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By Robert E. Barieau

This report gives the principles of the method used by the Helium Research Center of the Bureau of Mines when solving nonlinear-regression problems and contains the mathematical equations necessary to accomplish the following objectives: the evaluation of the parameters in such a way that the sum of the weighted squares of the residuals of an experimental observable is a true minimum, regardless of the functional relationship between the variables and these parameters; and the evaluation of all variances and covariances of the parameters by means of the usual approximation of the law for the propagation of errors.

Jan 1, 1967

By E. W. Geist

This paper is presented from the viewpoint of the mill operator and maintenance supervisor. Its purpose is to highlight the things that have been accomplished by the mill designers to lighten the load for the maintenance superintendent and to reduce the overall costs for the plant operator. The complexity of plant design, the civil and structural engineering problems encountered when the satisfactory maintenance layout is accomplished are appreciated, and the writer is fully aware of the complexities of these problems. However, it is not the purpose of this particular paper to dwell upon these problems, nor to emphasize or de-emphasize the problems of the civil, mechanical and electrical engineers. It is simply that the paper will attempt to review what these people have accomplished in spite of the many technical problems. This paper then is prepared with the operator and maintenance people?s viewpoint. What is their definition of design for maintenance? It is the writer's interpretation that the various design concepts which mean improved maintenance are such items as (I) maintenance areas, (2) laydown space for maintenance materials in specific maintenance jobs, (3) the inclusion of bridge cranes in the plant and specific design of the craneways to accomplish flexibilities for the cranes, and (4) the location of the piece of equipment to allow maintenance people to work around the equipment - - - this specifically includes the orientation of the particular piece of equipment.

Jan 1, 1967

By J. D. Campbell

"Coal is one of Alberta's major fuel resources, but its distribution, especially in the flat plains region, has been somewhat obscured by surficial deposits. After a period of neglect, easily strippable plains coal is presently approaching a position of dominance in electrical power production, a position it is likely to retain for a number of decades in the face of strong competition from hydro and nuclear power. Accordingly, the Research Council of Alberta has undertaken an inventory survey of the province's supplies of this resource.In the southern part of the province and in the north-central forest-fringe area, some strippable coal is found in the Belly River Formation and its equivalents, but major strippable coal reserves in large areas of central Alberta occur within the Edmonton Formation. The survey is planned on a reconnaissance scale, drilling test holes at 2-mile intervals in selected large areas. It appears to show that, in well-settled regions, large reserves of strippable coal are only to be expected where they have long been known; major presently unknown bodies of coal must be sought in unsettled regions or at depths too great for strip mining. However, such bodies might still be economically competitive with hydro and nuclear power in the production of electric power for some time to come."

Jan 1, 1967

By H. R. Cooper

Beginning from the point of view that process control of ore flotation can be approached by on-line analysis of processing behavior, an equation was developed which has characteristics useful for a multi-variable feedback loop. The application of this equation to optimizing control with a data acquisition system will be discussed in Part 11. OBJECTIVE OF CONTROL The purpose of developing a feedback method for concentrator control is to provide a means for determining ore processing behavior in order that data describing the ore can be used to make appropriate changes in control conditions while the ore continues to flow through the flotation circuit. In absence of simple linear relationships between pairs of variables in the flotation process, attention is directed to the need for a generalized relationship which possibly would incorporate all pertinent variables. It would be possible to apply such an equation to the control of variables in a concentrator in real time according to operational requirements as ore gradually changes in quality and processing behavior. To meet this objective, it is necessary to define relationships describing flotation performance in terms of performance variables capable of being measured on-line, either with on-line instruments and analyzers or with manual methods lending themselves to quick determination of meaningful information. Relationships derived to meet this objective form a model for the flotation process. The evaluation of flotation parameters of the ore and the execution of control on the basis of the derived information while the ore is continuing through the process would constitute a feedback control system. Data for the following control and performance variables can be made available: 1) ore feed rate, 2) collector addition rate, 3) lime addition rate, 4) pulp density, 5) assay or multiple assays in feed, tails, or concentrate sufficient for material balancing, 6) particle size distribution in flotation feed, 7) froth height, and 8) frother addition rate. Other process variables, such as flotation air input and mechanical agitation intensity, are usually not considered as control variables and were not taken into account in this analysis. Other data, such as that describing the ore, would be useful for concentrator process control. However, information of this type (such as ore hardness, grain size of the mineral, chemical species of the mineral, and ore surface properties) being not presently measurable in the on-line sense, has the effect of causing disturbances in the system which can be detected only indirectly. The process control system being sought must recognize disturbances by their effect on measured performance followed by determining control changes to compensate for them in meeting the objectives of improved performance (perhaps higher throughput, maximum return, etc.). A suitable model for the process having capability of recognizing the effects of ore disturbances should provide the means for introducing proper compensation through control changes. This would be done by processing on-line data with the model to calculate coefficients reflecting ore characteristics. This procedure can only be applied in a typical flotation system when on-line data can be processed at faster rates than the usual rate at which the ore in flotation feed takes on significantly different characteristics. For example, material balance data can be accumulated in approximately 5-min intervals using on-line X-ray fluorescence analysis. The flotation system time constant might be 15 min including grinding. Ore changes having time constants longer than 1 hr could be accommodated using on-line feedback control by this procedure. FORM OF A FLOTATION MODEL A suitable form for mathematical expression of the flotation process is an equation involving rates, when each of the components entering into the separation can be treated independently by a rate equation. A first-order, kinetic rate equation can be written on

