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By J. J. Gilman, T. A. Read

FOLLOWING the deformation 01 zinc monocrys-tals, sharply bent basal planes are observed near several types of inhomogeneities. Three of these in-homogeneities have characteristics which are quite regular so that they can be studied and analyzed. These are compressive kink bands, "deformation bands," and the inhomogeneities near end restraints. The present paper describes experiments in which "deformation bands" were artificially produced, and bend plane phenomena are discussed in terms of dislocation theory. Also, two new bend plane phenomena are described. The importance of bend plane phenomena in the deformation of crystals is not widely recognized. Many phenomena may be explained in a manner similar to the discussion in this paper. Jillson1 has pointed out that the "punching effect" in zinc is a bend plane phenomenon and is not caused by prismatic slip.' Bowles3 has suggested that they may be involved in diffusionless phase changes. Cahn4 has discussed the role of bend plane formation in the polygonization of zinc. Experimental Work Tensile Kink Bands: Because of the geometrical similarity between "deformation bands" and "kink bands" (compare Fig. 1 of this paper with Fig. 1 of the paper by Hess and Barrett"), the band shown in Fig. 1 of this paper will be called a "tensile kink band," and that shown by Hess and Barrett will be called a "compressive kink band." It is felt that the term "deformation band" should be reserved for banded structures in polycrystalline materials such as iron." Tensile kink bands seem to form spontaneously in aluminum crystals deformed by tensile loading.7-10 In zinc and cadmium crystals they do not form in good, carefully loaded specimens.'." However, tensile kink bands can be produced artificially in zinc crystals. The present authors did this by scratching one of the flat surfaces of triangular crystals transversely with a sharp needle. Natural tensile kink bands caused by inhomogeneities sometimes appeared in deformed crystals which were identical in appearance with the artificially produced ones. Zinc monocrystals were grown by the Bridgman method in graphite molds. Chemically pure zinc (99.999+ pct Zn) was used and the molds were sealed inside evacuated pyrex tubes during growth. The crystal cross sections were equilateral triangles with a typical base of 0.210 in. The artificial kink band shown in Fig. 1 is typical of tensile kink bands in zinc. The band lies between two bend planes which run from upper right to lower left and is inclined oppositely to the slip bands which are sharply bent at the two bend planes. The general form of the artificial tensile kink bands was independent of the scratch depth (1 to 5 mils deep) and also independent of which side was scratched. These variables did cause variations, however. Deep scratches produced more localized kink bands than light scratches. Also, if the angle between the slip plane traces and a transverse scratch varied appreciably among the three sides, then localization of the resulting kink bands also varied. Furthermore, if the slip direction lay nearly parallel to the scratched side, the band was more developed near the scratched side than at the opposite edge. Scratches produced tensile kink bands for crystal orientations from xo = 15" to x, = 75". Fig. 2 shows a scratched crystal after deformation. One triangular side lies in the plane of the photograph. The right hand tensile kink band was produced by a transverse scratch on the upper right side. The next two kink bands were the result of scratches on the front surface. The kink band at the left was caused by a scratch on the lower back side. All four bands have the same general form. A longitudinal scratch was also made on the crystal shown in Fig. 2 to determine the effect of a scratch on the critical shear stress. The critical shear stress of the scratched region was 33.9 g per sq mm compared to 24.4 g per sq mm for the un-scratched region above it. Fig. 3 shows Laue patterns of the crystal shown in Fig. 2. Fig. 3a shows the pattern of the undeformed crystal. The orientation was x, = 21°, A, = 31". After deformation, Fig. 3b was made of the homogeneously deformed portion of the crystal. The spots are compact but split into two halves. This region was elongated 45 pct and its orientation was x = 14", X = 20"; the sine law predicts x = 14", A = 20.5". Fig. 3c was taken near the center of the middle tensile kink band of Fig. 2. The pattern shows a range of orientations and polygonization in this region. The spread in orientation was due to the fact that the basal planes were curved (see Fig. 1) rather than flat as in the ideal case. Some may also have been the result of elastic distortions and "local curvatures." The orientation range was x = 23" to 32", A = 30" to 42". It is apparent from Fig. 3 that the material inside and outside the kink band rotated in opposite directions with respect to the tension axis during deformation. The orientation calculated from the ideal configuration of Fig. 9,

Jan 1, 1954

By S. F. Shaw

Fox some time it has been more or less recognized within the industry that a scientific control of flowing wells would result in increased production and a greater ultimate recovery of oil. About two years ago it was proposed by the writer that this control should follow principles worked out by him while handling large air-life operations. In the case of wells that had ceased to flow where a large quantity of liquid was present, the use of these principles would result in a large increase of production by using compressed air or gas to flow the well; in the case of a well flowing naturally it would take the form of controlling the gas associated with the oil, resulting either in immediate increase of production or in a reduction of the gas consumed per barrel of oil, and in both cases would result in a greater ultimate recovery from the sand. The Roxana Petroleum Corp., appreciating the advantages to be obtained by a scientific application of the principles of the air lift to oil wells, recently engaged, for a limited time, the services of the writer to work out some of the problems involved. The work was carried out at Braman, Garber and Tonkawa in Oklahoma, and at Oxford in Kansas. Following some suggestions of the writer a well was also equipped by the Roxana company at Smackover by A. S. Field.

