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By Craig R. Barrett, Oleg D. Sherby

The creep characteristics of four pure metals with widely Varying stacking-fault energies (silver, copper, nickel, and aluminum) were evaluated above 0.5Tm. Creep tests were performed under conditions of constant atomic diffusivity and constant stress over the elaslic modulus. The sleady-state creep rate, Es, was found to he a funclion of the THE most common empirical representation of the steady-state creep rate, Es, at high temperatures and intermediate stresses is of the form where a is the applied stress, E is an elastic constant, A and n are constants (n is typically stacking-fault energ, y, such that Es is proportional to y3,5. In addition, it was uncovered that the primary creep strain and the strain to fracture increased with increasing y, and that the ratio of initial to steady-state creep rate decreased with increasing y. about 5), Q is the activation energy for creep (usually equal to that for self-diffusion), and kT has its usual meaning. sherbyl and McLean and ale' have used this expression to correlate creep data for a number of pure metals. An interesting aspect of Eq. [I] is the absence of any dependence on the stacking-fault energy. While most creep data seem to obey the stress and temperature dependence predicted by Eq. [I], when data for several metals are put on a master plot they do not fall on a common line but form a band. The width of this band corresponds to a variation in Es of 102 to l03. sherbyl attempted to explain this band by assuming that a grain-size effect was present which led to the observed variation. On the other hand, Felt-

Jan 1, 1965

By H. R. Hardy

The study of the mechanical properties of geologic materials was initiated in the Mining Research Section of the Fuels and Mining Practice Division in 1951 as part of a fundamental study of ground stress in Canadian coal mines.1 Early in the investigation of the mechanical properties of geologic materials, however, it was realized that the test results are influenced by the rate and the duration of loading. For this reason, laboratory investigations2,3 were undertaken to study the effect of long-period uniaxial stress on the deformation and failure properties of these materials. A literature survey indicated that work on the time-dependent properties of geologic materials had been very limited in the past.

Jan 1, 1965

By N. E. Truitt, D. G. Russell

The transient pressure behavior of a well which produces a single compressible fluid through a singte-plane wrticat fracture has been investigated mathematically. The fracture is assumed to possess infinite flow capacity, to be of limited mdial extent, and' to penetrate the producing formation completely in the vertical direction. Previous studies of vertically fractured wells have been concerned primarily with production rate performance or semisteady-state pressure behavior. This study was undertaken to ascertain the influence of vertical fractures on transient pressure tests such as pressure build-ups and flow tests. In a vertically fractured system, flow in the region nearest the fracture is practically linear, whereas farther away from the fracture essentially radial flow prevails. Thus, transient pressure analyses based on radial flow theory are somewhat inaccurate. As fracture penetration increases radially, kh values calcutated from pressure build-up and flow test curves become increasingly larger than true values. Failure to consider the effect of fracture penetration also introduces inaccuracies into the catculation of fracture length from the apparent skin factor and into the determination of average reservoir pressure. If the total length of the fracture is 20 per cent, or greater, of the drainage radius of the well, corrections must be made to pressure build-up and flow test results. Methods for correcting such results are discussed in this paper. For wells with prefracturing pressure build-up or flow test data, it is possible to estimate fracture length by comparison with postfracturing build-up or flow test results. In new wells or wells without prefracturing build-up or flow test data, fracture length must be estimated to correct the values obtained from analysis of pressure tests after fracturing. Fracturing efficiency calculations should be made whenever possible to provide an estimate of fracture length. Tables of the dimensionless pressure drop as a function of time and fracture penetration are included in this paper. Using these values should permit analysis of other types of transient pressure behavior in vertically fractured wells. INTRODUCTION Hydraulic fracturing has been used quite successfully for over a decade as a completion and stimulation technique in oil and gas wells completed in low-permeability reservoirs During this period a considerable amount of theory has evolved on the performance of hydraulically fractured reservoirs and on more efficient means of artificial fracturing. Although theory has been developed, no rigorous investigation has been made of pressure build-up and flow test behavior in such wells. Prats et al.1 first discussed the performance of vertically fractured reservoirs for the case of a compressible fluid. Their work was primarily concerned with production performance at constant flowing pressure. These authors also considered large-time (semisteady-state) constant production rate behavior for vertically fractured wells; however, transient pressure behavior at constant rate was not investigated. McGuire and Sikora10 and Dyes, Kemp, and Caudle2 employed an electrical analog to investigate the influence of artificial vertical fractures on well productivity and pressure build-up. They found that fractures which extend beyond 15 per cent of the drainage radius away from the well alter the position and slope of the straight-line portion of the build-up curve. They concluded that these effects must be considered both in the determination of the effective permeability of the formation and in any calculations of final build-up pressure. Although these authors did not undertake an exhaustive study of the influence of vertical fractures on pressure build-up performance, their limited results were quite interesting from the standpoint of the effects they demonstrated. In a more recent paper, Scott- reported the results of an investigation of the effect of vertical fractures on pressure behavior, which was conducted with a heat flow model. Scott's results appear to be consistent with those reported in Refs. 1 and 2. However, the effects of different fracture lengths on performance were not investigated. Pressure build-ups and transient flow tests are among the most diagnostic tools available to the reservoir engineer or production engineer. Since a very high percentage of present-day well completions incorporate the hydraulic fracturing technique, a definite need exists for information on the effect of fractures on transient pressure performance. For these reasons we have undertaken a rigorous study of pressure build-up and flow test behavior in vertically fractured reservoirs. The objectives of this study were (1) to obtain synthetic pressure build-up and flow test