Jan 1, 1967

By Merton C. Flemings, Harold D. Brody

Analyses that include diffusion of solute in the solid phase are formulated to describe solute redistribution in dendritic solidification of metallic alloys. The analyses are based on conditions that include negligible undercooling before nucleation of solid phases, negligible increase of solute in advance of the tips of growing dendrites, complete diffusion within the liquid over distances the order of dendrite spacings, and a plate-like dendrite morphology. The classical nonequilibrium freezing equation, Cs = kCo(I - fS)k-l accurately describes solute redistribution between dendrite arms for the solidification processes considered, provided diffusion in the solid is negligible. To account for the effect of diffusion in the solid, an analytic expression is given which is similar inform to the classical expression. 172 addition, a numerical-analysis procedure is etnployed to examine in more detail the effect of diffusion both during and after solidification. The analyses are intended for application to solidification of castings and ingots to describe a) final solute distribution after solidification and cooling to room temperature (microsegregation) and b) local fraction solid as a function of ternperatcre within the solidifying casting or ingol. SOLUTE redistribution in cellular and dendritic solidification has been discussed quantitatively in recent papers'-3 and in a series of earlier work.4-6 However, none of the analyses developed have permitted close correlation of theory with final solute distribution (microsegregation) observed in castings and ingots. In this paper, discussion is given of approximations which may reasonably be made in mathematical treatment of microsegregation, and analyses are presented based on these approximations. Numerical results are given for Al-Cu alloys. In a second paper the analyses will be compared with exeriment.7 CLASSICAL ANALYSIS The classical quantitative treatment of solute redistribution within a closed "volume element" has been derived repeatedly, for example by Gulliver,4 Scheil,' and Pfann.' This "classical nonequilibrium solidification equation" is written for constant partition ratio: where Cs = interface composition of the solid when the weight-fraction solid within the "volume element" is fs (weight fraction, wt pct); k = equilibrium partition ratio; Co = initial alloy composition within the volume element (weight fraction, wt pct). Assumptions of Eq. [11 are: 1) There is negligible undercooling before nuclea-tion, or from curvature or kinetic effects. 2) There is no mass flow in or out of the volume