Jan 11, 1926

Jan 7, 1976

By Gilbert H. Cady

HE application of geology to problems arising A in coal mining engineering and coal preparation has, in general, been somewhat remote, or the geological problems have involved such simple forms of geological knowledge that the attention of specialists in this field has not been commonly thought necessary. Furthermore, the geology of coal beds and coal mining has received but scant attention in our educational system, even in mining education; so that coal mining engineers have become somewhat conditioned against geological thinking. Geologists, on the other hand, have commonly failed to realize that there are geological aspects to coal mining and coal preparation problems. A further reason why geology receives so little consideration in coal mining undertakings in this country lies in the fact that our coal supplies are, or have been thought to be, almost unlimited, have been easily accessible, and very cheaply mined. Conditions have been changing within recent years. Failures can be less easily endured. Great inroads have been made on our bonanza deposits of easily mined coal and the increasing cost of coal and the increasing difficulty of finding it in easily accessible and large quantities places greater and greater importance on accurate information and good technique in exploration. It seems probable, therefore, that the opinions and aid of geologists will be more commonly sought than in the past in the exploration for coal and in the development and operation of coal mines, and analyses of mining conditions, preparation, and utilization.

Jan 1, 1951

By Gilbert H. Cady

HE application of geology to problems arising A in coal mining engineering and coal preparation has, in general, been somewhat remote, or the geological problems have involved such simple forms of geological knowledge that the attention of specialists in this field has not been commonly thought necessary. Furthermore, the geology of coal beds and coal mining has received but scant attention in our educational system, even in mining education; so that coal mining engineers have become somewhat conditioned against geological thinking. Geologists, on the other hand, have commonly failed to realize that there are geological aspects to coal mining and coal preparation problems. A further reason why geology receives so little consideration in coal mining undertakings in this country lies in the fact that our coal supplies are, or have been thought to be, almost unlimited, have been easily accessible, and very cheaply mined. Conditions have been changing within recent years. Failures can be less easily endured. Great inroads have been made on our bonanza deposits of easily mined coal and the increasing cost of coal and the increasing difficulty of finding it in easily accessible and large quantities places greater and greater importance on accurate information and good technique in exploration. It seems probable, therefore, that the opinions and aid of geologists will be more commonly sought than in the past in the exploration for coal and in the development and operation of coal mines, and analyses of mining conditions, preparation, and utilization.

Jan 1, 1951

By A. L. Field

A. W. FAHRENWALD, Socorro, 'N. M. (communication to the Secretary*).-When asked to discuss Mr. Feild's paper, I felt most highly complimented to have the privilege of commenting on such a worthy and needed piece of apparatus. In consideration of the importance of the viscosity of blast-furnace slags and the relation existing between the' melting point of a slag and its viscosity, the introduction of this apparatus should be a welcome means or assistant in the study of the physical properties of a slag. Up to the present time, it is A fact that this side of the practical working of the blast furnace has been sadly neglected by those investigating slags. It is easily seen that the fluidity of a slag is of as great importance as its melting point. It is not necessarily true that a slag having a low melting point will have a correspondingly low viscosity or be highly fluid. For example, a slag having a melting point of 1,100° C. may have to be superheated to, say,1,300° C., in order to have as high a fluidity as another slag whose melting point is, say, 1,250° C. The latter in this case would be the more economical. This point has been brought out very nicely by Mr. Feild. Before discussing this paper further, I think it will be well to outline some of the points, a discussion of which may be in order:

Jan 3, 1917

By A. F. Witt, A. M. Gaudin, A. K. Biswas

Finite contact angles in the rutile-water-organic liquid system are traceable to contamination or are due to addition of a surface-active agent. Finite contact angles are invariably accompanied by hysteresis.1-7 Besides surfactant concentration and pH, the nature of the organic liquid is found to be a factor influencing the magnitude of contact angle hysteresis. In a recent paper the authors have reviewed principles and applications of measurement methods for contact angles and their hysteresis.22 In this paper, these methods are applied to a system consisting of rutile, an organic liquid (benzene, decane, or dode-cane) and water. Surfactant (dodecylamine hydro-chloride) was used at various concentrations and various pH values. MATERIALS A synthetic rutile crystal supplied by the Linde Co. was used. It is a cylinder 1/2 in. diam, with faces cut perpendicular to the c-axis. The crystal is stated to be alumina-free and to be 99.9% pure. Rutile is a high surface energy solid, its calculated average field strength being 2.7 x 105 e.s.u.,9 its dielectric constant10 is 114. The zero point of charge of rutile was measured11 and found to be at pH 6.0. The atomic distances and bond angles of the tetragonal crystal of rutile have been precisely determined.l2 The organic liquids were specially purified. Reagent grade benzene was repeatedly shaken with concentrated sulfuric acid to remove thiophene, then neutralized with sodium hydroxide solution, rinsed with distilled water, dried overnight over anhydrous calcium chloride and filtered. The refractive index of this chemically purified benzene was 1.4977 (at 25°C) - very close to that of pure benzene (n25 1.4979).13 Both n-decane and n-dodecane were washed with aqueous sodium hydroxide, concentrated sulfuric acid (repeatedly, until the acid layer was colorless) and again with alkali, to free the organic hydrocarbon from fatty acids and unsaturated hydrocarbons. The organic phases were subsequently washed with distilled water and dried over anhydrous sodium sulfate. The filtered hydrocarbons were then distilled under vacuum (9-10 mm pressure). Decane, thus purified, showed traces of unsaturated and of carboxylic compounds. On gas chromatographic analysis the purified n-dodecane showed the presence of two impurities. However, the relative retention times of these components did not change substantially when measured on a polar or a nonpolar column. This indicates that the compounds were probably in the same polarity class, i.e. the components were nonpolar like dodecane. Conductivity water has always been one of the liquids. Conductivity of the water used was 10-6 ohm-' cm". Dodecyl ammonium chloride was prepared from pure amine (supplied by Armour and Co., Chicago), by Li in the MIT Mineral Engineering Laboratory.14 The critical micelle concentration at 25°C is known, 0.0138 mol per liter15 or 3.06 gpl. All our experiments have been done at concentrations lower than the critical micelle concentration. The glass vessels, glass drop holder and the rutile crystal were all cleaned with hot chromic acid followed by distilled water, concentrated hydrochloric acid, and again distilled water, and conductivity water. During the experiments, a nitrogen atmosphere was maintained. For this purpose, commercially purified nitrogen was further purified by passing it over hot copper wire at 450°C, then through columns of acidic chromous chloride solution, concentrated alkali solution and distilled water. APPARATUS AND METHODS Hysteresis was produced by the "captive drop" or constant volume drop method as well as by the "expanding-contracting drop" or variable volume drop method. The image of the drop while it is expanding, contracting or moving is projected on a screen and photographed. The developed film is projected through an enlarger and the contact angles measured with a protractor.

Jan 1, 1964

By J. M. Roberts, N. Brown

The stress-strain behavior of zinc single crystals was measured over a strain range of 10-6 to 10-2. The phenomenon of macroyielding was observed in detail and plastic strains were detected at almost zero-stress. Closed hysteresis loops were observed during loading and unloading in the strain region of about 10-5. From the hysteresis a frictional stress on the dislocation of about 6 psi was obtained. A preliminary analysis indicates that impurities are primarily responsible for the friction. Nonelastic Strains as much as 10 -4 were recovered depending on the amount of prior deformation. Part of the recovered strain occurs instantaneously upon unloading and the remainder occurs at zero stress. The time dependence of the recovered strain was measured. THIS investigation is concerned with the details of plastic deformation preceding the ordinary yield point as measured with the usual strain sensitivity of about 10-4. The approach leads to internal friction observations in the hitherto neglected frequency range below 10-1 cycles per sec. It is believed that if the phenomenon of macroscopic yielding is to be understood, then the stress-strain curve in the neighborhood of the macroyield point should be greatly magnified. It may then be possible to determine whether macroscopic yielding is a unique event or whether it is a process which begins gradually at a lower stress. In the case of low-carbon steel a unique event obviously occurs at the macroscopic yield point as indicated by a drop in the load, but copper appears to exhibit a gradual transition from the elastic to the plastic state. In zinc the yield point is rather abrupt although the data indicates that some plastic deformation precedes large scale yielding.' One of the purposes of this investigation is to determine whether there is an abrupt transition from the preyield microstrain region to the region of macroscopic deformation. Such a rapid transition would support the concept that there is a critical stress for yielding. The concept that yielding is a unique event associated with such phenomenon as activating a Frank-Read source, freeing the dislocation from solute atoms, dislocations cutting through dislocations, or dislocations moving freely by one another, has been expounded widely on theoretical grounds. It is hoped that highly sensitive measurements of strain in the neighborhood of the macroscopic yield point will shed some light on the event known as the "Yield Point". EXPERIMENTAL METHOD 1) Specimens—High-purity zinc was cast into spherical graphite moulds in air and grown into spherical single crystals by the Bridgman method under a positive pressure of Argon gas. Spectro-graphic analysis of cleaved sections from four crystals showed a purity of 99.994 pet Zn. The specimens were acid machined with an 1/8 in. gage section in a form similar to those used by Parker and co-workers.2 Bausch type grips were fastened to the specimen by Epon VI adhesive. The specimens were oriented so that only [1120] (0001) slip occurred. Fig. 1 shows two of the specimens in the grips. Prior to each test, the gage section of the specimen was given a concentrated HNO3 chemical polish followed by alcohol rinsing and air blast drying. 2) Test Method- The shear tests were performed on an Instron testing machine and the experimental set-up was made very "hard". Strain could be measured to a sensitivity of 10 -6 by means of a capacitance gage extensometer. The design and calibration of this type of extensometer to measure microstrain, as applied to pure shear and tensile tests of metals, will be the subject of a separate paper—therefore, only a brief account will be presented here. The method essentially consists of attaching a

