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By P. N. Richards, M. K. Ormay

The present Paper extends the previous work on cold reduced, low carbon steels to preferred orientations developed after various heat treatments. In recrystal-lized rimmed steel, cube-on-comer orientations increased with cold reductions up to 80 pct. Above that {111}<112> and a partial fiber texture with (1,6,11) in the rolling direction dominated. During grain growth, cube-on-corner orientations have been observed to grow at the expense of {210}<00l>. In re-crystallized Si-Fe (111) (112) and cube-on-edge type orientations are dominant near the surface and the (1,6,11) texture near the midplane for reductions up to 60 pct. With larger reductions {111)}<112> and the (1,6,11) texture are dominant. In cross rolled capped steel a relationship of 30 deg rotation was observed between the (100)[011] of the rolling texture and the main orientations after re crystallization. Most orientations present in recrystallized specimens can be related to components of the rolling texture by one of the following rotations: a) 25 to 35 deg about a (110) b) 55 deg about a (110) C) 30 deg about a (Ill) THE orientation texture of recrystallized steel is of interest where the product is to be deep drawn, because preferred orientation is related to anisotropy of mechanical properties such as the plastic strain ratio (r value);1,2 and in electrical steel applications where a high concentration of [loo] directions in the plane of the sheet improves the magnetic properties of the material. It is interesting to note that both these aims are to a large extent achieved commercially, even though the orientation texture of cold rolled steel does not show large variation3 and the recrystallized orientations are generally given as being related to the as rolled orientations mostly by 25 to 35 deg rotations about common (110) directions.4-6 There is, as yet, no single completely accepted theory on recrystallization. The three mechanisms that have been investigated and discussed are: a) Oriented growth b) Oriented nucleation c) Oriented nucleation, selective growth Largely from the observations of the recrystalliza-tion process by means of the electron microscope,7-11 there is now considerable evidence that the "nucleus" of the recrystallized grain is produced by the coalescence of a few subgrains to form a larger composite subgrain, which finally grows by high angle boundary migration into the deformed matrix. From the intensive work on the recrystallization of rolled single crystals of iron, Fe-A1 and Fe-Si al-loys4-" he following observations have been made: 1) The change in orientation during primary recrys-tallization can usually be described as a rotation of 25 to 36 deg about one of the (110) directions. 2) The (110) axes of rotation often coincide with poles of active (110) slip planes. 3) If several orientations are present in the cold rolled structure, the (110) axis of rotation will preferably be a (110) direction that is common to two or more of the orientations. 4) With larger amounts of cold reduction (70 pct or more) departure from these observations became more frequent. 5) After larger cold reductions, rotations on re-crystallization about (111) and (100) directions have been observed. K. Detert12 infers that a rotation relationship of 55 deg about (110) directions is also possible, by stating that the recrystallized orientation {111}<112> can form from the orientation {100}<011> of cold reduced partial fiber texture A.3 The observation by Michalak and schoone13 that (lll)[l10] formed during recrys-tallization in fully killed steel containing (111)[112],— as well as (001)[ 110] which is related to the {111}<011> by a 55 deg rotation about <110>-implies a possible 30 deg rotation relationship about the common [Ill]. Heyer, McCabe, and Elias14 have recrystallized rimmed steel after various amounts of cold reduction, by a rapid and by a slow heating cycle and found that the preferred orientations strengthened with increased cold reduction. The most pronounced orientation up to about 70 pct cold reduction was found to be {1 11}< 110>, after 80 pct cold reduction both {111}<110> and {111}<112>, after 85 and 90 pct cold reduction, {111}<112>, and after 97.5 pct cold reduction it was {111}<112> and (100)(012). In the present work, the orientation textures of the recrystallized specimens are examined under various conditions of steel composition, amount and method of cold reduction, and method of recrystallization. The relationships between the preferred orientations of the as rolled and recrystallized specimens, and the conditions for the formation of the various orientations during recrystallization are investigated.

Jan 1, 1970

By C. F. Lucks, W. D. Wood, H. W. Deem

Electrical ad thermal-conductivity measurements have been made on titanium and 6 titanium alloys. The following expression was derived for calculating thermal conductivity from electrical conductivity: K = 0.626 s T x 10-8 + 0.00497 where K = thermal conductivity, cal sec-1 cm-2 cm0C-1 s = electrical conductivity, ohm-]cm-1 T = temperature, deg Kelvin This expression gives calculated thermal conductivities that are not in error by more than 10 pct from the experimental values for A-55 titanium and the 6 alloys measured; namely, A-110AT, C-110M, C-130AM, Ti-6A1-4V, Ti-140A, and Ti-155A, which are representative of the presently available commercial a and a-ß titanium alloys. THERMAL conduction in a gas, liquid, or amorphous solid is accomplished by energy diffusion from molecule to molecule, a relatively slow process. For this reason, such materials have a low thermal conductivity. When a material is crystalline, there is in addition a heat transfer by a vibratory motion of the crystal lattice. It is the contribution of this lattice conduction that makes a crystal a much better conductor than a gas, liquid, or amorphous solid. Lattice conduction, however, does not account for the relatively enormous thermal conductivity of a metal. This is explained by the freedom of movement of valence electrons. These valence electrons drift in a metal in a direction toward a drop in electrical potential and, to a lesser degree, in the direction of a temperature drop in the metal. Since both the electrical and thermal conductivities of a metal depend upon the presence of free electrons, there should be some relatively simple relation between the two. Wiedemann and Franz in 1653 first discovered an approximate empirical relation between the electrical and thermal conductivities of metals at the same temperature. This ratio varies appreciably with temperature, and Lorenz later showed that by adding a temperature factor to the Wiedemann-Franz ratio the value of K/(s T) is constant, where K is the thermal conductivity, a the electrical conductivity, and T the absolute temperature. This Lorenz constant shows a greater variation for alloys than it does for pure metals, the ratio increasing slightly as the proportion of alloying elements increases. It has been found that a closer correlation between electrical conductivity and thermal conductivity can be obtained by means of an equation of the form K - A s T + B [1] where A and B are constants. In this equation the term AsT is the contribution of electronic conduction and B is the contribution of lattice conduction to the total thermal conductivity. EXPERIMENTAL MEASUREMENTS Electrical-resistivity and thermal-conductivity measurements on titanium and 6 titanium alloys serve as the basis for determining an equation of the K = AsT + B type for titanium alloys. Specimens—Table I shows nominal compositions of the 7 metals on which electrical and thermal conductivities were measured. The electrical and thermal-conductivity specimens for each alloy were taken from stock of the same heat and usually from adjacent sections of the same bar. All of the metals measured were in a mill-annealed condition. Methods—Electrical-resistivity measurements

