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By J. Spreadborough, D. LaW. King, E. Anderson

Tmzsile tests were performed on Armco iron samples, at various ternpe.ralures and strain rates, ocer a wide range of grain sizes. Analysis of the data suggests that the plot of the lower yield stress, against d-1/2,where 2d is the acerage grain diameter, is not linear (as is often assumed) but is concave toward the d. axis over the range of d-from 7 to 53 . The different values of the parameters obtained by other workers can be explained, in part at least, by the observed curvature. This curvalure is shown to be consistent with a model of yielding based on dislocation pile-ups; however, the values of obtained by fitting our data to this model differ appreciably from the values generally reported. The equation proposed by Cottrell, viz.: is a plausible empirical fit to the experimental results. The purpose of this paper is to comment on the validity of the widely used linear relationship first proposed by all' and Petch and coworkers2"4 between ay, the lower yield stress, and 2d, the average grain diameter, for bcc metals, viz.: Many workers, see Refs. 2 to 7 and Table 11, have fitted this equation to their experimental results and have obtained acceptable fits over the relatively narrow range of grain sizes used by most of them. Indeed, in some cases, so few data points were available that any more sophisticated fit would have been irrational. In most of the interpretations,'-' oi is thought to be a measure of the friction stress accompanying dislocation movement, and ky was originally inter- preted as a measure of the dislocation locking but is now believed by Cottrell" to be a function of the dislocation creation rate. In the "unpinning" theories, k, is equated to where od is the unpinning stress and 1 is the average distance from the boundary of the grain where yielding is taking place to the nearest dislocation source in an unyielded grain. Other considerations (see, for example, Refs. 11 and 12) lead to equations with a similar form to [I] where different meanings may be attributed to the parameters. While there are doubts as to the physical significance of the parameters i and k, they continue to be used by many workers; interpretations of the variations in the behavior of ferrite materials following certain treatments, e.g., aging,'3 neutron irradiation,14 have been given frequently in terms of these parameters. Some theories of the mechanical behavior of bcc metals are based on this relationship. We have investigated experimentally the oy - d-'lZ relationship for Armco iron over a wider range of grain sizes and with more data points than those given in published results. The analysis of our data suggests that the oy—d-'" relationship is not linear but is in fact concave towards the d-'I2 axis. RESULTS AND DISCUSSION The experimental work was carried out on 3-mm-diam Armco iron rods which were prepared by wire drawing from 5-mm-diam rods. By annealing in vacuum at temperatures between 7000 and 1200°C for various times, grain sizes from 7 to 20,000 grains per sq mm were obtained, the grains in all cases being regularly shaped. Grain sizes were measured by lineal interceptand by area methods; only specimens with Amax/A values of 3 to 6 were used in the Petch-Hall plots (where A is the average area of a grain and Amax is the area of the largest grain observed). For all the specimens used, the number of grains in a cross section exceeded 50, which should be adequate to avoid grain size effects.'= Tensile tests were performed at 296", 219, and 17l°K, using

Jan 1, 1969

By C. Wagner

When an alloy solidifies and the composition of the solid differs from the composition of the liquid, atoms of the alloying elements rejected at the solid-liquid interface have to diffuse toward the bulk liquid. Diffusion may be supported by convection. Theoretical calculations have been made for a liquid without convection, for a liquid involving natural convection, and for solidification of a liquid alloy at the surface of a rotating disk as an example of forced convection. WHEN an alloy solidifies, the equilibrium composition of the originating solid phase differs in general from the composition of the liquid phase. Thus, segregation may take place, i.e., the composition of the solid phase formed at different times differs from the bulk composition. The degree of segregation depends on several factors such as the partition ratio of the alloying elements between the liquid and the solid phase, the rate of solidification, and convection. To clarify, a theoretical analysis has been worked out. The following presuppositions are made: 1—Calculations are confined to the solidification of binary alloys in which the concentration of component A (solvent) is much greater than that of component B (solute). 2—The equilibrium concentration of the alloying element B is assumed to be lower in the solid phase than in the coexisting liquid phase. 3—At the solid-liquid interface, partition equilibrium is assumed. 4—The dependence of the partition ratio of the solute between the liquid and the solid phase on concentration and temperature is disregarded since only small concentrations of the solute are considered. 5—The concentration of the alloying element B in the solid phase is supposed to be lower than the saturation concentration for the formation of a second solid phase. 6—diffusion in the solid phase is disregarded, since diffusion rates in the solid state are comparatively low. When the partition ratio of the solute between the liquid and the solid phase is greater than unity, a part of the solute is rejected at the solid-liquid inter- face and has to diffuse toward the bulk liquid. Thus there is necessarily a concentration difference in the liquid between the solid-liquid interface and the bulk liquid as has been pointed out by Hayes and Chipman,' Rutter and Chalmers,' Tiller, Jackson, Rutter, and Chalmers, and others (see Fig. 1). In view of the concentration gradient in the liquid phase, the ratio of the concentration of the solute in the solid phase to that in the bulk liquid differs from the equilibrium ratio, although at the solid-liquid interface, partition equilibrium is assumed. Under certain limiting conditions, the solid may even have virtually the composition of the bulk liquid as is shown below. General Equations Let u be the linear crystallization velocity in cm per sec, D the diffusion coefficient of component B in the liquid phase in cm2 sec-', c',, and c", the concentrations of component B in the liquid and the solid phase, respectively, in mol per cm", and s the distance from the solid-liquid interface toward the bulk liquid at a given time t. The partition ratio is assumed to be equal to a partition constant K. Thus. The difference in the specific volume between the liquid and the solid phase may be disregarded. In view of the discontinuity of the concentration of the solute at the interface according to Eq. 1, u(c', — c",), , , = tic', (S = 0)(1 — K) gram-atoms B per unit area per unit time are rejected at the interface and have to diffuse toward the bulk liquid. From Fick's first law it follows that uc',,(s = 0) (1 ~K) == - D(dc',,/?>s). _-„. [2] The concentration profile in the liquid near the interface depends on the interplay of diffusion and convection as is discussed in the following sections. A schematic concentration profile is shown in Fig. 1. The "effective thickness of the diffusion boundary

