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By R. J. Reynik

A semiempirial small flunctation theory of diff- sion in liquids is presented, which employs a fluctuation energy assumed quadratic for a small atomic or molecular displacement and Einstein's random-iralh model. The resulting diffusion equation is given by In these equations. D is the diffusivity, is the average liquid shite coordination number (at interatomic distance d. cm. T is the absolute temperature, xu. em, is (the diffusive displacement. K, is the quadratic fluctuation energy force constant, and rg, cm, are the radii oj diffusing atoms A and B, respectively. The quantities Xn and K are calculated from the computer-filled values of the slope and intercept. respectively. The radius of self-diffusing atom or radii and of diffusing atoms A and B are eta United and compared with values reported in the literature.. The predicted linear variation of diffusivity with. It tempera lure htm been observed in approximately thirty-iire metallic liquid systems, and in over seventy-fiee other liquid systems, including the organic .alcohols, liquified inert gases, and the molten salts, ALTHOUGH the average density within a macroscopic volume element of liquid is constant for fixed total number of atoms. pressure. and temperature, there exist microscopic: density fluctuations within the respective volume element. As such the microscopic volume available to an atom and its Z first nearest neighbors at any instant of time fluctuates above and below the average volume available to these atoms. If one assumes that liquid state atoms vibrate as in a solid. and further postulates that the mean position of any atom in the liquid state is not stationary. but shifts during every .vibration a distance 0 5 j 5 xo. then every atom in the liquid state continuously undergoes diffusive displacements which vary in the range 0 5 j 5 ro. Mathematically. for a binary liquid system consisting of atcrms A and B. the maximum diffusive displacement. .YO, is defined by the equation: where d is the average liquid state interatomic distance at specified liquid state coordination number Z. and v~ \ and vg are the effective radii of diffusing atoms A and B: respectively. For self-diffusion. r^ equals rg , and Eq. [I.] reduces to: It is interesting to note that Eq. [l] or [2] can be used to compute the radii of the diffusing atoms, provided one had an experimental evaluation of xo. As such. the computed radii could be compared with metallic or crystallographic ionic radii to ascerlain the electronic character of the diffusing atoms. Thus it is proposed that in the liquid state the n~otion of an atom relative to its original equilibrium position of oscillation represents the thermal vibration of any atom and its Z first nearest neighbors. while the small and variable displacements. 0 5 1 5 xc,. of the centers of oscillation represent the complex diffusive motions of the atoms at constant temperature and pressure. This is consistent with data obtained from slow neutron scattering by liquids1 ' and resembles an itinerant oscillator model of the liquid state.'" It is further postulated that the atomic displacements characterizing the liquid state diffusion process are essentially a random-walk process. As such. it nlay be described by Einstein's equation:' where D is the diffusivity. sq cm sec-'. j2 is the mean square value of the diffusive displacement. and i> is the frequency of density fluctuations giving rise to diffusion. FORMULATION OF DIFFUSION EQUATION The effective spherical volume occupied by an atom, as a consequence of a microscopic density fluctuation which enlarges the volume available to any atom, exceeds its average liquid state atomic volume by an amount: where AV is the enlarged spherical volume, v is the radius of the diffusing atom. and j is the elementary displacement distance from the original center of oscillation of the vibrating atom to a new center of oscillation position. For small atomic displacements. where c is a constant whose value depends upon the assumed geometry of the enlarged volume. For a spherical increase in volume, c equals 4nr2. Following the treatment of Furthl' and ~walin." assuming the enlarged volu~nes AL7 for the diffusing atoms are distributed in a continuunl. the probability of finding a fluctuation in the size range 0 5 j 5 xo defined by Where c includes the geometric constant cl and Eij) is the fluctuation energy causing the volume change. But the proposed model assumes all the Z first nearest-neighbor atoms are centers of oscillation. and hence the probability that any of these atoms is adjacent to a fluctuation of magnitude 05j5xo is unity. Thus:

Jan 1, 1970

By Charles W. Goodale

The ores of the Butte district present a variety of combinations, and their treatment by concentration is an interesting study. They may be classified in general as follows: 1. Copper-silver ores, which are produced by the mines of the Anaconda group, and by the Mountain View, Colusa, Silver Bow and Parrot. The high-grade ores from these properties are roasted and then smelted; but a large proportion of the output is low-grade and siliceous, and hence requires concentration. The copper-bearing minerals are chalcocite, bornite, enargite and chalcopyrite, in varying proportions in the different mines, the gangue, which breaks readily into grains, being quartz and feldspar. 2. Silver-copper ores, of which the Gagnon vein is the largest producer. The grade of the ores from this mine is such that nine-tenths of the output requires concentration. The silver- and copper-bearing minerals of this vein are massive wurtzite, sphalerite, bornite, chalcopyrite, pyrite, tetrahedrite, enargite, tennantite and galenite, with a quartz gangue associated with feldspar and small quantities of barite and fluorite. The gangue is very hard and not at all granular. 3. Silver-ores containing a small amount of gold, embracing the product of the Alice, Magna Charta and Moulton claims, on what is known as the Rainbow lode, and that of the Lexington, Blue Bird, Nettie, Burlington and other mines. The gangue is quartz, carrying pyrite, sphalerite, galenite, tetrahedrite and argentite, with manganese in the form of rhodochrosite and rhodonite. Good results on ores of this class cannot be obtained by concentration, because large percentages of the silver-bearing minerals are disseminated through the gangue in such minute grains that even the finest practicable crushing