Jan 1, 1965

By R. R. Boucher, O. J. C. Runnalls

A pronounced thermal effect has been observed on heating or cooling a1wninum-rich Al-U and Al-Pu alloys. From microscopic and X-ray diffractionstudies, the effectl has been attributed to trnsfor)nations in the inlemetallic phases UAl, and PuAl , involuing rearrangement or cluslering of vacancies The transformation obsrved in Al-20 wi oct U alloys occurred near the a Al-UAl4 eutectic tem-perature of 646°C making it difjicult to detect from heating curves. When cooling, howeoer, thermal mad X-ray analyses indicnted that the high-temperati~re phase labeled p UAL, precipitated initially during euitectic solidification. As solidification continued and after an induction period o-f 5 lo 20 tnin the nu-cleatiorz and growth of the low- twmperature phase, a UAl4 produced an euolution of energy which raised the observed alloy temperature by 1° to 2°C. in Al-Pu alloys the transformation occurred at 645°C, 5 deg below the eutectic solidification temperccture. The eslimated latent heat of transformation was 25 +5 cnl per g PuAl,. The high-tetnpevcl-ture forms of UAl, and PuAl, were easily 9-etccined by chill casting Al-U and Al-Pu alloys and on reheating the alloys the trcltzsforrnation to the a phase was sluggish even above 600°C. Separated single cryslals o-f UAl4, joy example, showed no evidence Of transformalion after heating for 16 hr at 620°C. The transformation rates increased yapidly enough with increasing temperature, however, that a a spontaneous liberation of energy lens observed on occasion when bealing cast Al-20 wt pet U to neal- the RECENT phase studies on A1-Pu alloys have indicated that earlier reported equilibrium diagrams should be modified to take account of several poly- morphic transformations in the intermetallic compound PuAl,.' During the course of the latter work an unexpected heat evolution was observed while cooling a solid alloy consisting of a mixture of a aluminum and PuA1,. The evolution occurred at 645°C, y below the a A1-Pu A1, eutectic solidification temperature. Subsequent thermal-analysis experiments with A1-U alloys showed that heat was evolved there also at a temperature nearly coincident with the a A1-UA1, eutectic solidification temperature of 646°. A search of the literature revealed that similar thermal effects had been observed before for both A1-U and A1-Pu but had never been fully explained.2,3 The purpose of the present paper is to describe thermal-analysis and X-ray diffraction experiments which have led to the conclusion that the thermal effects are due to transformations which involve the rearrangement of vacancies in the intermetallic compounds UA1, and PuA1,. EXPERIMENTAL PROCEDURE The A1-U alloys were prepared by heating super-pure aluminum (99.99 pct +) obtained from the Aluminum Co. of Canada in a graphite crucible surrounded by an induction coil. At 1000°C high-purity uranium metal produced by the Eldorado Mining and Refining Co., Ltd. was dropped into the liquid aluminum and was dissolved completely within 15 min. The impurities in the uranium were A1—4 ppm, Ca-4, C-70, Cr-3, Cu-6, Fe-30, Mg-2, Mn-10, Ni-25, Si-25, and Zn-2. The A1-Pu alloys were prepared by reacting plutonium dioxide with liquid aluminum under cryolite (3 NaF . AlF,) for 10 min at 1100°C in graphite crucibles exposed to the air. The plutonium was 99.8 pct pure, containing trace impurities of Ca, Cu, Fe, Pb, Si, and Zn. The liquid alloys were usually poured into water-cooled molds to provide castings of uniform composition from which samples could be cut for heat treatment and thermal-analysis experiments.

Jan 1, 1965

By J. L. Brimhall, R. A. Huggins

The structure of deformed internally oxidized alloys of siluer- cotztcrining magnesium and copper-containing aluminum in was studied by thin-film transrrzissiotz electron microscopy. With low to moderate amounts of stvain, the deformation structure in t11e dispersion-hardened alloys was found to consist of a high density of dislocations arranged it a random distribution or in a very fine, but poorly defined, cell stucture, depending on the fitness of the dbsbersion and amount of deformation. 112 contrarst, both pure copper and silver show relative1y Large, distinct cell structures. The particular structures in the alloys are believed to result from particles acting as both dislocaliot~ sources and deflector-s. The Inck of a pvorzolrr~ced deformation texture tr~ regiotzs qf' seoere loctll plastic curvature after heavy deformation can also be traced to the formation of clislocntions on many slip systemes and a lack 01 local concentrations of dislocations of predominantly one sign. THE presence of fine dispersions of a second phase has long been known to have a strong influence upon the mechanical properties of solids. Until recently, the influence of particles on the deformation mechanisms has been assumed to be solely that of barriers to dislocations. This is seen in the classic models of edge dislocations being restrained by the particles.1 4 There is, however, considerable evidence that this is not their primary effect, and that the particles can have a large influence on the defect structure generated by plastic deformation. The presence of particles causes changes in the surface topography observed after deformation. In overaged precipitation-hardened materials containing hard, noncoherent precipitates, fine intersecting slip lines are found after deformation of single crystals. indicating the activation of many slip systems. This has been extensively observed in the A1-Cu systen;, both by optical microscopy and replica electron microscopy.'"13 In some of the observations. the slip lines were seen to extend between the particles. Similar observations of extremely fine slip lines or the apparent absence of normal slip lines have also been found in A~-M~."