Jan 1, 1959

By D. G. Westlake

Polycrystalline tensile specimens of various Zr-0-H alloys have been tested at 298°, 178°, and 77°K. Solute oxygen and hydride precipitates in quenched alloys made individual contributions to the yield strength at 0.2 pct strain which combined to produce a resultant strength increment, a,., Ductility changes which were ohserved can he interpreted in terms of the various oxygen and hydrogen concentrations, testing tem -peratures, and dispositions of the hydride. ADDITIONS of oxygen in solid solution were known to increase the yield and tensile strengths of polycrystalline zirconium as early as 1951.&apos; More recently, the critical resolved shear stress (CRSS) for prism slip in zirconium single crystals was also shown to be affected by the solute oxygen impurity.&apos; This latter work also demonstrated that large increments of strength could be contributed by the finely dispersed zirconium hydride precipitates that are present in quenched Zr-H alloys.3 It was concluded that the combined strengthening due to alloying could be expressed by where to is the increase in the CRSS due to solute oxygen alone and TH is the increase due to finely dispersed hydride precipitates. Eq. [I] is analogous to one used to express the combined strengthening effects of work hardening and neutron radiation damage.4 Eq. [1] was verified only indirectly and for only small amounts of the impurities—up to 0.14 at. pct 0 and 0.63 at. pct H. The present investigation was undertaken to obtain a more direct verification of the validity of the form of Eq. [1] for this system and also to determine the combined effects of oxygen and finely dispersed hydride precipitates on the tensile strength and ductility of polycrystalline zirconium. EXPERIMENTAL PROCEDURE Tensile specimens were machined from the same rolled billet of Kroll zirconium used in the earlier study.&apos; These measured 38 by 4.7 by 0.5 mm and had 10-mm gage lengths which were 2.8 by 0.5 mm. Each specimen was ß-annealed in vacuo at 1173°K for 15.5 hr and a-annealed at 1073°K for 4 hr to D. G. WESTLAKE, Member AIME, is Associate Metal l ur-gist, Metallurgy Division, Argonne National Laboratory, Argonne, III. Manuscript submitted July 17, 1964. IMD______________ give an equiaxed structure with grain diameters averaging 0.06 mm. Oxygen was added by allowing the metal to react with a known quantity of oxygen during the 0 anneal and known quantities of hydrogen were added during the a anneal. Each alloy was encapsulated in Pyrex under vacuum, annealed at 873°K for 4 hr, quenched into ice water, and polished by immersion in a solution of 46.75 vol pct H2O, 46.75 vol pct concentrated HNO3, and 6.5 vol pct HF (49 pct) at 298°K. Special heat treatments given to a few specimens are described in the results below. Tensile tests were done on an Instron machine and were begun within 20 min after the quench, except where specified otherwise. Tests at 298°K were in air, at 178°K in acetone, and at 77°K in liquid nitrogen. All tests were at a strain rate of 8x sec-1. RESULTS AND DISCUSSION Yield Stress at 298°K. The compositions of alloys and the corresponding yield stresses (0.2 pct strain) are given in Table I. A plot of the yield stresses of the oxygen alloys, A, B, C, and D, indicates that varies linearly with CO1/2, where Co is the oxygen concentration, Fig. 1. This is in accord with Fleischer&apos;s6 theory for solution strengthening if the oxygen atoms do not cluster, or the cluster size remains constant with increasing oxygen concentration. In Fig. 1, it appears that if one could prepare some oxygen-free zirconium its yield stress would be very low. Therefore, we shall assume that for the oxygen alloys is equivalent to O0, the strength increment contributed by the presence of oxygen. The relationship between0.2and Co is expressed by 0.2 = 31.3 CO1/2, when the yield stress is in kg per sq mm and the concentration is in at. pct. Each of the hydrogen alloys, Al, A2, A3, and A4, contained 0.081 at. pct 0 as an impurity. In Fig. 1, it appears that this small amount of oxygen makes a significant contribution to the strength which cannot be ignored when we evaluate the contribution of the finely dispersed hydride. Let us assume the validity of the following equation: a0.2 = (a2o+a2R)1/2 [2] which is analogous to Eq. [I] for single crystals, and calculate values of UH for the hydrogen alloys by using the experimental values of 0.2 and o (0.081 at. pct) = 8.9 kg per sq mm. For 0.36 at. pct H, oH = 6.47; for 0.72 at. pct H, OH = 11.30; for 2.16 at. pct H, OH = 19.4; and for 3.60 at. pct H,

