Search Documents

By A. U. Seybolt

A FEW copper-zinc-base alloys meet die-casting requirements reason- ably well, although improvements are desired. Aluminum bronzes, high-tinbronzes and some copper-nickel-zinc alloys can be die-cast, accordingto Herb,1 but seldom are because of such factors as higher melting ranges and greater cost than certain of the brasses. Fox2 has summarized the copper-base die-casting alloys that were in commercial use in 1937 and has given the effects of different alloying constituents. Table 1 gives some of the properties of these alloys as reported by Fox. TABLE 1. Commercial Die-casting Brasses a Constituent Yellow Brass Low-silicon High-siliconb Brass Brass Nickel Silver Composition, Per Cent Cu 57-59 63-65 80 -81.5 42.0 Zn 40-42 33-35 13.5-16.0 41.0 Sn 0.5-1.5 Si 0.75-1.25 3.75-4.25 Pb 1.0 Ni 16.0 Properties Tensile, lb. per sq. in.. 55,000-60,000 65,000-70,000 85,000-95,000 85,000-95,000 Yield, lb. per sq. in.d.. 30,000-35,000 35,000-40,000 65,000-70,000 65,000-72,000 Elong., per cent in 2 in . 15-20 20-30 8-12 10-20 Brinell hardness 120-130 120-130 160-180 160 Specific gravity 8.47 8.50 8.15 8.45 Properties reported by Fox.2 b Trade name of Brastil, Doehler Die Casting Co., similar to Webert Alloy, 3,4 American Brass Co., and Tombasil Alloy,5 Ajax Metal Co. c Trade name Tinicosil, Titan Metal Manufacturing Co. Melting point (liquidus) of the yellow brass is given by Herb' as 1650° F., of the high-silicon Brastil (with 4.5 to 5 per cent Si) as 1600° F., and of the nickel silver as 1675° F. d Criterion not stated.

Jan 1, 1939

By C. C. Harris

An analytical solution of the integro-differential equation of batch grinding is proposed as a first appoximation to the xYt surface. The size distribution equation (xY plane) is a three parameter equation previously suggested. Possible refinements are outlined. Comminution kinetics research is presently following several related courses. Some are equivalent, in that they represent different ways of viewing the same facet of the problem, though the entire endeavor cannot be described as being completely integrated. The purpose of this note is to propose and discuss a framework into which the various approaches might be fitted. This must clearly be founded upon an analysis of the xYt surface.' (See also Fig. 1 of Reference 26.) The investigations referred to above comprise mainly researches into the following: (1) The kinetics of the creation of the finer sizes during relatively small grinding times. This is the Fahrenwald-Arbiter-Bhrany 2-3 approach which leads to equations equivalent to a special case of the charles4 relationship. It emerges that initial production of fines follow essentially zero order* kinetics. (2) Disappearance kinetics of the coarser fractions. This appears to be a first order relationship.5-6 (3) Prediction of the xYt surface via the selection and breakage functions utilizing computer-programmed or approximate solutions of the integro-differential equation of batch grinding.5,8-17 A recent discussion by Mika et al.5 references the relevant literature up to about 1966. In addition to these main-stream researches there is some work on the minor topic of extremely long grinding time considered as a limiting case.18-19 The field is supported by investigations into the size distribution of fragments produced by breakage processes, some of this work being most valuably statistical-mechanical in nature.20-25 Better fitting equations, however, are obtained by statistical and curve-fitting methods.26 This

Jan 1, 1969

By D. R. Mash

A strong yield point with attendant enhanced mechanical properties was found in commercially pure beryllium under certain conditions of heat treatment. Beryllium specimens also responded to both quench and strain aging treatments. Based on these results, a possible means of obtaining increased normal temperature mechanical properties is suggested. COMMERCIALLY pure beryllium has been found to exhibit the yield point phenomenon and several other aging manifestations under certain conditions of heat treatment. This behavior is not surprising in view of the present accumulation of experience regarding such effects in numerous metals; but in addition to extending this experience to include beryllium, the present study is of interest because aging effects are generally associated with the presence of small amounts of solute elements. The well known lack of tensile ductility in beryllium at normal temperatures is also considered to be due to impurities in some way. In the present investigation, the view was taken that beryllium of commercial purity (greater than 98 pct) should be considered as a dilute alloy and that precipitation phenomena may well exist which could lead to enhanced mechanical properties. In connection with this possibility, published data on the variation of mechanical properties with temperature are of interest. For example, Fig. 1 illustrates the variation of ductility (percentage of elongation) and ultimate strength as a function of temperature for beryllium of various histories.* Although these curves are somewhat schematic in nature, they clearly indicate the possibility that precipitation of an unstable phase and/or aging effects occur during tests in the region 400" to 700°C. The existence of such behavior should be recognized as affecting the properties of the commercial material and perhaps can be employed advantageously. Experimental Method All testing was done at room temperature using a Baldwin universal testing machine. A microformer extensometer was used in conjunction with a micro-former-type stress-strain recorder. All tests were conducted at constant loading rate, the slowest rates being used. This corresponded to 120 lb per min in the 1200 lb full scale range and 300 lb per min in the 6000 lb full scale range. After the rate of loading was set in the elastic range of the material during the early part of the test, no further adjustments were made, allowing the test to proceed at that setting. In the plastic region of the curve above the yield region, strain rates of from 0.002 to 0.006 in. per min were regularly obtained. All experimentation was carried out on specimens machined from the same lot of beryllium, lot No. Y5036BP. Table I shows the chemical analysis as furnished by the supplier, Brush Beryllium Co., as well as the standard specifications to which commercial beryllium is produced. Both 1/4 in. thick hot pressed plate and ½ in. round hot pressed and warm extruded rods were obtained. The history of the material is reported to be as follows: 1—Beryllium metal plates, produced from a standard hot pressed QMV beryllium metal block 4x15x40 in., were cut off and finished machined to 1/4x6x12 in. flat plates. The original hot pressed block was made by hot pressing —200 mesh vacuum cast attri-tioned powder at about 1050°C under vacuum. 2—Beryllium rod was hot pressed and warm extruded. Extrusion billets were machined from the regular hot pressed blocks followed by extrusion at 425°C. The extrusion was done without jacketing, and graphite was used as a lubricant. The rods were then straightened at 720 °C, after which they were annealed at 800°C for 15 min. Both flat tensile specimens and round tensile specimens were tested. The former were machined from the plate stock into standard specimens according to specifications shown in ASTM E8-52T. The nominal cross-section was 0.25x0.500 in. and the gage length was 2 in. The round specimens were

