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By J. L. Snoek

[ ] DISCUSSION J. L, SNOEK*-Stress-induced preferential diffusion in cubic body centered metals in the annealed state provides us with a powerful tool for determining the mobility of interstitially solved atoms as well as their location in the lattice and the exact nature of the distortion brought about in the lattice by their presence. Calculations given by D. Polder31 show that the distortion of the lattice, besides being proportional to the applied stress P, is also proportional to [VC, RT + xVCo] where T, V and Co are the temperature, molar volume of the solvent and molar concentration of the solute respectively and x is a constant describing the mutual interaction energy of the dissolved particles. This calculation obviously is no longer valid if x is negative and the abso¬lute value of xVCo surpasses that of RT. The lattice may then be expected to become tetragonal spontaneously. Such a spontaneous tetragonality seems to have been observed by W. Klemm and L, Grimm for the case of oxygen solved in vanadium.32 Measurements of the internal friction in cold worked iron containing carbon or nitrogen should provide us with information on the mobility as well as the preferential location of these particles in the iron lattice in the cold worked state. The work by T'ing-Sui Kê is a valuable contribution to this problem, The data obtained by T'ing Sui Kê and myself on cold worked samples of iron seem to indicate that carbon and nitrogen in these samples are found either in the normal (1/2 , 0, 0) interstices or in a new preferential position created by the cold working. The latter positions in my opinion can hardly by anything else but the edges of the dislocations. The observed larger distances of diffusion might be explained by assuming that the carbon atoms when freed from a certain dislocation by thermal agitation must diffuse over several atom distances before being caught in another dislocation. The theory however needs working out and no doubt will be much more complicated than the one valid for the annealed state. T'ING-SUI KÊ (author's reply)-It is highly encouraging to read the written discussion given by Dr, Snoek who initiated the theory of stress-induced preferential diffusion in cubic body centered metals in the annealed state, Since the presentation of this paper, the author has done more experimental work on this subject which seems to be able to settle several of the points raised by Dr. Snoek. It has been found that such stress-induced preferential diffusion occurs also in the solid solutions of carbon,33 oxygen,34 and nitrogen35 in tantalum which has a body centered cubic structure. Analysis of the shape of the observed internal friction. peaks indicates that the inter-

Jan 1, 1948

By B. Zondek, W. T. Cardwell, J. W. Sheldon

The fundamental equations that are used to describe two-phase fluid flow in porous media are Darcy's law for each phase and an equation of continuity for each component. The special case of one-dimensional, incompressible, two-phase flow has received much attention in the petroleum engineering literature.1-10 The basic paper on the subject is that of Buckley and Leverett.2 Buckley and Leverett showed that one could eliminate the pressure and obtain a single partial differential equation for the saturation. They solved this equation for the case when gravity and capillary forces are negligible. A frequently encountered property of the solution of the basic partial differential equation is that, as time progresses, the saturation becomes a multiple-valued function of the distance coordinate, x. Buckley and Leverett interpreted the formation of multiple values as an indication that the saturation-distance curve had be-come discontinuous. They developed a method of determining the position of the discontinuity from a material balance. We solve the Buckley-Leverett partial differential equation using the method of characteristics and the concept of shocks. Our treatment is analogous to treatments used in the theory of supersonic compressible flow." Although the numerical results obtained are the same as those obtained by previous methods, we believe that this approach is more logical and has broader applicability. It can, for example, be generalized to treat the case when the fluids are compressible. It is not clear how one would go about doing this using the method of Buckley and Leverett. To illustrate the power of the method of characteristics with shocks, we solve a problem in gravity segregation which has not been treated previously in the literature. A special case of the general method developed here was used by Welge, to solve a particular fluid displacement problem. We consider two-phase incompressible flow along the vertical direction x in a porous medium. We assume that there is no flow transverse to .x. We measure positive in the upward direction. The fundamental equations are obtained from Darcy's law and the mass conservation law. Since the two phases are incompressible, mass conservation is equivalent to volume conservation.

By C. J. Rosa, W. C. Hagel

An attempt is made to determine the diffusion coefficients of oxygen ions in hypostoichiometric zirconium oxide. A phenomenological theory is developed for three-phase, unidirectional volume diffusion of a gaseous species from a planar source. Knowledge about oxygen diffusion in a and ß zirconium and experimentally measured rates of movements of interfaces permit the evaluation of oxygen ion diffusivi-ties in ZrO2-x. The results conform to the relationship: sq cm per sec, for the temperature range of 875" to 1050° C. DIFFUSION coefficients of oxygen ions in stoichio-metric oxides have been studied by many investigators. The obtained results not only supplement the knowledge about the lattice-defect structures of oxides and conduction mechanisms but also provide information of technological importance. Rate processes such as oxide sintering, high-temperature creep deformation, and oxidation of metals and their alloys are directly dependent on diffusion phenomena. Unfortunately, diffusion coefficients obtained from studies on stoichio-metric oxides cannot be treated without restraints when applied to oxidation kinetics, if precise evaluations of oxidation rates are desired. Oxides formed on metals are usually nonstoichiometric and exhibit nonuniform distribution of either cation or anion vacancies across their thicknesses. Debuigne and Lehr1 extended Danckwerts'2 mathematical analyses and furnished a semitheoretical treatment for evaluating oxygen diffusion coefficients in zirconium oxide in terms of weight gain measurements during oxidation of zirconium in the temperature range 400° to 850°C. Their calculations are based on theoretical partitioning3 of the total amount of oxygen between a zirconium and its oxide phase. An inherent discrepancy appears to continue throughout their calculations. The amount of oxygen confined to the oxide phase should be corrected by multiplying the calculated oxide thickness by the inverse of Pilling-Bedworth ratio, if expansion of zirconium dioxide is taken into account. The purpose of the present investigation is to provide a new semitheoretical treatment for evaluating diffusion coefficients of moving species in hypostoichiometric oxide. The analyses are relevant to unidirectional volume diffusion. Although the presented method is quite general, its applicability will be discussed in terms of kinetic measurements from oxidation of zirconium at temperatures above the a/ß transition, for reasons stated in the later part of this paper. EXPERIMENTAL Pure, 99.93 wt pct, zirconium samples of approximately 2 by 1 by 0.35 cm were exposed to oxygen for various times at four temperature levels: 875°, 950°, 1000°, and 1050°C. High-purity, better than 99.9 vol pct oxygen was passed through a cold trap and columns containing anhydrous CaSO4 to remove residual water vapor. Before exposing to oxygen at a pressure of 500 Torr, specimens were subjected to wet abrasion on 200- through 600-grit Sic papers and polished with 1—p diamond dust. Prior to oxidizing, all zirconium samples were vacuum-annealed at 10-6 mm Hg for about 15 min at the test temperature. The temperature variation across the uniform heat zone was ±2°C from the preset value. Final polishing, for phase thicknesses measurements, was performed by using 8- and 1-p diamond dust and followed by vibrator polishing with 0.05-µ ? Al2O3 solution. Measurements of phase thicknesses were made by projection on a metallographic viewing screen. Conventional powder X-ray analyses for the oxide were employed. RESULTS Fig. 1 is an example of the cross section of oxidized zirconium. Designations of phases given below this figure are the same as those used in the three-phase diffusion system represented by Fig. 5 in the following section. Zirconium oxidized for longer exposure times showed two types of oxides: white oxide at the surface and an underlaying layer of gray oxide. X-ray powder patterns of these oxides at room tern-