Jan 1, 1967

By D. R. Uhlmann, T. P. Seward, K. A. Jackson, J. D. Hunt

microscopic ohservations on alloys of organic trzaterials show that dendrite arms can melt off under normal conditiorzs of growth. This occurs because of the interactiorz of' heat and matter fluxes during dendritic growth. The re melting occurs where the den-drite arms are joined onto the main deizclrite sterrz. Many detached crystals can be produced in this fashion. It is postulated that this remelting phenornenon occurs in metal alloys, giving rise to the equi-axed region in castings. Experiments peyformed orr castings of transparent materials support remelting as a primary source of detached crystals. Ob~ervations an equiaxed tones in metal castings are discussed in terms of this and other mechanisms. It is concluded that the partial remelting of dendrites is on important mechanisnl for producing the equiaxed regions in castings. THE freezing of a casting can be divided into three regions: a chill zone formed near the mold wall, a columnar region, and a third region, at the center of the casting, which is called the equiaxed zone. The origin of the grains that comprise the equiaxed region is the subject of this paper. We will first outline the mechanisms which have been proposed to account for the origin of the equiaxed region and discuss some recent experiments which cannot be explained by these theories. We will then present some microscopic observations of dendritic growth which have led us to conclude that the equiaxed zone in castings can arise from partial remelting of dendrites. This proposal is supported by observations on transparent castings. Finally, we will discuss several observations on metal castings which could not be explained previously, and which can be accounted for by the present proposal. Previous Mechanisms. Winegard and Chalmers3 pointed out that the molten central region of an ingot could be constitutionally supercooled, because of the solute layer at the growing interface. In this supercooled region, nucleation on particles could occur, giving rise to the equiaxed crystals. Another mechanism has also been suggested,4y5 that the nuclei originate in the chill zone then float or are carried by convection to the center of the casting, where they grow to produce equiaxed crystals. In this case, all the crystals nucleate immediately on casting, so this mechanism will be termed "big-bang" nucleation. Walker's Experiments. J. L. Walker has made observations on the solidification of nickel and Ni-Cu alloys which cannot be accounted for by either of the above mechanisms. In studying the grain size resulting from freezing of nickel at various undercoolings, walker6 found that at large undercoolings the grain size was small, due to mechanical nucleation, as discussed by walker7 and Horvay.' At small undercoolings, the grain size was large, and the growth dendritic. In Ni-Cu alloys, however, for initial undercoolings starting from just below the melting point and extending for a hundred or so degrees of undercooling, fine grains were also observed. Samples were undercooled 200 Centigrade degrees without nucleating, and were then heated 130 Centigrade degrees so that the undercooling was 70 Centigrade degrees, and nucleated. The samples had a small grain size, indicating multiple nucleation. There were no heterogeneous nuclei in the liquid which could operate at the temperature of growth. Constitutional supercooling could not have been greater than the supercooling of the initial melt, since the temperature rose as the freezing continued. walker -as also shown that a Ni-Cu alloy which can be undercooled to below its solidus will produce typical columnar and equiaxed regions when cast into a cold mold. This alloy could not reach a temperature below its solidus by constitutional supercooling. It could not, therefore, have nucleated heterogeneously. Neither the big-bang mechanism nor the Winegard-Chalmers mechanism can account for the fine grain

Jan 1, 1967

By A. Gene Collins

The Bureau of Mines undertook research to determine the bromide and iodide content of Mississippi and Alabama oilfield waters of the Tertiary and Cretaceous Period to determine genetic relationships of the ions, to determine their origin, and to determine their genetic relation to petroleum. The 280 samples were analyzed after a pretreatment to remove interferences. The iodide was oxidized to iodate and was titrated with thiosulfate. The bromide was oxidized to bromate and was determined iodometrically. A computer was used to calculate the correlation coefficients of iodide to bromide and to other ions. The other ions are sodium plus potassium, calcium, magnesium, chloride, bicarbonate, and sulfate. The mineral content of the samples ranged from 52 to 1,760 mg/l for bromide and from 2 to 65 mg/l for iodide. The mean bromide-to-chloride and iodide-to-chloride ratios were 0.0065 and 0.0002. The correlation coefficient matrix and linear plots indicated a definite bromide-to-calcium relationship for the brines investigated.

Jan 1, 1967

By Witold J. S. Ostrowski

Stabilization of water-bearing sediments by the freezing method for shaft sinking has been used for over 80 years on the European Continent. The real application of this method in Canada started with the development of the potash mines in Saskatchewan during the past fifteen years. The great depth to which it is applied creates a number of problems which have to be seriously considered by engineers in order to produce a safe and economical design. Freezing depth, thickness of the ice wall, number of the freeze holes, capacity of the freezing plant, pre-freezing time, etc., are the most important points which have to be established. Recent field experience in freezing to great depth in the Saskatchewan area is immensely interesting and important for further development of our potash mining and the application of the freezing method.