Jan 1, 1965

By M. F. Comerford

M. F. Comerford (Smithsonian Astrophysical Observatovy)- The authors' concern about the effects of preferred orientation is justified and emphasizes a phenomenon that can be a source of serious error, but the cogency of their concluding statement bears close examination. They contend that comparison of intensities from parallel planes of the two phases, as proposed by Averbach, Comerford, and Bever,13 leads to incorrect results. The state- ment is based on the fact that, in Fig. 3, intensity measurements at extreme angles of tilt, (2, lead to different values than those given by the average of all the data. The proposed explanation is that unsuspected superpositions of (110), reflections spuriously enhance the martensite intensity. However, it can be shown on appropriate stereographic projections that no superpositions occur which can affect the reflections in question. Hence, the ex-

Jan 1, 1965

By P. A. Tucker, C. R. Hudgens, D. E. Etter, D. L. Roesch, D. B. Martin

The equilibrium phase diagram of the Pu-Cd system is presented based on data obtained by differential thermal analysis, metallography, and electron-microprobe X-ray analysis. Liquidus temperatures range from 320° to 934°C. The system contains one congruently melting compound, PuCd, (945°C), and three incongruently melting compounds, PuCd, (800°C), PuCd, (730°C), and PuCd11 (410°C). A liquid-miscibility gap extends from 2 to 60 at. pet Cd with the monotectic reaction isotherm at 910°C. INTEREST in the potential use of plutonium alloys as reactor-fuel materials has prompted investigation of the phase equilibria in plutonium binary systems. A cursory investigation of the phase equilibria in the Pu-Cd binary system was conducted by differential thermal analysis (DTA), metallography, and electron-microprobe X-ray analysis (EMX). Extensive solid solubility of cadmium in both e and 6 plutonium was predicted1 based on atomic radii and electronegativities. Liquid immiscibility between these two elements was also predicted based on Mott's extension of Hildebrand's method. In the only previous investigation of the Pu-Cd system,2 two intermetallic compounds, PuCd11 (incon-gruent melting point 406°C) and PuCd8, were identified. EXPERIMENTAL The plutonium metal used in this work had a total impurity content of 500 ppm; the major impurities were: carbon (215 pprn), silicon (75 ppm), iron (60 ppm), nickel (40 ppm), and aluminum (25 ppm). The cadmium was reagent grade with a purity of 99.99 pet. The DTA technique for the study of plutonium alloys was previously described in detail.3 The alloys to be studied were prepared in tantalum DTA specimen capsules which were sealed by inert-gas welding. The alloys were homogenized in the liquid state in these sealed capsules which prevented the loss of cadmium by vaporization. Only the thermal arrests in the DTA heating curves were used to define the transformation temperatures of the system since supercooling affected many of the results during cooling. After the alloys were analyzed by DTA, the same alloys were used for the metallographic studies. Metallographic examinations were conducted in the manner described for plutonium alloys., No reaction was detected between the alloys and the tantalum capsules. Alloys for EMX analysis were placed in metallographic mounts together with specimens of unalloyed plutonium and cadmium which served as standards. The samples were highly polished but unetched. No protective coatings were applied to the surfaces of these radioactive specimens. Such coatings are detrimental to the excitation conditions and have been found to be unnecessary for the control of radioactive contamination. RESULTS The results of the DTA studies are presented in Table I. The phase diagram, constructed from these data plus the metallographic and EMX results, is presented in Fig. 1. The congruently melting compound, PuCd2, was identified by the occurrence of a maximum melting point (945°C) at 33.3 at. pet Pu-66.7 at. pet Cd and by the presence of a single phase in this composition.

Jan 1, 1965

By R. P. Marshall

This note describes positive evidence that hydrogen in titanium alloys diffuses under the influence of a thermal gradient. The experiments confirmed the expected similarity of this system to the H-Zr system and produced qualitative information on the magnitude of the heat of transport for hydrogen in titanium alloys. This effect has practical importance in applications where titanium alloys operate in a thermal gradient under conditions such that hydrogen embrittlement may develop within the expected lifetime of the structure, for example in supersonic aircraft service. The theories of thermal-gradient diffusion may be found in recent reviews and experimentation in this field by Shewmon,1 Sawatzky,2 Markowitz,3 and Darken and Oriani.4 The basis for Soret thermal diffusion is the "heat of transport", denoted by Q*. This is an energy term for the amount of heat (energy) transferred by atomic diffusion, and can be either positive or negative signifying a driving force for atomic diffusion to the cooler or hotter region, respectively. Experimentally, Q* is determined by plotting the natural logarithm of the point-to-point concentrations after exposure to a thermal gradient vs the respective point-to-point temperatures in units of the inverse absolute temperature scale. The slope of the straight line is Q*/R, R being the gas constant. For the titanium experiments, specimens (3 by 1 by 1/16 in.) of a) commercially pure titanium, b) the 8 Al-1 Mo-1 V titanium alloy, and c) the 6 A1-4 V titanium alloy were exposed to thermal gradients of 6° to 115°C per in. for 18 days at 250° to 550°C. The temperature gradient was in the direction of the 3-in. dimension. The hydrogen concentrations existing after exposure were determined on sections of the specimens by vacuum extraction. Three sections of unexposed sheet of each alloy were analyzed as standards to allow a check for hydrogen