Jan 1, 1897

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.'" 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 '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 R. E. Cook

This paper presents results of a study to determine to what extent errors in estimated free gas saturation affect the results of static pressure calculations from build-up curves in two-phase systems. Use is made of the method of pressure build-up curve analysis developed by Miller, Dyes and Hutchinson1 , with modifications for two-phase flow advanced by Perrine2. Cornhined fluid compressibility of gas-oil mixtures is included, with special attention given to the discontinuity that occurs in fluid compressibility at the saturation pressure and its effect on static pressure calculations from build-up curves. The sensitivity of static pressure calculations to errors in gas saturation is considered over wide ranges of formation and fluid properties and reservoir pressure conditions. It is concluded from this study that for analyses of two-phase pressure build-up curves (I) the use of under-saturated crude compressibility data, even when producing GOR's are at or near solution values, will result in very significant negative errors in calculated static pressrrre, and (2) except for large values of buildup curve .slope and/or very low crude gravities, rather large errors in calculated gas saturation can he tolerated without .significant effect on calculated static pressures. The conc1usions arc qualified as referring only to the effects of gas saturation and excludc possible errors in the nuumerous other factors that enter into the ancllysis of pressure build-up curves. INTRODUCTION As part of the analysis of basic data for several major Eocene reservoirs in the Bolivar Coastal field (Western Venezuela), it was necessary to analyze a large number of pressure build-up curves for oil permeability and static reservoir pressure. From performance data it became apparent that gravity segregation is very active in these reservoirs. As a result of this performance it was recognized that the free gas saturation within the oil leg of the reservoirs would be small but would be subject to certain errors in calculation due to the inaccuracy of relative permeability data in the low gas saturation region. Since all of the various methods of build-up curve analysis were originally derived for sin- gle-phase, constant compressibility systems, and since the presence of a small but rather indeterminate gas saturation would greatly affect the reservoir fluid compressibility, a study was undertaken to investigate the effect of gas saturation on the results of two-phase pressure build-up analyses. TWO-PHASE BUILD-UP CURVE ANALYSIS The method of analysis used in this investigation is basically that originally developed by Miller, Dyes and Hutchinson1, with modifications for two-phase flow advanced by Perrine2. Miller, et al, showed that the original equation for single-phase permeability away from the well bore, held for two-phase flow except that the calculated permeability is the effective permeability to oil away from the wellbore. This finding was acknowledged by Per-rine, who also presented the equation for effective gas permeability* as Since Eqs. 1 and 2 contain no terms influenced by fluid compressibility, no distinct problem should develop in calculating permeability from two-phase build-up curves. In regard to the calculation of static reservoir pressure from build-up curves in single-phase systems, the modified Miller, et al, method as presented by Perrine is briefly as follows. 1. From build-up curve data, PVT data for the reservoir fluid and the well spacing and sand thickness, calculate the climensionless shut-in time corresponding to the highest value of actual shut-in time (t, hrs) on the straight-line portion of a semi-log build-up curve. Dimenrsionless shut-in time is related to actual shut-in time by the relation, t- 0.000264 kt 2. From a graph of dimension less shut-in time vs dimensionless pressure difference (Fig. 1 1 ) find the value of dimensionless pressure difference corresponding to the value of 7 calculated under (1) above. Dimen-