Jan 1, 1967

By J. E. Cannaday, R. J. Austin, R. K. Saxer

PREVIOUS investigators have determined activation energies and have postulated various controlling mechanisms for creep.'-' Recently Barrett et 01.I5 have suggested, as the result of their work with cadmium, that the apparent activation energies for creep (AHc) above 0.5 T, could be correlated by means of activation energies for self-diffusion (AHSD) and modulus of elasticity functions: AHC = AHSD - (5RT/E) dE/dT. The wide disparity of apparent activation energies previously obtained with nickel compared to those reported for other fcc metals and the desire to test the postulate of Barrett el al. prompted this study. The as-received 17.5-mil nickel wire used during this work assayed 99.87 pct pure, Table I. X-ray analysis indicated that the wire was in a stress-re- lieved state and metallographic examination revealed an equiaxed grain size of approximately 0.01 mm. Specimens degreased in acetone and cut to 1-1/2 in. lengths were tested in a cam-mechanized constant-stress creep machine. A vacuum of at least lo-5 mm Hg was maintained during all tests. Stresses were applied when thermal equilibrium was established. When a measurable (at least 0.5 pct) secondary creep was observed, the temperature was pulsed to a higher temperature. Pulsing time varied from 30 sec at 480°C to 2 min at 1300'C and above. Slopes of creep curves were determined after the initial acceleration in the strain rate had subsided and steady-state creep was achieved. To confirm the results obtained, additional tests were performed incorporating a temperature pulsing method suggested by sherby. In this method the load was removed during temperature pulsing and reapplied after thermal expansion had occurred. No appreciable differences in results were obtained. Tests were performed over a wide range of temperature (470" to 1310°C) and stresses (250 to 17,000 psi). The expression was used to calculate activation energies. In this expression T1 and T2 are the initial and final temperatures, and el and i2 are the creep rates at T, and T2. The variation of the apparent activation energies with the mean test temperature calculated by means of Eq. [I] are shown in Fig. 1. The mean test temperature (Tmean) was calculated from the relationship

Jan 1, 1967

By V. R. Miller

The Bureau of Mines investigated methods for testing the tensile and sheer strength of cast specimens of bulk solder and of soldered joints in order to increase the strength and extend the useful temperature range of soft solders. A spread-area test for determining the wettability of solder on copper surfaces was developed. Mannitol was used as a flux in spread tests to control spreading and to avoid plating, etching, and other side effects of regular fluxes. Data on commercial and high-purity solders obtained by these methods show more consistency than those reported by others from similar tests.

Jan 1, 1967

By R. O. Pynnonen

This publication is an analysis of reports to the Bureau of Mines of 44 fatal accidents that occurred during the operation of rubber-tired, front-end loaders in the mineral industry. The causes of the accidents, the nature of the work being performed, and recommendations for preventing similar accidents are included.

Jan 1, 1967

By R. V. Higgins

This report presents computer instructions for calculating the performance of three-phase flow of gas, oil, and water. The calculated results for an illustrative example are presented. The example is the waterflood of a reservoir containing free gas in the reservoir as a result of the partial depletion of the oil by the expansion of the gas initially in solution. The flood pattern for the example is a 5-spot.

Jan 1, 1967

By N. Mungan

A study was made of the effects of wettability and interfacial tension on the immiscible displacement of a Iiquid by another Iiquid from porous media. The influence of viscosity ratio was also investigated. Porous media used were polytetrafluoroethylene (TFE) cores prepared by compressing TFE powder under different pressures. lt is shown that displacement of a wetting by a nonwetting Iiquid is always less efficient than the displacement of a nonwetting by a wetting fluid, all other things being equal. In the former case, the recovery efficiency can be increased substantially by either reducing the interfacial tension or increasing the viscosity of the displacing fluid. A qualitative discussion is given on the implications of this work to the recovery of crude oil by water flooding. INTRODUCTION The high cost of oil exploration and new recovery schemes makes it imperative that waterflooding be conducted under conditions favoring most efficient oil recovery. To improve oil recovery by waterflooding, it is essential that the role played by interfacial forces in the entrapment of residual oil be studied and understood. Interfacial phenomena in natural rock, connate water and crude oil systems are very complicated because of the complexity of the natural liquids found in petroleum reservoirs, because of our inability to adequately describe the geometrical structure of the porous media and because of a lack of understanding of physical and chemical interactions between the liquids and surface of the pores. The problem becomes further complicated when one tries to elucidate the role of interfacial phenomena in fluid flow. Numerous studies of the displacement of oil by water under different interfacial tension or wet-tability conditions have been made.lm3 These studies have been performed in silica, alundum or sandstone systems using water and paraffin oil and also some surface active material to control the interfacial tension s and the contact angle 0. Unfortunately, the high energies of various interfaces involved favor adsorption and orientation of the surface active material at the interfaces. Also the surface active material concentration at the interfaces exceeds that in the bulk of the liquid phases. Such surface excess may cause the surfactant distribution, the contact angle and the interfacial tension to differ from their measured static equilibrium values and makes interpretation of the displacement experiments difficult. Furthermore, as changes in s also lead to changes in cos 0, the role played individually by one of these parameters in the displacement becomes obscured by the effect of the other. To circumvent these difficulties, a low surface energy solid and true solutions or pure liquids should be used. Use of a low surface energy solid minimizes adsorption and orientation effects at the solid-liquid interfaces. By controlling s and cos 0 through use of selected pairs of pure liquids or true solutions rather than by surfactants, the adsorption effects at liquid-liquid interfaces are eliminated. In the present study TFE cores were used as the porous media. Liquids used were water, sucrose solutions, paraffin oils and benzyl, n-butyl and isobutyl alcohols. The interfacial tension was varied from 40 to 1.1 dynes/cm by suitably choosing the liquid pair. A surface active material was added to the water-oil system only in the case where interfacial tension of 0.5 dyne/ cm was desired. No precise changes of cos 0 were attempted. However, either the displaced or the displacing liquid could be made the one which preferentially wets the TFE surface. Using sucrose solutions and blends of paraffin oils proved to be a convenient way of changing the viscosity ratio between the displaced and displacing liquids. The present investigation examines the effect of interfacial tension, wettability and viscosity ratio on the immiscible liquid-liquid displacement from porous media. Observed data permit a