Jan 1, 1965

By J. Szekely

The paper discusses simultaneous heat conduction and diffusion. These problems may arise in slag-metal kinetics and in connection with rapid heating or cooling of specimens. A mathematical formulation is given and it is shown that the transients due to either the variability of the diffusion coefficient with temperature, or thermal diffusion, are unlikely to be important for molten or solid metals and slags. The negligibility of these effects is due to the large values of the ratio thermal diffu-sivity/molecular diffusivity. In many problems relating to transport-controlled metallurgical kinetics the diffusion process is accompanied by the transfer of heat; large-scale metal refining or metal reduction may be quoted as examples. It has been shown that due to turbulent mixing in these systems the relevant transport phe- nomena are best described in terms of "surface renewal models" which require the solution of the unsteady-state diffusion equation.1-1 Problems involving simultaneous diffusion and heat conduction are also encountered in the laboratory in connection with rapid heating or cooling of specimens. The effect of variable temperature on diffusion may be twofold: a) in the absence of "cross effects" the problem, due to variable temperature, is that of diffusion with a variable diffusion coefficient; b) if the Soret Effect is nonzero, thermal diffusion must also be taken into account in the formulation. Although information is available on thermal-diffusion transients in a steady-temperature gradient,4'5 little work has been done on the effect of unsteady temperatures on either the diffusion coefficient or on thermal diffusion.' In the following a formulation is given and solutions presented with a view of examining the areas where these effects may be important.

Jan 1, 1965

By R. V. Higgins

This paper presents a computer method to obtain the shape factors and equal cell volumes of the channels for any well spacing pattern from a potentiometric model. By using this program the authors have processed the data for the seven-spot, direct line-drive and the staggered line-drive patterns. The data for the five-spot pattern had been previously processed by a noncomputer method and are included for completeness. The shape factors and volumes for the channels are presented in tables for those who want to use them to process data using their own permeability relationships and viscosities of their reservoir oils. The authors have used the data and sets of representative permeability curves to process sample calculationr of waterflood performances. The comparison of the calculated results shows that the influence of well spacing is small. The permeabilities of the reservoir rock to oil and water had a greater influence on oil recovery for a given pore-volume throughput of water than the well spacing pattern. The more water-wet the reservoir rock, the better the possibility of permeabilities which are conducive to good recovery. The viscosity of the reservoir oil also influences the recovery more than the well spacing pattern. The reduction in the percentage recovery of oil with increase in viscosity of the reservoir oils is small when oil viscosities are in the range of 0.1 to 3. Above this range the reductions in recoveries are extensive. Sample comparisons of the time required for different patterns to recover the oil are presented. Results of an example calculation are given to show the effect of the permeability profile on recovery. INTRODUCTION The effect of well spacing pattern on the recovery of oil when flooding with either gas or water has been studied by many investigators. Muskat et al.1 presented an analysis using conductivity, sweep efficiency and unit mobility to the time of breakthrough. Dyes et al.2 used experimental techniques (X-ray shadowgraphs) and different mobility ratios. They presented quantitatively the relationship between mobility and sweep efficiency at and after breakthrough. Hauber3 presented a method to predict waterflood performance for arbitrary well spacing patterns and mobility ratios. Craig et al.,4 using techniques similar to Dyes et al. to determine sweep efficiency for a five-spot pattern, added the use of relative permeability curves at breakthrough and thereafter. Douglas et al.5 sed rela- tive permeabilities and continuously changing saturations throughout the entire five-spot flood pattern. In obtaining their solutions they used finite-difierence equations. Hig-gins and Leighton6,7 also used relative permeabilities and continuously changing saturations throughout the pattern before and after breakthrough. They employed techniques that process a flood-pattern calculation on the computer in about one minute. The methods of Douglas et al. and Higgins and Leighton both checked closely the laboratory results for a wide range of mobility ratios. This paper presents some sample performances calculated by the Higgins and Leighton method that show the effect on recovery of different permeabilities and viscosities using the seven-spot, the line-drive and the staggered line-drive, as well as the fivespot flood pattern. No previous paper has presented these data using different permeability curves and continuously changing saturations throughout the flood patterns. The paper also presents (1) the results and analyses of the flood-pattern prediction, (2) the computer techniques for determining the shape factors and volumes from the potentiometric models for the foregoing flood patterns, and (3) the shape factors and volumes of the channels of the flood pattern in the event reservoir engineers may like to process waterflood calculations using their own permeability curves and reservoir oils. DESCRIPTION OF METHOD VOLUMES AND SHAPE FACTORS The use of channels taken from a potentiometric model (see Fig. 1) to aid in calculating the performances of water floods of nonlinear patterns has been thoroughly explained in the literature.0,7 Therefore, very little theory, discussion, or proof regarding this phase will be repeated in this paper. The computer method presented in this paper to calculate the volumes and the shape factors of the channels of potentiometric models employs the trapezoidal rule for the volumes and the Pythagorean theorem (the hypotenuse equals the square root of the sum of the squares of the two sides of a right triangle) for the shape factors. In calculating the volume of a channel, the area of each cell in the channel is determined and then multiplied by the thickness to obtain the volume. In determining the areas of the cells, trapezoids are constructed whose vertical sides are spaced Ax apart, as shown in Fig. 2. The length of the sides is the difference between an ordinate cut off by the top and bottom of the cell — usually equipo-tentials. The coordinates of the points along an equipo-tential or streamline are obtained by Lagrange's8 equation of interpolation for which the constants are coordinate points at the intersections. Three intersections for con-