By George E. Cole

While many parts of Canada's pre-Cambrian shield are well served by railway, it is frequently necessary for prospecting purposes to proceed farther into areas inaccessible by rail. To such areas in summer the canoe was at one time the accepted means of travel for the prospector while the dog team was much used in winter. Although summer travel was much improved by the development of the outboard motor, the lack of facilities for cheap transportation has been a serious hindrance to the employment of capital in opening up the distant fields. The pre-Cambrian surface of Manitoba, like that of Ontario, is hummocky, with rounded hills and ridges of rock alternating with basinlike depressions and valleys occupied by lakes and rivers Or by many low-lying portions covered with muskeg' Routes to the mines have not usually been direct or easy and seasonal vagaries have presented problems in themselves. In summer, water transportation may be the cheapest method for the longer distances but it is not every water route that will satisfy the conditions of loading freight on to a boat or scow and of conveying it without interruption to its destination. By its location, a mine may require a large program of boat transportation in summer Over part of its route, to be followed by winter freighting for the remainder. In order to carry on development and produc- tion over a long period, it may be necessary to haul large quantities of supplies during the winter. This seasonal problem, particularly for the out-of-the-way properties, is SO important and demanding as to make it a major operation in the life of the mine. The -use of the tractor during winter months for heavy machinery and bulk supplies, and the use of the airplane throughout the year for the transportation of personnel and for emergency requirements, have greatly improved transportation to places that are inaccessible by rail. Canada has pioneered in both these methods. Development oF Transportation Twenty-two years have seen a marked change in transportation methods in Canada's mining country. Horse-drawn sleighs have given way to the tractor and that to some extent has been supplanted by the airplane. One of the earliest ventures involving transportation of considerable magnitude was that of the Mandy mine, on Schist at in northern Manitoba. According to accounts of early mining activities in Manitoba, the Mandy mine, beginning December 1916, had 3300 tons of ore hauled 40 miles by sleigh to Saskatchewan River and in summer this was conveyed by barge to The Pas, 130 miles, and then by railroad to Trail, British Columbia, 1200 miles. The mine shipped 6000 tons of ore in 1918 and 15,000 tons in 1919. In winter of the latter year, as many as 300 teams of horses were used on the 40-mile stretch to

Jan 1, 1943

By George E. Cole

While many parts of Canada's pre-Cambrian shield are well served by railway, it is frequently necessary for prospecting purposes to proceed farther into areas inaccessible by rail. To such areas in summer the canoe was at one time the accepted means of travel for the prospector while the dog team was much used in winter. Although summer travel was much improved by the development of the outboard motor, the lack of facilities for cheap transportation has been a serious hindrance to the employment of capital in opening up the distant fields. The pre-Cambrian surface of Manitoba, like that of Ontario, is hummocky, with rounded hills and ridges of rock alternating with basinlike depressions and valleys occupied by lakes and rivers Or by many low-lying portions covered with muskeg' Routes to the mines have not usually been direct or easy and seasonal vagaries have presented problems in themselves. In summer, water transportation may be the cheapest method for the longer distances but it is not every water route that will satisfy the conditions of loading freight on to a boat or scow and of conveying it without interruption to its destination. By its location, a mine may require a large program of boat transportation in summer Over part of its route, to be followed by winter freighting for the remainder. In order to carry on development and produc- tion over a long period, it may be necessary to haul large quantities of supplies during the winter. This seasonal problem, particularly for the out-of-the-way properties, is SO important and demanding as to make it a major operation in the life of the mine. The -use of the tractor during winter months for heavy machinery and bulk supplies, and the use of the airplane throughout the year for the transportation of personnel and for emergency requirements, have greatly improved transportation to places that are inaccessible by rail. Canada has pioneered in both these methods. Development oF Transportation Twenty-two years have seen a marked change in transportation methods in Canada's mining country. Horse-drawn sleighs have given way to the tractor and that to some extent has been supplanted by the airplane. One of the earliest ventures involving transportation of considerable magnitude was that of the Mandy mine, on Schist at in northern Manitoba. According to accounts of early mining activities in Manitoba, the Mandy mine, beginning December 1916, had 3300 tons of ore hauled 40 miles by sleigh to Saskatchewan River and in summer this was conveyed by barge to The Pas, 130 miles, and then by railroad to Trail, British Columbia, 1200 miles. The mine shipped 6000 tons of ore in 1918 and 15,000 tons in 1919. In winter of the latter year, as many as 300 teams of horses were used on the 40-mile stretch to

