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PRESIDENT. CHARLES F. RAND,1 NEW YORK, N. Y. PAST PRESIDENTS. CHARLES KIRCHHOFF,1 NEW YORK, N. Y. JAMES F. KEMP,2 NEW YORK, N. Y. FIRST VICE-PRESIDENT. BENJAMIN B. THAYER,1 NEW YORK, N. Y. TREASURER. GEORGE C. STONE,1 NEW YORK, N. Y. SECRETARY EMERITUS. ROSSITER W. RAYMOND NEW YORK, N. Y.

Jan 5, 1913

PRESIDENT WILLIAM L. SAUNDERS,1 NEW YORK, N. Y. PAST PRESIDENTS CHARLES F. RAND,1 NEW York , N. Y. BENJAMIN B. THAYER,2 . NEW YORK, N. Y. FIRST VICE-PRESIDENT PHILIP N. MOORE,1 ST. Louis, Mo. TREASURER GEORGE C. STONE,1 NEW YORK, N.Y. SECRETARY EMERITUS ROSSITER W. RAYMOND, NEW York, N. Y.

Jan 4, 1915

By P. E. Doherty, B. Chalmers

Subboundaries may be revealed in aluminum by the formation of pits on the surface during cooling from elevated temperatures. The pits do not form in the vicinity of high- or low-angle boundaries. They are attributed to the condensation of vacancies from a super saturation produced during coolirzg. Using the vacancy pit and Schulz X-ray techniques for observing low-angle boundaries, a study was made of the transition from the nearly perfect seed to the striated structuke characterist-ic of aluminum crystals grown from the melt. It was found that the individual striation boundaries develop by the coalescence of very small-angle boundaries, as well as by the addition of individual dislocations. Several mechanisms for the formation of striations are discussed. Evidence was found suggesting that a super-saturation of vacancies exists near a growing interface, and it is proposed that the resulting climb of existing dislocalions produces "half'-loops" at the interface, which combine to form the low-angle striation boundaries. LINEAGE, or "striation" boundaries, have been studied in detail by Teghtsoonian and Chalmers 1,2 in crystals of tin grown from the melt, and by Atwater and Chalmers3 in lead. They found that single crystals grown from the melt consist of regions which are separated by subboundaries that lie roughly parallel to the growth direction. A difference in orientation of 0.5 to 3 deg exists between the striated regions; the misorientation is such that the lattice of one region could be brought into coincidence with the lattice of its neighbor by a rotation about an axis approximately parallel to the direction of growth of the crystal. They observed an incubation distance for the formation of striations which increased with decreasing growth rate. They also found that in any crystal, the sum of all rotations of the lattice in one sense, in going from one striation to the next, is very nearly equal to the sum of all the rotations in the opposite sense. A striation boundary, which is a low-angle grain boundary, can be described as an array of dislocations. If it is assumed that suitable dislocations are introduced into the crystal during solidification, the formation of striation boundaries can be explained as a result of the migration of the disloca- tions into arrays. The formation of arrays is energetically favorable since the energy of an assembly of dislocations can be reduced by the interaction of the stress fields when a suitable array is formed. This investigation presents and interprets new information concerning the nature and origin of striation boundaries in aluminum. EXPERIMENTAL TECHNIQUE Single crystals of high-purity aluminum (Alcoa 99.992 pct) were prepared by horizontal growth from the melt.'' The specimens were subsequently electropolished in a solution of 5 parts methanol to 1 part perchloric acid kept between -10° and 0°C in a bath of dry ice and alcohol. The current density was approximately 6 amps per sq in. Doherty and Davis9 have shown that in aluminum sub-boundaries with misorientations of not less than several seconds of arc may be revealed by the vacancy pit technique. During cooling from elevated temperatures pits form on electropolished surfaces of aluminum crystals as a result of the condensation of vacancies.11 Pits do not form in the vicinity of small- or large-angle grain boundaries, presumably because such boundaries act as sinks for vacancies. Boundaries of misorientations down to 3 sec of arc are revealed as pit-free regions, see Fig. 1. The Schulz X-ray technique12 was used to determine the angular misorientations of subboundaries. In this method, white radiation from a micro-focus X-ray tube is used to produce an image of a fairly large area of a single crystal surface. Subboundaries cause splitting in the diffracted image, see Fig. 2. Misorientations down to about 15 sec of arc may be observed with this technique. OBSERVATIONS AND DISCUSSION Figure 1 shows a striated aluminum crystal grown at 10 cm per hr etched by the vacancy pit technique. An incubation distance of about 1 cm is observed before the initiation of striation boundaries. Fig. 2 is a Schulz X-ray photograph of a striated crystal similar to that shown in Fig. 1. A large area of the crystal was studied by means of a series of photographs. Fig. 2, which is a reflection from the (100) plane, included about the first 4 cm of crystal to freeze. There is an incubation distance of about 1 cm, and a distance of about 2 cm over which the angle of misorientation builds up to its final value of approximately one degree. Some twist component can be seen in Fig. 2 at the right side of the photograph. From Fig. 2 it can be seen that the sum of all rotations of the lattice in one