Jan 1, 1956

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 John Chipman

Published data on the equilibria of carbon in binary Fe-C austenite with H2-CH4 and CO2-CO gas mixtures are used to obtain the constants of an equation repre -senting the activity coefficient of carbon throughout the stable austenite range of temperatutre mid compositiotl. Calculated values for the solubility of graphite are found to be in agreement with the best-published direct observations. Its heat of solution is 10,680 calper g-atom. The free energy of formation of cementite is culculated from the equilibrium compositions of austenite and of gas. Its entropy and heat of formation are also obtained. BASIC knowledge of the high-temperature properties and treatment of steels is contained in the Fe-C diagram and its extensions for the effects of alloying elements. The application of thermodynamics to the Fe-C system, with addition of alloying elements, can serve to simplify and systematize this knowledge. The points of beginning are the binary fee solution, austenite, concerning which our information is reasonably complete, and the binary carbide, cementite. Further studies must include the other phases of the binary system, a and liquid, and for these an accurate knowledge of the ? phase boundaries is essential. These studies should provide a firm base for systematic study of the effects of alloying elements on all phases of the system, their transformations, and precipitation phenomena. With the aid of the simplifying thermodynamic concepts of activity coefficients and interaction parameters it is to be hoped that the results of these studies will be amenable to computer solution thus making the information on multicomponent systems more readily available than would be possible in multidimensional diagrams. Studies of the thermodynamic properties of austenite have utilized equilibrium measurements on the reactions:

Jan 1, 1968

By George D. Graffin.

The first use of graphite is lost in the mists of time. It was used by primitive man to make drawings on the walls of caves and by the Egyptians to decorate pottery. As early as 1400 A.D. graphite crucibles were being made in the Haffnerzell district of Bavaria. Through the Middle Ages graphite was confused with other minerals, especially galena and molybdenite. Two common names that are still used for the mineral are "Plumbago," meaning leadlike, and "Black Lead." The latter name implied that graphite is either composed of lead or at least contains a large percentage of it. Gessner is credited with having recognized it as a separate mineral in 1565, but its composition was not determined until 1779, when Scheele demonstrated that graphite oxidized to carbon dioxide, thus proving its carbon constitution. In 1789, Werner named it "graphite" from the Greek word "graphein," meaning to write. The United States has long relied on foreign countries for its graphite supplies. This reliance has been due more to the lack of suitable domestic graphites than to any particular preference for buying minerals overseas. Ceylon (now Sri Lanka) graphites were imported as early as 1820, and Madagascar graphites have been imported since the properties on that island were opened up about a hundred years later. Mexico has long supplied the United States with most of its requirements for amorphous graphite. Physical Properties and Classification Graphite is found in laminated, flaky aggregates disseminated in schistose rocks. It also occurs in veins and exhibits a foliated or fibrous structure. Graphite is a black lustrous mineral that crystallizes in the hexagonal system, with rhombohedral symmetry. The crystals have tabular form and are six-sided; the faces are commonly striated. The flakes have perfect basal cleavage and are opaque. When well crystallized, the flakes have a black metallic luster while the amorphous material is black and earthy, with a microcrystalline compactness. The flakes feel greasy. Graphite is an excellent conductor of heat and electricity. It melts at approximately 3550°C at a triple point under 1250 psi. It sublimes between 3300-3500°C at 14.7 psi. At 3726°C a second triple point occurs at approximately 100,000 atmospheres. Thermal oxidation in the presence of oxygen begins at 300°C and the rate increases with temperature. The three forms of carbon (charcoal, graphite, and diamond) are distinguished by chemical and physical tests. The specific gravity of charcoal is 1.3 to 1.9, of graphite 2.266 g/ cm3 (crystal density), and of diamond 3.5. Graphite has a hardness of 1 to 2 (Mohs' scale). Natural graphite can be divided into three classes: disseminated flake, crystalline vein (fibrous or columnar), and amorphous. Flake graphite is a lamellar form found in metamorphic rocks, such as marble, gneiss, and schist. Each flake is separate, having crystallized as such in the rock. Crystalline vein graphite is found in the form of well defined veins or as pocket accumulations along the intrusive contacts of pegmatites with limestones. The graphite of such deposits is of two types, foliated and columnar. The important Sri Lanka (Ceylon) deposits are vein type. Amorphous graphite is commonly found as minute microcrystalline particles more or less uniformly distributed in feebly metamorphic rocks, such as slates and shales, or in beds consisting practically entirely of graphite. The latter usually are metamorphosed coal seams and carry as much as 80-85% graphitic carbon, while the former, being altered carbonaceous sediments, commonly range from 25 to 60%