Jan 1, 1961

By H. M. Manasevit, R. L. Nolder, L. A. Moudy

The observation that silicon-on-sapphire crystallo-graphic relationships exist which are unrelated to one another implies that there are regions of sapphire orientations containing these relationships which are separated by boundaries. The presence of these boundaries is demonstrated, initially on rounded cylindrical surfaces md more definitively on flat sapphire substrates with orientations along primary crystallograPhic zones. By means of reflection electron and X-ray diffraction techniques the crystallographic relationships have been studied. Two new relationships have been found, viz., (111) Si (1014) sapphire and (001)Si (1012) sapphire. Also found were multicrystalline relationships. The approximated boundaries between the crystallographic regions for each relationship are shown by means of a stereo-graphic projection. These studies also clarify discrepancies in the literature concerning the silicon-sapphire relationships on the (1120) sapphire substrate. SINCE the first report of the deposition of single-crystal silicon on sapphire in 1963' this epitaxial system has been the object of study by many semiconductor laboratories. In particular, there has been strong interest in the crystallographic relationships between the two materials. In 19652,3 we demonstrated that at least four distinct modes of orientation relationships can occur, namely, (100)Si (0112) sapphire, (111)Si 11 (1124) sapphire, (111)Si (1120) sapphire, and (111)Si (0001) sapphire. Each relationship could be obtained when the substrate plane was at the particular orientation indicated. Other workers as well as our laboratory concurred in general with the initial results. However, two discrepancies were observed. First it was observed by Joyce et a1.4 that on a (1120) substrate a (110) silicon deposit could be obtained. This was actually consistent with the (111)Si (1124) sapphire mode. Second, two other laboratories,5,6 as well as our own,7 have found a deposition on the basal plane which is different than our initial findings. Even though a (111)Si deposit was obtained, the crystallographic relationships were not identical to those previously found. Subsequent work in our laboratories has confirmed that the form found in these later investigations of the basal plane is by far the more predominant, and the original finding was an anomaly. The relationships which have been previously estab1.ished are summarized in Table I. It is seen that at present a rather small number of possible substrate orientations has been investigated. Therefore, it seemed appropriate that a systematic investigation of silicon epitaxy on various sapphire substrate orientations would be of value. It was expected that the answers to three questions could be obtained from such an investigation. These are as follows: 1) Since we know of at least four distinct modes of orientation relationships, over what range of substrate orientation do these modes occur and what is the form of the boundary expected between the different regions in which each mode occurs? 2) Are there other modes which occur on substrate orientations not previously investigated? 3) What is the explanation for the discrepancy between our laboratory's findings and those results reported by Joyce et al.4 concerning the relationships occurring on (1120) substrates? APPROACHES AND EXPERIMENTAL METHODS Two different approaches were used. Initially, depositions were carried out on rounded cylindrical surfaces which lay perpendicular to the (0112) plane.* By this means the presence of boundaries and their approximate positions could be determined. Finally and more definitively, depositions on flat sapphire substrates with a variety of orientations, mostly along primary crystallographic zones and about the (1120) plane, were studied by means of reflection electron diffraction and X-ray diffraction (using back-reflection Laue patterns and full circle goniometer techniques) in order to determine crystallographic relationships. The sapphire orientations investigated by these means

Jan 1, 1969

By H. A. Schwartz

THE spheroidal form of the temper carbon nodules in malleable cast iron and of the graphite mottles of "mottled" cast iron suggests that in both all the graphite in a given mottle or nodule grew from a single center of crystallization or nucleus. ? There is, however, a distinct metallo-graphic difference between the mottle and the nodule; the area of mother metal impoverished in combined carbon by the crystallization of graphite in a mottle is practically coextensive with the ramifications of the graphite, while the impoverished zone of metal corresponding to a given nodule is always larger, and usually much larger, than the approximately spherical mass of graphite crystals forming the nodules. Furthermore, the mottle probably is formed during freezing and the nodule almost always at a considerably lower temperature. Assuming that the nodules or mottles can be used as a measure of the existing nuclei (capable of germination) we propose to record certain observations as to the graphitizing reaction in the light of the number and habits of growth of these nuclei. The present authors, in cooperation with others1-7, have reported upon various cognate aspects of the problem. The fact that temper carbon is a mass of flakes and not a solid granule has become well recog-nized since the introduction of an improved polishing technique8,9,10 for cast iron. The problem of deriving from the circular planar intercepts