Jan 1, 1969

By Gerhard Bockstiegel

Kuczynski's formula has been derived for the case of nonspherical particles. TWO formulae of Kuczynski's type have been derived, one describing the increase in tensile strength, the other describing the progress of shrinkage of a powder compact. It has been strength,shown that the exponents of all three formulae each contain two magnitudes of different physical characters, viz, the geometrical factor a and the kinetic factor ß. The interrelationships between the three exponents are stated. SOME years ago Kuczynski1 experimentally showed that the radius, x, of the area of contact between very small spherical metal particles and a metallic block is related to the time of sintering, t, by the following equation x = constant tk [11 where k has the value 1/5 or 1/7. Assuming that the metal particles were perfect spheres and the metallic block was perfectly flat, he derived the foregoing equation from theoretical considerations of the process of material transport in metals, and he showed that exponent k is different for different mechanisms of transport, e.g., k = 1/2 for viscous flow (according to Frenkel2), k = 1/3 for evaporation and condensation, k = 1/5 for volume diffusion, and k = 1/7 for surface diffusion. From this Kuczynski concluded that the mechanism of transport was either volume diffusion or surface diffusion, depending on whether the value of k, as found in his experiments, was 1/5 or 1/7. Subsequently. Cabrera8 corrected Kuczynski's calculations with regard to surface diffusion, showing that the theoretical value of exponent k is 1/5 for both volume and surface diffusion. He supposed that the different experimental values of k were due to slight differences in the shape of the metal particles. An exponential relationship similar to the aforementioned was found by Okamura, Masuda, and Kikuta,4 Masuda and Kikuta, and Takasaki8 when studying the rate of shrinkage on powder compacts during sintering. The authors measured the shrinkage by means of the fraction w = Vp — V./Vp — V,,,, where V,, is the volume of the green compact, V, is the volume of the sintered compact, and V,,, is the volume of the compact in its densest state. This fraction, w, they found, is related to the time of sintering, t, by the equation w == constant tm. [21 Further, Bockstiegel, Masing, and Zapf7 observed that the tensile strength, s, of sintering iron powder compacts can also be related to the time of sintering, t, by an equation of the foregoing type, i.e., s = constant tn. [3] For exponent n the values 0.28 (S=2/7) and 0.35 ( 2/5) were obtained, and the authors pointed out that there might exist a simple interrelation between exponent n as found in their experiments and exponent k in Kuczynski's equation. The authors supposed that 2k = n, since the strength of adhesion between a metal sphere and a block (as in Kuczyn-ski's experiments) must approximately be proportional to their contact area, p. x2. Theoretical Considerations This paper is an attempt to correlate the fundamental experiments of Kuczynski's type with the results obtained with powder compacts as represented by Egs. 2 and 3. In particular, the paper is to show how the rate of sintering is influenced by the geometry of the sintering particles and by the type of material transport. As the geometry of particles conglomerating in a powder compact is very complex, some simplifying assumption has to be made, of course, in order to adapt the problem to mathematical treatment. In the following paragraph a suitable simplification is introduced, and Kuczynski's formula is derived for the case of nonsphcrical particles. Relation Between Area of Contact and Sintering Time—As the face of contact between two particles in a sintering powder compact is not necessarily a circle (as in the case of spheres sintering to a block), Kuczynski's formula is modified as follows: Let the perimeter of the face of contact be described by means of polar coordinates R, 4, as shown in Fig. la, so the area of contact, f, is determined by f= 1/2 . S112p[R(Æ) ]2 dÆ [4] Then, let the two particles be intersected by a plane perpendicular to area f. The intersection is shown in Fig. lb. According to the nomenclature in this figure, the distance, h, between the surfaces of the two particles is a function of T and Æ: h = h(r,Æ). For the particular case of spherical particles, as in Kuczynski's theory, this function becomes: h = constant r2. It shall be assumed here that in the close neighborhood of their