Jan 1, 1965

By R. D. Pehlke, J. V. Gluck

The limiting activity coefficient of zinc in a "binary " solvent has been described for several dilute ternary solutions by combining literature data from recent interaction studies in the terminal regions with thermodynamic data for the central regions. Results are discussed in terms of the Alcock and Richardson random solution model. The observed behavior agrees semiquantitatively with predictions using the model. RECENT efforts in the thermodynamics of dilute ternary liquid metallic solutions have been mainly concerned with the interactions between two dilute solutes, that is, the terminal region at an apex of the composition diagram.&apos;-&apos; A more general case is that of the behavior of a dilute solute over the full range of a ternary system, or, more specifically, the limiting activity of solute i as projected to the k-j binary side of the i-j-k composition triangle. An implication of this is that the interaction between i and j at the k apex should connect in some way to the interaction between i and k at the j apex. A model to characterize various types of expected behavior has been discussed by Alcock and Richardson.9,10 Such behavior can range from a simple linear relation for In yi over the 1-k binary to more complex curved relations which depend on various assumptions regarding the heat of solution in the j-k binary system and the presence or absence of clustering with solute i. Quantitative data to assess these concepts have been limited primarily to the cases of nonmetallic interstitial solutes in ferrous solutions. Alcock, Richardson, and various coworkers9-13 have discussed the behavior of oxygen, sulfur, silicon, or hydrogen in dilute solution over the range of iron + metal systems; however, the only data considered by them for substitutional nonferrous metallic solutions were the results of Elliott and Chipman concerning the activity of cadmium in the Pb + Sn, Pb + Bi, and Pb + Sb systems.9 These data were limited and did not cover the terminal regions in detail. An opportunity to extend the Alcock and Richardson considerations to the dilute solution of zinc in various "binary" solvents has been afforded by combining results of several of the recent investigations of ter-minal-region interactions with previous data from the literature for the same more concentrated solutions. RESULTS AND DISCUSSION The results of the analysis are shown in Figs. 1 to 5 where the log activity coefficient, (In yZn)xzn--o, is plotted vs the composition of the "binary" solvent. In these plots the end points are the values for In yzn in the appropriate binary solution with Bi, Pb, Sn, Cd, or In at the indicated temperature—usually 550°C (823°K). For the terminal regions the slopes were drawn using the first-order interaction parameters taken from various studies reported in the literature. The data points shown in the central regions were obtained by the short extrapolation to infinite dilution of the logarithm of the activity coefficient calculated from thermodynamic studies reported in the literature for the same systems. The sources of the data are indicated on each figure. Second-order effects were not considered. Reasonably smooth curves can be drawn to connect the central region with the terminal regions for the Zn-Pb + Bi system, Fig. 1, the Zn-Pb + Zn system, Fig. 1, and the Zn-Bi + Cd and Zn-Bi + Sn systems, Fig. 2. As shown in Fig. 2, where central region data are available from two independent investigations, the agreement is quite good. The Zn-Pb + Cd system does not appear to be as well behaved as the previous four, Fig. 3; however, this type of behavior has also been

Jan 1, 1970

By E. R. Macgregor, J. Halpern

The kinetics of the reduction of cupric salts in aqueous solution by molecular hydrogen to metallic copper are described. The rate of reduction appears to be homogeneously determined and shows a marked inverse dependence on the hydrogen-ion concentration. Precipitation of copper is more rapid and complete in sulfate than in per-chlorate solution. A mechanism is proposed which accounts for this behavior. IN recent years a number of important hydro-metallurgical processes have been developed in which metallic salts in aqueous solution are reduced by gaseous hydrogen, usually at elevated temperatures and pressures, and thereby precipitated either in metallic form (e.g. Ni, Co, Cu) or as an oxide or salt of lower valence (e.g. VO, and VA).1 ; In connection with applications such as these, most of which involve heterogeneously catalyzed reactions, recent demonstrations"-" that salts of certain metals, e.g., Cu", Ag&apos; , Hg" , and Hg,+ can activate molecular hydrogen homogeneously and thus catalyze hydrogenation reactions in aqueous solution, are of considerable interest. For example, cupric salts catalyze the otherwise slow homogeneous reduction of dichromate and ceric salts by hydrogen, i.e. Cr,O; + 3HL. + 8H1 ? 2Cr&apos;- -- 7H,O [1] 2Ce &apos; ! H.. ? 2Ce" | 2H . [2] In perchloric-acid solution, where Cu" is not appreciably complexed, the kinetics have been found" " to be of the form -d [H,] _- k,[HJ [CU"]&apos; dt -LCu+&apos; l+ (k ,/k,) [H] [3] where, K = 1x10"&apos; exp [—26,600/RT] 1, mole-&apos; min-&apos; ... [4] and (k ,/k,) - 0.25 at 110°C. This kinetic behavior suggests that the reaction proceeds by a mechanism involving the following sequence of steps kt Cu" +H1CuH&apos; 4-HA [51 k., CUH + CU" ? + 2Cu f H&apos; [GI 6Cu&apos;+ Cr,07 + 14H&apos;+ 2Cr- (¦ 7H,O + 6Cu" [&apos;i] fast The catalytic activities of the undissociated cupric-sulphate and cupric-acetate complexes are somewhat greater (by factors of 6.5 and 120, respectively) than that of the simple hydrated Cu" ion.&apos;" These considerations suggest that, in contrast to the other hydrometallurgical hydrogenation reactions, referred to previously, reduction of cupric salts in aqueous solutions by molecular hydrogen, should proceed homogeneously, and in the absence of an extraneous catalyst. This has already been demonstrated" for acetate-buffered solutions where the product of the reaction is a precipitate of cuprous oxide (Cu,O). In the present paper, an investigation of the reduction of cupric salts in perchloric-acid and sulphuric-acid solutions, leading to the precipitation of metallic copper, is described. Some results for the sulphate system, which is of considerable hydrometallurgical interest, have been reported previously by Ipatieff",&apos; " and by Schaufel-berger&apos; but these do not give a quantitative account, of the kinetics and mechanism of the reaction. Experimental The reduction experiments were conducted in the 1-gal, titanium-lined autoclave described in connection with earlier related investigations," " and using a similar procedure. The solutions were made up by dissolving known amounts of CP grade Cu(ClO,), and HC10, (or CuSO, and HISO,) in dis-tilled water. While in the autoclave, the solution was stirred and maintained at a constant temperature (±loc) and under a constant partial pressure of hydrogen gas. It was ascertained that the agitation (provided by two 3-in., four-bladed stirrers, rotating at 900 rpm) was adequate so that at no time was the rate of reaction limited by solution of hydrogen. During each experiment, samples of the solution were withdrawn periodically, allowed to cool, and the concentration of copper remaining in solution was then determined electrolytically. Some Cu&apos; is formed during the reaction, but undergoes disproportionation when the solution is cooled to room temperature. For purposes of kinetic calcula-