Jan 1, 1967

By R. G. Davies, R. H. Richman

Several techniques, X-ray diffraction, transmission electron microscopy, conventional, metallography, and mechanical property measurements are combined to investigate decomposition in the suPersaturated solid solution Fe-27 at. pct Be. The following sequence of structures for aging temperatures below 400°C is established: massive short-range order, pseudo-FeBe (L2o) order, Fe3Be (DU3) order, sinusoidal modulation of composition, general or continuous precipitation, and discontinuous or cellular precipitation. In addition to this sequence itself, several features of the individual stages are noteworthy; for example, when coherent modulations occur, their development is parallel to (100) everywhere in the specimen apparently without incubation, and both the wavelength and the composition amplitude of the modulations increase with aging time. Two types of discontinuous reaction are observed, depending upon the aging temperature. At low temperatures (<550°C) the boundary-nucleated variety of discontinuous precipitate predominates; but at higher temperatures (>600°C) the crystallographic variety occurs instead. Hardness and flow-stress measurements clearly reflect the quoted structure sequence. Some qualitative aspects of the structure changes and of the relationship between mechanical properties and structure are discussed. BERYLLIUM in solid solution markedly strengthens iron.&apos;" A recent study demonstrated that not only were supersaturated single crystals of Fe-27 at. pct Be very strong, but they deformed primarily by mechanical twinning.3 Such behavior, coupled with the decrease in solid solubility of beryllium in a Fe from about 33 at. pct at 1165°C to about 10 at. pct at 500°C4 as shown in Fig. 1, leads naturally to questions about property changes with aging in this system. In 1929 roll,1 and later Seljesater and Rogers,5 reported that useful increases in strength could be obtained by aging quenched Fe-Be alloys, but it was not until quite recently that any of the details of precipitation in these alloys were studied. Richman6 observed that both an Fe3Be superlattice (with a DO3 crystal structure the same as Fe3A1, illustrated in Fig. 2) and a modulated structure preceded the appearance of a discrete second phase in the 20 at. pct Be composition. Here, a modulated structure refers to a periodic composition fluctuation within one crystal, while its lattice remains coherent. Subsequent work on a Fe-Be alloys by Heubner7 and von Heimendahl and Heubner8 confirmed the existence of the modulated structure, although only an FeBe (L20) ordered structure was detected (also shown in Fig. 2). Both Rich-man and Heubner corroborated the large increases in hardness during aging reported earlier, but other mechanical properties were not examined. Since modulated systems are encountered relatively infrequently, the influence of coherent modulation upon mechanical properties is not well-known. With the accumulation of information about age-hardening systems, it has become clear that many precipitation reactions cannot always be described by the concept of heterogeneous nucleation at some lattice discontinuity followed by diffusional growth. Rather, complex sequences involving prior "preparation" of the matrix are quite common; that is, a transition structure occurs in the parent phase, instead of in some "nucleus" form. Delineation of such subtle sequences appears to be a worthwhile step toward the understanding of solid-state precipitation. Since not many structural progressions of comparable nature have been reported, the objectives of the present survey are to identify and elucidate the various