Jan 1, 1957

By T. K. Redden

Protective coatings based on the formation of a surface coating of nickel aluminide (NiAl) were applied to the nickel-base superalloys IN 100, SEL 15, and U-700. Coated specimens were exposed to an oxidizing environment at temperatures between 1600 and 2200 F for times up to 1000 hr. The oxidation resistance and stability of the coating were evaluated by weight gain measurements, metallographic examination, and X-ray diffraction study of surface oxides and coating. The composition of the coating and diffusion zone was determined by electron microprobe traverse of samples before and after high-temperature exposure. Intermediate phases formed in the coating and diffusion zone were identified by X-ray diffraction in situ and after electrolytic extraction. The outer coating was found to consist of the inter-metallic compound, NiAl, while the diffusion zone contained MC, M23C6 or M6C carbides, and a phase in a matrix of NiAl + Nidl. Oxidation resulted in formation of an A1203 n'ch scale containing some Tz02. Depletion of aluminum during oxidation resulted in degradation of the outer coating to Ni3Al and the nickel alloy matrix. Diffusion of aluminum into the base metal was found to be slight and did not influence coating life significantly. The o formed in the diffusion zone during coating decomposed during elevated-temperature exposure to form stable carbide phases characteristic of the base metal. Diffusion zone phase changes were found to have no effect on the life of the aluminide coating in the oxidizing envzron?nent. THE oxidation resistance of many high-strength nickel-base superalloys is inadequate for extended exposure at temperatures above about 1600°F. In addition, some applications for these materials require that they be exposed to environments containing sulfur compounds and sodium salts which can cause surface attalk known as sulfidation or hot corrosion. In order to provide the necessary corrosion resistance to the high-strength alloys, protective coatings based on an aluminizing process have been developed. These processes, usually based on a pack cementation technique, result in the formation of a NiAl-rich outer coating layer either during the coating process or by a subsequent diffusion treatment. The performance of the aluminide coatings is affected by interactions between the coating layer and the base metal both during the coating process and during subsequent exposure at elevated temperatures. Knowledge of these interactions is required to guide the development of coatings capable of longer life and improved reliability. Goward et al.' recently reported the metallurgical factors which influence coating per- formance on MAR-M200. The present work is concerned with correlating the interactions and performance of coating compositions on several representative materials. EXPERIMENTAL PROCEDURES Materials. Three cast nickel-base superalloys which are used for turbine buckets in air-breathing engines were studied: IN 100, U-700, and SEL 15. Their chemical compositions are given in Table I. The alloys were vacuum-induction-melted and cast to slabs approximately 0.3 in. thick from which rectangular specimens 0.25 by 0.5 by 1 in. were machined. Coating Procedures. The machined specimens were coated by CODEP processes which were developed at the author's laboratory. These are based on pack cementation in various media to deposit either aluminum or aluminum in combination with titanium. The coating process which deposits only aluminum is designated CODEP-C, while the CODEP-D process deposits titanium in combination with aluminum. The CODEP-D process was applied only to IN 100. Both CODEP processes are applied at 1950" or 2000°F for 4 hr without need for a subsequent diffusion treatment. An outer coating about 1 mil in thickness is produced by these processes. Test Procedures. Coated specimens were exposed to static oxidation for periods ranging from 24 to 1000 hr at temperatures of 1600" to 2200°F. Terminal weight gain measurements and visual examination were used to evaluate oxidation resistance. including oxide spalling and coating failure. Both as-coated and exposed specimens of each alloy were studied by metallographic examination, electron microprobe analysis (EMA), and X-ray diffraction analysis either of the exposed surfaces or of phases extracted from the coating and diffusion zone. RESULTS As-Coated Condition. The microstructures of as-coated conditions were generally similar, irrespective of base materials or the particular coating process. They are typified by IN 100 coated by CODEP-D as shown in Fig. 1. The predominately single-phase outer layer, area A, Fig. 1, was identified by X-ray diffraction as the intermetallic compound NiA1. The NiAl zone extended inward to the original base metal interface. The diffusion zone, area B, Fig. 1, included carbide phases, a lamellar phase oriented perpendicular to the base metal surface, and a matrix phase consisting of a mixture of NiAl and Ni3Al. The phases in the diffusion zone were electrolytically extracted using a 10 pct HCl in methanol solution at approximately 1.3 amp per sq cm. The extracted phases were found to be M6C, MC, or M=C6 carbides and o as shown in Table I1 for each of the alloys. The d spacings from a typical diffraction pattern are

Jan 1, 1969

By Tenney, J. B.

DEVELOPMENT of complex ores in the south- western part of the Rocky Mountain region has been retarded by the prohibitive distance to the nearest suitable zinc treatment plants. In the north- western and central Rocky Mountains the building, cluring tlie past decade, of electrolytic zinc plants at Anaconda, Great Falls, Trail, and Burke has tremendously stimulated the mining and exploiting of such .ores, greatly increasing the production of lead, zinc, copper, gold, and silver. Selective flotation permits the making of high-grade led, copper, and zinc concentrates. If the zinc concentrates could be made free from lead, copper, gold, and silver, they could be shipped economically to Mid- Western retort plants designed for such concentrates. Unfortunately a considerable proportion of the precious metal content accompanies the zinc blende in the ores of this region. Although some of it is saved in 'retort residues, the treatment cost is thereby increased so materially and the proportion saved so small, that .concentrates of ordinary grade cannot stand treatment charges and freight.

Sep 1, 1928

By C. G. Durdaller, W. H. Robinson, G. M. Pound

The nucleation rate of the a (pay) to 0 (white) tin transformation was measured as a function of temperature and a tin particle size using an X-ray diffraction technique. The powder specimens of a tin were essentially monodisperse and the small dinzension of the particles of these specimens was varied from 13 to 75 p. Several types of nucleation sites of differing potency were fbund to be operative in the nucleation process, but it could not be determined whether these sites were on the free surface of the tin particles or within the volume. Assuming that they were on the free surface, the average density of the most potent sites was calculated to be 2.5 to 5.3 x 10' sites per sq cnz through the application of a Poisson distribztion finction to the isothermal data. Analysis of the temperature dependence' of the rate constmts at a given fraction transformed suggests that the active sites are regions of higher free energy and not catalytic interfaces. Appreciable induction periods were observed at the lower temperatures of transformation. Experimental studies1 of solid-solid phase transformations have led to the belief that the new phase nucleates at structural imperfections. The purpose of the present work was to learn more about the mechanism of nucleation in solids and the nature of the singularities at which nucleation occurs. In this investigation nucleation rates in the isothermal transformation of gray to white tin were measured by an X-ray diffraction technique using essentially monodisperse powders of gray tin. This particular phase transformation was chosen for study because it presented fewer experimental difficulties than most others. The experimental temperature-control problems were minimal because the two phases coexist in equilibrium at 13.3"C, and measurable transformation rates occur at temperatures only slightly above room temperature. The growth rate of the P phase into the a2 is sufficiently fast to make the measured transformation rate equivalent to the nucleation rate, provided that the particle size of the samples is small enough; for the experimental temperatures used in this study, the particle diameter must be less than 100 p. EXPERIMENTAL TECHNIQUE The P tin used in this study was obtained from Capper Pass and Son Ltd., North Ferriby, Yorkshire, England, and was of 99.999 pct purity. It was transformedS to the a phase and ground into a fine powder in an agate mortar. This powder was separated by a Roller air classifier into seven fractions whose dimensions, as determined by microscopic measurement of many thousands of particles, are given in Table I and whose distribution of size within each fraction is given in Figs. 1 and 2. The shape of the particles was roughly that of an oblate spheroid,