Jan 1, 1959

By Philip D. Anderson, Ralph Hultgren

Heat contents of extremely pure iron were measured over the range 300"to 1433"K, using a diphenyl ether calorimeter. Results from three samples containing widely differing impurities agreed with one another and with Previously reported results at higher temperatures (1184 ° to 1809°K) by Olette and Ferrier. From these data a table of heat contents of iron has been Prepared which is believed to be more accurate than those previously available. CP values have been derived which are consistent with these heat contents, with the best experimental Cp data, and with the thermodynamic conditions of equilibrium between bcc and fcc iron. The opinion is expressed that low-temperature extrapolations of presently known Cp values for y-Fe are not reliable. It would seem that the thermodynamic properties of iron, which is by far our most important metal, should have been well established long ago. This is not the case, however. As discussed by Olette and Ferrier,&apos; there is objection to every earlier heat content measurement. While the best true Cp determinations agree well at temperatures below the Curie point, there is wide divergence at higher temperatures. Several investigators have examined available data and attempted to calculate thermodynamic functions for iron that are consistent with the two equilibrium temperatures of bcc and fcc iron. The two primary efforts were those of Austin&apos; in 1930 and Darken and smith3 in 1948. The recommended values differ considerably; integration of Austin&apos;s Cp values leads to a heat content at 1100°K which is 300 cal per g-atom higher than the value recommended by Darken and Smith. The compilation of Fisher4 in 1949 was based on the selection of Austin. In 1956, Weiss and Tauer obtained yet another set of values by resolving Cp values into components due to dilation, lattice vibration, electronic excitation, and magnetism. The magnitude of contribution by each component and its dependence on temperature was estimated by semiempirical means. Their values are not self-consistent in that they do not form smooth curves when plotted vs temperature; moreover, their calculations cannot easily be repeated since they do not give the values of some of the parameters used. Clearly, experimental values for iron were in a most unsatisfactory state. The presently described measurements of the heat content of iron were therefore undertaken, covering temperatures as high as 1433°K. While the work was in progress, the high-temperature (1193" to 1789"K) heat content measurements of Olette and Ferrier&apos; were published; in the region of temperature overlap the present results agree with Olette and Ferrier well within experimental accuracy. It is believed that the present results, combined with those of Olette and Ferrier, provide for the first time a reliable set of heat contents of iron from room temperature to the melting point. From these data, guided by available Cp measurements, it proved possible to derive Cp, entropy, and free energy function values for @-iron from room temperature to the melting point, and for y- iron in the temperature region of its stability. Exhaustive study led to the conclusion that extrapolations of y-iron functions to room temperature were not reliable enough to be useful; hence these have been omitted from the tables. EXPERIMENTAL Materials. Three samples of extremely high purity iron from different sources, containing widely different impurities, were measured. The first of these, designated "Chipman", was kindly supplied by Dr. K. K. Kelley of the U. S. Bureau of Mines from a lot which was made many years ago by Dr. John Chipman of the Massachusetts Institute of Technology. The second, designated6&apos;Teddington", was supplied by the National Physical Laboratory, Teddington, England, from a lot zone-refined by them. The third sample, designated "Irsid", was supplied by the Institute de Recherches de la