Jan 1, 1967

By J. L. Shultz

The Bureau of Mines extended its investigation of methanation catalysts. The noble metals (platinum, palladium, ruthenium, rhodium, osmium) and rhenium), molybdenum, and tungsten were tested in hydrogenations of carbon monoxide and carbon dioxide at 21 atmospheres in a temperature range between 200° and 600° C. From the 8 metals studied) 25 catalysts represent 5 catalyst types were prepared and tested. The impregnated 0.5-percent-ruthenium catalyst proved to be the most active and versatile of all the catalysts produced. Tungsten and the noble metals other than ruthenium were low in activity and usually required temperatures above 500° C for appreciable production of hydrocarbons. Molybdenum was moderate in activity, but further improvement in molybdenum catalysts seems possible.

Jan 1, 1967

By Roy L. Grant

The Bureau of Mines investigated the up-and-down method with factorial designs to determine if shorter, and therefore less costly, trial sequences could be used. Although sequences of 50 trials are usually recommended, sequences of 20 trials were arbitrarily chosen for the experiments with permissible coal mine explosives described in this report. These explosives were fired from a cannon pointed into a flammable natural gas-air atmosphere at the Bureau of Mines Explosives Research Center gallery to ascertain their safety properties. The investigation demonstrated that the shorter sequences led to useful conclusions with a reduction in cost of the experimental program.

Jan 1, 1967

By L. R. Woodyatt, H. J. Beattie, C. T. Sims

Theories correlating the formation of u and related intermetallic compounds to the electron-per-atom density of binary and ternary alloys have appeared regularly in recent technical literature. These same principles can be modified and applied to complex precipitation-strengthened alloys such as the iron-, cobalt-, and nickel-base superalloys and the stainless steels. Since these complex alloys contain carbides and other phases that normally precipitate before the U-type phases, the nature and amount of the precipitated phases must be calculated first. The following general formula is then applied to the residual matrix composition of the alloy: element. The magnitude of the resulting number is indicative of whether the alloy will form a a -type phase. When these calculations (which are computerized) are systematically applied to alloys of knoun phase analysis, a breakoff in average electron-vacancy number is noted between U-free and U-prone alloys. Alloys with an average electron-vacancy number higher than the breakoff form a-type phases, while those with lower ones do not form these phases. This method could then be used to eliminate from consideration all experimental compositions that would precipitate undesirable phases. It also is useful in evaluating analyzed heats of alloys where minor heat-to-heat variations determine whether the alloy is o-free or o-prone. THE highly significant development of strong, ductile superalloys to provide reliable construction materials in the 1000" to 2500° F temperature range has been due principally to unremitting application of Edisonian techniques and logic by the dedicated physical metallurgists who have shouldered this responsibility. Tools such as the electron microscope, phase analysis, and computers to accomplish regression analyses have been used heavily, but the effort has been essentially practice of an art, rather than a science. The objective of this paper is to describe and illustrate application of some relatively fundamental principles to certain of these alloy systems in an attempt to remove some of the empiricism from the technology. Specifically, the work presented here deals with the use of periodic-group relationships to predict the formation of intermetallic phases which can occur in primarily austenitic (fcc) structures. Calculations that have been developed might be applied in the design of new alloys and the evaluation of known alloys, and thus have the potential of eliminating vast areas of unnecessary alloy preparation and evaluation. ALLOYING CONCEPTS AND STRUCTURAL FEATURES OF SUPERALLOYS Strength is produced in austenitic superalloys by three principle mechanisms: 1) precipitation of y&apos;; 2) formation of carbides; 3) solid-solution hardening by soluble refractory metals. The first mechanism requires the addition of aluminum and titanium, the second requires carbon and carbide-forming elements, while the third calls for the addition of molybdenum and/or tungsten. A considerable concentration of chromium is usually maintained to resist oxidation/corrosion, but it is also an important carbide-forming element. Fig. 1 shows a sketch and electron micrograph of the structure of a typical wrought nickel-base super-