Jan 1, 1964

By A. G. H. Andersen, A. W. Kingsbury

SILICON bronzes containing iron are used to a considerable extent in industry, under the trade name of P.M.G. alloys. Various classes of wrought alloys fall in the composition range 1.5 to 3.5 per cent silicon, and 0.5 to 2.5 per cent iron. Castings may contain as much as 6 per cent silicon and 3 per cent iron at present. The constitutional diagrams of these alloys are thus of considerable practical importance. Copper-silicon-binary alloys have been thoroughly investigated by a number of workers, the latest reports being those of C. S. Smith1 and of A. G. H. Andersen.2 Although much work has been done on iron-copper alloys,3 recorded investigations on the copper-rich copper-iron binary constitutional diagram are not numerous. Tammann and Oelsen4 determined the solubility limits of iron in copper by means of magnetic measurements, and found that the solubility of iron in copper amounts to a fraction of one per cent at 400°C., increasing slowly to one per cent at 800°C. From 800°C., the solubility increases rapidly and attains 4 per cent at 1100°C. Hanson and Ford,5 using electrical resistivity measurements and the microscope, determined a somewhat different solubility limit. Of earlier X-ray works on the copper-iron system, very little has been published. The work by Bradley and Goldschmidt6 on copper-iron-aluminum alloys includes some information on the copper-iron binary. These investigators conclude that substitution of iron in the copper lattice decreases the spacings, which is contrary to the evidence of the present work. Hanson and West7 have investigated the ternary alloys of copper with iron and silicon. Although their diagrams are valuable contributions to the understanding of these alloys, they did not recognize the kappa phase,12, 7,8 and their diagrams do not everywhere conform to the phase rule. The present work contains a check by means of X-rays of the solid solubility limit of iron in copper, and an X-ray investigation of the ternary-phase diagram, which, owing to present conditions, it became necessary to curtail considerably. PREPARATION OF SAMPLES Castings weighing about 75 grams were melted under vacuum. The charges were made up of ingot iron, copper cathodes from Laurel Hill, and refined silicon supplied by the Electrometallurgical Co. Alundum crucibles were generally used. The exceptions were alloys 77 and 78, which were melted in graphite crucibles. The ingots were annealed at 800°C. for one week, then samples were cut for chemical analysis. Longitudinal sections of the binary alloy ingots were hammered into plates 3 in. thick. Wherever possible, these plates were homogenized at temperatures ensuring

Jan 1, 1942

By K. Barron

The glass insert stressmeter, or photoelastic stressmeter, is an instrument designed to determine stress changes occurring in rocks. It has several potential advantages over other such devices in that it is a biaxial device, it is simple and it is cheap to make. The object of this study was to assess the behaviour of the meter under biaxial loads and to examine some of the problems associated with measurement and interpretation of the fringe pattern. This assessment has been carried out by comparing theoretical and laboratory behaviour of the meter. It has been shown that: a) There are certain optimum measuring points in the meter at which measurements should be made for best accuracy. The position of the points depends on the ratio, n, of the biaxial stresses. b) The meter&apos;s sensitivity can be assumed to be independent of the rock modulus E provided that the rock modulus is < 2.5 x 106 psi and not, as previous workers have assumed, if E < 5 x 106 psi. c) There are several methods of separating the principal stresses; some of these are unsatisfactory. A new method is proposed and discussed. d) The meter sensitivity decreases as the ratio of the biaxial stresses approaches unity; the accuracy thus also decreases. e) The axes of symmetry of the fringe pattern give an excellent indication of applied stress direction. f) Laboratory calibrations are in good agreement with theory. The glass insert or photoelastic stressmeter is an instrument designed to determine stress changes occurring in rocks. It has several potential advantages over other such devices in that it is a biaxial device, it is simple and it is cheap to make. This stressmeter has been described in detail.l,2 Basically it is a hollow glass cylinder that has at one end a light source and filters producing circularly polarized light. The glass cylinder and source are grouted into a borehole in rock and the face of the cylinder is viewed through a quarter wave plate and an analyser. If, after installation, a stress change occurs in the rock, then a distinct colored isochro-matic fringe pattern is seen in the meter. The fringe order at any point in the meter can be determined by counting the fringes and measuring the fractional fringe orders by the Tardy compensation method. The relation between the fringe order at any point and the applied stress change can be determined either by calculation or by calibration. The object of this study was to assess the behavior of this stressmeter under biaxial loading conditions and to examine some of the problems of interpretation of the fringe pattern. THEORY Hiramatsu et a14 have determined the stress distribution in a hollow cylindrical inclusion in an elastic host material when subject to uniaxial stress. Using this solution, the biaxial case of stress p in the x direction and stress q in the y direction (Fig. 1) can be solved by superposition. This has been done in Appendix 1. It is shown that the principal stress difference (s1 -s2) at any point (r,?) in the cylinder is given by:

Jan 1, 1965

By A. G. H. Andersen, A. W. Kingsbury

SILICON bronzes containing iron are used to a considerable extent in industry, under the trade name of P.M.G. alloys. Various classes of wrought alloys fall in the composition range 1.5 to 3.5 per cent silicon, and 0.5 to 2.5 per cent iron. Castings may contain as much as 6 per cent silicon and 3 per cent iron at present. The constitutional diagrams of these alloys are thus of considerable practical importance. Copper-silicon-binary alloys have been thoroughly investigated by a number of workers, the latest reports being those of C. S. Smith&apos; and of A. G. H. Andersen .2 Although much work has been done on iron-copper alloys,3 recorded investigations on the copper-rich copper-iron binary constitutional diagram are not numerous. Tammann and Oelsen4 determined the solubility limits of iron in copper by means of magnetic measurements, and found that the solubility of iron in copper amounts to a fraction of one per cent at 400°C., increasing slowly to one per cent at 800°C. From 800°C., the solubility increases rapidly and attains 4 per cent at 1100°C. Hanson and Ford," using electrical resistivity measurements and the microscope, determined a somewhat different solubility limit. Of earlier X-ray works on the copper-iron system, very little has been published. The work by Bradley and Goldschmidt6 on copper-iron-aluminum alloys includes some information on the copper-iron binary. These investigators conclude that substitution of iron in the copper lattice decreases the spacings, which is contrary to the evidence of the present work. Hanson and West7 have investigated the ternary alloys of copper with iron and silicon. Although their diagrams are valuable contributions to the understanding of these alloys, they did not recognize the kappa phase,1,2,7,8 and their diagrams do not everywhere conform to the phase rule. The present work contains a check by means of X-rays of the solid solubility limit of iron in copper, and an X-ray investigation of the ternary-phase diagram, which, owing to present conditions, it became necessary to curtail considerably. PREPARATION OF SAMPLES Castings weighing about 75 grams were melted under vacuum. The charges were made up of ingot iron, copper cathodes from Laurel Hill, and refined silicon supplied by the Electrometallurgical Co. Alundum crucibles were generally used. The exceptions were alloys 77 and 78, which were melted in graphite crucibles. The ingots were annealed at 800°C. for one week, then samples were cut for chemical analysis. Longitudinal sections of the binary alloy ingots were hammered into plates h in. thick. Wherever possible, these plates were homogenized at temperatures ensuring