Jan 1, 1962

By Rudolph G. Wuerker

THE scarcity of values of tensile strength of rocks has been explained by the lack of successful testing procedures. In the case of mine rock a description is given' of the difficulties encountered in testing a cylindrical specimen, such as a core, by conventional methods. Over a period of years the following method has given definite and reproducible results with the weakest as well as with the strongest rocks. It does not completely supersede the use of cores with special fixtures but is a supplement in all cases where cores cannot be obtained, as from soft rocks, or in cases where it is less expensive to prepare test specimens by cutting them out of the rock instead of drilling cores. Principle and equipment are the same as for the test for tensile strength of hydraulic-cement mortar.' The test specimen, Fig. 1, has the shape of a briquet. While in the original cement mortar test the briquet is cast in a special mold, it is prepared from rocks in different ways, depending on how easily they can be cut and shaped. Soft rocks, which cannot be core-drilled with a carboloy or diamond bit, are simply hand-cut. Only two dimensions need be watched. The first is the 1-in. diam at the narrowest cross-section of the briquet. The other critical measure is the radius of curvature of the waistline, as the roller supports in the grips have a fixed distance. This radius is ground out of the solid by means of a carborundum grinding wheel having a 3/4-in. radius. Medium hard rocks can be core-drilled with a carboloy bit. The resulting core can be used for nondestructive sonic testing first, and after that for any destructive test. By using an EX-bit and by carefully placing the coreholes, preferably by using a tenplate such as shown in Fig. 1, it is possible to obtain from the rock a punched sample from which numerous tensile briquets can be made. The outside radius of the EX-bit differs from the radius of curvature of the briquet by 1/8 in., but this still permits placing and aligning the specimen in the grips. In the case of bedded rocks the core might have bedding planes normal to the plane of the briquets, and rocks can be tested in any arrangement of the bedding planes desired. Hard rocks, limestones, igneous, and metamor-whic rocks can only be diamond-drilled or diamond-cut. Here the method of getting the tension briquets by accurate placing of EX-drill holes is especially economical. The tops of the briquets made from hard rocks cannot be rounded; they are straight cuts made with a diamond cut-off saw and rounded off on a polishing wheel. Results: As long as specimens broke over the waistline the results were considered acceptable. Further statistical treatment of the tests' showed a satisfactory percentage of standard deviation. The tensile strength values obtained by this method do not represent true values because of the stress concentration caused by the curvature of the side of the piece and because of the closeness of the grips. The ratio of maximum to average stress at the plane of failure has been determined to be about 1.75." All tensile strength values listed in Table I are corrected accordingly. To avoid this stress-concentration, if there are a sufficient number of cores, tensile strength can be measured by imbedding the cores in mortar in the two outer briquets in the gangmold.4 Strain-Measurements: The applicability of the briquet specimens for strain observations was tested in the case of sandstone and shale. Two element Rosette SR-4 strain gages were used. Young's modulus and Poisson's ratio, both in tension, were computed and found to be different from those in compression, determined during the same test series and from the same rock, see Table I. References 1 L. Obert, S. L. Windes. and W. I. Duvall: Standardized Tests for Determining the Physical Properties of Mine Rock. U. S. Bur. Mines R.I. 3891 (1946). 2 Test for Tensile Strength of Hydraulic-Cement Mortar, ASTM Standard C 190-44. S F. O. Auderegg, R. Weller, and B. Fried: Tension Specimen Shape and Apparent Strength. Proc. ASTM 11939) 39, pp. 1261-1269. 4 API Code 32.

Jan 1, 1956

By M. B. Bever, A. B. Michael

The solidification of aluminum-rich aluminum-copper alloys was investigated for different solidification rates. The measured amounts of nonequilibrium eutectic were compared with the amounts calculated on the assumption of no diffusion in the solid. The morphology of the eutectic was studied and dendritic spacings were measured. Compositions of the cored primary solid solutions were determined by quantitative autoradiography after activation of the solute copper by neutron irradiation. CONSIDERABLE progress has been made in recent years toward an understanding of the solidification of metals. This is especially true for the factors involved in nucleation, the controlled growth of metal crystals from melts, and various aspects of the freezing of ingots and castings. Many features of the solidification process, however, are not understood adequately and much further work is required. In the research reported here the solidification of a series of aluminum-rich aluminum-copper alloys was investigated. Different degrees of deviation from the idealized case of equilibrium solidification were attained by varying the rate of solidification. Thermal analysis and microscopic examination were supplemented by lineal analysis and autoradiography. The latter required the use of radioactive tracers and was adapted to the quantitative determination on a microscale of concentrations of copper dissolved in aluminum. The tracers were produced in situ by activating the copper with neutrons. These techniques permitted a correlated interpretation of the temperature-time history, the amounts of nonequilibrium eutectic and the general morphology of the alloys, and yielded quantitative data on microsegregation. Nonequilibrium Solidification In the general case of the solidification of a solid solution in accordance with the phase diagram, the composition of the coexisting liquid and solid must change continuously. This change requires diffusion, which at best remains incomplete in the solid during solidification. The resulting inhomogeneity of the solid solution crystals is well-known as coring, dendritic segregation, or microsegregation. The generally accepted analysis of coring assumes that, 1—no diffusion occurs in the solid, 2—diffusion is complete in the liquid, and 3—the composition of the solid formed on cooling through any infinitesimal temperature interval is given by the solidus of the phase diagram. On this basis, In this equation m designates mass, x designates the concentration of solute and the subscripts L and S refer to the liquid and solid phases, respectively; the subscript o indicates the initial state, in which the liquid is identical with the entire system. Eq. 1 or its equivalent has been derived repeatedly'-7 and an analogous equation, known as Rayleigh's equation, has been used for distillation. The assumptions on which Eq. 1 is based do not include an infinitely fast cooling rate as sometimes stated. In fact, Olsen and Hultgren %ave shown by experiment that very high solidification rates suppress coring, presumably by preventing diffusion in the liquid and by the effect undercooling has on the composition of the nucleus. Coring thus occurs at rates of cooling which are too fast for a close approach to equilibrium in the solid and too slow to suppress diffusion in the liquid and to cause marked undercooling. If the liquidus and solidus approximate straight lines, Eq. 1 simplifies to The fraction of liquid present at any temperature during nonequilibrium solidification can be calculated from Eqs. 1 or 2. By the lever relation it is