Jan 1, 1962

By A. S. Emanuel

A correlation has been developed for calculating the phase behavior of, gas-condensate systems at reservoir conditions. The correlation is based on the principle of corresponding states and has been coded for an IBM 7094. Experimental K-values were determined for several gas-condensate systems at reservoir conditions to evaluate various semi-empirical parameters of the correlation. The approximate range of application of the correlation is 150 to 300F and 1,500 to 6,000 psi. INTRODUCTION The rapid development of digital computers during the past several years has made feasible the calculation of hydrocarbon phase behavior by methods based on rigorous thermodynamic principles. Good correlationsl have been developed for low to moderate pressures, but these techniques have not yet been extended successfully to reservoir fluids at high pressures. Consequently, the determination of phase behavior of oil and gas systems at reservoir conditions is still based almost entirely on generalized data correlations or on experimental studies of the fluid in question. While these methods have been used successfully many times, they do have inherent limitations that restrict their applicability. Generalized correlations, such as the NGShlA K-charts, are limited to the range of pressure, temperature and components for which the data were determined. The accuracy of these correlations is often questionable because the effect of total system composition is not well defined. Experimental studies offer a reliable method for determining phase behavior, but usually the studies are costly and time consuming. Recently, Leland and co-workers presented a new approach to calculating phase behavior from the principles of corresponding states.6-8 Corresponding states methods determine the thermodynamics properties of a given system by comparison with a reference substance whose properties are known. The accuracy of this approach depends on close chemical and structural similarity between the reference substance and the system in question and between components within the system itself. For high accuracy, it is usually necessary to correct for chemical and structural dissimilarities. In principle, however, the corresponding states method should be no less accurate at high pressures than at low pressures, provided reference substance properties are known. This paper describes an empirical modification of the basic correlation proposed by Leland, et al.6 for the specific purpose of calculating the phase behavior of gas-condensate fluids at reservoir conditions. The modified correlation, which has been programmed for an IBM 7094, may be used for either approximate or precise determination of fluid behavior depending on the amount of analytical and, experimental data available for the system. BASIC THEORY The basic theory of the corresponding states phase equilibria correlation was first published by Leland, Chappelear and Gamson.6 Subsequently, Leland, Chappelear and Leach published methods for improving the accuracy of the original theory.7-9 The aim of the correlation is to calculate the K-value of each component of a given system as a function of pressure, temperature, and over-all composition, where Once the K-values are known, the phase behavior may be determined directly by an appropriate flash calculation. The basic equation for calculating component K-values was taken from the work of Joffe. 4 For any component i of a mixture, the K-value is given by

Jan 1, 1969

By J. Serra, M. Turpin, R. Alberny

A new method is proposed to obtain automatically an unbiased estimate of the interdendritic spacing A. It is shown that the structure can be built by a random distribution of a rectangular basic unit. The usual definition of the interdendritic spacing yields a value 1 which, coupled with A, gives the shape of the basic rectangular unit. A study of the relationship between dendrite arm spacing and solidification rate was conducted as a part of a research program on dendritic solidification. For any comparison between theory and experiments to be meaningful, it is necessary to measure reproducible and clearly defined spacings. Fig. 1 shows clearly that even in a fairly simple structure such measurements are difficult. if we compare photos (a) and (b), we can hardly assess which one shows the larger spacing. Moreover, the quantity to be measured can be defined in several ways. On a small scale, dendrites seem to be distributed in a very regular and ordered way. However, on a larger scale, this regularity no longer exists. The usual way to measure spacings is to pick up some rows of dendrite stalks; such measurements are obviously biased since less orderly regions are not taken into account. A more objective method is to section the picture with randomly oriented straight lines and average the measured interdendritic spacings. The purpose of this paper is to show that such measurements, which can be conducted automatically, yield objective and reproducible results which are directly related to characteristic features of the dendritic structure. I) THEORETICAL ANALYSIS 1-1) Mathematical Morphology and Function of Co-variance. Matheronl and Serra2 enlarced- the definition and geometrical meaning of the notion of covariance to encompass problems in mathematical morphology. A brief review of part of their theory can be stated as follows. Let A&apos; be an isolated particle, and let us consider a group of two scanning points h is the vector joinlng these points, h its modulus, and a its direction. Let us also define a boolean function, k(x), whose value is 1 if x lies inside the particle and 0 if it 1s outside. The total number of events in which both points are inside A&apos; IS the covariance Ii&apos;,(h): is the measure of the intersection of A&apos; with the particle ALh obtained by translating A&apos; of -h Obviously K,(O) is the volume of the particle A&apos;, or its area if A&apos; is a two-dimensional body. The average value of K,(h), when the direction of a vector h of constant modulus is rotated, is: An important property of the covariance is illustrated on Fig. 2: if the shape of a particle shows some regularity along a direction a, K,(h) generally presents a maximum. We now consider a group A, made of many particles A&apos; distributed in space; then k(x) is taken as the realization of a stationary random f~nction.~ The volume fraction (or fraction of area if the problem is two-dimensional) occupied by A equals the average value q of k(x): meaning "average value of"). We also replace

Jan 1, 1970

By J. A. Cahill, A. D. Kirshenbaum

Using an alumina or zirconia crucible with an alumina sinker or a molybdenum sinker coated with zirconium dioxide, the density of liquid iron was determined by the immersed-sinker method over the temperature range of 1800" to 2500°K. The density, with respect to temperature, is ex-Dressed by the equation Dg/cm = 8.523 - 8.358 X 10 T&apos;K The molar Volumes and thermal coefficients of expansion were calculated. Iron, upon me1ting, was found to expand 3.5 pct. A basic knowledge of the physical properties of materials at high temperatures is becoming increasingly important. A check of the literature shows, that in spite of the importance of iron, very few measurements have been made of its physical properties in the liquid state. Density measurements have been made by Benedicks and his collaborators1g using the method of balanced columns, by Desch and smith4 using the immersed sinker method with an alumina sinker, by Lucas using the maximum bubble method5 and by Stott and endall&apos; who used an alumina pyknometer. In the method of balanced columns, the difference in level of molten iron in two arms of a U-tube, together with the corresponding difference of pressure had to be measured. The formation of gas bubbles in one or both arms was a great source of error. These values are very erratic. They vary from 6.83 to 7.45 g per cm3 at the melting point (1805"~) and from 6.45 to 7.15 g per cm3 at 1890°K. Stott and Rendall determined the density at 1837"K, with a reproducibility of *0.2 pct. They used an alumina pyknometer fired to 1973°K. The vessel was filled in a vacuum furnace by immersion in the liquid metal. When thermal equilibrium was attained, the pyknometer was withdrawn, cooled, the ingot removed and then weighed. The chief disadvantage of the method was the difficulty of inserting the pyknometer without cracking it. The authors have been able to determine the density of liquid iron from its melting point up to 2500°K, by using the immersed-sinker method, with A1203 or ZrOz crucibles and A1203 or molybdenum sinkers coated with Zr02, Fig. 1. EXPERIMENTAL Apparatus. In these studies the source of heat was the carbon tube resistance furnace with an argon atmosphere described previously.7 Experimental runs were made using either Ala3 or ZrOz crucibles. The sinkers used were 1) pure A1a3 and 2) molybdenum coated with ZrOz. The crucible, 2 1/8 in. in diam and 3 in. high, was centered in the furnace on an Ala3 of Zr02 pedestal. The sinker, 1/2 in. in diam and 1 1/2 in. long, together with a counter weight, was suspended from an analytical balance into the melt by a molybdenum wire. Procedure. The procedure, as described previously,&apos; consisted in measuring the weight loss of the sinker in the liquid iron while determining simultaneously the liquid iron temperature by means