Jan 1, 1955

By N. A. D. Parlee, I. D. Shah, W. C. Phelps

THIS note reports on a continuation of a program on the thermodynamics of Fe-S-X systems in the "steel-burning" temperature range begun by Bock, Barloga, and parlee.' Small coils of 0.039-in.-diameter pure iron (Ferrovac-E) wire were equilibrated with Fe-S-0 melts in ingot iron crucibles under argon at 1324°C in the assembly shown in Fig. 1, the lower part of which was heated in a large Globar furnace. Fig. 1 shows (R) the coiled iron wire sample, (M) the Fe-S-0 melt prepared from desired proportions of ferrous sulfide and ferric oxide, (K) the iron crucible, (I) a mullite guide tube, (J) an alumina crucible, (L) alundum sand, (N) crushed mullite, (Q) hollow cylinders of K30 brick, (C) a steel rod, (B), (El, (F), (G), (P), and (O), details of brass water-cooled head, and (H) a mullite tube 2-3/4 in. ID and 26 in. long. The rod (C) bearing the sample could be removed at will and be replaced by a tube for sampling the melt, or by a thermocouple for comparing the melt temperature with a control thermocouple not far from the 2-3/4-in. mullite tube. After equilibration the iron coils were treated with acid to remove the outer layer of metal and then they were analyzed for sulfur by a standard combustion method. The melt samples were analyzed for oxygen by a variation of Lander's2 hydrogen-reduction method for mattes, and for sulfur by the ASTM combustion-iodometric method NO. E 30-47. When the results of some forty-two runs were examined it was found that the sulfur and oxygen contents of the equilibrated melts showed good consistency, in that the plotted compositions fell along the smooth curve shown in Fig. 2. The points on this curve represent the experimental compositions of melts in equilibrium with ?-iron (Fe-S-0) solid solutions. These solid solutions are saturated with sulfur and oxygen with respect to the melt and therefore have the same sulfur and oxygen activities as the melt. The curve drawn through the points therefore delineates the ? liquidus. It falls in such a position as to roughly confirm the liquidus curves of Hilty and crafts3 at 1200" and 1300°C which are

Jan 1, 1965

By Gordon B. Brox, Joseph F. Mcaleer, Charles C. Goddard, Edward P. Shea, Robert G. Ingersoll, Lester G. Zeihen, George J. Burns, John M. Guilbert, Richard N. Miller, Charles Meyer

The Boulder batholith is a composite intrusive in which the Butte quartz monzonite is the dominant rock type. Quartz porphyry dikes intruded the quartz monzonite in directions which were subsequently followed by the eastwest- striking Anaconda system of veins, the earliest major veins in the district. Anaconda veins are faulted by northwest-striking veins of the Blue system, which are most prominent in the central third of the district. Anaconda veins are the major producers in the western third of the district and also in the eastern third, where the "horsetail" zones break off from them. Individual oreshoots are thousands of feet long as well as deep on both systems of veins, but they are generally more persistent and thicker on the Anaconda veins. Viewed broadly, the mineralization in the big veins is arranged in crudely concentric zones of zinc and manganese around a central zone of copper. Only slightly offset from these zones, but earlier structurally, is a zone in which quartz-molybdenite veinlets are prominent. This zone tops at about the 2800 level and widens downward. The pattern of distribution of Cu-Fe-S series minerals in the large veins of the copper zone is not symmetrical with respect to the metal zones. There is a fringe of chalcopyrite-bornite all around the copper front. However, within the copper zone, pyrite-chalcocite-enargitecovellite- digenite assemblages are prevalent near its eastern edge from the 3800 level to the surface, whereas deep on the large Anaconda veins in the western part of the copper zone, chalcopyrite is dominant. Here the chalcopyrite grades upward into bornite-chalcocite ores and eastward into the high-sulfur assemblages of the Leonard mine. Sericite-biotite-K-feldspar alteration envelopes, containing up to about 2 per cent copper as chalcopyrite, are present on some of the quartz-molybdenite veinlets at deep mine levels in the molybdenite zone. These envelopes contrast sharply mineralogically and chemically with the later sericitic and argillic alteration envelopes around Main Stage veins. K'0-Ar'0 ratios indicate that they may be older by about 4 m.y. Secondarily enriched copper ores are mined in the Berkeley pit in the southeastern part of the district. At the present time they account for about half of Butte's production of copper.