Jan 1, 1955

By D. R. Parrish, W. E. Lamoreaux, W. W. Owens

Several methods are now being used by the industry for determining the gas-oil flow characteristics of reservoir rock samples. Most of the laboratory experirnerltal rlzethods can be classified either as steady-state, unsteady-state, or Hassler-type tests. Although the validity of the results obtained by any specific method is not questiorzed, in general, the complexity of these methods leaves much to be desired. This investigation dealt primarily with the development of a simplified unsteady-state (gas drive) laboratory test method for measuring kg/ko re1ationships of small core samples. A procedure for selecting uniform and representative sandstone rock samples was developetl since it was observed that the reliability of the test resu1ts was dependent upon having a sample which was uniform in porosity and permeability. The importance of factors known to influence the results of this type test, such as oil viscosity, gas expansion, and pressure differential were eva/uated. The method of calculating the test results was found to give valid data over a wide range of gas expansion. The limits of pressure differential and oil viscosity which would insure reliable results were defined. In cornparisorz with other presently used testing methods, the gar drive method requires considerably less apparatus, is less time consuming, and is more readily adaptable to a routine type core test. INTRODUCTION The detcrmination of the gas-oil flow characteristics of reservoir rocks has been given concentrated study by the oil industry for the past decade. Both analytical and experimental methods have been considered. The analytical methods have generally relied on a simplified characterization of porous materials in order that the fundamental laws of fluid flow and capillarity could be utilized. More direct experimental methods have been proposed by numerous production research laboratories with the primary goal being a simple and inexpensive, yet reliable method for measuring the gas-oil flow characteristics of reservoir rock samples. The experimental methods which have been reported in the literature generally can be grouped into one of the following classifications: 1. Steady state1,2,3,4 in which a fixed ratio of flowing fluids is forced through the test sample until equilibrium conditions of saturation and pressure gradient are established. 2. Hassler or stationary liquid method5,6,7 in which a uniform liquid saturation is attained, usually through capillary desaturation, then gas or oil is flowed through the sample at a pressure drop insufficient to disturb the pre-established saturation. :. Non-steady state method1,8,9,10 In which only the gas phase is injected into the sample, causing displacement of the oil phase and resulting in a system of continually changing average saturation and saturation gradient. The steady-state and Hassler methods have been most popular because, no doubt, of the simplicity of the actual relative permeability calculations. The problems involved in these methods were limited to apparatus design and measurement techniques. In the steady-state method, for instance, a constant flowing fluid ratio is established which, at equilibrium, results in an essentially uniform saturation over the entire length of the test sample. Therefore, the basic flow characteristics could be obtained by correlating the average saturation of the test sample with the kg/ko determined at various flowing gas-oil ratios.

Jan 1, 1957

By Meguru Nagamori

DURING the smelting of the sulfide ores of copper, nickel, and certain other metals, a matte phase is formed. For a better understanding of the physico-chemical properties of mattes, binary systems such as Cu-S, Ni-S, Fe-S, and so forth, should be studied, especially in the vicinity of liquid compounds such as Cu2S, Ni3S2, FeS, and so forth. These compounds are relatively stable in the solid state although they can exhibit appreciable deviations from stoichiometry. With small deviations from stoichiometry there are large changes in the activity of both sulfur and metal this is a characteristic of both solid and liquid sul-fides near the stoichiometric compositions. In the vicinityof molten Cu2S,1 for instance, the activity of sulfur increases about 100 times for a 0.012 increase in the mole fraction of sulfur and, correspondingly, the activity of copper decreases greatly. In this sens the minor deviations from stoichiometry should be carefully taken into account in studies of such metal-sulfur melts. Metal-sulfur melts may be considered to have properties intermediate between metallic solutions and molten salts, i.e., neither entirely metallic nor entirely ionic. The radius of the ion sZ- is 1.84 as compared with 1.04? for a single bond covalent s.2 It is therefore inferred that when the sulfur is more ionic its partial molar volume is larger, although metal-metal, metal-sulfur, and sulfur-sulfur interactions may bring about further complexities. Thus, it is to be expected that the molar volumes, which are derived from density-composition relations, will help in resolving the structure of the melts. In this study the maximum bubble pressure method with bubbling gases of H2, H2S, and Ar, .was employed to measure the density. EXPERIMENTAL Materials. Silver of 99.95 pct purity was melted in an alumina crucible and hydrogen gas was then bubbled through the liquid for the deoxidation. In preparation of Cu2S, electrolytic copper powder (>99.9 pct Cu) was mixed with precipitated sulfur and heated to 1200°C in an alumina crucible under a hydrogen atmosphere. Mixtures having the approximate compositions FeS and Ni3S2 were prepared by heating reagent grade electrolytic iron or reduced nickel powder with precipitated sulfur under a hydrogen atmosphere. The H2S gas was of 98.5 pct purity, the impurities being mostly CO2 and CS2 which hardly contaminate the melts. Apparatus. The crucible system is shown schematically in Fig. 1. To minimize the variation of melt composition during a density measurement, the apparatus was designed in such a way that either Ar, H2, H2S, or mixtures of these gases could be used as the bubbling gas. When the melt had a high partial pressure of sulfur, H2S gas was used. When the partial pressure of sulfur was so low that oxygen might dissolve in the melt, the use of H2 was preferred. In intermediate cases, argon or mixtures of H2-H2S were used. Density of Dibutylphtalate. Dibutylphtalate was used as the manometer fluid. Relative to distilled water, the density of the dibutylphtalate, pdib g per cc, was measured and found to be: pdib (25°C) = 1.046 i 0.002. With the use of the temperature coefficient reported by Kemppinen and Gokcen,3 the following value was

Jan 1, 1970

By M. T. Hepworth, A. K. Stewart

Iron containing 0.1 pct A1 and -0.9 pct P by weight was internally oxidized in the temperature range 900° to 1300° C, where the bcc structure is stabilized by phosphorous. By measuring the depth of penetration of oxygen with time in an internally oxidized zone for an imposed surface oxygen potential, oxygen permeability was determined. The dgfusion coefficient of oxygen in iron was then calculated using known solubility data, yielding the expression: where Do is the diffusion coefficient of oxygen in bcc iron in sq cm per sec and T is temperature in OK. RECENTLY Hepworth, Smith, and Turkdoganl measured the diffusivity of oxygen in bcc iron and reported the temperature dependence of diffusivity from data determined in the a, and 6 temperature ranges. Subsequently Swisher and Turkdogan' have measured the diffusivity of oxygen in fcc iron. Internal oxidation techniques were employed by these investigators and in this current study. The analysis of this technique is developed by wagner3 (presented in English by Hauffe4 and Rapp 5). In this present study bcc iron stabilized by phosphorous was used to determine oxygen diffusivity in the temperature range 900° to 1300°C. Meijerin 6 has studied oxygen permeability in this temperature range using bcc iron stabilized with 5 pct Sn. Other inves- tigators who have studied oxygen permeability in bcc iron at other temperatures are Schenck et al., 7 Bohen-kamp and Engell, 8 and Bradford. EXPERIMENTAL Electrolytic iron of 99.99 pct purity was alloyed to contain 0.897 pct P and 0.093 pct Al. The maximum weight percent phosphorous required to stabilize bcc iron between 910" and 1392°C is 0.51 pct as determined by Haughton,10 0.42 pct by Roquet and jegaden," and 0.58 pct by vogel,12 with the latter value preferred by Hansen.13 Microprobe analysis indicated that there was no segregation of the phosphorous either before or after permeability studies; therefore, the quantity of phosphorous added was assumed to be sufficient to stabilize the bcc structure. Furthermore, the permeability results of studies on this alloy agreed substantially with interpolated values from previous data on bcc iron.' An ingot of the Fe-P-A1 alloy was hot-rolled to a l-in.-thick slab. Specimens were machined to dimensions: 13/8 by $ by 1/4 in. The experimental apparatus and procedure used have been described before.' A constant oxygen potential was established by passing argon and hydrogen through a column of oxalic acid dihydrate, which has a water vapor pressure which is well-known as a function of temperature. Slab specimens were exposed to a gas mixture sufficiently lean in oxygen to prevent the formation of a surface oxide for predetermined temperature for selected times. The specimens were then quenched, sectioned, and examined metallo-graphically. All quenched specimens were iron-plated to provide protection from the outside sample edge during polishing. Fig. 1 shows a typical microstruc-ture for a specimen oxidized at 953°C for 48.00 hr at a water vapor-to-hydrogen pressure ratio of 0.20. DISCUSSION AND RESULTS The following equation was derived by Hepworth et al.' from Wagner's kinetic expressions for internal oxidation:

Jan 1, 1969

By W. G. Pfann

In zone-melting, a small molten zone or zones traverse a long charge of alloy or impure metal. Consequences of this manner of freezing are examined with impurerespect to solute distribution in the ingot, with particular reference to purification and to prevention of segregation. Results are expressed in terms of the number, size, and direction of travel of the zones, the initial intermsofsolute distribution, and the distribution coefficient. IF a charge of binary solid-solution alloy is melted and then frozen slowly from one end, as for example in the Bridgman method of making single crystals,' coring usually occurs, with a resulting end-to-end variation in concentration. Such coring, or normal segregation, is undesirable where uniformity is an object. On the other hand, for certain systems, it can be utilized to refine a material by concentrating impurities at one end of the ingot.'. ' In the present paper a different manner of freezing will be examined with respect to the distribution of solute in the ingot. A number of procedures will be indicated which have in common the traversal of a relatively long charge of solid alloy by a small molten zone. Such methods will be denoted by the general term zone-,melting, while the process described in the preceding paragraph will be called normal freezing. It will be shown that, in contrast to normal freezing, zone-melting affords wide latitude in possible distributions of solute. Segregation can either be almost entirely eliminated or it can be enhanced so as to provide a high degree of sttparation of solute and solvent. A number of simplifying assumptions will be invoked which, while not entirely realizable in practice, nevertheless provide a suitable point of departure for more refined treatments. Moreover, our own experience with zone-melting has shown that, for certain systems at least, the analysis holds quite well. The present paper will be confined to a discussion of principles and a general description of procedures. Comparison with experiment is planned for later publication. Normal Freezing Before considering zone-melting, segregation during normal freezing will be reviewed briefly. If a cylinder of molten binary alloy is made to freeze from one end as in Fig. 1, there usually will be a segregating action which will concentrate the solute in one or the other end of the ingot. If the constitutional diagram for the system is like that of Fig. 2, then the distribution coefficient k, defined as the ratio of the concentration in the solid to that in the liquid at equilibrium, will be less than one and the solute will be concentrated in the last regions to freeze. If the solute raises the freezing point, then k will be greater than one and the solute will be concentrated in the first regions to freeze. The concentration in the solid as a function of g, the fraction which has solidified, can be expressed by the relation: C = kC0 (1-g)k-1 [I] where C, is the initial solute concentration in the melt. Eq 1 is based on the following assumptions: 1—Diffusion in the solid is negligible. 2—Diffusion in the liquid is complete (i.e., concentration in the liquid is uniform). 3—k is constant. Concentration curves representing eq 1 for k's from 0.01 to 5.0 are plotted in Fig. 3. This equation, in one form or another, has been treated by Gulliver,³ Scheuer,4 Hayes and Chipman5 for alloys and by McFee2 for NaCl crystals. It is derived in Appendix I. It should be pointed out that the k which is calculated from the phase diagram will be valid only in the ideal case for which the stated assumptions are correct. In all actual cases, the effective k will be larger than this value for solutes which lower the melting point, smaller for solutes which raise the melting point, and will probably vary during the beginning of the freezing process. For simplification it will be assumed that the ideal k is valid. Zone-Leveling Processes The processes of this part are designed to produce a uniform, or level, distribution of solute in the ingot. Single Pass: Consider a rod or charge of alloy whose cross-section is constant and whose composition, C2, is constant, although permissibly varying on a microscopic scale." Such a charge might be a rapidly frozen casting or a mixture of crushed or powdered constituents. Cause a molten zone of