Jan 1, 1962

By D. E. Hartman, J. M. Roberts

A detailed study of the temperature dependence of the critical stress, TB . necessary to cause a damping loss of 1.41 x 10-6 g mm per mm3 in pre-strained magnesium single crystals has been carried out in the temperature range 82" to 320°K. Tb is found to be linearly related to the reciprocal of the ahsol~cte temperature in this temperature range. The temperature dependence of the anelastic limit, TA, defined as the stress necessary to form open unidirectional stress-cycle damping loops has been measured between 82" to 320°K. ta is found to be independent of temperature in this range. It is suggested that TA is determined by the stress necessary to activate Frank-Read dislocation NUMEROUS studies1-9 have been reported concerning the details of yielding and microstrain near and below the generally discussed macroscopic flow stress. The work of Kramer and coworkers10-13 is helpful in determining certain qualitative facts. concerning preyield phenomena. The absence of a stress-dependent delay time in annealed copper and aluminum single crystals between 83" and 298 suggests that the preyield mechanism is temperature-independent in this range. This is not sources. The temperature and stress dependence of the effective activation volume (Veff) has been measured in the damping-loop region in prestrained magnesium single crystals. The data suggests that Veff/kT is approximately constant, equal to 2 4.5 sq mm per g in the temperature range 130°to 298°K, and that Veff is almost independent of stress at stress levels greater than 10 g per sq mm. A restricted model is developed to predict the stress (rb) necessary to cause a small fixed damping loss as a function of temperature, effective activation volume, and dislocation density. Various possible dislocation mechanisms controlling TB are discussed. true for zinc, p brass, and iron crystals in the same temperature range, however, since the existence of a stress-dependent delay time suggests a thermally activated preyield mechanism in these materials.10-13 The work by Vreeland et a1.14 confirms the work by Liu et al.ll on delayed yielding in zinc single crystals. A stress-dependent delay time between 82" and 298°K was found12 in prestrained aluminum and copper crystals. These results suggest that the preyield phenomena may be different between prestrained and unstrained or annealed crystals. The temperature dependence of the yield point at 2 x 10-8 plastic strain found by Rosenfield and Averbach3 in annealed copper and aluminum is not in agreement with the delay-time data, unless possibly the delayed yielding experiment only de-

Jan 1, 1964

By R. W. Gurry, L. S. Darken

The solubility of cementite in austenite is computed by thermodynamic methods from the observed solubility of graphite. It is found that the solubility of cementite is greater than that of graphite in the entire austenite temperature range. Thus the prior discrepancy between this portion of the phase diagram and the observed metastability of cementite is partially resolved. FOR several years it has been apparent that a serious discrepancy exists in certain observations pertaining to the Fe-C system. Direct experimental data indicate: 1-That the curve representing the solubility of graphite in austenite&apos;" crosses that for cementite4 at about 945°C as shown in Fig. 1. 2— That graphite and austenite saturated therewith are stable1 relative to cementite at all temperatures between the eutectoid, about 723°C, and the eutectic, about 1153°C. These observations are mutually incompatible in view of a well-known consequence of the second law of thermodynamics, namely, that the stable phase (presumably graphite at all temperatures) has a lower solubility than the metastable phase (presumably cementite). Hence either 1 or 2 above must be in error; either the measured solubility of graphite or of cementite, or the observation as to the stability of graphite, is in error. Our present purposes are: 1—To collate the available data on cementite and prepare a table of HO — HO° and of (Fa— HO°)/T. This tabular method seems the best and most convenient way to represent the heat and free energy of formation. 2—To determine whether the measured solubilities of cementite and graphite in austenite are in accord with the above table and the measured thermodynamic properties of austenite, in order to resolve, if possible, the existing paradox of these two solubilities. Enthalpy of Cementite The enthalpy of cementite at 273 °K, H279 — HOcem, was computed by integration of the low temperature heat capacity as measured by Seltz, McDonald, and Wells" 68" to 298 °K) and as given by the Debye functions recommended by them (0" to 68°K); the result is included in Table I. At higher temperature HCem — H,,"" is given by Kelley who used the data of Naeser7 (298" to 1037°K) and of Umino8,9 (273° to 1923°K). We have recalculated Hcem — H273 cem from the data of UminoO in the following way. In the equilibrated alloy at temperature the weight fraction of cementite Pct c -Pct cr is PctC -PctCr designated f(C), and the