Jan 1, 1968

By A. Chakravarti, C. C. Harris

First-order kinetics adequately describe the recovery of a single floatable species. The conditions under which cell behazior can be simulated by a single-phase model are discussed; deviations from the multiphase model are accountable. The rate coefficient depends upon operating conditions besides particle size and mineralogy and the physicochemical properties of the pulp constituents. The model for a real flotation system combines the first -order, single-phase model with a distribution of noninteracting species. Methods for determining the distributions are discussed. Applications of the procedure to flotation studies are outlined. The mathematical description of flotation as a rate process can be traced to Garcia1 who reported cases in which the fraction of solid remaining in a cell in semi-batch operation, F (for Notation used throughout, see Table l), decays exponentially with experimental time T. F = e-k>r. (1 The differential equation leading to Eq. 1 is dF ----= -k,F (2) dT which is recognized as the algebraic analog of the chemical kinetics first-order reaction equation.' This has led to suggested mechanisms for flotation and mathematical relationships other than first order: with very little foundation other than analogy. The flotation rate coefficient kl can be accounted for as the product of several probabilities concerning bub-ble-particle attachment and detachment, aggregate entry from pulp into froth and return from froth to pulp, and removal from froth as concentrate. These factors clearly contribute to the magnitude of the overall flotation rate, and there are others also, but describing flotation merely as the overall probability of consecutive gross events hardly appears a significant advance in understanding. More recently, it has been described in terms of a stochastic process, which promises to provide a more satisfactory approach? The present paper will be more concerned with a phenomeno-logical description of the flotation process than with an account of the internal mechanics of the process. This is not a statement of priorities, or a judgement of the relative importance of these options but rather an assessment of what is presently possible. Previous investigators'" have developed methods for interpreting semi-batch flotation data in terms of species distribution. These methods have been used in an attempt to explain flotation behavior in response to changes in operating conditions." Inspection of examples given in the literature" reveals discrepancies between theory and experiment, and data obtained in the Colum-

Jan 1, 1971

By Pei-Yung Huang, Carle R. Hayward

IN order to understand more fully the actual state of copper lost in copper reverberatory slags, a systematic study on the various reactions between certain metallurgically important copper compounds and synthetic copper reverberatory slags was undertaken by the authors in the Massachusetts Institute of Technology from 1942 to 1945.1 This paper, being only a part of the work completed, is published first because it furnishes the first experimental evidence of the formation of copper ferrite from reactions between cuprous oxide and copper reverberatory slags. CHOICE OF SLAG COMPOSITION The choice of the composition of the synthetic reverberatory slags to be used was much deliberated. Commercial copper reverberatory slags, neglecting minor constituents, average:2.3 45 to 47 pct FeO; 38 to 42 pct Si02; 5 to 6 pct CaO; 5 to 6 pct A1203. Since the ternary system CaO-FeO-SiO2 has been much more thoroughly studied4 and is much simpler than the quaternary system CaO-FeO-Si02-A1203, it was decided to use calcium oxide only instead of calcium oxide and alumina in the synthesis of the slags. Fortunately the composition of the average copper reverberatory slag with calcium oxide substituted for alumina lies in the region of the phase diagram clarified by the investigators. A survey of the phase diagram (Fig I) suggested two compositions: (I) the com¬position near the invariant point S, which is made up of 46 pct ferrous oxide, 37 pct silica and 17 pct calcium oxide; (2) the composition near the invariant point K with 45.5 pct ferrous oxide, 43 pct silica and 11.5 pct calcium oxide. Composition S has the advantage that the percentages of ferrous oxide and of silica almost exactly coincide with those of the average reverberatory slags, and that of the lowest melting point (1093° ± 3°C) in the whole ternary system. The calcium oxide content, however, obviously is high. Since we have already substituted calcium oxide for alumina, and since calcium oxide is more basic than alumina, the resulting slag is decidedly too basic. Composition K has a slightly higher melting point (1105° ± 3°C) and a higher silica content, but this is preferred because the slag is saturated with respect to tridymite and thus should not corrode siliceous refractories. Besides, it is less basic than composition S. The final slag composition, therefore, was chosen to

Jan 1, 1947

By David J. Mack

A SURVEY and critical appraisal of published information about Young's modulus was originally made by the writer because of a complete lack of information about this very important quantity in works on mechanics, physical metallurgy, physics, and other sciences. It was felt that a comprehensive summary of such information about Young's modulus might be of general interest and may suggest new problems or lines of attack on other problems that involve E. Hence this paper has been prepared even though it is only a review, with no new ideas or experimental data. The references are only those used in assembling the paper. No attempt was made to compile a complete bibliography on the subject of Young's modulus. CALCULATION OF YOUNG'S MODULUS FROM THEORETICAL OR EMPIRICAL CONSIDERATIONS Many attempts have been made to compute E from theoretical considerations. The earliest calculations were probably those of Tomlenson (1883) and Southerland (1891), but Fessenden 41,42 made extensive calculations a few years later and arrived at the relationship: [2E = 78. 101 (_L V] where V is the atomic volume. In 1923, Peczalski,43 working from the same stand-point but with more information available on atomic structure, arrived at an identical relationship, which he expressed as: [E=B(m) 2] where B is a constant of value about 8 • 10 7, p is density and m is atomic weight; the atomic volume, of course, being m/p. Portevin44 immediately pointed out that while the equations of Fessenden and Peczalski were true of the common metals, they gave low values for the refractory metals with high moduli (Fig. I). He showed (Fig. 2) that much better concordance was obtained by means of an empirical equation of the form: [E _ KT'Vb] where K is a constant; T the absolute melting point; V, atomic volume, and a and b constants of value approximately I and 2 respectively. This constant K in the Portevin equation is not necessarily the same for all elements, as shown by Thompson.45 Other equations for E based upon theoretical considerations have been derived by Honda and Yamada49 and Lasareff. 50 The most recent calculations of elastic moduli based upon quantum mechanics are probably those of Fuchs.46-48 He extended the method of Wigner and Seitz for calculating the lattice energy and compressibility of monovalent metals and computed the elastic constants of lithium,