Jan 1, 1953

By Lawrence H. Van Vlack, Otta K. Riegger

Periclase-type oxides were examined microscopically after being exposed to siliceous liquids. The rate of grain growth was found to be inversely proportional to the grain diameter. Grain growth proceeds more rapidly at higher temperatures, but is retarded by increasing liquid contents. aMag-nesiowiistites with higher MgO contents grow less rapidly than those with higher FeO contents. The growth rate is reduced by the presence of a second solid phase. The silica-containing liquid penetrates as a film between the individual magnesiowus tite grains. This is independent of time, temperature, amount of liquid, or the MgO/ Fe0 ratio. When present, olivine and spinel-type phases can provide a solid-to-solid &apos;&apos;bridge" between magnesioustite grains. THIS paper presents the results of a study of the microstructures of periclase type oxides in the presence of a silicate liquid. The purpose was to learn more about the effect of service factors such as 1) time, 2) temperature, and 3) liquid content upon A) grain growth, and B) liquid location among the solid grains. This study was prompted by the fact that periclase refractories are known to have very little solid-to-solid contact when the phases which are present are limited to periclase and liquid. Such a micro-structure gains industrial significance because it permits fracture during service when stresses are applied at high temperatures. The details of ceramic microstructures have not received extensive attention. This is in contrast to the extensive attention given to a) the phase relationships pertaining to refractory compositions, and b) the details of the microstructures of comparable metallic materials. A brief review will be made of the pertinent phase relationships and microstructural considerations in general, as well as of refractory compositions. a) Phase Relationships. This investigation was limited to those compositions in which (Mg, Fe)O was the solid phase. MgO and FeO form a complete series of solid solutions. Pure MgO has the name of periclase. The related FeO structure is called wustite. Both have the NaC1-type structure: however, wustite possesses a cation deficiency so that the true composition is Fe<10 even in the presence of metallic iron. The phase relationships involving solid (Mg, Fe)O and a silicate liquid are shown in Fig. 1. In this case. the liquid is saturated with (Mg, Fe)o. There-fore its SiOz content is below that encountered in orthosilicate liquids. As a consequence the liquid phase specie:; are primarily the following ions: and 0-&apos; plus occasional Fe+ ions. Two features are of importance: a) the liquid contains relatively small species and b) the liquid contains large quantities of the same species as the solid. viz., Fig. 2 shows the system, FeO-SiOz, which will be used in some of the discussions that follow. This diagram is the right side, vertical section of Fig. 1. Here, as pre\iously, the composition at the FeO end of the diagram is nonstoichiometric, varying from Feo.950 when the liquid oxide is in contact with the solid iron, to about Fe 0, when the solid oxide is in equilibrium with an atmosphere of equal proportions of CO and C02 at the solidus temperature. The Fe/O ratio will be maintained in wustite in the presence of SiO,. However, the FeM/Fe++ ratio in the liquid will be lower because of the effect OIF the SiO, on the activity of the FeO. With the addition of MgO to wustite, the over-all composition (IvZg, Fe)@, has a value of x lying between 0.9 and 1.0 when the COz/CO ratio is 1.0&apos;. b) Microstructures. In general, published attention to refractory microstructures has been directed toward the phase analyses that accompany compositional variations. This is illustrated by Harvey6 in his work on silica brick and by wells7 in his work on periclase brick. In each case, a series of altered zones is encountered which provides a sequence of phase associations. If due consideration is given to reaction kinetics, such an examination reveals phases that are compatible with equilibrium studies. Admittedly, however, it is often necessary to determine more complicated polycomponent systems to account for all the phases present.8 Relatively little attention has been given to microstructural geometry in ceramic materials. Certainly less attention has been given to this aspect of ceramic microstructures than to the size, shape, and distribution of the constituent phases in metals. Burke has pointed out that the grain size of oxides follows the same growth rules as for metals, viz.,

Jan 1, 1962

By A. H. Geisler, R. F. Mehl, C. S. Barrett

The mechanism by which the supersaturated solid solution of 20 per cent silver in aluminum decomposes has been reported in two previous publications.1&apos;2 The analysis of streaks in Laue photograms showed that thin platelike particles (the so-called Guinier-Preston aggregates) form upon matrix planes in the early state of decomposition.1 The size of these particles is larger, the higher the temperature at which they form in accordance with nucleation theory;³ at all temperatures they increase in size with aging.2 When they have grown thick enough to afford three-dimensional diffraction, powder X-ray photograms show that the structure is not that of the equilibrium precipitate but that of a transition lattice . Sincc this is also platelike in shape and also lies upon the (III) matrix planes with the [IIO] direction in the matrix parallel to the [II.O] direction in it seems likely that the original platelet particles are merely in an early stage of formation, and thus finely dispersed. The atomic spacing and pattern on the (00.1) plane in y&apos; are identical with those on the (111) matrix plane to which it lies parallel, and since comparable directions in the two planes are parallel, the lattices are thus coherent at the interface; an analogous coherence has been found in aluminum-copper alloys.3 The structures y&apos; and y are both close-packed hexagonal and are oriented alike; they differ only in interatomic distances. Consequently, y&apos; is regarded as y strained from its ordinary dimensions by the lattice coherency between it and the matrix.2 The lattice movements that transform the matrix to the equilibrium precipitate appear to be very simple.2 The mechanism of precipitation in this system is simpler and is more precisely known than that in any other system hence the system should be a profitable one for the difficult task of correlating property changes with structural alterations. The present report provides additional studies on powder X-ray diffraction from alloys of 10 per cent, 20 per cent and 30 per cent Ag, and presents the correlation of crystallographic changes with changes in microstructurc, Brinell hardness and electrical resistivity of the three alloys. Preparation of Samples and Experimental Procedure The preparation of the 20.2 per cent Ag alloy has been described2 Alloys containing 9.9 and 29.7 per cent Ag were prepared from 99.97 per cent A1 and 99.99+ per cent Ag using a similar procedure. Rolled

Jan 1, 1943

By R. F. Mehl, C. S. Barrett, A. H. Geisler

The mechanism by which the supersaturated solid solution of 20 per cent silver in aluminum decomposes has been reported in two previous publications.1&apos;2 The analysis of streaks in Laue photograms showed that thin platelike particles (the so-called Guinier-Preston aggregates) form upon matrix planes in the early state of decomposition.1 The size of these particles is larger, the higher the temperature at which they form in accordance with nucleation theory;³ at all temperatures they increase in size with aging.2 When they have grown thick enough to afford three-dimensional diffraction, powder X-ray photograms show that the structure is not that of the equilibrium precipitate but that of a transition lattice . Sincc this is also platelike in shape and also lies upon the (III) matrix planes with the [IIO] direction in the matrix parallel to the [II.O] direction in it seems likely that the original platelet particles are merely in an early stage of formation, and thus finely dispersed. The atomic spacing and pattern on the (00.1) plane in y&apos; are identical with those on the (111) matrix plane to which it lies parallel, and since comparable directions in the two planes are parallel, the lattices are thus coherent at the interface; an analogous coherence has been found in aluminum-copper alloys.3 The structures y&apos; and y are both close-packed hexagonal and are oriented alike; they differ only in interatomic distances. Consequently, y&apos; is regarded as y strained from its ordinary dimensions by the lattice coherency between it and the matrix.2 The lattice movements that transform the matrix to the equilibrium precipitate appear to be very simple.2 The mechanism of precipitation in this system is simpler and is more precisely known than that in any other system hence the system should be a profitable one for the difficult task of correlating property changes with structural alterations. The present report provides additional studies on powder X-ray diffraction from alloys of 10 per cent, 20 per cent and 30 per cent Ag, and presents the correlation of crystallographic changes with changes in microstructurc, Brinell hardness and electrical resistivity of the three alloys. Preparation of Samples and Experimental Procedure The preparation of the 20.2 per cent Ag alloy has been described2 Alloys containing 9.9 and 29.7 per cent Ag were prepared from 99.97 per cent A1 and 99.99+ per cent Ag using a similar procedure. Rolled