Jan 1, 1983

By Jean Howard

RECENT attempts to produce secondary recrystalli-zation in high-purity iron have given conflicting results. Coulomb and Lacombe1'2 did not find it but Dunn and Walter3,4 did. The latter workers have stated that (100) [001] and/or (110) [001] orientations develop depending on the oxygen content of the annealing atmosphere. This Technical Note records results which are in agreement with Dunn and Walter in so far as it shows that secondary recrystallization can be produced in high-purity iron, but does not confirm that both types of orientation are obtainable. Similar observations have been made on chromium-iron and molybdenum-iron, although when this technique is used on 3 1/4 pct Si-Fe, both types are obtained as in the work of Dunn and alter.' Pure iron strip was cold-rolled from sintered compacts prepared from Carbonyl Iron Powder-Grade MCP of the International Nickel Co. (Mond) Ltd. The powder contains about 0.5 pct 0, 0.01 pct C, 0.004 pct N, (0.002 pct S, $0.005 pct Mg and Si, and 0.4 pct Ni—that is, it is substantially free from metallic impurities other than nickel, which is thought to be unimportant in the present work. The iron powder was (a) pressed at 25 tons per sq in. into blocks measuring 3 by 1 by 0.3 in., (b) deoxidized in hydrogen (dewpoint -60°C) by heating first at 350°C and then at 600° C until the dewpoint returned to -60°C at each temperature and (c) sintered in hydrogen (dewpoint -40°C) at 1350°C for 24 hr. (when dewpoint is referred to in this Note, it is the value as measured on the exit side of the furnace). The sintered compacts were cold-rolled to 1/8 in., annealed in hydrogen (dewpoint -60°C) at 1050°C for 12 hr and cold-rolled to 0.004, 0.002, and 0.001 in. with inter-anneals at 900°C for 5 hr and a final reduction of 50 pct. Final annealing of strip between alumina or silica plates at 875" to 900°C in hydrogen with dewpoints of -20°, -55" and -80°C produced secondary grains with the (100) in the rolling plane; the extent of secondary recrystallization was greatest when the dewpoint was -55°C. Annealing in a vacuum of 2 x 10"5 mm Hg at the same temperature produced no secondary recrystallization at all. With strip thicker than 0.002 in. very few secondary crystals developed whatever the conditions of annealing. Using a processing schedule somewhat similar to that described above, secondary recrystallization was produced in two bcc alloys of iron, viz. 80 pct Fe + 20 pct Cr and 96 pct Fe + 4 pct Mo. The former was reduced to final thicknesses of 0.001 to 0.004 in. and the latter to final thicknesses of 0.001 to 0.016 in. With the chromium-iron, a final anneal at 1250°C (found to be the most effective temperature for developing secondary crystals in the 0.004-in material) with a dewpoint of -25°C produced a greater degree of secondary recrystallization than with dewpoints of -50°C or -20°C. Secondary crystals developed in strips of all thicknesses from 0.001 to 0.004 in. Final annealing in vacuum produced no secondary crystals at all. For the molybdenum-iron a temperature of 1200°C was most effective. It was found that a dewpoint of -50°C during the final anneal gave better results than a dewpoint of -25 "C on the 0.008 in. material. Final annealing in vacuum gave slightly worse results than annealing in hydrogen with a dew-point of -50°C. Secondary crystals were developed in strips of all thicknesses up to 0.008 in. The experiments show that the extent of secondary recrystallization is a maximum for certain critical values of oxygen content of furnace atmosphere and annealing temperature, and that these values are different for different alloys. The thinner the material, the less critical these values are. The general conclusions are that secondary recrystallization can be obtained in high-purity iron, chromium-iron, and molybdenum-iron, using a processing schedule similar to that which will cause the phenomenon to take place in high purity 3 1/4 pct Si-Fe. Unlike the silicon-iron, however, only the (100) (0011-- orientation has been produced in these alloys, irrespective of the temperature of final annealing and the oxygen content of the furnace atmosphere. The information used in this Note is published by permission of the Engineer-in-Chief of the British Post Office.

Jan 1, 1962

By Margaret G. Scroger, Luke L. Y. Chang, Bert Phillips

Using the sealed-system technique, isothermal sections at 1000°, 1400°, and 1700°C for the system Co-W-O hare been determined. The equilibrium data were obtained by microscopic and X-ray diffraction examination of samples winch had been equilibrated in pellet form fit sealed capsules and subsequcelly quenched. The only ternary phase in the system is CoWO, which mells congruentlly at approximately 1280°C. At 1000°C, this ternary phase exists in equilihrinm with all the allows and oxide compounds in the hounding binary systems. At 1400°C, liquid forms in thin oxygen-rick region near the CoWO4 composition and only one phase assemblage in the system (W + WO2 + H'5CV7) contains no In order for tungsten to be used to its full potential as a refractory metal. it is necessary that coatings be developed which will preclude oxidation of the metal. It is true that coatings now in use do protect tungsten for short periods at temperatures near 1700 °C. but no coating has been developed which protects adequately at or above this temperature where the use of tungsten is most required. This situation exists despite the great effort in recent years to develop such coatings. and it has become evident that success in this area can be achieved only after a more fundamental knowledge of the thermochemical and therrnophysical propertics of tungsten oxidation and tungsten -metal oxidation is obtained. In our 1aboratories. a project liclrriel. At 1700°C, tungsten is the ouly solid phase which is stctble, and a large range of compositions melt to two liquids, one metallic and one oxidie. The sealed-system method of etjuilibra lion prevents the determination of the partial pressure of oxygen and the total gas pressure orer the condensed phases at equilibrium. This data is not available and can be obtained only by some other method. We can generalize on these unknowns and indicate that both partial pressure of oxygen and total pressure of the gas phase must increase as compositions change from the W-Co binary toward the oxygen apex and as temperatures increase. has been initiated which is directed at providing some of this fundamental information through a study of metal-tungsten-oxygen reactions and equilibria and the properties of any intermediate phases which result. This paper is based on a part of this program in which the system Co-W-O was studied between 1000° and 1700°C. I) RELEVANT INFORMATION FROM THE LITERATURE A) The Notable Lack of High-Temperature Work on Metal-Tungsten-Oxygen Systems. It should be pointed out that there has been no published report (of which we are aware) which deals with the study of a metal-metal-oxygen system at 1700°C. Also, there has been no report on a complete metal-luugsten-oxgen system at any temperature. As a matter of fact. before this program started. The

Jan 1, 1965

By Joseph W. Roe

MaNY questions arising in the work of the mining engineer may be solved quickly and with suffcient accuracy by the methods of descriptive geometry; but, unfortunately, this subject is more often considered from a mathematical view-point than as an effective tool for solving practical problems. Some of the principles involved are merged into the ordinary operations of mechanical drawing, and are used unconsciously by the engineer in his every-day work. The rest are stowed away on the book-shelf with his forgotten or rarely-used college text-books. One reason for this condition of " innocuous desuctude " may lie in the uifortunate and often cumbersome notation which it has been found necessary to introduce. If some of these principles can be recalled to the engineer's attenti011 in terms of' every-day use they may prove of practical hearing. Recently, in talking with several mining engineers, I used some of the drawing-room methods of a machine-designer, to the evident surprise of those around me. These men were perfectly familiar with the methods, but their application to mining-work had not occurred to them. At their suggestion the present paper is offered, not in ally way as a treatise, but merely to suggest a certain point of view, in hope that it may lead others far more familiar with mining-problems to pursue the subject further. I. To Find the Strike. As the simplest and most fundamental problem, let it be required to find the strike of a vein when the location and elevation of three points on the outcrop are known. It mill be assumed for the present that the rein is a plane.