Jan 1, 1936

By M. N. Pathasarathi, P. A. Beck, T. J. Koppenaal

EARLIER work1 indicated that in rolled and annealed copper the volume fraction of the cube-texture component may increase on continued isothermal annealing. Merlini found2 that in rolled copper the well-known increase in the amount of cube-oriented material with increasing annealing temperature3 is concurrent with grain growth, which takes place after recrystallization is complete. It was found that both in copper2 and in aluminum4 the texture resulting from primary recrystallization, even if this is followed by some grain growth, may in general comprise, in addition to the cube-texture component, four symmetrical texture components of the general type (123)[412], i.e., components not very far from the ideal orientations of the rolling texture. The volume fraction of the cube-texture component increases on further annealing at the expense of these four components.' The present work was undertaken to study quantitatively the increase in the volume fraction of the cube-texture component in the course of normal grain growth, under varying conditions. Since the grain-gr3wth behavior of A1-Mn alloys has been already investigated in some detaiL5 an A1 + 0.8 pct Mn alloy was chosen for this work, in which the extent of normal grain growth can be effectively controlled by the inhibiting effect of a dispersed second phase. EXPERIMENTAL PROCEDURE High-purity aluminum of the following composition was used: A1 99.997 pct, Cu 0.0004 pct, Fe 0.0005 pct, and Si 0.001 pct. A high-purity A1-Mn master alloy was prepared by dehydrating manganese chloride at 500°C and reacting it with molten high-purity aluminum at 750°C in a graphite crucible.5 The Mn metal reduced from the salt by the molten aluminum goes into solution in the latter. The master alloy? containing 13 pct Mn, was solidified under conditions suitable for minimizing segregation. An ingot of the final alloy, to be used in the experiments, was per pared by melting high-purity aluminum and the necessary amount of master alloy in a graphite crucible, and by pouring the molten alloy into a graphite mold preheated to 700°C through a box containing graphite baffles designed to intercept most of the aluminum oxide films floating in the melt. The melt was then solidified by placing the mold on a water-cooled copper plate and by keeping the top of the mold hot, in order to minimize piping. The 6 1/2 in. long, 11/4-in.diam ingot consisted largely of a single crystal. Chemical analysis showed that there was little segregation from the bottom (0.83 pct Mn) to the top (0.81 pct Mn). Spectrographic analysis of the ingot showed that the impurity content remained essentially the same as that of the aluminum used. The ingot was processed so as to obtain a uniformly small grain size. without banding. The ini-tial steps of rolling in the form of a flat bar and of annealing, down through a thickness of 0.4 in., are shown in Table I. At this point the bar was cut into four sections, each approximately 3 in. long, which were processed separately as shown in Table If. The table also gives the penultimate grain sizes obtained in each section by annealing prior to the final rolling of 90 pct RA. During the final rolling the strips were reversed end to end between passes. Annealing treatments were given in a salt pot furnace, with the temperature controlled to 1°C. All annealing of section "6s" was carried out above the solvus point to avoid the formation of second-phase precipitate. The penultimate annealing was sufficiently short to give a relatively fine grain size in spite of the high temperature. Section "6L" was processed in a similar manner, except that the penultimate annealing was much longer, so as to allow considerable grain growth. Section "4" was given the two final

Jan 1, 1961

By R. K. Govila, E. H. Parkison

THE interplanar angles for hcp metals vary with c/a ratio, and therefore must be computed separately for each particular metal or alloy. Manual computation of these angles is laborious and time consuming, and for this reason computer programs have been developed to accomplish this task.1"3 However, these programs have certain disadvantages. For example, they require prior knowledge and understanding of ALGOL or FORTRAN languages. Further, they will not print out specific angles but instead give all angles between given limits—thus program2 prints out a total of 26,649 angles between planes with indices and in the range from (4 4 4) to (4 4 4) for any given c/a ratio. The purpose of this note is to present a simple and inexpensive computer program for accomplishing this task. This program is written in BASIC language4 which does not require any prior knowledge of computer programming, and is ideally suited for nonprofessional programmers. It also provides flexibility for the user by allowing him to select any indices for as many or few planes as desired for any given c/a ratio. The computer program proposed below is based on the relationship in which + is the angle between any two planes and . TO illustrate use of the program, consider the problem of calculating the interplanar an-