Jan 1, 1945

US 4,134,944-Production of iron oxide ore pellets of uniform size and excellent strength. Small pieces of ore are rolled into nuclei in a first pellet-rolling circuit in the presence of a binder, the nuclei sized and hardened by sintering or cold-bonding of the binder, the nuclei rolled in additional ore to form product pellets, the pellets sized, the suitable size fraction taken as product, and undersize pellets returned to the rolling operation. P. A. Ilmoni and R. Drugge, assigned to Luossavaara-Kiirunavaara AB Jan 16, 1979. 5 pp. (264-37) Filed- 5-25-77 (800,278) Priority: Sweden, 6-2-76 (76/06,¬241). Same British 1,553,763, dated Oct 10, 1979. US 4,145,210-In the induration of pellets of iron oxide ore or iron works dust or sludge, a charge of dried pellets and 2-20% by weight of coke having a size range of from 5 to 30 mm, a drum index of more than 70, a reactivity index of less than 50, and a tumbler index of more than 50 is charged into a rotary kiln The charge is heated and passed through the rotating kiln to indurate the dried pellets without burning the coke Powder-coated coke is recovered from the kiln for reuse. Ring formation in the kiln is substantially prevented. K. Kato and K Kadota, assigned to Sumitomo Metal Industries, Ltd, and Sumitomo Heavy Industries, Ltd. Mar 20, 1979 10 pp (75-3) Filed- 2-22-77 (770,947) Priority: Japan, 2-24-76 (51/19,754) US 4,145,211-Method of cooling hot metallized iron oxide ore agglomerates from a direct reduction furnace Agglomer¬ates ranging from 3/a in to 41/2 in in cross-section and at a temperature of 1000-2000°F are formed into a moving bed while at rest relative to each other Air at ambient tempera¬ture is passed through the bed at a velocity sufficient to cool the agglomerates rapidly to a temperature no greater than about 500°F without substantial reoxidation of the metal in the agglomerates and by using air as the sole cooling gas. C A Czako, A Berzins, and M J Greaves, assigned to Arthur G McKee & Co Mar. 20, 1979 15 pp. (75-34) Filed: 7-18-77 (816,467)

Jan 1, 1980

By David J. Mack

A survey and critical appraisal of published information about Young's modulus was originally made by the writer because of a complete lack of information about this very important quantity in works on. mechanics, physical metallurgy, physics, and other sciences. It was felt that a comprehensive summary of such information about Young's modulus might be of general interest and may suggest new problems or lines of attack on other problems that involve E. Hence this paper has been prepared even though it is only a review, with no new ideas or experimental data. The references are only those used in assembling the paper. No attempt was made to compile a complete bibliography on the subject of Young's modulus. CalculatioX oP YouNg's Modulus from Theoretical or Empirical CoNsidera-tions Many attempts have been made to compute E from theoretical considerations. The earliest calculations were probably those of Tomlenson (1883) and Souther-land (1891), but Fess'enden4',~ made extensive calculations a few years later and arrived at the relationship: £ = 78.TOw(i)* where V is the atomic volume. In 1923, Peczalski, working from the same standpoint but with more information available on atomic structure, arrived at an identical relationship, which he expressed as: where B is a constant of value about 8 . 107, p is density and mis atomic weight; the atomic volume, of course, being ml p. Portevind4 immediately pointcd out that while the equations of Fessenden and Peczalski were true of the common metals, they gave low values for the refractory metals with high moduli (Fig. I). He showed (Fig. 2) that much better concordance was obtained by means of an empirical equation of the form: F- KT" where K is a constant; T the absolute melting point; V, atomic volume, and a and b constants of value approximately I and 2 respectively. This constant K in the Portevin equation is not necessarily the same for all elements, as shown by Thompson. Other equations for E based upon theoretical considerations have been derived by Honda and Yamada49 and Lasareff.50 The most recent calculations of elastic moduli based upon quantum mechanics are probably those of Fuchs He extended the method of Wigner and Seitz for calculating the lattice energy and compressibility of monovalent metals and computed the elastic constants of lithium, 18

