting upon gold-, silver-, lead-, zinc-, copper- or iron-

Jan 1, 1905

By Jack Green

Within three major tectonic time frames of earth history: Microplate (±3.8 - ±2.6 billion years), intraplate (±2.6 - ±1.3 b.y.), and macroplate (=1.3 b.y. - present), precious - metal deposits are confined to specific structural, depositional and physico-chemical environments. Precambrian primary gold deposits are localized in two microplate greenstone episodes (±3.7 and ±2.7 b.y.); secondary gold in Witwatersrand placers (±2.6 b.y.). Precambrian primary platinum group metals are in anorthositic facies of layered mafic intrusions (±2.8, ±1.8 and ±1.0 b.y.). Most radioisotope mineral dates cluster - at these times and are coincident with inflections on polar wandering curves. These coincidences may reflect episodicity in lunar tidal disruptions and global deceleration effects in crust and outer core during micro- and intra- plate phases. Macroplate tectonics and an oxygenated atmosphere created favorable conditions for strata-hosted and plate suture gold and silver deposits. "Black smokers" at constructive plate margins and calc-alkalic calderas at destructive plate margins are loci for hydrothermal gold and silver.

Jan 1, 1984

By Y. C. Liu, W. R. Hibbard

An analysis of the relationship between the deformation and recrystallization textures in face-centered-cubic metals is presented. The analysis assumes that orientations of the secondary as well as the primary textures are related to the deformation texture. The effect of alloying elements on the recrystallization texture of copper-base alloys is also discussed. ROTATIONAL relationships based on prior orientations have been used to derive both the primary and secondary recrystallization textures."" This similarity suggests that, if the secondary texture arises from grains formed during primary recrystallization, as proposed by Dunn: and if primary recrystallization derives its lineage from the deformation structure, then the orientations obtained in secondary recrystallization .as well as those obtained in primary recrystallization should be related to the deformation texture. The following discussions are

Jan 1, 1956

By R. T. Mishler

I wish to express my keen appreciation of the article on the above subject by Coe and C1evenger.l It has been doubly interesting to me, for the reason that the experience recorded and the principles evolved practically parallel the results of similar investigations made by myself and others at The Lucky Tiger Mine, El Tigre, Sonora, Mex. An outline of the work at El Tigre may aid in confirming the principles expressed by Coe and Clevenger. El Tigre has the unenviable distinction of possessing a slime with a much lower settling rate than any recorded in the article discussed. Under most favorable conditions the settling rate is about one-third that reported for the Liberty Bell mill, and one-tenth that reported for the Nipissing, Golden Cycle, and Presidio mills. This slow settling characteristic of Tigre ore has necessitated careful investigation of settling phenomena throughout the various evolutions of the plant. Previous Settling Investigation at Tigre During construction work at the mill, the metallurgical engineer in charge, D. L. H. Forbes, ran a series of experiments on settling. His tests proved that deep settling tanks were not ordinarily necessary. The use of tanks 2 or 3 ft. in depth was suggested.2 Later experiments demonstrated that the following principles of settling applied to Tigre pulp.3 1. In settling dilute pulp, settling rates are independent of pulp depth. 2. In settling thick pulp, settling rates are approximately proportional to pulp depth.4

Jan 1, 1918

By M. O. Abo-el Fotoh, J. B. Mitchell, J. E. Dorn

The effect of strain rate and temperature on the tensile flow stress of a polycrystalline bcc alloy of magnesium containing 14 wt pct Li and 1.5 wt pct Al was investigated for strain rates of 3.13 x lom5 to 3.13 x 10-3 per sec over the range from 20° to 300°K. From about 180° to 300°K the alloy exhibited an ather-ma1 deformation behavior where the flow stress was independent of strain rate and increased only slightly with decreasing temperature. At lower temperatures the flow stress was strongly strain-rate- and temperature-dependent, characteristic of deformations controlled by thermally activated mechmzisms. The activation volume for thermally activated plastic defornzation was between 5 and 30 cu Burgers vectors, independent of plastic strain. This low-temperature thermally activated deformation behavior was found lo be in satisfactory agreement with the theoretical dictates of the Dorn-Rajnak1 formulation of the Peierls mechanism where deformation is controlled by the rate of nucleation of pairs of dislocation kinks over the Peierls energy barriers. SEVERAL studies of the low-temperature thermally activated deformation of bcc metals and alloys (molybdenum,1 tantalum,1 Fe-2 pct Mn,2 Fe-11 pct MO,3 and AgMg4) have revealed that the strain rate is controlled by the activation of dislocations over the Peierls-Nabarro energy hills. Although there is some uncertainty as to the nature and effect of solute atom-dislocation interactions during low-temperature deformation of bcc metals, it has been concluded by Dorn and Rajnak,1 Conrad,1 and Christian and Masters6 among others that overcoming the Peierls-Nabarro stress which arises from the variations in bond energies of atoms in the dislocation core as it is displaced is the probable mechanism controlling low-temperature deformation. The purpose of this research was to investigate the low-temperature plastic deformation of the bcc alloy Mg-14 wt pct Li-1.5 wt pct A1 to determine if the behavior of this alkali metal alloy might be analogous to that for other bcc metals. This alloy was selected because of its availability and its current industrial importance as a lightweight material for aircraft and aerospace applications. I) EXPERIMENTAL PROCEDURE Polycrystalline tensile specimens having cylindrical gage sections 2 in. long by 0.2 in. in diam were machined from as-received alloy sheet stock of Mg-14 wt pct Li-1.5 wt pct Al. Specimens were annealed in an argon atmosphere at 423°K for 4 hr and maintained in a kerosene bath together with the sheet stock to prevent corrosion. The resulting specimen microstructure consisted of a coarse uniform dispersion of incoherent precipitate MgLi2Al particles7 in a bcc 0 phase matrix having an average grain size of 150 p. Prior to testing the specimens were chemically polished in dilute hydrochloric acid. Comparison of tensile properties and microstructures of specimens cut from center and edge sections of the sheet stock revealed no effects of inhomogeneities in the sheet material. Tensile tests were performed on an Instron machine at crosshead speeds corresponding to tensile strain rates of 1.56 x 10-5 and 1.56 x 10"3 per sec. Stresses were determined to ±2 x 106 dynes per sq cm and strains to within ±0.0001. Average values of shear stress t and shear strain y reported were taken as one half the tensile stress and three halves the tensile strain, respectively. Flow stresses were taken at 0.05 pct strain offset. Test temperatures down to 77°K were obtained by immersing the specimens in constant-temperature baths. Lower-temperature tests were performed in a liquid helium cryostat to within ±2°K of the reported values. Prior to testing at the various temperatures and strain rates all specimens were prestrained at 2 35°K at a shear strain rate of 3.13 x 10-5 per sec to a stress level of 0.606 x 10' dynes per sq cm to obtain a uniform initial state. Additional tests were made to determine the effect of changes in strain rate and strain on the flow stress by rapidly changing the crosshead motion during testing. Shear moduli of elasticity, needed for analyses of the data, were obtained at several temperatures by a common technique of determining the resonant frequencies of vibrations of rectangular test specimens. 11) EXPERIMENTAL RESULTS Fig. 1 shows the experimentally determined flow stress vs temperature for two strain rates. Two distinct regions of behavior are evident. Below about 180°K the strong increase in flow stress with increased strain rate and decreasing temperature indicates that deformation is controlled by a thermally activated dislocation mechanism. At higher temperatures an athermal region is evident where the flow stress is independent of strain rate and only slightly dependent on temperature. The applied stress t to cause plastic flow was separated into two components:

Jan 1, 1969