Jan 1, 1942

By J. P. Hammond, C. J. McHargue

THERE have been no publications on the wire texture, on the cold-rolled sheet texture, nor on the recrystallized sheet texture of vanadium. Since it has a body-centered cubic structure, it would be expected to show strongly preferred orientations such as are found in iron&apos; and molybdenum.&apos; The wire textures of body-centered cubic iron,3 tungsten," molybdenum,5 antalum,6 iobium,6 and brass6 have been found to have [110] directions lying parallel to the wire axis. Wires of iron,&apos; containing 1.95 pct V or 1.95 pct Si,7 and steel8 retain their texture upon recrystallization. Molybdenum9 and tungsttln&apos; wires retain their texture after recrystallization at low temperatures. A [loo] recrystallization texture has been reported for mo1ybdenum9 and for a Fe-Ni alloy (53 atomic pct Ni).10 The cold-rolled sheet texture for iron,&apos; mild steel," and molybdenum chiefly one in which the [110] directions lie parallel to the rolling direction and the (100) planes lie parallel to the rolling plane with a deviation from this position chiefly about the rolling direction as an axis. This paper presents the cold-rolled and the re-crystallized wire textures, and the cold-rolled and the recrystallized sheet textures for vanadium. The results show that the textures in vanadium are not significantly different from those reported for other body-centered cubic metals. The vanadium used in this investigation was the so-called "ductile" vanadium which has a nominal composition within the following limits:12 0, 0.05 to 0.12 pct; H, 0.001 to 0.004; N, 0.02 to 0.04; C, 0.03 to 0.07; and V, 99.8 to 99.9. The wires were formed by rolling annealed rods of 0.280 in. diam to 0.028 in., a reduction in diameter of 90 pct. The wires were then electrolytically etched to 0.005 in. diam and used as such for specimens. Annealed sheet was reduced 95 pct in thickness from 0.100 to 0.005 in. with a two-high, 4-in. diam mill using reductions no greater than 10 pct per pass. In order to avoid temperature effects, the sheet was allowed to cool between passes. X-ray specimens were made in the form of posts from the sheet. The sheet was mounted in a fixture and the edges were polished using metallographic technique. Each edge was alternately polished and etched during the last stages in order that all worked material would be removed. These post specimens were approximately square in cross-section. The specimens to be recrystallized were wrapped in tantalum foil, sealed in evacuated quartz tubes, and annealed at 1600°F. The X-ray data were obtained from transmission shots made with a 0.030 in. pinhole camera, and molybdenum radiation with a zirconium filter inserted between the specimen and film. The grain size was sufficiently small in both the cold-worked and recrystallized material to give satisfactory results with the specimens stationary. In order for the wire texture to be determined, transmission X-ray patterns were taken with the

Jan 1, 1953

By George L. Montgomery

In a recent article Heckler, Elias, and woods1 have described an automatic computer technique for plotting of pole figures. To anyone who has constructed pole figures manually from raw X-ray data, the development of computer plotting techniques has been a very welcome development. The purpose of the present note is to describe an alternative computer plotting method which, if somewhat less precise than the method described by Heckler et al., has the advantages of being faster and of not requiring the availability of a plotter. The plot is made directly by the printer of the terminal system and, by its nature, has a good deal of visual impact. Each character of output symbolizes a level of intensity. For example the numerals 1 to 9 might represent intensities referred to some reference obtained from a randomly oriented sample. Should more levels be required (this is seldom necessary) alphabetic or other characters may be used in addition. When these are arranged in the proper fashion, the result is a pole figure such as is shown in Fig. 1. It is the purpose of the computer program to transform the data and carry out the arrangement in a suitable manner. The computation is carried out on a line by line basis in order to reduce the amount of storage required and thus keep the program "small". It is, thereby, well within the limitations of the time-sharing systems which are becoming increasingly available. The inaccuracies introduced are slight and the plot can easily be made as precise as the technique used to collect the data. Comparison of pole figures produced by this method with those constructed manually shows a high degree of equivalence. To the present, the technique has been applied to reflected X-ray data only. X-ray data are collected in a manner identical to that described by Heckler et al. That is, as the goniometer rotates the specimen, a series of counts, accumulated over a preset time, is recorded. The method by which the proper symbol, representing an intensity level, is assigned to each print position is up to the ingenuity of the programmer. Perhaps the simplest method is to section the stereograph in the fashion of a polar net, and to assign all print positions lying within each segment a symbol representing the level of intensity recorded at the data point nearest to the center of the segment, see Fig. 2. The number and arrangement of the segments are selected to conform more or less with the number of accumulated counts and the geometry of the goniometer path used to collect them. Since the angular distance between accumulated counts is usually not infinitely controllable, it is impossible to locate one reading within each segment and, at the same time, maintain symmetry in the sectioning of the stereograph. This latter requirement is essential to keep the computer program simple and flexible. As an expedient it was found that the number of data points could be increased to conform with the number of segments, with very little loss of