Jan 1, 1970

By Erwin Pink

It has been pointed out in a previous publication' that, for a given strain rate, serrated yielding can be observed only at certain test temperatures. Fig. 1 shows the results obtained for polycrystalline and re-crystallized tantalum, Va group in the periodic table of elements, where serrations in the course of deformation match the decrease of total elongation. However, there was no evidence of repeated yielding when testing molybdenum or tungsten, VIa group, at similar conditions, i.e., annealed and air-cooled samples (serrations have been found in quenched tungsten2). The reason for the observed serrations in the stress-strain curve are dissolved impurities on interstitial sites of the lattice. Of importance is the concentration of oxygen, carbon, and nitrogen, which are in random solution. Two methods to calculate the limiting concentrations for serrated yielding have been evaluated and applied with more or less success in estimating the role of carbon and nitrogen in mild steel.3 J. Friedel4 has given two equations, which determine the upper and lower strain rates i for the appearance of serrations at a certain test temperature: W denotes the binding energy of the interstitial atom, -1 ev for refractory metals;5 e' the portion of continuous strain in the discontinuous stress-strain curve, measured as -3x10-3; b the Burgers vector, c the concentration, see Table 11, in atom fractions; p the dislocation density, -2 X l09 per cm2 at an average stress ?, -15 kp per mm2 at medium strain. k stands for the Boltzmann constant, T for the absolute temperature, and D for the diffusion coefficient. Table I. Eq. [1], for a given strain rate, determines the minimum temperature, and [2] the maximum temperature, below or above which no "dynamic strain-aging" can occur. According to the calculation, which uses the given quantities, serrations should only be observed within the cross-hatched temperature regions in Fig. 1, and this is in good agreement with the experiment. The effect of varying impurity concentrations is indicated schematically in Fig. 2: only Eq. [I] is affected. Setting Eq. [I] equal to [2], one can calculate the limiting concentration cmin which first causes serrations. The second method uses the aging condition by Cottrell and Bilby6,7 \£i/ \ n. a / where n(t) is the number of impurity atoms, which segregate at a dislocation line of 1 cm length after the time t (t in our case is the time between "repeated yield drops" in the serrated curve, or, the time until the above mentioned strain E' is obtained, i.e., -1 sec for medium intensity or serrations). no is the number of impurity atoms in 1 cm3 and A = Qb4ep[(1 + v)/(l - v)], derived from equations given in Ref. 7. p is the shear modulus, 18,800 kp per mm2 for tantalum, 12,200 for molybdenum, AE the tetragonal distortion caused by interstitial impurities in a bcc lattice (approximately 0.4 for both tantalum and molybdenum) and v Poisson's ratio (0.35 for tantalum, 0.30 for molybdenum). From Eq. [3], combined with the condition for a pronounced yield drop as formulated by cottrel16 (at least one impurity atom segregated at the unit length of a dislocation), again a no min, and hence the concentration Cmin can be calculated.

Jan 1, 1970

By A. C. Emery

The physical and chemical properties for the metalliferrous feed materials to the Imperial Smelting Process blast furnace are defined and the means of achieving these properties by the sintering or briquetting routes discussed. Modern sinter plant performance data is included with a plant flow sheet showing draughting patterns. The necessity for ensuring an adequate SO2 content in sinter machine gases when roasting sulphide materials to enable conversion to sulphuric acid in a contact acid plant is described. The ability of the process to consume limited quantities of oxide materials, residues from other processes and other secondary sources is discussed. The argument for a briquetting route is developed out of this limitation and the merits of cold and hot briquetting examined. Development work on the hot briquetting route for this purpose is briefly described and several flow sheets outlining possible applications for hot briquetting to different raw material situations including the preparation of low lead charges for the furnace are presented.

Jan 1, 1977

By J. B. Conway

RECENT studies of first-stage creep data have led to a special least-squares procedure for use in calculating the Andrade creep-equation constants. This procedure is easy to apply, uses only experimental data, and yields results which do not vary with the individual making the analysis. Taking logarithms of the Andrade equation I = lo(1 +ßl1/3)ekt leads to In l = In lo + In(1 + ßl1/3) + kt A residual can then be defined as the difference between the logarithm of an experimental length value and the logarithm of a calculated length value. Following the usual least-squares approach differentiation with respect to 10 and k of the expression for the sum of the squares of the residuals leads to two equations which cannot be solved directly for the three constants involved. However, values of ß can be assumed and corresponding values of lo and k can then be calculated. Then the sum of the squares of the residuals can be calculated. For a certain value of ß this sum will exhibit a minimum value to identify the least-squares values for ß, lo, and k. An illustration of the application of the above least-squares approach is obtained by employing the creep data for lead originally presented by Andrade' in the development of the one-third creep law. A plot of the sum of the squares of the residuals as a function of ß is shown in Fig. 1 along with the corresponding lo and k values. The minimum is seen to occur at ß = 0.0143 from which lo = 39.149 and k = 7.27 x 10-5. Based on these results the Andrade equation for these lead data is 1 = 39.149(1 + 0.0143 t1/3)e7.27 x 10-5t compared to the equation I = 39.13(1 + 0.01457/l/3)e6.95 X 10-5t developed by Andrade (calculation procedure not given but was probably a graphical solution). Calculating length values using the above equations and comparing with the experimental length values, residuals corresponding to the difference between experimental and calculated length values can be obtained. The sum of the squares of the residuals can then be calculated. For the case of the least-squares approach a value for this sum was found to be 2.37 x 10-3 compared to a value of 3.47 x 10" for the equation originally proposed by Andrade. In other words, while the constants proposed by Andrade provide an excellent fit for the lead data, a still better representation is afforded by applying the least-squares approach discussed above. A similar result was obtained for the lead data at 162oc.l The least-squares approach led to 1 = 9.866(1 + 0.0497 t1/3)el.011 x 10-2t compared to the equation I = 9.94(1 + 0.0433 l1/3)e1.06 X 10-2t given by Andrade. In this case, too, the sum of the squares of the residuals is slightly smaller for the equation based on the least-squares approach. It should be pointed out that a double trial and er-