Jan 1, 1965

By Alan T. Gorton, T. L. Joseph, Gust Bitsianes

High-temperature X-ray diffraction techniques were used to determine thermal expansion coefficients of iron and its oxides. Lattice parameters of a and iron, wiistite, magnetite, hematite, and goethite were determined and plotted as a function of temperature. From these results, the true and mean linear thermal expansion coefficients were calculated. In the case of noncubic crystals, the expansion coefficients were determined along each of the crystallographic axes. The effect of the magnetic transformation on lattice parameter was measured for a iron and magnetite at their respective curie temperatures. COEFFICIENTS of expansion for iron and its oxides were determined from the temperature dependence of their lattice parameters. From these data, the true linear coefficients were derived by means of the formula: at =[(l/ao )(dao/dt)] [1] where at is the true linear coefficient of expansion, a, is the lattice parameter in angstrom units, and all variables are referred to the temperature, t, in OC. Thus the true expansion coefficient represents the instantaneous change in lattice parameter on a unit basis and at a particular temperature. A second expansion coefficient is also often used. It is termed the mean linear coefficient and is defined in the following way: am = [ao(t) - ao(O)]/ao(0) l [21 This coefficient represents the average change in lattice parameter on a unit basis but at a specified parameter length, ao at O°C, and over a specified temperature range,1 to 0°C. Generally the true co-

Jan 1, 1965

By Harry C. Gatos, Frank J. Bachner, Mario D. Banus

The portion of the Nb-Sn phase diagram between 75 and 79 at. pct Nb at temperatures near the liquidus has been investigated by melting alloys of known composition and examining the microstmc-tzlres resulting when these melts were quenched. The Nb-Sn samples were contained in magnesia sleeves, and were mounted in a high-pressure apparatus. It was shown that Nb3Sn me1ts by a peri-tectic decomposition and that the composition of the compound Nb3Sn at the peritectic horizontal lies between 77 and 78 at. pct Nb. Analysis of the phases present in the samples was accomplished by anodic staining techniques and an electron-microbeam analyzer. DURING the past several years a great deal of work has been devoted to the Nb-Sn system, and the bulk of this work has been primarily concerned with the intermetallic phase Nb3Sn. However, the melting characteristics of Nb3Sn have not been investigated because of the difficulty in maintaining known compositions due to tin losses by vaporization, and the added difficulty of containing Nb-Sn alloys without sample-container reaction at the high temperatures involved. This paper reports on the development of a technique for containing Nb-Sn alloys under pressure high enough to prevent tin losses at temperatures in excess of the liquidus. Using this technique, melts of known composition were made and a phase diagram near the liquidus is proposed based on the microstructures resulting when these melts were quenched. EXPERIMENTAL The Nb-Sn alloys weighing 0.7 g each were prepared in the form of cylinders. Niobium powder, -200, +325 mesh, and tin shavings with a minute amount of tin powder for a binder were mixed in the desired proportions and cold-pressed at 50,000 psi in a 0.150-in. die. This cylinder was then enclosed as shown in Fig. 1, and the entire arrangement mounted in a 2.6-in. pyrophyllite tetrahedron.' The desired temperatures (-2500°C) presented several problems in high-pressure container materials. Boron nitride, the usual sample holder, was found to react with niobium to form the nitride. However, MgO cans and plugs machined from refractory rods did not melt nor react with the sample. Thick tantalum contact disks were used to carry the large currents (~450 amps) to the graphite heater, since tantalum did not melt and had enough strength to prevent extrusion of the sample. It was further observed that the graphite heater and tantalum disks could not be in direct contact with the pyrophyllite because it melts and decomposes at these temperatures to kyanite and coesite (SiO2),2 the former reacting with graphite and the latter with tantalum to form the silicide. The use of a MgO outer sleeve