Jan 1, 1969

By J. C. Savins

The practical analysis of the hydrodynamics of the wellbore has long been a subject of interest to engineers. This paper presents a simplified solution to the problem of computing the pressure drop for the flow of drilling mud in the annulus of the wellbore. This solution is, however, an exact and rigorous solution under the assumptions which have been imposed. These assumptions are that the drilling fluid is a Bingham plastic fluid* and that the annulus is formed by two concentric, stationary, cylindrical pipes. It is further assumed that the fluid is incompressible and that its motion is isothermal and in a steady state. This problem under the same assumptions has been attacked by previous authors. Beck, Nuss and Dunn&apos; proposed that the equation for the flow of a Bingham plastic fluid in a cylindrical pipe could be applied to an annulus if the pipe radius were replaced in the equation by the hydraulic radius. This equation, known as the Buckingham-Reiner equation&apos; (see Appendix 1), was also used in an approximate form. Van Olphen pointed out that even for a simple or Newtonian- fluid the pipe equation (Poiseuille&apos;s law) could not be converted to the Lamb equation escriptive of flow in an annulus (see Appendix 1) by using the hydraulic radius. Van Olphen further attempted to give a solution for the annular flow of a Bingham plastic fluid by introducing approximations similar to those which have been used in the case of the Buckingham-Reiner equation. Other attempts to provide approximate or exact solutions have been made by Grodde&apos; and by Mori and Ototakeq. The present authors some years ago in unpublished work derived the correct expressions relating the pressure drop and flow rate for this problem. It was found that the solution consisted of two simultaneous equations, one of which contained a logarithmic term. Thus, obtaining numerical results for any particular case of interest involves very tedious trial-and-error computations. Very recently Laird presented the correct derivation of the two equations which are given in full detail in Appendix 1. In order to reduce the amount of calculation time which would be involved in providing a complete tabular or graphical solution to the problem, a high-speed electronic digital computer has been utilized. For this purpose the two simultaneous equations were transformed into more compact expressions by introducing reduced variables. These expressions are given in the following theoretical section. A similar procedure in this problem has been developed by Fredrickson and Bird1" Their tabular results, however, are very incomplete in the range of practical interest for problems of wellbore hydrodynamics. We have furthermore been able to express our graphical results in terms of convenient and familiar dimensionless groups. THEORETICAL DEVELOPMENT Use of Reduced Variables In terms of reduced variables the two simultaneous equations just discussed take the following form, The reduced variables q, x, a and z are defined in terms of the various measured quantities, where Q is volumetric flow rate, AP/L is pressure gradient, Dl is OD of inner pipe, D, is ID of outer pipe, is plastic viscosity, and is yield point. Thus, we have a dimensionless volume flux, a dimensionless reciprocal pressure gradient, and the ratio of the pipe diameters Before introducing the fourth reduced variable, z, it is of interest to consider the physical significance of the parameter x. As may &apos;be seen from the velocity profile of Fig. 1 the Bingham plastic fluid has the interesting property that a portion of the stream flows at a uniform velocity without shearing action. This section of the stream is situated approximately in the center of the conduit and is known as the "plug flow" region. Its existence is due to the fact that the shearing stresses within the region do not exceed the yield point, which is one of the two flow properties characterizing the fluid. The parameter x then turns out to be the ratio of the

By Gregoire Gutzeit

THE development reported in this paper was begun by the author a number of years ago, while he was a lecturer on complex chemistry and metallurgy at the University of Geneva, Switzerland, and in charge of that institution&apos;s research laboratory. Completion of the development and reduction to practice did not occur until last year at the Westport mill, laboratories and testing plant of the Dorr Company, where this method is now in general use for identifying and localizing the mineral constituents of both metallic and nonmetallic ores. It has proved to be a practical tool of the metallurgical staff at the Westport mill, devising unusual milling flowsheets for complex and refractory ore bodies. In a number of instances the findings have been successfully used as fundamental factors in the design and specification of complete metallurgical plants. Seven examples of the use of this method in solving practical milling problems are included in this paper. GENERAL OUTLINE The microscopic study of an ore, at first only of scientific interest, has proved extremely useful both in practical geology and in ore dressing. The binocular magnifying lenses for rough observation of the products of an ore-dressing plant have been in use for a long time; but only within the last few years has a systematic microscopical examination of ore samples become a normal tool of any research laboratory dealing with ore-dressing problems. Such an investigation avoids considerable loss of time as well as empirical trials and useless experimentation. It will generally indicate the correct grinding and often will suggest the proper method of treatment. The petrographic determination of transparent minerals in thin sections, or even in grains, has been perfected, and very accurate methods have been devised to meet any requirement, such as Feodorof&apos;s rotating stage on the petrographic microscope. Almost all transparent minerals can be positively identified by their optical properties; i.e., isotropism, anisotropism, color, pleochroism, refractory index, cleavage, crystal form, birefringence, and others. The identification of opaque minerals is a much more difficult problem and can be done only by using polished specimens. Unfortunately, most of the valuable metallic ores, and even some of the nonmetallic ones, are not transparent; therefore it has been necessary to develop a special technique for the determination of these minerals. Some optical properties-for instance, isotropism, anisotropism, color, cleavage, reflecting power-are often adequate in roughly classifying the mineral. Only "reflecting power" is a measurable value, provided special photometric equipment (ocular photometer or Orcel&apos;s photoelectric cell) is available. The other optical properties mentioned are more or less relative,