Jan 1, 1965

By H. H. Rachford, and J. D. Rice

The effectiveness of digital computing machines in making technical calculations depends on how well the work is arranged to utilize the capability of the machines. This note presents a particularly useful way of calculating hydrocarbon vapor-li.quid equilibrium in the flash vaporization (or condensation) system. The method is well suited to sequence-controlled computing equipment. It is not limited to equilibrium calculations and may be used for solution of most implicit equations in one variable. INTRODUCTION There is increasing interest in the use of electronic digital computers in research and engineering calculations. This is a fortunate and inevitable trend in view of both the increasingly extensive numerical work which is becoming a routine part of many daily production operations and growing demand for the overwhelming amounts of calculations required by newly developed numerical methods for solving heretofore unsolved problems. Machines are in many ways ideally suited to the task but of necessity present certain difficulties. for a particular poblem to be solved must often be formulated quite differently from the way it would be arranged for manual solution. This is done in order to take advantage of the inherent speed and precision of electronic computers and at the same time to limit the need for number storage to the capacity of the machine. Therefore, this note is submitted to present a general and quite powerful method of finding solutions of the frequently encountered implicit equation: F(x,y1,y2,...ya)=0.......(1) where the root, x, is to be found for a given set of y1, ... yn.. The procedure is well suited for use with computing machines, for it usually requires but little storage or programming beyond that necessary to evaluate F. HYDROCARBON EQUILIBRIUM The method is described in terms of the problem it was designed to solve, i.e., the calculation of hydrocarbon vapor-liquid equilibrium in flash vaporization. Given the composition of a hydrocarbon mixture and appropriate values of the equilibrium ratios K, to find the phase ratio and compositions in a closed system: let z, be the mol fraction of the i-th component in the mixture. If K, is the ratio yl/xl, where y, and x,

Jan 1, 1952

By R. E. Collins, Paul B. Crawford

Mathematical equations have been derived to show the effect of the slippage phenomomenon (Klinkenberg effect) on unsteady-state gas flow through porous media. The assumption is made that the slippage may be represented by an equation of the type It is pointed out that most of the existing data on unsteady gas flow may be corrected for slippage by a simple change in definition of the dimen-sionless groups. INTRODUCTION Several solutions to the various problems associated with the unsteady-state flow of gas through porous media have been recently presented in the literature.','" The cited publications have resented solutions for flow under ideal conditjons. The principal assumptions involved include: (a) the density of the gas obeys the perfect gas law; (b) the viscosity of the gas is constant; and (c) the gas permeability is constant. Few, if any, actual gases under reservoir conditions are believed to conform with the above, but the ideal solutions do provide the basis for making improved estimates on the performance of gas reservoirs. The purpose of this paper is to show the performance characteristics when assumption (c) is corrected for the slippage phenomenon or the Klinkenberg effect. This is believed to be a step nearer to reality. MATHEMATICAL DEVELOPMENT Case 1. Gas Flow — Ideal Conditions The equations describing the flow of gas under ideal conditions have been clearly presented in the cited literature; however, for completeness of this work they are repeated here. The basic differential equation describing the flow of gas is Equation (6). It may be derived as follows: The continuity equation, the perfect gas law and Darcy's law are combined to give: Manuscript received in the Petroleum Branch office Aug. 3, 1963 or If — is constant, Equation (5) is rewritten to form the basic Equation (6). or for the linear case A dimensionless equation is obtained by dividing through by (pl)z and making the substitutions shown below: The resulting equation is A similar procedure for the radial case leads to the following equations: where and Equations (11), (12), and (13) are those used by Bruce, et al., and Jenkins and Aronofsky for their computational work.

Jan 1, 1953

By M. J. Scoble, N. Rowlands, L. Piciacchia

Pronounced non-linear behaviour of mine backfill arises from the influence of confining pressure, cementing agent content, curing time, void ratio and water content. Past research into backfill behaviour under stress is reviewed and related to the needs for constitutive laws which can be integrated into numerical modelling for mine design where structures employ backfill support. A method for representing non-linear backfill behaviour is proposed, which is based upon numerical regression treatment of triaxial laboratory data. The non-linear behaviour observed from a program of laboratory triaxial testing of cemented hydraulic backfill is presented. The particular influence of confining stress and curing duration is high- lighted. The paper concludes by considering the alternative means of accounting for such behaviour in mine design.