Jan 1, 1967

By R. Lagneborg, R. Gullberg

An X-ray method for determinig volume fractions of phases in textured materials has been developed. The method involves measurements of the integrated intensities of reflections of each phase for one single orientation of the sample. The method was checked by evaluating the phase contents in samples from two stainless Cr-Ni steels containing austenite and ferrite in known amounts. In the present case measurements of about five reflections from each phase were required. The agreement between calculated and known volume fractions was found to be very close. AN X-ray diffraction method is often employed for determining the amounts of two or more phases in a material. The details of the method have been described at several instances.&apos;" In short, the method is based upon the fact that the integrated intensity of a reflection is directly proportional to the volume fraction of the phase considered. In principle, the method only requires the measurement of the intensity of one reflection for each phase. The most severe shortcoming with this method is that it disregards influences from preferred orientation in the material. In a diffractometer, where this type of analysis is most conveniently carried out, the geometry is such that the diffracting planes for a specific Bragg peak are all parallel to the surface of the specimen. This implies that it must be required that the occurrence of the diffracting planes parallel to the specimen surface must be as frequent as for any arbitrarily oriented physical plane of the sample. This requirement will generally only be fulfilled for a material free of texture. Since all materials in reality always exhibit a preferred orientation to some extent. the deficiency of the method is quite serious. In cold-deformed material the texture is appreciable, but also annealed material will in many cases display a considerable texture. The problem of quantitative phase analysis in textured material is one of obtaining the integrated intensity averaged over all orientations of the specimen with respect to the X-ray beam. Lopata and ~ula~ have shown that this can be accomplished by integration of intensities over the whole pole figure, or by random rotation of the specimen in the X-ray beam, or by a combination of both. Hence, in this method the average integrated intensity for a specific reflection is obtained by directly determining the intensity for a sufficient number of physical orientations of the sample. However, since an excess of diffracting planes in a certain surface plane necessarily must be accompanied by a deficiency of another type of diffracting plane, it appears to be possible to obtain the correct average intensity for a specific diffracting plane by performing an appropriate averaging of intensities belonging to a large number of diffraction planes of different hkl when all intensities have been produced from one single orientation of the specimen surface. In the present work such a method has been attempted and tested experimentally for two stainless Cr-Ni steels containing austenite and ferrite. 1) THEORY The expression for the integrated intensity of a Bragg reflection diffracted from a phase in a polycrys-talline sample in a diffractometer is: where C is a constant only dependent on the incident X-ray power and the diffractometer geometry, v the volume of the unit cell, F the structure factor, m multiplicity of the diffracting plane, L Lorentz factor, P polarization factor, e-2 temperature factor, p average linear absorption coefficient of the irradiated vO1umej and V volume fraction of the phase &apos;Onsidered. Hence, the factor R in the abbreviated form of Eq. [I] can be calculated and depends only on 0 and the diffracting plane {hkl}. For an alloy containing two phases, a and y, we can write