Jan 1, 1952

By W. C. Hardy, B. W. McArthur

The purpose of this work is to show application of laboratory data in calculating solution gas-drive performance of the Cisco K-I reservoir. Included herein is a diagram showing the graphical relationship between six variables common to all solution gas-drive mechanisms. With an iterative process one may assume existence of any of these six variables at a particular pressure and calculate the production performance likely to occur in a reservoir produced by solution gas drive. Four unique pressure values are described at which the material balance equation alone is sufficient to predict the cumulative volumes of gas produced. Information derived from these pressure points establishes a criterion for determining compatibility of the pressure-volume-temperature (PVT) analysis of the produced crude with the gas production history. Two averaging procedures are used to arrive at a relative permeability-saturation relationship which describes the field-wide performance. INTRODUCTION The Cisco K-1 reservoir is a lenticular-type sand structure lying at approximately 6,300-ft subsurface. It is located in the H. and T. C. Railroad Co. Block 97, SW 1/4 S 392 and NW 1/4 S 385, Scurry County, Tex. Correlation of data from logs indicated that the Cisco K-1 reservoir occupied approximately 3,218 acre-ft of space with a closure of from 15 to 20 ft. Analysis of the production data indicates that the initial formation pressure and temperature were 2,450 psig and 121°F, respectively. The bubble point occurred at 1,715 psig after production of 12,256 STB oil and 11,520 Mcf gas. Only traces of water have been produced since initiation of production. Successive material balance calculations from June, 1952, to June, 1957, showed that no initial gas cap or water influx has contributed to production of oil and that the Cisco K-1 reservoir originally contained approximately 1.44 X 10" STB of oil. THEORY Methods for calculating solution gas-drive perform-

By R. C. Ku, A. J. McEvily, T. L. Johnson

AS reported in a recent paper,&apos; we attempted to measure the response to stress of as-quenched Fe-Ni-C martensites (Ms of -35°C) in both the micro-and macrostrain regions. To avoid effects associated with the diffusion of carbon, tensile specimens were quenched from room temperature at 78°K and tested after 15 min in situ. It was assumed that the transformation had terminated and that the retained austenite was essentially stable. In the tensile tests microplastic strains of the order of 10"* were measured at stresses below 20 ksi. It was concluded that the observed strains were due to the motion of dislocations in the martensite, the dislocations having been introduced during transformation. It was argued that transformation or plastic deformation of the retained austenite did not contribute to the non-elastic deformation measured in the microstrain region. In contradiction to the above argument, Magee and paxton2 have more recently shown that the strain due to isothermal transformation of retained austenite to martensite can contribute to plastic deformation at low stresses even at 78°K. Moreover we were unaware (nost)-a culpa) of a paper by Machlin and cohen3 in which it was clearly shown by resistance measurements that isothermal transformation at 78°K leads to the formation of an additional 1 pct or so of martensite after the initial athermal transformation, even in the absence of external stress. We have verified Machlin and Cohen&apos;s results in the following manner. A capacitance microstrain gage was placed on a tensile specimen before immersion in liquid nitrogen. After 15 min at 78°K detectable burst phenomena had ceased and it was then possible to obtain a continuous record of the additional extensional strain due to spontaneous isotherma1 transformation. The results for the Fe-Ni-C series studied are shown in Fig. 1, and are similar to those of Machlin and Cohen who investigated a low-

Jan 1, 1968

This report presents the comments of members of the Institute&apos;s Sub-committee on Physics of Mine Ventilation on the proposals of a special committee of the Institute of Mining Engineers (London). This report is as follows: THEORY OF MINE VENTILATION Abstract of a report submitted June 16, 1925, to the Council of The Institution of Mining Engineers by a Special Committee Laws of Flow of Aib The law of flow of air in mine galleries is, at present, expressed by two formulas differing slightly in shape but both derived from the original hydraulic formulas of Chezy and others. These formulas are: The Atlcinson Formula.—Pa = KsV2, which in transformation becomes a3 where P = pressure producing flow; K = coefficient of friction; s = surface of the mine galleries; V = velocity of flow; Q = rate of flow; a = area of mine galleries. This formula is especially applicable to mine galleries, but is unwieldy in application, as in many problems we are dealing with changes produced in the same set of airways when K, s, and a are assumed not to change, and the only variables are P and Q. Great uncertainty prevails as to the exact values to be assigned to the coefficient K in different types of airway, as different workers have given widely differing values. This formula assumes: (I) That resistance to flow is independent of the pressure within the gallery. (2) That changes in volume within the limits of pressure ordinarily met with may be neglected. (3) That changes in density and viscosity and mode of flow of the air may be neglected. (4) That the coefficient K is a constant. (5) That P is proportional to the square of the velocity. We cannot find any reliable experimental work leading us to conclude how far these assumptions are justifiable in mining practice. Equivalent Orifice Formula.—The fundamental form of this formula is Q = ~nA.\/2~11

Jan 1, 1927

By M. J. Marcinkowski, R. M. Fisher

The flow stress-grain size relationship has been determined at room temperature in both a disordered and a fully ordered FeCo for plastic strains up to 30 pct. The results are in agreement with a Hall-Petch relation of the type given by Of =a,+kd-1/2 where of is the flour stress and a, increases mono-tonically with increasing strain to a maximum value which is much higher for the ordered than for the disordered alloy. The slope, k, is found to increase FOLLOWING the original work of Halll and petch relating the effect of grain size to the lower yield stress of iron and steel, it has been generally found that the yield stress oy.s. of polycrystalline metals with strain to a maximum and then decrease for both ordered and disordered alloys. However, k for the ordered alloy is in general higher than that for the disordered alloy and the critical strain for k max somewhat larger. All of these observations can be satisfactorily accounted for quantitatively and in some cases semiquantitatively by using a slip band-grain boundary intersection model, and by taking note of the fact that, in general, moss slip, while quite common in the disordered alloy, is extremely difficult in the ordered alloy. obeys a relation of the form oy.s.=a0+kd-1/2 [1] where a, and k are constants and d is the mean grain diameter. For convenience, and in accord with prevailing custom, Eq. [I] will be referred to simply as the Petch relation. Tjerkstra3 and Armstrong, Codd, Douthwaite, and petch4 showed that the flow stress af of iron or steel measured at strains of up to at least 20 pct also obeyed a relationship of the type given by Eq. (11. The latter investigators have also shown that Eq. [I] applies to fcc and hcp metals and alloys.