Jan 1, 1946

By C. M. Schwartz, J. R. Bridge, D. A. Vaughan

THERMAL expansion coefficients of a uranium were originally reported' on the basis of X-ray diffraction measurement of lattice constants at 25°, 300°, and 650°C. These data have been reproduced by Katz and Rabinowitch.' CuK radiation had been used in this work, with consequent crowding of the patterns. Considerable overlap of the back-reflection lines was observed as the temperature was raised. Subsequent reexamination of the data led to the conclusion that errors had resulted from failure to obtain unequivocal indexing of the high angle reflections at elevated temperatures. The measurements have been repeated, using FeK radiation, which provided sufficient dispersion to assure proper indexing of the reflections, at each temperature level. The unit cell dimensions were re-determined at ten temperatures, from 25" to 650°C. Schuch and Laquer easured the macroscopic contraction from room temperature down to —253°C, and reported a negative value from —210" to —253°C; they suggested the possibility of the occurrence of a phase change. In the present work, the lattice constants of uranium have been measured down to —253°C, to test this hypothesis. Filings were prepared from a single piece of pure uranium bar stock. They were carefully cleaned with a magnet and pickled in nitric acid to remove traces of iron from the file. They were then annealed at 600°C in a sealed evacuated silica tube. The annealed filings were pickled in strong nitric acid to remove any oxide layer, washed in water and alcohol, quickly dried, and sealed in evacuated thin-walled silica capillary tubes. If properly sealed, the sample could be heated to the a-ß transforination temperature without significant buildup of the diffraction pattern of oxide. The high temperature X-ray diffraction camera was modified from the design of Hume-Rothery and Reynolds.' The thermocouple used to record the specimen temperature was calibrated from lattice-constant measurements of a standard silver specimen, using the Hume-Rothery and Reynolds values for silver over the temperature range from 25" to 700°C. Temperatures were reproducible to 210°C. Temperatures to —210°C were attained by passing precooled gas over the sample. The gas from the cooling train was directed over the sample capillary tube and thermocouple by means of a chimney of 1-mil polystyrene. The 36-gage Cu-constantan thermocouple had been calibrated by

Jan 1, 1957

By David J. Mack

A survey and critical appraisal of published information about Young's modulus was originally made by the writer because of a complete lack of information about this very important quantity in works on. mechanics, physical metallurgy, physics, and other sciences. It was felt that a comprehensive summary of such information about Young's modulus might be of general interest and may suggest new problems or lines of attack on other problems that involve E. Hence this paper has been prepared even though it is only a review, with no new ideas or experimental data. The references are only those used in assembling the paper. No attempt was made to compile a complete bibliography on the subject of Young's modulus. CalculatioX oP YouNg's Modulus from Theoretical or Empirical CoNsidera-tions Many attempts have been made to compute E from theoretical considerations. The earliest calculations were probably those of Tomlenson (1883) and Souther-land (1891), but Fess'enden4',~ made extensive calculations a few years later and arrived at the relationship: £ = 78.TOw(i)* where V is the atomic volume. In 1923, Peczalski, working from the same standpoint but with more information available on atomic structure, arrived at an identical relationship, which he expressed as: where B is a constant of value about 8 . 107, p is density and mis atomic weight; the atomic volume, of course, being ml p. Portevind4 immediately pointcd out that while the equations of Fessenden and Peczalski were true of the common metals, they gave low values for the refractory metals with high moduli (Fig. I). He showed (Fig. 2) that much better concordance was obtained by means of an empirical equation of the form: F- KT" where K is a constant; T the absolute melting point; V, atomic volume, and a and b constants of value approximately I and 2 respectively. This constant K in the Portevin equation is not necessarily the same for all elements, as shown by Thompson. Other equations for E based upon theoretical considerations have been derived by Honda and Yamada49 and Lasareff.50 The most recent calculations of elastic moduli based upon quantum mechanics are probably those of Fuchs He extended the method of Wigner and Seitz for calculating the lattice energy and compressibility of monovalent metals and computed the elastic constants of lithium, 18

Jan 1, 1946

AN intermetallic compound, Ni3A1, has an ordered fcc structure of type Ll2, and shows peculiar dependence of the yield stress upon temperature; i.e., the yield stress increases by a factor of six upon raising the temperature from 77" to 900K1, 2 This compound is technologically important, since many nickel-base superalloys owe their high-temperature strength to the peculiar yield stress behavior of Ni3Al. The only study of the elastic behavior of this compound was made by Davies and Stoloff,1 who determined Young's modulus of poly crystalline Ni3A1 between 300" and 730°K. The determination of single-crystal elastic constants of Ni3A1 is therefore of interest in connection with dislocation dynamics and is reported in this paper. A single-crystal specimen, 1 by 1 by 3 cm, was cut from an ingot generously supplied by Dr. B. H. Kear of Pratt & Whitney Aircraft. Following initial machining with a Servomet and a surface grinder, the specimen was etched and annealed at 1100°C for 5 hr in vacuum followed by furnace cooling. Two parallel faces were oriented normal to within ±l deg of a [I101 crystallographic axis by the back-reflection Laue technique. The parallel faces were hand-lapped, etched, and polished by the usual metallographic procedures. Final thickness along the [I101 axis was (0.9325 * 0.0005) cm. Chemical analysis gave an average composition of 87.35 pct Ni. Total impurity content is esimated to be no more than 0.1 pct. The elastic constants were calculated from measurements of ultrasonic waves which were propagated along the [110] axis. A longitudinal wave and two shear waves whose displacements are aligned along the [ 110], [li~], and [001] directions, respectively, are necessary in order to completely specify the three elastic constants. Two 3/6-in. quartz transducers were bonded to the parallel faces of the sample with ~ac-seal.3 Although this bond was sensitive to thermal shock, it performed satisfactorily over the entire temperature range for both longitudinal and shear wave propagation. A frequency of 5 mHz was employed in the method of Williams and Lamb4 in order to measure the absolute value of the ultrasonic velocity. The pulse-overlap technique of Mcskimin5 was also used at this frequency in order to determine the shift in the ultrasonic velocity