Jan 1, 1984

By R. B. Gilmore

It has been the custom of the Railroad Commission of Texas to hold hearings each month with respect to existence and imminence of waste of oil and gas in Texas and its prevention, and to issue orders restricting the production of oil to the reasonable market demands and allocating production to the various fields in Texas. The practice of designating the actual days during the month on which wells are to be shut down was discontinued in the order for November 1942, and orders issued thereafter contain only the number of shut-in and producing days for the month. Orders issued by the Railroad Commission are divided into two main subdivisions, the first a general shutdown order of all oil wells in the various fields in Texas, and second, the exception of certain fields to this general order. Table I shows the producing days for all of the fields in Texas for 1944 under the first of these classifications : The fields that have producing schedules varying from the general order may be divided roughly into three subdivisions, as follows: Table 2 shows the producing days for certain fields that were prorated as a group throughout 1944. Other fields which were occasionally included with this group were also prorated under the general order and by special orders. The producing days for these irregular fields are shown in Table 4. In Table 3 are listed fields that were exempted from any shutdown days during December 1944, the majority retaining this exception throughout 1944. Certain fields included in the general order were added to this group on the first day of the month shown.

Jan 1, 1945

By R. Maddi, I. R. Kramer

The delay time for the initiation of slip was studied in single crystals of a brass, aluminum, and ß brass. A delay time for slip was found in ß brass when the specimens were tested below room temperature; however, one was not found for a brass or aluminum. A general theory for the existence of the brittle transition temperature is proposed. A LTHOUGH a considerable amount of effort has A been devoted to the study of the deformation and fracture of single crystals, the vast majority of the work was concerned with static tests or with tests carried out at relatively slow strain rates. The necessity for the study of a possible incubation time for slip becomes apparent when the various theories which have been postulated for the elucidation of the mechanism of slip are considered. The existence of an incubation period would strongly indicate that slip occurs by a process of nucleation and growth; whereas the absence of an incubation would present rather convincing evidence that slip occurs by a cataclysmic process. In addition to shedding light on the process of plastic deformation, an understanding of the early stages of plastic deformation may be helpful in finding an explanation for the brittle behavior of the body-centered metals under certain conditions. It is well known that these metals, such as iron, molybdenum, tungsten, ß brass, etc., will become brittle as the test temperature is lowered or the strain rate is increased. In spite of the fact that this subject has received considerable attention since the turn of the century, no adequate theory exists today which explains the phenomenon. In the ductile temperature range the metal breaks with a "fibrous" fracture after considerable slip has taken place. In the brittle temperature range the metal fails essentially by cleavage on the {loo) planes: however, some plastic flow is always present even in the most brittle fractures. It is possible, as will be explained later, to ascribe this brittle behavior to the length of the incubation time for slip. Clark and Wood,' using polycrystalline metals, showed that a delay time existed for the yield point in mild steels and that the delay time depended upon the applied stress. These authors stated that the delay time was observed only with those materials for which the stress-strain curve showed a definite yield point. In their work only the mild steel specimens exhibited a delay time at the yield point, while the other materials studied-type 302 stainless steel, SAE 4130 normalized steel, SAE 4130 quenched and tempered steel, 24s-T aluminum—did not show a delay time. These authors' in an extension of their work, found that as the temperature was lowered the delay time was increased. It is, then, the purpose of this investigation to measure or to set an upper limit on the delay time for plastic flow in single crystals of a brass, aluminum, and ß brass. The delay time will also be studied as a function of temperature. The incubation time may be measured by determining the length of time the specimen will support a stress without slip occurring when the stress is greater than the static critical resolved shear stress. In order to accomplish these measurements use was made of a pendulum which was so designed that a single crystal specimen could be placed at various positions along its length. When a pendulum is struck by another pendulum of the same length, an elastic wave is transmitted down the bar with the velocity of sound in the material and is reflected from the far end of the bar. The reflected wave then travels back and unloads the stress until it reaches the impacted end of the bar and the two pendulums separate. The length of time that the specimen is subjected to the stress is equal to the time it takes for the stress wave to travel twice the distance from the specimen to the end of the bar. The stress applied to the specimen is governed by the velocity of impact of the two pendulums. The stress at which the specimen first suffers plastic: deformation was determined in these experiments by examining the specimen under the microscope for the first appearance of slip lines and by measuring the residual strain after each impact. In these experiments the critical resolved shear stress was approached from the low stress side and no attempt was made to determine it exactly. To determine it exactly, it would have been necessary to find that stress at which slip would have just started. However, since the stresses were increased in rather small increments the critical stress is believed to be approached rather closely, as will be seen from the experimental results. The critical stress will be taken as the highest stress obtained before the onset of plastic deformation. The stresses

Jan 1, 1953