Jan 1, 1911

By J. P. Heller

The purpose of this discussion is to comment briefly on one of the points raised in the paper. The topic is that referred to in the Conclusion 2, in which the authors note a "disproportionate increase in mixing rate" as they proceed from a displacement performed at viscosity ratio 0.998 to one at 1.002. The recovery curve of this displacement, Fig.2A, shows a quite noticeable difference between the two runs in which displaced and displacing liquids were interchanged. This difference is ascribed by the authors to the change in viscosity ratio between the two experiments. This interpretation of the experimental results must certainly be based on rather precise measurements of the fluid viscosities or, at least, of the ratio of their viscosities. The ordinary Ostwald viscometer, employed in the usual way, is only just able to distinguish between liquids whose viscosities differ by two or three parts per thousand. The experimental refinements which then must have been necessary to measure with any precision a viscosity ratio of 1.002 would be worthy of mention. Indeed, one would have expected the authors to devote at least a paragraph to the display of this technique. For the same reason - to emphasize that the details of such unusually critical experimental work should be reported and discussed in the literature — I would have liked to see some comment by the authors on the requirements for temperature control during both the viscosity measurements and the displacement experiments. The temperature coefficient of viscosity of Soltrol C at room temperature has been measured in this laboratory at about - 1.9%/1°C. How much did the coefficients for the fluid mixtures used in the experiment differ from this and from each other Even if the two fluids were identical in this respect, it would appear that a temperature difference of .l°C between them in the flow system would produce a viscosity con- trast equal to that imposed by their composition. Reference to the experimental solutions of these problems would render Conclusion 2 more credible. Published theoretical work on the stability problem contains no indication of such extreme sensitivity to the viscosity ratio in the immediate neighborhood of unity. On the contrary, perturbation calculations such as those made by Chuoke1 and Perrine2 lead to initial finger growth rates proportional to the first power of the viscosity difference. The later instability growth calculated by Scheidegger,3 using the assumption of zero pressure gradient perpendicular to the average flow, is also simply proportional to the viscosity difference. The conflict regarding the sensitivity of the dependence of instability growth or mixing rate on the viscosity contrast needs explicit recognition in the literature. In particular, it would seem that the experimental work reported here should be supported by a more detailed description of the viscosity controls. Further discussion of possible alternative interpretations of the data would also be in order. For instance, is it possible that the unconsolidstted bead pack used changed its characteristics between the runs (due, perhaps, to the handling and inverting involved in the injection of the front) Or, are the data points of Fig. 2A averages from several runs performed in a series in which the two liquids alternated as displaced and displacing fluids? To summarize, it seems to me that the relationship asserted by Conclusion 2 in the paper needs the support of more detailed experimental evidence. REFERENCES 1. Chouke, R. L., van Mews, P. and van der Poel, C.: "The Instability of Slow Immiscible Viscous Liquid-Liquid Displacements in Porous Media", Trans., AIME (1959) Vol. 216, 188.

By Rollin E. Hook, Attwell M. Adair

The response of CrzO3 and C~304 to various heat treatments was studied in are-melted iodide chromizim over the temperature range 1000" to 1750°C. These oxides, which are present as impurity phases in this material, were identified by X-ray diffraction teclzniques which were supplemented by optical metallop-aphy. As a function of increasing temperature, Crs04 is first observable in samples annealed at 1300°C and coexists with Cr2O3 (the low-temperature oxide) over a temperature range exceeding 200°C. As the temperature decreases, Cr3O4 dissolves with the concomitant precipttation of Cr2Y2. Both oxides precipitate predominantly at pain boundaries. The reactions which occur are involved with at least ternary equilibria, possibly due to iron which is present as an impurity in arc-melted iodide chromium. HILTY, Forgeng, and Folkman' reported in their investigation of the Fe-Cr-0 system that Cr3O4 (with about 8 pct Fe substituted for chromium) is a primary phase found in alloys with 9 or more pct Cr. They reported that this phase is stable only at high temperatures and that below the liquidus Cr3O4 is disproportionated into Cr2O3 and chromium-rich metal for both Fe-Cr-O alloys and in oxygen saturated pure chromium. Further, they proposed that CrsO4 forms by a peritectic reaction between Cr2O3 and the liquid. On the other hand, Hook, Garrett, and Adair2 found in their investigation of impurity phases formed in "pure" chromium (material consolidated from iodide chromium crystals) that Cr3O4 forms intergranularly and is stable as low as 1500°C which is 375OC below the melting point of chromium. The purpose of the research described herein is to determine the temperature range of stability of Cr3O4, and to show the nature of its decomposition. This further investigation indicates that Cr3O4 undoubtedly occurs in this material as low as 1300°C. The chromium studied was consolidated and fabricated from iodide chromium crystals (ICr-5) and contained Fe r 135 ppm, Si = 20 to 100 ppm, and 0 = 35 to 137 ppm. A complete chemical analysis is given elsewhere.' Annealing was conducted in 1 atm of purified helium and all samples were rapidly cooled (-200°C per sec) by withdrawing them from the furnace hot zone under a high flow rate of helium. The details of the electrolytic-etching technique and electrolytic-digestion techniques for preparation of insoluble residues for X-ray examination are given elsewhere also.' EXPERIMENTAL RESULTS The Starting Material. The as-swaged rod (final swaging done at 900°C) had a wrought grain structure and contained a dispersion of CrzO3 inclusions of maximum particle size of about 2 or 3 p, Fig. 1. The microstructure also contained a dispersed