Jan 1, 1970

By B. B. Rath, Hsun Hu, R. S. Cline

FOLLOWING the techniques used by Beck and co-worker~ "~ the characteristics of selective growth in the recrystallization of a zone-refined aluminum single crystal, rolled 80 pct at -78°C in the (110)[112] orientation, have been studied. The material was 99.999+ pct pure. The as-grown crystal had a resistance ratio, R(298°K) /R(4,2°K), of approximately 5000. The method of preparation of the single crystals and the necessary precautions in handling them during rolling in order to avoid recrystallization in locally distorted regions were described in an earlier paper.3 The rolling texture of this zone-refined aluminum crystal is practically identical with that of less pure aluminum crystals rolle! in the same orientation, i.e., a very sharp (110)[112]. Random nuclei were provided by artificial nuclea-tion by abrading one face of the rolled crystal on 600-grit emery paper in a random fashion. The thin layer of disturbed metal recrystallized at room temperature into fine grains almost immediately. An X-ray diffraction pattern was taken from the abraded surface of the crystal, and the relative intensities of the various reflection peaks were compared with those obtained from a powder specimen. As shown in Fig. 1, the relative intensities of the various peaks from the recrystallized layer varied somewhat from experiment to experiment, depending presumably on the abrading technique. However, the texture of the recrystallized layer produced by this method is nearly as random as that of a powder specimen. Fig. 2 shows the texture determined from the "growth side" (face opposite the abraded surface) of the crystal after it was kept at room temperature for 100 hr. The specimen was only partially recrystallized, as shown by the remaining deformation texture. The new orientations are derived from the recrystallized grains grown through the thickness of the crystal from the "nucleation side" (the abraded surface). Fig. 3 shows the texture after complete recrystallization produced by annealing at 60°C for 1 hr. The arrows indicate 40-deg rotation around the (111) axes of the deformation texture. The microstructure of a completely recrystallized specimen is shown in Fig. 4. As shown in Figs. 2 and 3, the texture of the re-crystallized grains grown from the nucleation side to the growth side is essentially the same as that observed in less pure aluminum' (99.994 pct) and dilute alloyz crystals rolled in the same orientation. How-

Jan 1, 1968

By Jacob T. Wainwright

AS a means for increasing the efficiency in modern blast-furnaces by supplying to them blast of a much higher temperature than is now possible, the writer offers as a suggestion a modification in the construction of regenerative hot-blast stoves. Stated briefly, the plan proposed is to pre-heat both the gas and the air for its combustion in a manner similar to that generally adopted in Siemens openhearth furnaces. After thus carrying the temperature of the stove to a point much higher than that common in hot-hlast stoves, the cold blast passes through it. Without entering into the details relating to the reversing valves and the system of flues, the general plan may be outlined as follows, referring to the accompanying drawings: The valves are so placed in heating up the stove that the blast-furnace gas enters at B, Fig. 1, and the cold air for combustion at A. Ascending in flues, F and E, respectively, combustible gas and air meet and mix in the combustion-chamber, I. Flowing through K, they descend through the flues, G and H, escaping through the chimney. In this manner the walls of the combustion. chambers, I and L, are highly heated, and the right-hand side of the stove is carried to a higher temperature. By reversing the valves, blast-furnace gas enters at C and cold air for combustion at D. Both are pre-heated in their ascent through the flues, G and H. They burn in the combustion-chamber, L, and the hot gases of combustion, flowing through K, I, E and F to A and B, heat the left-hand side of the stove. In this manner the stove is carried to a temperature greater than that of those now generally in use, in which air and gas are burned without preliminary pre-heating. In the plan proposed, that side of the stove will, of course, be relatively cooler through which cold air and furnace-gas last passed in its ascent to its combustion-chamber. After having sufficiently heated the stove in the manner outlined, the cold blast is admitted through all the flues, A, B, C and D. It ascends through the highly-heated regenerative material to the chambers at the top and descends through the flue, P, Fig. 2 (dotted

Jan 1, 1889

By Charles S. Larkey

Numerous papers have been published on the use of graphic methods for determining the best curve for estimating the production decline of oil wells but, as far as the writer has been able to ascertain, nothing has been published showing how curves may be worked out mathematically that will conform most closely to the production data under consideration in any given instance; hence the writer has endeavored to show just how such application can be made. Among the valuation engineers, two types of curves are in current use for the representation of the decline in production of oil wells. One may be represented by the equation, y = krx; this is sometimes known as a percentage curve, for the production for any period is multiplied by a constant rate or percentage to obtain the production for the succeeding period. It appears as a straight line on semilogarithmic cross-section paper. The other curve may be represented by the equation, y = kxn, and is shown as a straight line on logarithmic cross-section paper. In each equation, y represents the number of barrels produced in a given period of time, and x the successive periods of time. The other letters are constants to be determined for each well, or group of wells considered in arriving at the most probable curve to represent the rate of production for a given property. From this the underground reserves may be estimated by extrapolation, or by extending the curve beyond the last known period of production to show the most probable production values for the future. Application to the Burbank Pool Fig. 1 relates to a property in the Burbank Pool, Osage County, Okla. The production is shown as an average per well per month, is plotted to the vertical scale of barrels on the left-hand margin and to the horizontal scale of months at the bottom of the chart. In column y, the number of barrels is listed beginning with May, 1922, as the first month on which to base a decline curve. The type of curve used is of the form, y = krx, or, expressed in logarithms, log y = log k + x log r, in which log k and log r are constants to be determined so that the curve will most closely approximate the production data given.