Jan 1, 1943

By J. C. Fisher, J. H. Hollomon, David Turnbull

Understanding of the diffusion problem has recently been furthered by the analysis of Birchenall and Meh1.l They pursued the problem of the variation of the diffusion coefficient with composition for non-ideal solid solutions. Their analysis follows the tradition of Wagner,l Jost, Dehlinger, and Darken & who assumed the net flux of diffusing material to be proportional to the gradient of a quantity related to free energy. The basic assumption in Birchenall and Mehl&apos;s formulation of the problem is that the net flux of diffusing material is proportional to a thermodynamic activity gradient. To estimate the applicability of the derived relations, they corrected the diffusion coefficients of carbon in austenite by utilizing Smith&apos;s6 activity data for carbon, and the diffusion coefficients for zinc in copper with activity data computed from the vapor pressure measurements of Har-greaves.&apos; The corrected coefficients for carbon were virtually independent of carbon concentration. For the diffusion of zinc in copper a moderate variation of diffusion coefficient with concentration remained after the correction. The problem of diffusion can be formulated in another way than that used by Birchenall and Mehl. The method is that of chemical rate theory and has been used by Eyring and his coworkers8,9 as well as by Eyring and Zwolinskilo in a discussion to Birchenall and Mehl&apos;s paper. As yet the method has not been applied to substitu-tional solid solutions. On the basis of their assumptions, Eyring and Zwolinski derived a relation between the diffusion coefficient and activity that is identical with that of Dehlinger and Darken but which does not correct for the variation of the diffusion coefficient with concentration as well as does the relation derived by Birchenall and Mehl. It was thought that the theory of diffusion would be more complete if the inconsistency between the two analyses could be rationalized and if diffusion in substitu-tional alloys were analyzed on the basis of the concepts of the chemical rate theory. Chemical Rate Theory According to the theory of absolute reaction ratess the reaction +..... +X, Eq I is viewed as taking place in two steps. First the reactants A1, A², . . . A; combine to form an activated complex M with which they are in equilibrium: A1 + A1+ . . . + A=M. Eq 2 Second the activated complex decomposes to give the products XI, XZ, . . . Xi: M?X, + X²+ . . . +Xi Eq g It has been showns that the number of activated complexes decomposing per unit volume per unit time is given by the expressiont kT -h CM † The transmission coefficient has been taken as unity.

Jan 1, 1949

By David Turnbull, J. H. Hollomon, J. C. Fisher

Understanding of the diffusion problem has recently been furthered by the analysis of Birchenall and Meh1.l They pursued the problem of the variation of the diffusion coefficient with composition for non-ideal solid solutions. Their analysis follows the tradition of Wagner,l Jost, Dehlinger, and Darken & who assumed the net flux of diffusing material to be proportional to the gradient of a quantity related to free energy. The basic assumption in Birchenall and Mehl&apos;s formulation of the problem is that the net flux of diffusing material is proportional to a thermodynamic activity gradient. To estimate the applicability of the derived relations, they corrected the diffusion coefficients of carbon in austenite by utilizing Smith&apos;s6 activity data for carbon, and the diffusion coefficients for zinc in copper with activity data computed from the vapor pressure measurements of Har-greaves.&apos; The corrected coefficients for carbon were virtually independent of carbon concentration. For the diffusion of zinc in copper a moderate variation of diffusion coefficient with concentration remained after the correction. The problem of diffusion can be formulated in another way than that used by Birchenall and Mehl. The method is that of chemical rate theory and has been used by Eyring and his coworkers8,9 as well as by Eyring and Zwolinskilo in a discussion to Birchenall and Mehl&apos;s paper. As yet the method has not been applied to substitu-tional solid solutions. On the basis of their assumptions, Eyring and Zwolinski derived a relation between the diffusion coefficient and activity that is identical with that of Dehlinger and Darken but which does not correct for the variation of the diffusion coefficient with concentration as well as does the relation derived by Birchenall and Mehl. It was thought that the theory of diffusion would be more complete if the inconsistency between the two analyses could be rationalized and if diffusion in substitu-tional alloys were analyzed on the basis of the concepts of the chemical rate theory. Chemical Rate Theory According to the theory of absolute reaction ratess the reaction +..... +X, Eq I is viewed as taking place in two steps. First the reactants A1, A², . . . A; combine to form an activated complex M with which they are in equilibrium: A1 + A1+ . . . + A=M. Eq 2 Second the activated complex decomposes to give the products XI, XZ, . . . Xi: M?X, + X²+ . . . +Xi Eq g It has been showns that the number of activated complexes decomposing per unit volume per unit time is given by the expressiont kT -h CM † The transmission coefficient has been taken as unity.

Jan 1, 1949

By J. D. Mote, A. Rosen, J. E. Dorn

The effect of strain rate and temperature on the critical resolved shear stress for (1100) [1120] prismatic slip was determined for the intermediate hexagonal phase containing about 67 at. pct Ag and 33 at. pct Al. Whereas the flow stress increased only slightly as the test temperature was first decreased below room temperature, a rapid increase inflow stress was obtained with yet greater decreases in temperature from about 240" to 4°K. The effect of both temperature and strain rate on the flow stress over the low-temperature range could be completely rationalized in terms of the Peierls mechanism when the deformation is controlled by the rate of nucleation of pairs of kinks. A few years ago Mote, Tanaka, and Dorn1 observed that the critical resolved shear stress for prismatic slip of a 67 at. pct Ag plus 33 at. pct A1 hexagonal intermediate phase by the (1100)[1120] mode decreased precipitously as the test temperature was increased from 4" to about 160°K. Their results for both basal and prismatic slip are given in Fig. 1. It is obvious that only the flow stress for prismatic slip is strongly temperature-dependent, whereas the flow stress for basal slip is independent of temperature. If the temperature dependence of the flow stress were primarily due to interstitial impurities, it might be expected that they would influence the flow stress for basal slip as well. Since the activation volume at 115°K for prismatic slip was determined to be about 15b3, where b is the Burgers&apos; vector, this thermally activated deformation process was tentatively ascribed as being due to the Peierls mechanism. But the various analyses of the Peierls mechanism then available as formulated by Seeger2 and also by Lothe and Hirth3 did not agree well with the experimental data. Since that time a more realistic theory for the operation of the Peierls mechanism under conditions where the strain rate is determined by the rate of nucleation of pairs of kinks has been presented by Dorn and Rajnak.4 The present investigation was, therefore, undertaken in order to provide the essential data for a careful check on the agreement between this theory and the low-temperature deformation by prismatid slip of the above-mentioned Ag2A1 intermediate phase. EXPERIMENTAL TECHNIQUE Single-crystal specimens so oriented that the [1120] direction and the normal to the (1100) plane were at 45 * 2 deg to the tensile axis were grown from the congruent melting composition of about Ag2Al for the intermediate hexagonal phase by the