Jan 1, 1967

By C. B. Alcock, M. G. Hocking

The kinetics of the growth of sulfate layers on blocks of Cu20 has been studied between 688" and 800°C. At 788c the over-all weight increases followed the parabolic rate law, with k = 216 30 sq mg per cm4 min, using a 1:1 entering gas mixture of SO2:02. At 757 after an initial linear period the parabolic rate law was followed, with k = 57.8 10 sq mg per cm4 min. The gas mixture required a platinum catalyst to produce the maximum SOs pressure. The sulfation rate at 757&apos; and 788c was high until all the CUZO had changed into a core of CuO, when it became very much lower. At 757°C marker experiments showed that the sulfates (CuO. CuS04 and CuSO4) grow outwards from the oxide surface, but CuO. CuS04 mixed with CuO was found beneath the markers. At 688 markers were found at the CuO. CuS04/CuS04 interface. Visual observations at 757 showed a liquid eutectic moving beneath the sulfate surface. causing very rapid sulfation and extruding to solidify as thick &apos;needles" up to 8 mm long. Marker experiments have shown conclusi.cely that CuO grows on Cu20 in air by the outward migration of copper. ThermODYNAMIC measurements on the sulfate and basic sulfate of copper, reported recently,&apos; are followed here by measurements of the rates of formation of these sulfates on cuprous oxide, in order to provide a background for the understanding of roasting processes. peretti2 and McCabe and Morgan3 have shown that the phase Cu20 lies next to Cu2S when the sulfide is roasted under conditions where sulfates will be formed. Since this would present too complex a system for kinetic study, the present work4 has been based on the kinetics of sulfation of the oxide phase. The results of a study of the kinetics and mechanism of the sulfation of cobaltous oxide have recently been reported.4,5 Results on the sulfation of cuprous oxide have also appeared,6 but are at variance with those to be reported here. This seems to be because the previous workers6 did not obtain constant SO3 pressures from the SO2/O2 sulfating gas mixtures used, as will be discussed later. Wadsworth, Leiter, Porter, and Lewis found that the sulfates produced when SO2/O2 mixtures are passed over Cu20 at red heats are CuS04 and the basic sulfate CuO.CuSO4. When the decomposition of CuS04 was followed&apos; by differential thermal analysis, a stage corresponding to CuO .CuS04 was reached before decomposition into the oxide occurred. APPARATUS The vertical furnace used for quantitative studies was a conventional resistance-heated and propor- tionately controlled furnace with an even zone (1 deg) which was 4 cm long. The gas mixtures of SO2 and 02 were made by mixing measured flows from capillary flowmeters and drying over phosphorous pentoxide before passing them into the Pyrex top-piece of the furnace assembly. A mullite tube of bore 2% cm was used as reaction vessel and at the bottom of this tube was a trap for SO3, which condensed as a colorless liquid. The residual gas was led into a fume cupboard for ventilation to the atmosphere. The furnace used for visual observations of needle growth and other phenomena consisted of a transparent silica reaction tube of bore 3 cm, having an optically flat silica window sealed into its wall. The reaction tube was clamped vertically, inside a mullite tube of bore 4 cm and length 42 cm which was heated by Kanthal windings. The window in the silica reaction tube was arranged opposite a hole 3 cm wide and 2 cm tall which had been cut in the wall of the mullite winding tube 19 cm from its top end. A binocular microscope was used to look through the window, illumination being provided by a focusing microscope-lamp offset sideways and downwards. The oxide block to be sulfated was suspended from the removable Pyrex top-piece to the reaction tube, by means of which it was inserted at the start of the experiment, and through which entered the S02/02 gas mixture. The variation of the temperature inside the reaction tube with horizontal and vertical displacement from the window was investigated, and, while it can be said that the temperature was constant 1 deg, its value at a given position was known only to 12 deg. In both furnaces, the oxide block to be sulfated was suspended from a small silica hook immediately downstream from a platinum thimble used as catalyst, which was held on a long silica rod from a Pyrex spring attached to the removable Pyrex top-piece of the furnace. The spring was only included in the quantitative sulfating furnace; its sensitivity was 1.4 cm per g and it was found to be free from creep in a 16-hr test when carrying the working load. The extensions were followed by a cathetometer which could be read to 0.001 cm, corresponding to i0.7 mg. Extensions of the spring were measured on adding weights between 5 and 500 mg to the working load (thimble + oxide block), and Hooke&apos;s law was closely obeyed. SAMPLES Cuprous oxide blocks were prepared by oxidizing Johnson Matthey "Specpure" copper sheet of 1 mm thickness (impurities: iron at 3 ppm, silver at 2 ppm, lead, nickel, sodium, and silicon each at 1 ppm, calcium, chromium, magnesium, and manganese each at less than 1 ppm) for 6 days in air at 1000°C in a re-crystallized alumina boat. It has been reported7 that when Cu20 is prepared by heating copper sheet for 1 day the central plane of the blocks produced consists

Jan 1, 1967

By James T. Curry

The steady growth of the Northwest portion of the United States over the past two decades, and the very rapid development of Northern California, Western Nevada, and Oregon in particular, led the Calaveras Cement Company people to Shasta County, California in 1957. The presence of a large deposit of high calcium carbonate limestone had been recognized for many years, but it required the momentum of an expanding economy to make these long known reserves valuable. This, plus the availability of a reliable supply of fuel in the form of natural gas, and the ready means of shipping the product to the consumer both by highway and railroad, seemed to offer the proper combination to launch a successful venture. The Calaveras Cement Company had been manufacturing cement by the wet process since 1925 at their plant at San Andreas, California. Starting with two small kilns, the plant in Calaveras County started an expansion program in 1945 that ultimately resulted in the plant as it exists today, consisting of five kilns with a combined production of 4.5 million barrels annually.

Jan 1, 1967