Jan 1, 1965

By A. E. Dwight, A. F. Berndt

Binary and ternary alloys of uranium with transition metals were prepared with U2X stoichiometry. The compounds U2Tc, U2Rh, U2Os, and U2lr were formed by peritectic or peritectoid transformations, and were shown to be isostructural with U2Ru. The lattice constants are presented. Miscibility relationships obtained from the study of ternary alloys are graphically summarized in terms of an area-of-stability plot. The compound U2Re is not isostructural with either U2Ru or U2Mo. A series of compounds with stoichiometry U2X has been prepared in which X is technetium, rhodium, rhenium, osmium, or iridium. The only other U2X compounds, for which X is related to the above transition metals by proximity in the periodic table, are U2Mo and U2Ru. The structure of U2Mo is the tetragonal C11b type (MoSi2 type)1 and U2Ru is monoclinic, with a new structure type.' This investigation was undertaken to determine if any of the above compounds are isostructural with either U2Ru or U2Mo and to find the range of occurrence of these phases. EXPERIMENTAL Alloys were prepared from stoichiometric amounts of electrolytic uranium (99.99 pet pure) and transition metals of 99.5 pet purity (98+ pet pure Tc), by arc melting on a water-cooled copper hearth under an Ar-He atmosphere. Weight losses were negligible. The buttons were homogenized at temperatures between 700o and 800°C (900°C for U2Tc) in evacuated capsules and air-cooled. The X-ray powder specimens were annealed briefly at the temperature of homogenization. Except in the case of the technetium alloy, metallographic examination was used to determine the number of phases present. The radiation hazard involved in handling technetium precluded the use of metallography to examine U2Tc. The temperature and mode of formation of the U2X phases were determined by heating the metallographic specimens to successively higher temperatures, until examination indicated the presence of chilled liquid or a peritectoid transformation. RESULTS The U2X compounds investigated were found to be formed under the following conditions: UzTc unknown U2Ru peritectic 897o ± 3°C U2Rh peritectoid 755o ± 5°C U2Re peritectoid3 below 750°C Uas peritectic4 920°C U2Ir peritectoid 775o ± 5oC Debye-Scherrer patterns for the above U2X phases were made with CuKa radiation (nickel filter). The similarities in the positions and intensities of the strongest lines in the front-reflection region strongly suggested that U2Tc, U2Ru, U2Rh, U2Os, and U21r are isostructural with only minor differences in the unit-cell dimensions. The known lattice constants and intensities of the Debye-Scherrer rings for U2RU2 were used as a guide in order to index the low-angle X-ray reflections of the U2TC, U2Rh, U2Os, and U2Ir powder patterns. Approximate lattice constants for these compounds were thus obtained and were used along with the intensities observed for U2Ru to index the strongest lines in the back-reflection regions. A sin2 2? correction term was included and the lattice constants were refined and standard deviations estimated by least squares. Comparison of observed and calculated values of Q(= 4 sin2?/?2) used in these calculations are given in Table I. In each case when the positions of lines could not be resolved on the films they were not measured. The final lattice constants, with their standard deviations, are given in Table 11, along with the unit-cell volume and X-ray density. The values of the atomic volume5 of the transition ele-

Jan 1, 1965

By R. A. Sharma, F. D. Richardson

Manganese oxide acitivities and sulfide capacities have been measured at 1650°C in mixtures of MnO + A1203 and MnO + SiO2 - Al2O3. Sulfide capacities have also been measured at 165O0C for melts of MnO + SiO2, MgO + SiO2, MgO + SiO2 + Al2O3, MgO + MnO + SiO2, and SiO2 + Al2O3 and for crystalline CaO. The activity coefficients of the sulfides of manganese and magnesium have been derived where possible. It looks as though the activity coefficients of sulfides are greatest at compositions where the free energies of formation of the silicate mixtures have their maximum negative values. The amphoteric nature of alumina is reflected in the results for the binaries and ternaries in which it is present with silica. The limiting solubility of CaS in CaO at 1650°C is 6.3 x 10-4 mole fraction. THE activities of manganese oxide have been measured in a variety of silicate and aluminate melts by use of the equilibrium (MnO)slag = [Mn]pt .½O2 [l] and the experimental techniques described previously.' Sulfide capacities (CS = wt pct S (PO2/PS2)½) have also been determined in a series of melts, by use of an established method2 which exploits the equilibrium (O°) + ½S2 = (S") . ½O2 [2] If CS and the activity of a metal oxide are known in a melt, the activity coefficient of the metal sulfide can be calculated by use of the equilibrium constant K, for the pure phase reaction MO i ½S2 = MS + ½O2 [3] The activity coefficient of the sulfide is then given by the equation