Jan 1, 1942

By M. H. Mueller, P. A. Beck, W. P. Chernock

HARRIS introduced the term inverse pole figure for the diagrams previously used by Barrett&apos; to represent the volume fraction p(a,ß) of material in various orientations with respect to the fiber axis in a specimen with fiber texture. The direction of the fiber axis with respect to the crystal lattice is specified by the two independent angle variables a and ß. In such a diagram p gives the fiber axis density distribution over the various crystallographic directions. The p(a,ß) may be given in a two-dimensional diagram by means of contour lines (p=con-stant) in a stereographic projection. The inverse pole figure incorporates in a single contour line diagram all the information given conventionally in pole charts for various (hkl) reflections and, therefore, it represents a considerable degree of condensation. Also, it gives this information directly in terms of the volume fraction of the specimen in various orientations, and it obviates the necessity of referring back and forth between the various pole charts in an attempt to interpret them in terms of orientations. Inverse pole figures undoubtedly represent the most adequate method for describing a texture in a quantitative manner and, at least in the case of fiber textures, this method is certainly a practicable one. Harris described1 a simple procedure for determining at least the rough outlines of a quantitative inverse pole figure. This method depends on the measurement of the intensity of X-ray reflections from various (hkl) planes lying parallel to the same specimen surface. In the case of a rod, reflections from a plane specimen surface perpendicular to the rod axis (fiber texture axis) are to be used. Harris has shown that the measured intensities I,,, reflected by crystal planes (hkl), aligned perpendicularly to the fiber axis of a specimen with unknown fiber texture, and the corresponding intensity Iu nkl from a random specimen are related to the p(a,ß) value for the unknown texture by the following equation IAkl/I°Aklw=c/c°.p(a, ß) [1] where C and C° re parameters depending on the crystal imperfections (extinction), surface preparation (e.g., thickness of oxide layer), the absorption coefficient in the specimen, effective line breadth, and instrumental factors. The values of the variables a and ß1 defining the crystal orientation, depend only on the indices hkl of the reflecting plane perpendicular to the fiber axis. Since p, as described by Harris1, is normalized in such a way that upon integration over the total orientation range its mean value is 1, the parameter C/C may be calculated approximately by the summation of Eq. l over all available X-ray reflections hkl, corresponding to a set of discrete orientations (rather than by integration over the complete range of orientations represented by the continuous variables a and ß). From the summation of Eq. 1 1/n SI AKL/I° Akl = C/C. SP(a,ß)/n is obtained where, as stated above 2p(a,ß) =1. n Therefore

Jan 1, 1959

By F. H. Buttner, E. R. Funk, H. Udin

Gold wires, 5 mil in diam, are found to creep viscously up to approximately 5.5x106 dynes per sq cm around 1300°K. Beyond this point, an additional slip mechanism appears. The average coefficient in the viscous range at these temperatures is 18.9 ± 7x10 12 poises. This observation and other visual observations made during the experiments agree with Herring&apos;s predictions. EARLY creep studies by Chalmers on single crystals of tin produced some of the first experimental evidence to suggest that metals deform viscously under very light stresses. That is to say, over a small initial stress range up to 150 g per sq mm, the single crystals of tin elongated at a rate proportional to the stress. The proportionality constant between strain rate and stress is by definition the coefficient of viscosity. Chalmers named this range of proportionality the microcreep range. One of the first theoretical attempts to explain the microcreep phenomenon was given by Kauzman,&apos; who applied Eyring&apos;sQ eneral statistical mechanical theory of shear rates to creep data then available. From the rate theory, he deduced the general hyperbolic sine law for shear rate on the assumption that the distortion of the reaction path due to stress is negligible and that the system is an infinite continuum. In order to fit the available data to the equation, it was necessary to assume that creep occurs by shear of rather large blocks of material, rather than by an atomistic shear process as in diffusion. The size of the shear units was shown to increase with increasing temperatures and lower stress, or lower strain rates. In applying the hyperbolic sine law equation to the microcreep data of tin, it was shown by Kauzman that the unit shear blocks became quite small, which suggested to him that microcreep might be a self-diffusion process. Making this an assumption, Kauz- man reworked the rate theory and arrived at an equation where the shear rate is proportional to the stress. In the form of viscosity coefficient, the equation is: o- _ \LkT V = 2qAlA where u is the stress; S, the shear rate; X, the distance in shear direction moved by flow units relative to one another in the unit process; L, the distance between layers of units of flow; T, the absolute temperature; k, Boltzmann&apos;s constant; qAL, a constant proportional to the size of flow units; and kT A, the diffusion coefficient = ------kTe-Q/RT = K X2 h Kauzman applied the expression to molten lead with a fair degree of success, the calculated viscosity being low by a factor of four. For solid lead the result is 5000 times too high. Taking q = 1, and X = dA = L = 21 = nearest neighbor distance, Udin, Shaler and Wulff8 found the equation low by a factor of lo7 for solid copper. On the basis of the discrepancy in lead, Kauzman indicated that microcreep is probably not a simple diffusion process of molecular shear units, but one involving preferential diffusion paths, or even that diffusion in solids does not involve shear at all. Cottrell and Jaswon4 treat the microcreep phenomenon on the basis of slow moving dislocations and apply it to Chalmers&apos; data on tin with fair success. Nabarro Suggested a microcreep model in which mass movement in the direction of pull is effected by the diffusion of holes. The tension on the crystal effectively creates a greater hole concentration at regions near the crystal surfaces perpendicular to

Jan 1, 1953

By E. L. Kamen, H. D. Kessler, M. Hansen, D. J. McPherson

The highly reactive Ti-Mo and Ti-Cb alloys were prepared and heat treated under protective conditions. Phase diagrams were established based on micrographic and X-ray diffraction analysis and detection of incipient melting. ß titanium forms a continuous series of solid solutions with both molybdenum and columbium, whereas these metals are only slightly soluble in the a titanium modification. PREVIOUS work on the Ti-Mo and Ti-Cb systems was very limited and is discussed in succeeding sections of this paper relating to the respective phase diagrams. The diagrams in the present work were determined principally by micrographic analysis, because other methods such as thermal analysis and dilatometry are not suitable, due to the low diffusion rates of these alloys in the transformation range. X-ray analysis was believed less useful than micrographic analysis because: 1—On quenching certain high titanium alloys from above their transformation range, the body-centered cubic ß phase decomposes into acicular a (hexagonal close-packed) which room temperature X-ray diffraction techniques cannot differentiate from isothermal a. 2— High temperature X-ray techniques might be used, but are difficult to apply and are subject to error because of the high reactivity of titanium with gases such as oxygen and nitrogen. Although metallo-graphic study was the basic method used, X-ray diffraction analysis was applied to a limited extent, to further substantiate the findings. The transformation ranges on the titanium side of the Ti-Cb and Ti-Mo systems were studied both with DuPont Process A (magnesium-reduced) titanium alloys and with iodide titanium alloys. The Process A metal was used chiefly to bracket the transformation range in order to reduce the number of alloys given a particular treatment for the more accurate final study with iodide titanium alloys. Experimental Procedure The analyses of the metals used in the preparation of alloys for this study are presented in Table I. Melting Practice: Early in the work, a consumable electrode, arc melting furnace was used in the preparation of the Process A Ti-base Mo and Cb alloys. This type of furnace has been described by other investigators.&apos;, &apos; One of the major difficulties of the consumable electrode melting process was the prep- aration of homogeneous electrodes (with the mixture of coarse titanium sponge and fine powder alloying addition) which would give homogeneous ingots. Composition gradients encountered may have been due to a tendency for powdered alloying metals to drop away from the electrode in handling. This difficulty in the preparation of homogeneous alloys was overcome by the use of a nonconsumable electrode furnace for later work. This furnace is similar to the one used by Mc-Pherson and Fontana a Ohio State University. A diagram of the nonconsumable electrode arc furnace is given elsewhere.&apos; The source of power was a 400 amp dc welding generator. Electrode tips of tungsten (% in. in diam) were used for all columbium melts and for a limited number of molybdenum melts. Molybdenum tips were used for the majority of molybdenum alloy melts. Columbium tipped electrodes were tried, but disintegrated rapidly at currents above 300 amp. In the Process A titanium melting practice the metals were charged into the water-cooled spun copper crucible in the following forms: l—titanium: sponge (—4 + 16 mesh); 2—molybdenum: sections of 0.003 in. sheet (approximately ½ in. sq); and 3— columbium: powder compacts (? in. lumps broken from large section). After alternately evacuating and purging the furnace several times with argon or helium, the arc was struck against the metal charge,