Jan 1, 1964

By Henry M. Rowe

Professor Ruff's most illuminating paper' describing his extremely valuable investigation of the carbon-iron equilibrium diagram assigns definite temperatures to certain very important lines in the diagram, viz.: the eutectic temperature EB (Fig. 1) and the " near-eutectic " temperature E'B', but without indicating clearly enough the reasoning which warrants these assignments. These temperatures are of such primary importance that it is well to indicate the apparent gaps in the reasoning, in the hope that they may be filled in. In his diagram, Fig. 1, the point X and the liues B'D'lII represent the experimental results reached by Ruff and Goecke;a AB, AEB, and SE represent the liquidus, the solidus, and the solubility of the carbon in solid austenite in the absence of graphite according to Gutowsky,3 AB being also in accordance with Spiecker's data; S'E' the solubility of carbon in solid austenite in the presence of graphite according to Ruer and Iljin;5 GS the line A3 after Ooerens and Meyer; 6 and EBC the true eutectic line as inferred by Prof. Ruff from Gutowsky's data. B'D' is the carbon content found in cast-iron which had apparently saturated itself with carbon in the presence of the graphite of the enclosing graphite crucibles in which the determinations were made. From its straightiiess and its sharp inflection near 6.67 per cent. of carbon, the carbon content of

Jan 1, 1913

By D. J. Weintritt, R. G. Hughes

Statistics show arz increase in the average depth of wells drilled in recent years. As a corollary to this trend, drilling fluids have been improved in an effort to meet the problems inherent at temperatures approaching 500°F. Of importance are (1) deterioration of mud components and (2) the effect of solids on filtration and rheological properties. High-temperature, stable water-base and oil-bare muds are discussed. Those areas in which differences exist are pointed out. Results are based on data taken from the Fann consistotneter, rheometer and shear-strength measurements, static and dynamic filtration tests, methy-lene blue test for bentonite solids and specific heat measLrrenlents of muds. INTRODUCTION Higher well temperatures go along with the fact that the average depth of wells continues to increase. Recent data by Gardner' lists 137 completions deeper than 15,000 ft for the first half of 1964 with a record second-half total of 167 wells drilling or proposed. In addition, there has been an increase in drilling for steam for power production or mineral recovery. In this application the depths are modest, but the mud may approach the critical pressure and temperature of water. Scearce and Magnon' report drilling mud used at temperatures of about 700°F in the Salton Sea area of California. Most deep wells have been drilled with water-base muds. In recent years, however, there has been a substantial increase in the use of oil-base muds because of technological advances in effective additives. The significance of this development was dealt with in considerable detail by Simpson and his co-workers.3 Additiona1 field data have now been obtained to indicate that oil muds are competitive in control, performance and cost with the best types of water muds for use at high temperaturc. This parallel offer of two very different fluid systems, each offering a similar variability in performance, cost and convenience, has created the need to evaluate the merits of these fluids under specified conditions so that the advantages and disadvantages of each can be weighed in relation to the over-all drilling program. This paper is not intended as a review of all the factors. Rather, it attempts to emphasize: (1) important condltions and facts peculiar to high-temperature drilling muds, (2) that more than one imposed test condition or testing method is necessary to describe the quality of a mud at high temperature and (3) that elaborate experimental precautions are necessary whenever laboratory data are used in selection of a mud for field use. WHAT IS A HIGH-TEMPERATURE DRILLING FLUID? For the purpose of this discussion, a high-temperature drilling fluid is any system so formulated or treated to economically minimize the effects of temperature on the properties of the fluid. Our experience in drilling fluids suggests that these effects become obvious for many mud materials at temperatures of 300F or higher. It is understood that hydrolysis of starches, depoly-merization of certain organic thinners, or irreversible chemical reactions (such as that of clay and lime) can affect filtration, viscosity and shear strength at less than 300F. However, the temperature level is not a serious point and in no way affects the precautions and techniques used in this study. An up-to-date review of the literature on high-temperature drilling fluids and the many variations was treated by Rogers'in 1963. EXPERIMENTAL REQUIREMENTS TESTING EQUIPMENT AND PROCEDURES With the advent of deeper drilling and increased demand for temperature-stable drilling fluids, new testing equipment and laboratory techniques were devised for the evaluation of drilling fluids subjected to elevated temperature and pressure. While the equipment has not been standardized, it is in widespread use. Milligan et al. Qescribe a filtration cell for determining the filtration properties of drilling fluids at temperatures in excess of 300F. They showed the effect of variations in temperature and pressure on oil and water muds filtered in the 300 to 400F range. The dynamic filtration apparatus described by Simpson6 permits the study of the filtration properties to temperatures of 350F for drilling fluids circulated over sandstone cores. Watkins et al.' describe the use of pressure bombs for studying the effect of prolonged periods of elevated temperature upon the gelation or solidification of drilling fluids. Chisholm et a1.' describe the use of a modified cement consistometer adapted for use in drilling fluid evaluations. A similar consistometer is used in this study, although the application and data-recording method have been changed. The consistency of a mud sample is measured by timing the movement of a soft iron bob which is magnetically moved up and down in the sample container.* Changer in the time of travel and the temperature of the mud at that moment are plotted with a two-point Brown Elec-tronik Recorder. A 10-in. chart with a speed of 4-in./hr is used. Fia.- 1 is a generalized internretation of the data ob-

Jan 1, 1966

By W. G. Matteson

The Gulf Coastal plain of the southern United States is that area bordering for a large part, the Gulf of Mexico and extending inland and northward to the main interior highland region. It is more or less V-shaped and includes the States of Florida, extreme southern Alabama, all .of Mississippi and Louisiana, the eastern and southern half of Arkansas, and the eastern, southeastern, and southern portions of Texas. While the contents of this paper apply to. the Gulf Coastal plain in general, they are intended to refer more specifically to that portion of the plain included between the 90th and 97th meridians, and the 29th and 33d parallels, an area that may be described geographically as comprising western Mississippi, all of Louisiana, part of eastern and all of south-eastern Texas. It is within this area that numerous and prolific oil pools have been developed during the last 17 years.