Jan 1, 1965

By W. W. Mullins, F. A. Nichols

Solutions are developed, assuming surface diffusion and both internal and external volume diffusion, for the relaxation of bodies slightly perturbed from spherical and cylindrical geometries. Combined with those previously published for the nearly planar case, these results provide a means of gaging the relative contributions of the two diffusional proc-cesses in any given case. It is shown that in all sintering experiments to date, and probably in any attainable in practice, surface diffusion has played the dominant role, although most previous authors have assumed otherwise. It is also shown that surface diffusion predominates in normal field-emission tip blunting and also for the coalescence of gas bubbles introduced into metals by a bombardment. The surface-diffusion solutions for a perturbed sphere are combined with previous results for volume diffusion to show that the inclusion of interface diffusion permits considerably larger spheres to develop in diffusion-controlled precipitate growth before the onset of instability. A mechanism is also proposed for the spheroidization of precipitate platelets as well as rods. In a previous paper1 the relaxation of a nearly plane surface to flatness by the combined action of the transport processes of viscous flow, evaporation-condensation (in a closed system), volume diffusion, and surface diffusion has been analyzed under the assumption that all surface properties are independent of orientation. In this treatment, criteria were developed for deciding which process predominates, and solutions valid in the latter stages of the sintering of small wires and particles to a plane were obtained. A numerical solution, valid throughout the entire particle-sintering process for the case of surface diffusion, was subsequently obtained by the present authors.' It was found that the analytic solution (which assumed small slopes everywhere) is accurate to within -10 pct when the maximum slope of the profile is less than 0.3; the wire-sintering problem has also been solved nu- merically for the case of surface diffusion and here again the results converge to the analytic small-slope solution at late stages of the process, the two solutions agreeing in this case to within 10 pct when the maximum slope of the profile is less than -0.6. The purpose of this paper is to extend the perturbation solutions to nearly spherical and nearly cylindrical geometries. We treat only the two principal diffusional processes, i.e., surface and volume, but for these geometries we discuss volume diffusion both inside and outside of the solid. Our results, when coupled with Mullins' solutions1 for nearly planar surfaces, provide criteria for gaging the relative contributions of surface and volume diffusion to the over-all transport process in three basic geometries. A very interesting feature in the cylindrical case is the occurrence of instability for longitudinal perturbations with wavelengths greater than the cylindrical circumference, a classical result. This instability of the cylindrical surface is applied to give a quantitative explanation for the often-observed "erratic" pore closure in the late stages of the sintering of wire compacts; also, the theory previously presented for the spheroidization of rod-shaped precipitates by surface (interface) diffusion' is expanded now to include volume diffusion inside and outside of the particle. The results for circumferential perturbations on a long cylinder allow quantitative estimates for gaging the relative importance of surface or volume diffusion in the early stages of the sintering of spheres or wires. The results here demonstrate clearly that surface diffusion has played a very important, if not dominant, role in all sintering experiments discussed in the literature, although the surface-diffusion contribution to the kinetics has usually been ignored. The results for the sphere (surface-diffusion case) are added to the results obtained previously by Mullins and sekerka3 concerning instabilities of a growing spherical precipitate particle (with interface diffusion disallowed) to obtain a general solution to this problem including interface diffusion. The inclusion of interface diffusion is found to increase significantly the range of stability of a growing spherical precipitate for typical metallurgical cases. The following assumptions are made: (i) the initial surface lies everywhere near and has a slope differing only slightly from that of the reference

Jan 1, 1965

By J. L. Stokes, L. J. Demer

It has recently been shown' that epitaxial films of silicon carbide deposited on silicon single crystals possess desirable properties for semiconductor applications. There is one apparent disadvantage to such a system, however; since epitaxial deposition is a high-temperature process, it can result in plastic deformation of the silicon substrate. The accompanying Berg-Barrett X-ray diffraction photographs reveal plastic deformation in two silicon semiconductor crystals which occurred when the crystals were coated with an epitaxial layer of silicon carbide at 1150°C. Due to differences in thermal expansion between the silicon substrate and the epitaxial silicon carbide, the silicon was subjected to stresses while still in the plastic temperature range. Both crystals shown were 0.7 in. in diam and 0.0055 in. thick. The crystals were sliced from a larger crystal so that their polar axes were parallel to the [ill] direction. After cutting, the crystals were polished with diamond paste, and etched in HC1 vapor to remove surface damage re- sulting from the cutting and polishing operations. This provided clean, damage-free surfaces on which to deposit the silicon carbide. Figs. l(a) and l(b) are reflection and transmission photographs, respectively, of the same crystal. A smaller portion of the crystal is shown in the transmission geometry, because a vertical slit was

Jan 1, 1965

By G. R. Speich, R. A. Oriani

The rate of coarsening (Ostwald ripening) of copper precipitate Particles in an a-iron matrix has been studied in three Fe-Cu alloys containing 2.3, 4.0, and 5.4 wt pct Cu in the temperature range 730° to 830°C. The kinetics of Ostwald ripening ohevs the law as deduced by Lifshitz and Wagner so that matrix diffusion controls the process. The equilibrium shape of the particles is that of rods with hemispherical caps, and is due to the BOTH Lifshitz and slyozov and wagner3 have recently solved the complex problem of determining the rate of coarsening of an assembly of precipitate particles. Both workers, although using somewhat different mathematical approaches, arrive at the same equation for the relation between the mean radius 7 of a distribution of spherical particles and the bulk solubility co, diffusivity D in the matrix, large anisotropy in the copper/a iron interfacial free energy (y,/y, = 4). A Lifshitz -Wagner equation, modified for both the nonsphericity of the diffusion field and the reformulation of the Gibbs-Thomson equation for the case of nonsphencal particles, is derived. Using the modified equation, the calculated values of the mean radius are smaller than those observed by a factor of about one -half. absolute temperature T, gas constant R, surface free energy y of the precipitate/matrix interface, and the time t of aging: where V, is the molar volume of the precipitate and v is a stoichiometric factor. Wagner's treatment is restricted to the case of spherical particles growing in a liquid matrix where strain energy is not a factor. Lifshitz and slyozov have discussed the effect of anisotropic particle shapes and internal strains on the rate of coarsening. Oriani4