Jan 1, 1964

By R. W. Smith, T. J. Smolik

Recent work indicates that fluosilicate ions and or fluosilicate amine complex ions play important roles in fluoride activation of bery and feldspars in cationic flotation systems. In an attempt to further confirm conclusions reached in this earlier work, an infrared and X-ray diffraction study of the action of fluorides in cationic flotation of silicates was undertaken. It should be noted that in recent years considerable use has been made of infrared spectroscopy in studies of surface phenomena,2-4 and these studies have established the excellence of the technique. In the present study infrared spectra were obtained for various products of the reaction of HF and dode-cyclamine hydrochloride with quartz, microcline and beryl. These spectra were compared with one another and spectra of several inorganic and organic substances. In addition to infrared spectra, X-ray diffraction patterns were run on many of the reaction products obtained. A model 137 B Perkin Elmer Infracord double beam spectrophotometer containing sodium chloride optics was used to obtain the spectra. Infrared samples, except for the dodecylamine sample, were prepared by thoroughly mixing the substance to be analyzed with purified KBr in steel vessels on a Wig-L-Bug amalgamator. One-half in. pellets weighing 100 mg were than pressed under vacuum. Details concerning percentage of the substance to be analyzed in the pellets are indicated on the spectra. In all cases except for dodecylamine a KBr pellet was placed in the reference beam of the spectrophotometer to cancel bands due to possible impurities in the KBr. The dodecylamine sample on which an infrared spectrum was obtained was prepared by placing pure dodecylamine between two salt plates. X-ray diffraction patterns were obtained with a Norelco instrument, using a copper target tube, nickel filter and Geiger tube detector. The samples were ground into powders and either placed on glass slides with glue or placed into regular powder sample holders for diffraction studies. Goniometer scanning speed varied from 1°/min to 1/8°/min. EXPERIMENTAL RESULTS AND DISCUSSION Infrared spectra of microcline, beryl and quartz were obtained first and are shown in Fig. 1. These spectra agree reasonably well with previously reported spectra.5,6 The microcline (Fig. 1 a) and beryl (Fig. 1 b) were from good Black Hills crystals. The quartz (Fig. 1 c) was from a large, clear Brazilian crystal. It is not clear whether absorption bands of minerals are due to molecular vibrations, lattice vibrations or both. Fig. 2 shows infrared spectra of dodecylamine (Fig. 2 a) and dodecylamine hydrochloride (Fig. 2 b). The dodecylamine spectrum checks quite closely with that reported in Sadtler.8 Little is known of the spectra of hydrochloride salts of amines,9 and a spectrum of dodecylamine hydrochloride could not be

Jan 1, 1965

By R. P. Smith

The carbon content of a number of alloys ranging (before carburitation) from purified iron to purified cobalt was determined for fixed activities of carbon by equilibration with each of six CO-CO2 atmosphere at 1000°C. At fixed carbon activity, the carbon content decreases continuously with increasing cobalt content. For concentrations of 0 to 50 at. pct Co the results can be expressed by a linear interaction equation of the type In y2 = 7.76n2/(n1+n3)+ 2.30 n3/(n1+n3) where y2 is the activity coefficient of carbon (standard state such that y2— 1 as n2 — 0 in the Fe-C binary) and n1, n2, and n3 are the number of atoms of iron, carbon, and cobalt per unit weight of alloy. The results are also given in terms of the a functions. In the same concentration range, the results are in accord with the regular solution theory of Alcock and Richardson. THE carbon content of Fe-Si, Fe-Mn, and Fe-Ni alloys at fixed activities of carbon has been reported previously.&apos;-, The present work extends R. P. SMITH, Member AIME, is Research Chemist, E. C. Bain Laboratory for Fundamental Research, United States Steel Corp., Research Center, Monroeville, Pa. these measurements to a series of Fe-Co alloys. These alloys, like the Fe-Ni alloys, are fcc ("aus-tenitic") over the entire range of composition at 1000°C. EXPERIMENTAL PROCEDURE The alloys were made from electrolytic cobalt and Plast-Iron in a small vacuum-melting furnace. A small amount of graphite was added to each melt to keep the oxygen content low. The ingots were analyzed for iron and carbon: the amount of cobalt was obtained by difference. Analysis of the top and bottom of the ingots indicated that they were uniform in alloy content. Except for the pure cobalt the ingots were hot-rolled to approximately 0.15 cm thickness, cleaned by sandblasting, then cold-rolled to about 0.045 cm. We were not successful in cold rolling the pure cobalt; therefore it was hot-rolled to the final thickness. The last traces of surface oxide were removed by acid pickel, then the samples were treated in a hydrogen-2 pct water vapor mixture at 1100°C to remove carbon and most of the oxygen. The carburizing procedure was similar to that previously described.1,2,4 The alloys in the form of strips about 1.7 cm wide, 7.5 cm long, and 0.04 cm thick, together with a similar specimen of purified iron, were equilibrated with each of six CO-CO2 mixtures of fixed composition, then quenched in the