Jan 2, 1918

By Frederick N. Rhines, William A. Anderson

The investigations of Wymanl have demonstrated that copper deoxidized with several of the commonly used agents that confer immunily to ordinary hydrogen em-brittlement can still be embrittled if it is annealed alternately under oxidizing and reducing conditions. During the oxidizing cycle, oxygen diffuses into the copper and frequently deposits a subscale composed of the oxide of the residual deoxidizing agent. Upon subsequent reduction with hot hydrogen, the copper becomes ruptured along the grain boundaries to a depth sharply limited by the previous penetration of oxygen as delineated by the inner boundary of the subscale. Obviously the sensitivity to this kind of hydrogen embrittlement is engendered by the introduction of oxygen during the oxidizing anneal, but beyond this the mechanism of the process, and hence the controlling factors, remain obscure. There are several possibilities: (I) oxygen dissolved in the copper matrix of the subscale may, upon cooling prior to the hydrogen anneal, precipitate as cuprous oxide which is subsequently reduced by hydrogen as in the familiar case of hydrogen embrittlement; (2) oxygen in solid solution in copper may itself confer susceptibility to embrittlement by hydrogen; (3) the normally refractory oxides such as those of aluminum, silicon and titanium may themselves be reduced by hydrogen when in contact with copper; or (4) the precipitated oxides of the subscale may be complex compounds such, perhaps, as SiO2.Cu2O, which are partially reduced by hydrogen. These possibilities have been examined, and it has been concluded that the first three and possibly the fourth are operative collectively or individually under more or less predictable conditions. Effect OF Precipitated Cuprous Oxide and Dissolved Oxygen The literature provides no definite proof that oxygen in solid solution in copper can confer susceptibility to hydrogen embrittlement; indeed, the research of Leiter2 seemed to indicate the opposite—that to produce the effect, cuprous oxide must be present in massive form and in a more or less continuous network along the grain boundaries. To test this point, pure copper has been annealed in hydrogen under conditions designed to ensure the presence in various samples of: (I) precipitated cuprous oxide, (2) dissolved oxygen only, and (3) no oxygen in any form. Very pure copper" said to contain no oxygen and no spectro-scopically detectable traces of any other element (that is, no individual detectable impurity in quantity greater than 0.0001 per cent) was used. Strips of this material cold.-rolled 75 per cent to 1/8 in. in thickness were subjected to the following treatments, the results of which are noted:

Jan 1, 1941

By Frederick N. Rhines, William A. Anderson

The investigations of Wymanl have demonstrated that copper deoxidized with several of the commonly used agents that confer immunily to ordinary hydrogen em-brittlement can still be embrittled if it is annealed alternately under oxidizing and reducing conditions. During the oxidizing cycle, oxygen diffuses into the copper and frequently deposits a subscale composed of the oxide of the residual deoxidizing agent. Upon subsequent reduction with hot hydrogen, the copper becomes ruptured along the grain boundaries to a depth sharply limited by the previous penetration of oxygen as delineated by the inner boundary of the subscale. Obviously the sensitivity to this kind of hydrogen embrittlement is engendered by the introduction of oxygen during the oxidizing anneal, but beyond this the mechanism of the process, and hence the controlling factors, remain obscure. There are several possibilities: (I) oxygen dissolved in the copper matrix of the subscale may, upon cooling prior to the hydrogen anneal, precipitate as cuprous oxide which is subsequently reduced by hydrogen as in the familiar case of hydrogen embrittlement; (2) oxygen in solid solution in copper may itself confer susceptibility to embrittlement by hydrogen; (3) the normally refractory oxides such as those of aluminum, silicon and titanium may themselves be reduced by hydrogen when in contact with copper; or (4) the precipitated oxides of the subscale may be complex compounds such, perhaps, as SiO2.Cu2O, which are partially reduced by hydrogen. These possibilities have been examined, and it has been concluded that the first three and possibly the fourth are operative collectively or individually under more or less predictable conditions. Effect OF Precipitated Cuprous Oxide and Dissolved Oxygen The literature provides no definite proof that oxygen in solid solution in copper can confer susceptibility to hydrogen embrittlement; indeed, the research of Leiter2 seemed to indicate the opposite—that to produce the effect, cuprous oxide must be present in massive form and in a more or less continuous network along the grain boundaries. To test this point, pure copper has been annealed in hydrogen under conditions designed to ensure the presence in various samples of: (I) precipitated cuprous oxide, (2) dissolved oxygen only, and (3) no oxygen in any form. Very pure copper" said to contain no oxygen and no spectro-scopically detectable traces of any other element (that is, no individual detectable impurity in quantity greater than 0.0001 per cent) was used. Strips of this material cold.-rolled 75 per cent to 1/8 in. in thickness were subjected to the following treatments, the results of which are noted:

Jan 1, 1941

By N. A. D. Parlee, I. D. Shah

The solubilities of oxygen in liquid Ag-Au, Ag-Pt, and Ag-Pd alloys have been determined in the range of 940° to 1200°C at 1 atm pressure of oxygen using an improved Sieverts technique. The additions of gold (0 to 57 pct), platinum (0 to 27 pct), and palladium (0 to 22 pct) to liquid silver continuously decrease the solubility of oxygen in liquid silver. Activity coefficients and interaction coefficients of oxygen in these alloys and have been calculated. The interaction coefficientscan be described by the following equations: Approximate second-order interaction coefficients (pM have been calculated. The contribution of the product, pMxNM, to In yo only becomes significant at high alloy concentrations. RECENTLY several investigators1"3 have redeter-mined the solubility of oxygen in liquid silver. In general the recent findings1" for Po, = 1 atm are in good agreement with the equation:4 log %O = 695.4/T + 1.086 [1] It is established1, 2 that the solubility of oxygen follows Sieverts' law reasonably well, at least up to 1 atm partial pressure of oxygen. It should be noted that a very slight deviation from Sieverts' law has been reported by Lupis and Elliott.3 Only recently has the solubility of oxygen in Ag-X binary liquid systems received much attention, and only the Ag-Cu, Ag-Au, Ag-Pt, and Ag-Pd systems have been studied. Par lee, Sacris, and zoellners reported that the solubility of oxygen in liquid silver increases progressively with the small additions of copper (0 to 0.5 pct) up to the point where the copper oxide phase appears. Lupis and ~lliott~ have reported that the solubilities of oxygen in liquid silver decrease progressively with the additions of gold, platinum, and palladium. However, their investigation was limited to 0 to 5 pct of these alloying elements, a range too limited to satisfy the requirements of the research program of this laboratory, where the solubilities of oxygen in the range of 0 to 30 pct were required for the calculation of chemical diffusion coefficients of oxygen in these alloys. The present paper deals only with the solubilities of oxygen in these alloys while another paper will deal with the diffusion of oxygen in these alloys. EXPERIMENTAL METHOD A Sieverts technique was employed which involved an improved design of the reaction tube, Fig. 1, as described briefly in a previous communication.4 Liquid melts (70 to 100 g) were held in Norton Alun-dum crucibles. The induction furnace used had a maximum output of 2.5 kw with very fine control. This induction system had excellent stability and the final equilibrium temperatures measured by calibrated Pt-Pt, 10 pct Rh thermocouples are believed to be within ±2C. These thermocouples were checked against the melting point of pure gold wire, and the results agreed with standard tables (±l°C). Each run involved a careful sequence of operations. The sample was heated to and held at about 900°C in vacuum for 3 to 4 hr with the thermocouple in a retracted position. After melting, the melts were usually exposed to a small amount of oxygen (0.5 to 2.0 cu cm) and then degassed slowly for 1 to 2 min to remove any oxidizable volatile impurities such as carbon and sulfur as CO, CO2, SO2, and SO forth. Argon gas was then allowed to enter the system. The protection tube containing the thermocouple was then

Jan 1, 1969

By D. S. Tomalin, D. F. Stein

The effect of reducing oxygen to low concentrations on the fracture of high-purity iron single crystals has been examined at 78° and 20°K. It is found that iron single crystals grown by the strain-anneal method usually contain a few occluded grain boundaries which may become embittled in the presence of oxygen, thereby nucleating cleavage fractures. High purity with respect to interstitial elements was found to inhibit twinning and evidence is presented for an orientation dependence of the resolved yield stress. Deformation occurred by slip rather than twinning at both temperatures of testing with elongations of as much as 9 pct at 20°K. THE fracture properties of iron single crystals have been observedl-3 to be a function of temperature, orientation, and purity. Allen, Hopkins, and McLennan1 demonstrated that at 78°K iron single crystals became increasingly brittle as the tensile axis approached the (001) pole of the stereographic unit triangle. Iron crystals with the tension axis near a (001) pole were completely brittle and orientations near the (011)-(111) boundary were very ductile, achieving a 100 pct reduction in area prior to fracture. Later work of Biggs and pratt2 and of Edmondson3 demonstrated that by reducing the carbon content of the single crystals the transition between brittle and ductile failure at 78°K could be shifted to orientations nearer the (001) pole. Ed-mondson went further and pointed out that any mechanism which tended to increase the yield strength of the iron (i.e., carbon addition, pre-strain) also increased the tendency for brittle behavior at 78°K. Thus by a reduction of carbon content Biggs and Pratt were able to obtain ductile behavior to within 20 deg of the (001) pole, and Ed-mondson was able to obtain ductile behavior to within 26 deg of the (001) pole. Edmondson's material had a total interstitial content (carbon, oxygen, and nitrogen) of approximately 60 ppm and, although Biggs and Pratt reported no analysis, indications were that their iron contained comparable impurities. Stein, Low, and seybolt4 purified iron single crystals to a total carbon, oxygen, and nitrogen content of approximately 20 ppm. They observed a lowering of the yield stress with this increased purity, and thus one might have expected an observation of increased ductility. Although they tested specimens of orientations which the previous workers had indicated should be ductile, the crystals failed at a 78°K in a brittle manner with little elongation. Stein noted,' however, that about 90 pet of the failures could be traced in origin to occluded grains. Allen et al.1 and Edmondson3 do not report examination of their cleavage surfaces, but Biggs and pratt2 reported that microscopic examination of the cleavage surfaces of many of their specimens revealed the presence of small occluded grains. Honda and cohen6 and Keh7 have also observed the initiation of fracture at occluded grains in iron single crystals. Therefore, the additional complication of occluded grains must be considered in studying the properties of iron single crystals and the origin of fractures determined if the ductility exhibited by the crystals is to be considered meaningful. Various investigators8-12 have studied the effects of impurities on grain boundaries in high-purity polycrystalline iron. Rees and Hopkins10 showed that the addition of oxygen to low-carbon (0.002 pet) iron weakened the grain boundaries, causing a shift from transcrystalline to intercrystalline fracture and a progressive decrease on the brittle-fracture stress with increasing oxygen content. In addition, it has been shown by Low and Feustel11 that the addition of carbon to polycrystalline iron containing oxygen eliminated grain boundary brittleness. Thus, oxygen can embrittle grain boundaries in high-purity polycrystalline iron, but the addition of an appropriate amount of carbon can eliminate the oxygen-induced brittleness. The oxygen content (19 ppm) of the iron "single crystals" employed by Stein el al. was large enough to suspect impurity effects at the occluded grain boundaries. Allen et al.1 Biggs and pratt,2 and Edmondson3 may have masked any occluded grain problem in their specimens considering the relatively high carbon levels they employed. stein13 demonstrated that the addition of as little as 0.9 ppm C to previously purified (less than 5 x 10-3 ppm C) "single crystals" would increase the elongation from a few percent to more than 20 pet at 78°K and the fracture was not associated with grade boundary initiation.