Jan 1, 1925

The State Mining Experiment Station, Missouri School of Mines and Metallurgy, Rolla, Mo Charles H. Fulton, Director of the School of Mines Martin H. Thornberry, Director of the Mining Experiment Station. From the State Mining Experiment Station are issued all the general and technical bulletins of the School of Mines The latest bulletin containing a complete list of publications will be sent upon application to the Director of the Station Residents of the state may obtain bulletins as issued without charge, or may ask to be placed on the mailing list. Nonresidents should write to the Director for further information concerning specific bulletins. From the long list of bulletins the following have been care¬fully selected as being most likely to interest the geologist and the mining engineer. Vol 8, No. 1 (1916), Bibliography of concentrating ores by flotation, by J Cunningham, vol 1, No 3 (1912), Some apparatus and methods for demonstrating rock drilling and the loading of drill holes in tunneling, by L E Young, vol 2, No 1 (1915), Comparative tests of piston drill bits, by C R Forbes and L M Cummings; vol 2, No 3 (1916), Cupellation losses in assaying, by H. T Mann and C. Y Clayton; vol 4, No 1 (1917), The hydrometallurgy and electrolytic precipitation of zinc, by F D. James; vol 4, No 2 (1917), The effect of additional agents in flotation, pt 1, by M. H. Thornberry and H T. Mann, vol 5, No 1 (1919), The carbonization of Missouri cannel coals, by H L. Dunlap, K. K. Kershner and V. X Smiley. Vol 5, No. 4 (1921), Coal mining methods in Missouri, by W W Weigel, vol 6, No 1 (1921), The problem of the St Peter sand¬stone, by C L Dake, 50 cents, vol 6, No. 2 (1922), Bibliography on the electrothermic metallurgy of zinc, by B M. O'Harra, vol 6, No. 4 (1923), Experiments on the distillation of zinc from complex zinc-lead-silver ores, by B M. O'Harra and E S. Wheeler, vol 7, No 3 (1924), Underground loading devices, by C. E. van Barneveld, 81; vol 7, No. 4 (1924), Briquetting of zinc ores, by B. M. O'Harra; vol. 8, No 2 (1925), A treatise of Missouri clays, by M. H. Thornberry.

Jan 1, 1933

By B. D. Cullity

GOLD and beryllium form an intermediate phase composed of the two metals in equal atomic proportions and having the formula AuBe. According to Winkler,1 this phase probably exists in two modifications: beta, stable below about 600°C, and alpha, stable between 600°C and the melting point, about 740°C. Only the low- temperature beta form will be considered in this paper. EXPERIMENTAL PROCEDURE The gold used had a fineness of 999.75 to 999.85, balance mainly silver, and the beryllium purity was better than 99.8 pct. AuBe was prepared by melting the constituents in a beryllia crucible in an evacuated induction furnace. After melting and thorough mixing, the alloy was allowed to solidify in the crucible. No difficulty was encountered in obtaining a homogeneous ingot. Both chemical analysis and microscopic examination of the ingot showed that the alloy was essentially one phase, containing 50 at. pct gold. The alloy was quite brittle and powder samples could easily be pre- pared by grinding in an agate mortar. The X-ray diffraction patterns were made with CuK-alpha radiation in a Debye-Scherrer powder camera 57.3 mm in diameter. The film was placed unsymmetrically in the camera in order to afford a basis for am-shrinkage corrections. A sample homogenized at 5o0°C gave the same diffraction pattern as a sample taken from the as-melted ingot. GENERAL RESULTS The diffraction pattern of AuBe was readily indexed on the basis of a simple cubic lattice with ao = 4.659 ± 0.001kX. If the unit cell is assumed to contain four AuBe "molecules," the calculated X-ray density is 13.46 grams per cc as compared with the measured density of 13.55 gm per cc. The only missing reflections in the dsraction pattern are (100) and (220) (see Table I). Since these missing reflections are not those characteristic of body or face centering, the lattice of AuBe must be simple cubic. To locate the positions of the atoms within the unit cell, two possibilities had to be considered: I. The structure was disordered and there were eight positions to be filled by an "average" gold-beryllium atom. That the structure was disordered seemed unlikely since the lattice parameter did not vary with composition in alloys containing some- what more and somewhat less than 50 at. pct gold, indicating a fixed composition for AuBe.