Jan 1, 1965

By J. C. McKinnell

The appraisal of an oil lease may often be mad,? through production decline analysis, which requires description of the functional relationship between the oil production rate and either cumulative production or time. Heretofore, attempts to define the function appropriate to a given set of production data have depended to some extent on subjective procedures. The purpose here is to introduce an objective solution, obtained by combining the principle of least squares with the theory of equations. MATHEMATICAL ANALYSIS The fundamental differential equation appropriate to a general class of decline curves may be written. Solution of Eq. 1 for general boundary conditions may be written in terms of either the cumulative oil production or time: These equations constitute the mathematical expression of the so-called hyperbolic decline. Their complete description for a given set of production data requires the numerical evaluation of the three parameters1.&apos;, n, D, and (go),. For the special case of n = 0, Eq. 2 becomes q. = (q.), - DiN with the corresponding expression in terms of time being q. = (qa),e...........(5) Similarly, for the special case of n = 1, Eq. 3 becomes with the corresponding expression in terms of cumula- tive oil production being q. = (q.),e " &apos;.......(7) Eqs. 4 and 5 constitute the mathematical description of the so-called exponential decline; Eqs. 6 and 7 are the mathematical description of the harmonic decline.&apos;,&apos; Returning to the hyperbolic expressions, Eqs. 2 and 3 may also be written, q: = sNp + b........ (8) and where a = 1 - n; s = (n— 1)D,(q0);"; b = (go):-"; a&apos;=-n;s/= nD,(qo);"; and b&apos; = (go);-. Note that both Eqs. 8 and 9 are linear in either time or cumulative production with respect to an exponential function of the production rate. In other words, a straight line relationship results for both variables when associated with the appropriate power of q,. This fact is of prime importance in the application of statistical analysis. . STATISTICAL ANALYSIS For a given oil lease, the time, production rate and cumulative production are recorded records. To establish predictive formulas from Eqs. 2 and 3, it remains to determine numerical values for the three parameters [n, D, and (q,) .] through an investigation of the past history. Upon interpreting a, s and b as parameters, Eq. 8 may be expressed for every time interval of interest, i, over the past history as follows. (q,): = s(Np), + b........(10) In general, Eq. 10 will not be satisfied exactly, because of the assumptions in the expression of Eq. 1, and the errors and anomalies universally associated with production data. It will instead define the residual, s(Np), + b- CO=d......(11) Squaring both sides and summing over all the data points, m, under consideration yields

By Donald T. Hawkins, Ralph Hultgren

The lorsion effusion method has been used to measure the vapor pressure of lead over pure lead and eight Pb-Sn alloys ranging from 9.1 to 87.9 at. pct Pb in the temperature range 950° to 1125°K. The resulting ?H°y 298 = 46,630 ± 200 cal per g-atow for pure lead is in excellent agreement with previous work. Deriued ?Gph values for the alloys were smoothed and correlated with previous heat of formation data to obtain entropies for the liquid alloys. values for the tin component were calculated by Gibbs-Duhem integmtion. Surfhce depletion of these liquid alloys was found to be absent, as shown by the fact that the measured pressure remained substantially constant with time in contrast with previous measurements on iron-rich solid Fe-Mn alloys. The activities and Gibbs (free) energies of the liquid Pb-Sn system are not well known although the heats of formation have been accurately determined by K1eppa.l Vapor pressure determinations of the activity of lead by Voronin and Evseev2 disagree with those of Predel.3 Elliott and chipman4 measured activities by the electromotive -force technique in the ternary Pb-Sn-Cd system. From the resulting values of the activity of cadmium, they were able to calculate the activities of lead and tin for the binary Pb-Sn system at the compositions xsn = 0.33 and 0.67. Atarashiya, Uta, Shimoji, and Niwa5 determined the activity of tin from Hz-H2O equilibrium measurements, but their results are subject to question due to uncertainty in the final state of their samples. To resolve these differences, measurements of the activity of lead were made using a torsion-effusion apparatus. Among other advantages, this apparatus rapidly detects errors caused by surface depletion, which tends to reduce the apparent vapor pressure of the more volatile component. If the measured torques remain nearly constant with time, only bulk depletion is occurring. This contrasts with the rapid decrease in torque found in solid Fe-Mn alloys at high temperatures and low manganese contents.6 EXPERIMENTAL 99.999+ pct Pb was obtained from the American Smelting and Refining Co. and 99.999 pct Sn from Vulcan Detinning Co. Eight Pb-Sn alloys were prepared by melting together weighed amounts of the pure metals in evacuated Pyrex tubes and quenching the melts in water. Loss of weight in preparation was less than 0.02 pct in all cases. The effusion cells were made from high-purity, nonporous graphite. Graphite was chosen because of its resistance to reaction with lead and tin and because it can be accurately machined with precision orifices. Two cells were used with overall dimensions as shown in Fig. 1. The orifices of cells 1 and 2 were, respectively, 1 and 1.5 mm in diam.

Jan 1, 1968

By M. G. Corson

The iron-silicon alloy series has always been one of the most puzzling among the binary alloys. Examining the well-known mechanical properties of the iron-rich alloys only we meet the following situation: The ultimate strength and yield point of alloys worked and annealed under the usual conditions represent nearly a straight line function of the silicon content up to 1.5 per cent. silicon (Fig. I). Starting at the ultimate strength of 35,000 lb. and at a yield point of 16,000 lb. for pure electrolytic iron, one reaches a maximurn strength of 93,000 lb. and a maximum yield point of 74,000 lb. at 4.5 per cent. silicon. This corresponds to an increase in ultimate strength by 13,000 lb, per each per cent. of silicon added and nearly the same rate applies to the yield point. The data mentioned are taken from the investigation by T. D. Yensen,1 and while they do not exactly corroborate the results obtained by earlier investigators, they seem to be the most correct. Plastic properties of the alloys are controlled by a much more complicated relationship. Up to 2..5 per cent. Si, the elongation stays close to 50 per cent. (in 2 in.) and the area reduction amounts to 85 per cent., a situation that forms the usual feature of all alloys representing strictly solid solutions. The plasticity of the latter is always nearly equal to that of their base metal. Beyond 2.5 per cent. silicon, the situation becomes much more complicated. Yensen observed an enormous drop in elongation and area reduction at about 2.65 per cent. silicon, where the first hardly reaches 10 per cent. and the second is still lower; he found, however, a considerable recovery in plasticity at about 2.8 per cent. Si and up to 1.5 per cent. Si it is represented by 20 per cent. for the elongation and 30 per cent. for area reduction. Yensen&apos;s graphs, as shown in Fig. 1, indicate also a considerable drop in strength and yield point at the same point of 2.65 per cent. Si,