Jan 1, 1965

By A. L. Jr. Pozzi, A. O. Garder, D. W. Peaceman

A new numerical method is proposed for the solution of multidimensional miscible displacement problems. Besides the usual stationary grid associated with numerical procedures, the method uses moving points for which positions and concentrations are computed each time step. Based on the method of characteristics for treating combined transport and dispersion, the method applies equally well to any number of dimensions and, in contrast with other numerical procedures, properly takes into account the physical dispersion, no matter how small. Extensive tests show that accurate solutions of one-dimensional problems can be obtained over a wide range of values of the dispersion coefficient, including zero. They also show that the moving points do not need to be uniformly spaced, and that increasing the number of moving points beyond 2/grid interval does not significantly improve the accuracy of the solution. Two-dimmsional calculations using the new method were carried out to simulate laboratory model displacements in which gravity caused overriding of solvent. Good agreement between observed and computed profiles and measured and computed concentrations of produced fluid was obtained for a viscosity ratio of 1.89; at higher viscosity ratios, fair agreement was obtained Computed results were found to be significantly affected by vertical dispersion, and negligibly affected by dispersion in the direction of flow, in agreement with conclusions based on experimental observations. INTRODUCTION Although miscible displacement processes are potentially of great economic significance, limited progress has been made in developing mathematical methods for predicting the outcome of a solvent flood. Because of the complexity of the partial differential equations which describe multidimensional miscible displacement, numerical methods are a natural approach to their solution. The task of finding suitable numerical approximations to one of the partial differential equations, which involves both dispersion and convective transport, has been particularly difficult. Dispersion in the absence of transport is described by the heat flow equation, a second-order equation of parabolic type. This equation has been very successfully treated by numerical methods. Transport in the absence of dispersion is described by a first-order equation of hyperbolic type. This equation has been treated numerically with some success in one dimension, both by Lagrangian and Eulerian techniques, 1.2 but extension to two or more dimensions has not been satisfactorily accomplished. Usually one of two things happens: either the numerical solution develops oscillations or it becomes smeared by artificial dispersion resulting from the numerical process. When transport and dispersion are considered simultaneously, this numerical dispersion may dominate the low physical dispersivicy that generally characterizes miscible displacement. Stone and Brian2 have developed a new difference equation for treating combined transport and dispersion in one dimension. By suitable choice of certain parameters, they succeeded in markedly reducing both oscillation and numerical dispersion. However, a satisfactory extension to higher dimensions has not yet been found. Peaceman and Rachford3 presented a centered-in-time and centered-in-distance difference equation combined with a 1,transfer of overshoot" procedure which was demonstrated to work well in one dimension. The technique was applied to the two-dimensional miscible displacement problem, but subsequent calculations with zero dispersivity showed little change in results compared with the calculations they presented. This indicates that their method involved a numerical dispersion of the same order as the physical dispersion. The present paper describes an alternate method for solving the combined transport-dispersion

Jan 1, 1965

By W. F. Sullivan, J. R. Coleman

The use of radioisotopes in obtaining basic information on large scale industrial processing is illustrated with two examples. The first is concerned with the operating characteristics of a kiln scrubbing tower and the second with those of a Hardinge ore mill. The examples show the advantages associated with the industrial use of tracers as well as the limitations. The Atomic Energy Commission regulations governing the use of radioisotopes in this manner are also discussed. The nuclear properties of radioactive isotopes have provided a new technique for obtaining basic information on large scale industrial processing. A small portion of the process stream is made radioactive by mixing with a suitable radioisotope or by irradiation in a nuclear reactor. The "tagged" portion is then part of the normal process stream and can be followed by detection and measurement of the associated radioactivity. The advantages of radioactive tracing over other forms of tracers are well known, and include such factors as chemical similarity, capability of precise determination of very small quantities due to the high sensitivity of detection apparatus, and the absence of foreign element contamination of the final product. This report will illustrate two applications of the use of radioactive tracers in large scale industrial processing which have provided information that would have been hard to obtain by other means. The first is concerned with the operating characteristics of a kiln scrubbing tower and the second with those of a Hardinge ore mill. ATOMIC ENERGY COMMISSION REGULATIONS Atomic Energy Commission approval can be obtained by qualified personnel if the proposed quantity of radioactivity does not exceed AEC's standards for

Jan 1, 1965

By A. Ahmadieh, J. E. Dorn, Jack Mitchell

A detailed investigation of the disloccrtion mechanisms controlling prismatic, slip in a solid solutions of magnesium containing up to 15.9 at. pel Li revealed that low-temperature prismatic slip is controlled by the Peicrl's mechanism for all alloy compositions. At higher temperatures slip in the 7.9 at. pet Li alloy was found to follow the diclates of the cross-slip mechanism from basal to prism planes, while the higlier-lilhium alloys exhibited an athermal dejormation process which might be due COARSE-GRAINED polycrystalline aggregates of distilled magnesium exhibit very limited ductility at low temperatures.' The ductility of polycrystalline magnesium, however, is much improved by solid-solution additions in excess of about 8 at. pct to shot-range ordering. The major effect of lithium additions on the low-temperature Shear] stress. for prismatic slip appears to be due to its efftct in lowering the Peierl's stress whereas (1 increase in the shear stress with increased lithium conlent at higher temperatures might he due to short-range order strengthening. Additions rip to 7.9 (at. pel Li appear to have only minor effects on the slackiug-jaidt energy. Li.2 Although the relative amounts of basal slip and twinning are not materially altered by such alloying, a substantial change takes place in the relative amounts of prismatic slip. Whereas prismatic slip is negligible and limited to regions of high stress concentrations in the vicinity of the grain boundaries in pure magnesium, extensive prismatic slip over entire grains occurs in the higher lithium content alloys. Furthermore, as the lithium content is increased above 8 at. pct, the flow stress for polycrystalline aggregates decreases. Comparison of the single-crystal data on pure magnesium for basal slip by Sheely and Nash3 and those for prismatic slip by Flynn, Mote, and Dorn4 indicates that the critical resolved shear stress for prismatic slip is much above that for basal slip.

Jan 1, 1965