Jan 1, 1947

By B. D. Cullity

Gold and beryllium form an intermediate phase composed of the two metals in equal atomic proportions and having the formula AuBe. According to Winkler,' this phase probably exists in two modifications: beta, stable below about 600°C, and alpha, stable between 600°C and the melting point, about 740°C. Only the low-temperature beta form will be considered in this paper. Experimental Procedure The gold used had a fineness of 999.75 to 999.85, balance mainly silver, and the beryllium purity was better than 99.8 pct. AuBe was prepared by melting the constituents in a beryllia crucible in an evacuated induction furnace. After melting and thorough mixing, the alloy was allowed to solidify in the crucible. No difficulty was encountered in obtaining a homogeneous ingot. Both chemical analysis and microscopic examination of the ingot showed that the alloy was essentially one phase, containing 50 at. pct gold. The alloy was quite brittle and powder samples could easily be prepared by grinding in an agate mortar. The X-ray diffraction patterns were made with CuK-alpha radiation in a Debye-Scherrer powder camera 57.3 mm in diameter. The film was placed unsym-metrically in the camera in order to afford a basis for film-shrinkage corrections. A sample homogenized at 500°C gave the same diffraction pattern as a sample taken from the as-melted ingot. General Results The diffraction pattern of AuBe was readily indexed on the basis of a simple cubic lattice with ao = 4.659 + 0.001kX. If the unit cell is assumed to contain four AuBe "molecules," the calculated X-ray density is 13.46 grams per cc as compared with the measured density of 13.55 gm per cc. The only missing reflections in the diffraction pattern are (100) and (220) (see Table I). Since these missing reflections are not those characteristic of body or face centering, the lattice of AuBe must be simple cubic. To locate the positions of the atoms within the unit cell, two possibilities had to be considered: I. The structure was disordered and there were eight positions to be filled by an LCaverage" gold-beryllium atom. That the structure was disordered seemed unlikely since the lattice parameter did not vary with composition in alloys containing sornewhat more and somewhat less than so at' pet gold, indicating a fixed composition for AuBe.

Jan 1, 1947

By H. J. Engell, W. Frank, A. Seeger

SWISHER and ~urkdogan' have determined the solubility of oxygen in a iron. They found it to lie between 7 and 10.5 at.-ppm at 881°C. Using earlier work on the permeability of oxygen in bcc iron,' they arrived at the following expression for the diffusion coefficient of oxygen in bcc iron (k = Boltzmann's constant, T = absolute temperature): where The present authors3 have estimated the activation energy QD for the diffusion of oxygen in bcc iron in two different ways from various experimental data.2'4"6 In the first method QD + QS (QS = heat of solution for oxygen in bcc iron in thermodynamic equilibrium with solid FeO) was determined either from data on the reduction of FeO with hydrogen4 or from measurements of the internal oxidation of silicon in a iron.5 Using an estimate of QS from investigations of the oxygen solubility in 6 iron2 (in thermodynamic equilibrium with molten FeO) Q = 0.97 ev or Q~ = 1.06 ev were obtained. From the magnitude of these values it was concluded that oxygen migrates interstitially in bcc iron and that consequently the activation energy QD for diffusion of oxygen has to be identified with the migration energy E~ of the oxygen atoms. Therefore, for a second estimate of QD from the diffusion coefficient of oxygen in 6 iron at 1450" ~,~ we used the theoretical expression:3 (a = length of elementary cube edge, m = mass of interstitially diffusing atom, sM = migration entropy), applicable to diffusion via the octahedral interstices in bcc lattices. Taking sM = 3.8 k (migration entropy of carbon in a iron), one gets Q = 0.90 ev. Hence, in Ref. 3 Q = (0.98 *0.1) ev was proposed as a plausible value for the diffusion energy of oxygen in bcc iron. sM + 9 (9 = solution entropy for oxygen in bcc iron) can be determined from permeability measurements.4 Using the above-mentioned estimate for QS , the following expression for the solubility c (atomic concentration) of oxygen (in thermodynamic equilibrium with solid FeO) in bcc iron was derived: From [4] the solubility of oxygen at 881°C in a iron is calculated to lie between 0.6 and 12 at.-ppm. We see that the solubility determined by Swisher and

Jan 1, 1969

By B. D. Cullity

Gold and beryllium form an intermediate phase composed of the two metals in equal atomic proportions and having the formula AuBe. According to Winkler,' this phase probably exists in two modifications: beta, stable below about 600°C, and alpha, stable between 600°C and the melting point, about 740°C. Only the low-temperature beta form will be considered in this paper. Experimental Procedure The gold used had a fineness of 999.75 to 999.85, balance mainly silver, and the beryllium purity was better than 99.8 pct. AuBe was prepared by melting the constituents in a beryllia crucible in an evacuated induction furnace. After melting and thorough mixing, the alloy was allowed to solidify in the crucible. No difficulty was encountered in obtaining a homogeneous ingot. Both chemical analysis and microscopic examination of the ingot showed that the alloy was essentially one phase, containing 50 at. pct gold. The alloy was quite brittle and powder samples could easily be prepared by grinding in an agate mortar. The X-ray diffraction patterns were made with CuK-alpha radiation in a Debye-Scherrer powder camera 57.3 mm in diameter. The film was placed unsym-metrically in the camera in order to afford a basis for film-shrinkage corrections. A sample homogenized at 500°C gave the same diffraction pattern as a sample taken from the as-melted ingot. General Results The diffraction pattern of AuBe was readily indexed on the basis of a simple cubic lattice with ao = 4.659 + 0.001kX. If the unit cell is assumed to contain four AuBe "molecules," the calculated X-ray density is 13.46 grams per cc as compared with the measured density of 13.55 gm per cc. The only missing reflections in the diffraction pattern are (100) and (220) (see Table I). Since these missing reflections are not those characteristic of body or face centering, the lattice of AuBe must be simple cubic. To locate the positions of the atoms within the unit cell, two possibilities had to be considered: I. The structure was disordered and there were eight positions to be filled by an LCaverage" gold-beryllium atom. That the structure was disordered seemed unlikely since the lattice parameter did not vary with composition in alloys containing sornewhat more and somewhat less than so at' pet gold, indicating a fixed composition for AuBe.

Jan 1, 1947