Jan 1, 1965

By C. A. Eligwe, F. W. DeVries, A. E. Torma

This study is an investigation on using hydrogen peroxide for tank-leaching of uranium with sulfuric acid. The optimum sulfuric acid concentration was found to be 0.03 mole 11 -&apos;for a 25% pulp density suspension. The order of reaction with respect to sulfuric acid concentration was found to be ns0.75. The best results vith hydrogen peroxide were obtained at a 4.64 molar ratio of 6202 to U in the ore. The order of reaction was found to be zero with respect to hydrogen peroxide concentration. The theoretical maximum rate effect of Hz02 on uranium extraction was derived as Vm = 8.15 x mole &-&apos;min-&apos;. The highest rate experimentally attained was 8.09 x mole kL&apos;min-&apos;. It was found that the uranium extrac- tion was not affected by the pulp density up to the 50% used in this study. However, the final yieldswere significantly higher (over 90%) for leaches carried out in the presence of Hz02 than (less than 90%) for leaches carried out in the absence of H202. The reaction was found to follow a first order course with respect to substrate concentration (pulp density) regardless of the presence of H202. The effect of temperature was more explicit at moderate tempetatures (30 to 55 C) than at lower (10 C) or at higher (70 C) temperatures. At this latter temperature an almost complete extraction was realized even without H202. The apparent activation energies were found to be AEa = 2.68 kJ mole-&apos; in the absence of H202, 0.5 kJ mole-&apos;with Hz02 at 40 C to 70 C. and 4.72 kJ mole-&apos; with Hz02 at 10 C to 40 C. All these activation energy values suggested that the uranium extraction process is diffusion controlled regardless of the presence of H202. Further, the change in activation energy in the presence of Hz02 indicates the possibility of change in the reaction mechanisms at lower and higher temperatures.

Jan 1, 1980

By R. H. Richards

In October, 1891,I read a paper before the Institute on a "A HandTelescope for Stadia-Work" (Bans., xx., 732), and promised to report at an early date some results showing the degree of accuracy attained with the instrument. I am now able to report on these results and also on certain improvements that I have made in the target since the first paper was read. I may say that I prefer the title, "Prismatic Stadia-Telescope," to that used in my earlier paper, for while the instrument can be used with perfect satisfaction for short sights up to, say, 300 to 600 feet when held in the hand, it is impossible to read milch longer distances without the use of a tripod, as a steady support for the instrument. Results are here given upon four combinations of prism and telescope. No. 1. A telescope made by Alvan Clark & Sons, 3-inch objective, 28 inches focal length, magnifying 60 diameters, the prism covering half the objective: Feet measured Reading of Distance reduced Reeding of rod pro by tape. the rod. to feet. portional to 100 ft. 127.66 1.1825 100 .92629 211.35 1.9585 100 .92666 326.59 3.0265 100 .92669 484.88 4.4925 100 ,92652 606.91 5.6225 100 .92641 Average,,92651 The value of this prism therefore is .92651 feet on the rod for 100 feet of distance, or 1 foot on the rod corresponds to 107.931 feet of distance. No. 2. A Bardou telescope having a 1-inch objective, magnifying 20 diameters, and a prism covering half the objective:

Jan 1, 1893

By Donald Barton

THE theory of gravitation is based on Newton&apos;s law that any two bodies exert a mutual attraction which is proportional to the product of their masses and inversely proportional to the square of the distance between them; i. e. A= K MM/R2 (1) where K is a constant, M and m are the respective masses of the two bodies, and R the distance between them. In the earth&apos;s gravitational system, the earth is one of the bodies; the other may be any body within or without the earth. In theoretical discussions and calculations in regard to gravity, that other body usually is taken as a unit of mass: in the C. G. S. system, a body of one gram in mass.

Jan 1, 1928

By J. L. Huiatt, G. M. Potter, R. B. Tippin

The US Bureau of Mines and Great Salt Lake Minerals and Chemical Corp. have developed a froth flotation process for concentrating potassium salts from Great Salt Lake solar evaporites containing about 6% K2O. The crude evaporites, which were predominately halite (NaCl) with smaller amounts of kainite (KCl.MgS0, 2.7Hp0) and schoenite KeS0,MgS04.6H,0), were conditioned in a saturated brine solution., thus converting nonfloatable kainite to the floatable mineral schoenite. Schoenite was then selectively floated with a medium-molecular-weight fatty acid. Continuous small-scale pilot-plant testing indicated that 80% of the potassium could be recovered from the crude evaporites in flotation concentrates assaying about 13% K2O.

Jan 1, 1976

By R. C. Kadyk, C. J. Bise

High-voltage cable couplers are convenient and widely used accessories in modern coal-mine power distribution systems to help extend and retract power-feeder cables throughout a mine. Coupler design has tried to keep pace with the industry&apos;s desire to move to higher distribution levels, but the increase in recorded failures of 15-kV class couplers, which serve the 12.47-kV and above distribution levels, has inhibited this transition. Problems associated with the effects of partial discharge on high-voltage cable couplers are analyzed. The phenomenon of partial discharge is discussed, a testing standard is developed, and various coupler designs are subjected to its requirements. An analysis of test results and results based on field applications are provided.

Jan 1, 1985