Jan 1, 1965

By W. A. Tiller, S. O’Hara

Grain refinement in stirred melts has previously been shown to arise from dendrite segmentation. The present work discusses experiments capable of distinguishing between remelting and mechanical effects which result from fluid motion. Nucleation of still un-dercooled Sn-1 pct Pb melts with a single-crystal seed shows that the grain size of the resulting ingots decreases as the undercooling at nucleation increases up to about 1Z0C, then increases again for larger undercoolings. Pure melts exhibit little refinement as a result of nucleation at any undercooling up to 12°C. The presence of fluid motion gives rise to grain multiplication in pure melts, but the magnitude of this effect is partly obscured by solid-state pain growth. The results indicate that two grain-multiplication pvocesses can operate, one which involves dendrite remelt ing, and another associated with fluid motion. Small ingot experiments indicated that an equiaxed transition can be caused by fluid motion. THE presence of forced convection during recales-cence of undercooled Sn-1.3 pct Pb melts has been shown to give rise to extensive grain refinement during solidification of small ingots of this alloy.''2 In Ref. 2, this refining was shown to result entirely from dendrite fragmentation and not from any nucleation mechanism. The purpose of the present work is to establish what processes lead to dendrite segmentation. Experiments were therefore carried out to determine the resulting structure of both pure tin and Sn-1 pct Pb melts, nucleated at various undercoolings by single-crystal seeds in the absence of forced or natural convection. By comparing the information obtained from these experiments with the results of Refs. 1 and 2, the effects of fluid motion on the ingot structure, and the details of the segmentation mechanisms, should become clear. The results of these experiments should also be helpful in understanding the solidification structures of larger ingots since natural convection, which is known to play an important role in determining ingot structure13 differs only in degree from the fluid-motion effects studied here. I) EXPERIMENTAL PROCEDURE The apparatus shown in Fig. 1 was constructed to permit controlled nucleation of stirred or unstirred supercooled melts using a seed oriented in the tin dendrite growth direction. Because the melts, in all cases, were capable of larger supercoolings than the one used in each experiment, the structure observed always resulted from a single nucleation event at the surface. The sequential procedure was as follows: Tin was melted under purified hydrogen and the oxide removed at a temperature of 450°C . Electromagnetic stirring was then used to clear the surface completely and during this time the guide tube was lowered underneath the melt surface. A pointed Czochralski-like crystal was then propagated from a specially prepared tin dendrite seed4 inside the guide tube while the temperature of the bulk melt was held just above the melting point, ensuring a perfectly clean seed which was epitaxial with the original dendrite. The dendrite and epitaxial seed, still in the guide tube, were withdrawn from the melt which, in turn, was undercooled to 2C° below the temperature at which the nucleation experiment was to be performed. The melt was held there for several minutes, both in stirred and in still-melt experiments. The temperature was next raised to the required value and the melt nucleated by the carrot seed inside the guide tube, the heater power being shut off just after nucleation. In experiments where quenching after nucleation was required, a high-density graphite crucible was used, but otherwise the procedure was as described above. The temperature gradient in the melt before nucleation was kept below 1C° per cm by carrying the experiment out just below the center of the heater shown in Fig. 1.

Jan 1, 1968

By M. A. Dayananda, R. E. Grace, P. F. Kirsch

Ternary diffusion experiments were carried out at 750°C with vapor-solid diffusion couples in single-phase copper-rich Cu-Zn-Sn alloys. The Philibert-Guy method was used to calculate intrinsic diffusion coefficients at compositions corresponding to the plane of inert markers imbedded in the diffusion couples. Inter diffusion coefficients were determined at common composition points of intersecting diffusion paths. Intevdiffusion coefficients were also obtained at compositions corresponding to maxima in the tin concentration pvofiles Relations between the interdiffusion coefficients and the expansion of vapor-solid diffusion couples are described in detail. Such relations permit the calculation of constant interdiffusion coefficients in binary couples from expansion data directly. In ternary couples expansion data provide an additional constraint on the interdiffusion coefficzents. ThE phenomenological analysis of diffusion in ternary solid solutions has been developed extensively, and various approaches taken in the determination of diffusion coefficients have been reviewed recently by Guy et al.' Finite,' semi-infinite,3 and infinite4 diffusion couples have been used in studies of ternary diffusion, but most of the work has been done with infinite diffusion couples. Semi-infinite diffusion couples3 (vapor-solid couples) have been used to determine both intrinsic and interdiffusion coefficients in the Cu-Zn-Mn system, in which two diffusing species, zinc and manganese, were supplied from the vapor phase. If only one component has a sufficiently high vapor pressure to be supplied from a vapor source, vapor-solid diffusion couples may still be used. In this case the boundary conditions at the gas/solid interface may be governed by partial equilibria rather than by virtually complete equilibrium between the phases. In the present work diffusion measurements were carried out at 750°C with vapor-solid couples of Cu-Zn-Sn alloys. Only zinc was transported between the vapor source and the diffusion disks, because the vapor pressures of both copper and tin are at least 108 lower than that of zinc. Both intrinsic and interdiffusion measurements were made at several compositions. A secondary objective was to relate expansion of the diffusion couples with the interdiffusion process. Such measurements for binary couples yield average values of the interdiffusion coefficients over composition increments. In ternary diffusion couples ex- pansion data provide an additional constraint on the interdiffusion coefficients. COMPOSITION-DEPENDENT INTRINSIC AND INTERDIFFUSION COEFFICIENTS As shown by Philibert and GUy5 the determination of intrinsic diffusion coefficients in a ternary system requires two independent diffusion couples containing marker planes with identical composition. In the case of vapor-solid couples such a requirement torresponds to two couples set up with the same vapor source exposed to two diffusion disks of different composition. Inert markers placed initially on the disk surfaces become imbedded during diffusion. If the pair of couples exhibits appreciable marker burial with marker planes of virtually the same composition, the intrinsic diffusion coefficient may be evaluated at the composition of the marker planes. Fig. 1 is a schematic diagram of the concentration of of a Cu-Zn-Sn ternary vapor-solid couple after diffusion of zinc from a vapor source into a binary Cu-Sn alloy. The areas, Ai correspond to the cumulative intrinsic fluxes of the three diffusing species across the marker plane:5 where Ji is the intrinsic flux of component i, t is the diffusion time, and D3i are the intrinsic diffusion coefficients. For the determination of interdiffusion coefficients a pair of diffusion couples with intersecting diffusion paths is needed. At the composition point of intersection (C1, C2) the coefficients are evaluated from the equation:3

Jan 1, 1969