Jan 1, 1952

By J. E. Burke, C. S. Barrett

THE fine lines shown in Fig 1 are typical of markings that may be detected after polishing and etching deformed specimens of alpha brass and other alloys. Although they have long been the subject of discussion by metallurgists their nature is still uncertain and the names that have been applied to them, such as deformation lines or strain markings, indicate this uncertainty. In this paper which reports the results of a further investigation of their nature, they will be called strain markings. INTRODUCTION Matthewson and Phillips1 in 1916 concluded that strain markings appeared only after deformations that exceeded 20 pct. They objected to the markings being called slip lines believing this term should be reserved for surface markings produced by plastic deformation. In 1921, Vogel2 described similar striations which appeared after polishing and etching the roughly ground surface of numerous alloys. He reported that the markings were crystallographic in nature, and since they resemble Neumann bands in iron, at least superficially, he assumed them to be mechanical twins. In 1928, Matthewson3 reported work by Phillips which indicated that the lines were more readily produced by impact than by slow deformation and that in many cases the twins inside recrystallized grains were parallel to strain markings in the original deformed grains. This was taken as evidence that the markings coalesce into annealing twins, and hence that they themselves are mechanical twins. Many attempts have been made to [ ] demonstrate directly that the markings are mechanical twins. In 1934, Samans4 described the results of X ray studies of two deformed crystals of alpha brass. Evidence was obtained which could be interpreted to indicate that the strain markings are mechanical twins, and this remains the only direct evidence to this effect. Several other attempts to obtain similar evidence by X ray diffraction have failed5,6,7 although in no case was the original method of Samans employed. An

Jan 1, 1948

By Howard Scott

INVAR is the preeminent low-expansion metal by virtue of the fact that it can be prepared with a zero coefficient of expansion at atmospheric temperature. This fact suggests that there is little room for improvement in the expansion properties of the low-expansion nickel steels. The inference is true, however, only so far as the expansion at and near atmospheric temperature is concerned, because the expansivity of invar starts to increase rapidly on heating above 100° C. and soon reaches the value of copper. Guillaume1 met this situation by increasing the nickel content above that of invar. By that expedient, alloys having low expansivity under higher temperatures were obtained, but not without a large increase in minimum expansivity. The increase in minimum expansivity with increasing nickel content severely limits the technical applications of these alloys at high temperatures. Prospects of improving the expansion characteristics of the nickel steels is offered by alloying. Search for an advantageous alloying addition by analogy with other alloy systems, however, is not productive because the low-expansion characteristic is unique with that system. The rule of mixtures usually gives a fair value of the expansivity of other solid-solution alloys, but in the iron-nickel systems gives a value of 18 X 10-6 per deg. C. whereas the actual value is 1 X 10-6 per deg. C. Apparently suitable additions are not to be deduced from such ingenuous considerations. Recognition of the fact that the temperature range of low expansivity in nickel steels is terminated with loss of magnetism affords a more promising basis for the selection of an advantageous element. One may expect from that fact that additions of nonmagnetic elements to the iron-nickel alloys are detrimental to the low-expansion characteristic. Indeed, carbon, manganese, silicon, copper and chromium are detri-mental to the expansion properties and no nonmagnetic element is reported to be beneficial. From the same viewpoint, the addition of a magnetic metal offers prospects of improvement. As two of the three ferromagnetic elements are already present in the

Jan 1, 1930

By J. E. Burke, C. S. Barrett

The fine lines shown in Fig I are typical of markings that ma): be detected after polishing and etching deformed specimens of alpha brass and other alloys. Although they have long been the subject of discussion by metallurgists their nature is still uncertain and the names that have been applied: to them, such as deformation line4 or strain markinas, indicate this uncertainky. In this paper which repotts the results of a furthcr investigatinn of their nature, they will be called strain mxrkings. Introduction Mathewson and Phillips1 described strain markinps in 1 916 and concluded that they appear only after 20 pet deformation. They objected to the markings being called slip tines believing this term should be sewrved for surface markings protluced by plastic deformntion. In 1921. vogel² described similar striations which appeared after polishing and etching the roughly ground surface of numerous alloys. He reported that the markings were crystallo-graphic in nature, and since they resemble Seumann hands in iron, at least superficially, he assumed them to be mechanical twins. In 1928, Matherwson reported work by Phillips which indicated that the lines were more readily produced by impact than by slow deformation and that in many cases the twins inside recrystallized grains were parallel to strain markings in the original deformed grains. This was taken as cvirlence that the markings coalesce into anncaling twins. and hence that they themselves are mechanical twins. Many attempts have been made to demonstrate directly that the markings are mechanical twins. In 1934, Samans described the results of X ray studies of two defomed crystals of alpha brass. Evidence was obtained which could be interpreted to indicate that the strain markings arc mechanical twins, and this remains the only direct evidence to this effect. Several other attempts to obtain similar evidence by X ray diffraction have failed5.8.7 although in no Ease was the original method of Samans employed. An

Jan 1, 1949