Jan 1, 1943

By C. S. Matthews, P. Hazebroek, F. Brons

A method has been developed for calculating the average pressure in a bounded reservoir. The reservoir is first divided into the individual drainage volumes of each well, by using the criterion that at steady state each individual drainage volume is proportional to a well's production rate. The average pressure in each drainage volume is then calculated by a method developed in the report. By volumetrically averaging these individual drainage volume pressures, the average pressure in the entire reservoir is obtained. To calculate the average pressure in each drainage volume, a correction is applied to the ordinary extrapolated pressure, i.e., the pressure obtained by extrapolating to infinite time the linear portion of the graph of closed-in pressure versus log[?t/(t + ?t)], where At is the closed-in time and t the production time. The correction, which is a function of the production time, is presented in graphical form for different shapes of the drainage area (horizontal cross section of the drainage volume). INTRODUCTION It is important to be able to find the volumetric average pressure in a reservoir so that the size of the reservoir may be determined from material balance calculations. It is also desirable to be able to find the approximate distribution of pressure within a reservoir for detection of fluid movement. 'The purpose of this paper is to present a method for calculating both the average reservoir pressure and the approximate distribution of pressure within a bounded reservoir — that is, a reservoir with no water drive. In reservoirs where the pressure builds up rapidly after wells are shut in, the determination of average pressure generally poses little problem, for one often need only average the final buildup pressures. It is when pressure buildup is slow that difficulties arise. For practical and economical reasons, the time allowable for closing in wells is limited. If at the maximum allowable closed-in time the pressure has not reached a con- stant value (and this is more often the case than is generally realized), calculation of average pressure presents difficulties. One method which has been used in the past for obtaining an "average" pressure involves the extrapolation to infinite closed-in time of curves of pressure as a function of closed-in time. Contour maps of these extrapolated pressures are used in arriving at an average pressure. In some cases wells are shut in for arbitrary Lengths of time, and contours of these arbitrary shut-in pressures are used for calculation. All these methods are somewhat arbitrary and suffer from lack of fundamental theoretical basis. For example, no precise meaning can be given either to the extrapolated or to the arbitrary shut-in pressure. Furthermore, there seems to be no reason why either set of pressures should be contourable. It was because of the vagueness of these old methods and their lack of a sound theoretical basis that, the present method for determining average reservoir pressure was developed. SYMBOLS A = drainage area of a well, cm' A, = drainage area of well j, cm2 A , = total drainage area of all wells in a reservoir, cm2 c = coefficient of compressibility of fluid at reservoir temperature, atm-1 f = hydrocarbin-filled porosity, fraction h = net thickness of formation, cm k = permeability of formation, darcy p = pressure at a well, atm p0 = initial reservoir pressure, atm p* = pressure obtained by straight-line extrapolation of linear portion of plot of p versus log [At/(t+ At)] p = volumetric average pressure inside drainage volume of a well q = volume flow rate at a well, cc/sec a: prevailing reservoir conditions q, = total volumetric flow rate from a reservoir, cc/sec at prevailing reservoir conditions rw = radius of well bore, cm T = kt/fµcA t = corrected time of production of a well, seconds, defined by

Jan 1, 1955

By T. P. Harrington, P. G. Doctor, K. A. Prisbrey

Crushing and grinding ore consumes so much energy that it represents a major component of total processing costs. While it has been estimated that only about 0.6% of the total energy expended in grinding is actually used to create new surfaces, accurate measurement of this quantity is difficult. If energy expended in crushing and grinding could be more directly measured, alternatives for increasing efficiency of the processes could be evaluated more effectively. Since the energy intensity associated with rock fracture is related to fracture sonority, it should be possible to use this sound (acoustic emission) to measure the actual energy expended. However, it is difficult to apply this approach because the mill environment is so noisy. To make the approach practical, a method for differentiating acoustic emissions caused by rock fracture from those caused by extraneous noises must be found. Pattern recognition analysis may provide such a method. This paper presents the results of pattern recognition analysis to make two types of differentiations: acoustic emissions caused by crushing two types of minerals (quartz and chrysocolla) and those caused by two extraneous noise sources, and acoustic emissions produced by each mineral.

Jan 1, 1982

By M. Bevis, A. G. Crocker

A. G. Crocker and M. Bevis (Battersea College of Technology)— Richman and Richman and conard17 have recently published the very interesting results of their studies on the plastic deformation of Fe-Ni-C martensites and of an Fe-5 wt pct Be alloy. Other work on the range of Fe-Be alloys containing between 16 and 27 at. pct Be has also been reported by Richman." One of the fascinating features of this work is that the materials investigated deform primarily by means of twinning and that several twinning modes are operative in addition to the well-established (112 ) mode of bcc materials The composition planes of these unusual twins were determined using a single-surface analysis and reported as (0131, "{045)" or "{089)", and It is now thought1' that the "{0,1,13)" habit reported for the Fe-Ni-C alloys'' is more likely to be near "{127)". Although the full twinning elements of these unusual twinning modes could not be determined directly from the experimental results, the authors attempt to deduce the elements by considering twin intersectionslQ and by using the projection technique of Jaswon and Dove. The basic assumption of their approach is that the (013) habits are truly rational planes but that the other habits are irrational and merely approximated to by the indices quoted above. They thus deduce that the twinning mode describing the (013) habit is either Type I or compound and that the modes describing the other habits are Type 11. This deduction must however be false as all twinning modes in cubic structures obeying the classical orientation relationships of deformation twinning must be compound. Type-I and Type-I1 modes can occur in all of the other crystal systems (indeed in the triclinic system compound modes are not allowed), but in the cubic system only compound modes can arise. This fact, which does not appear to be well-known, fol- lows immediately from the relations between the four twinning elements defining a twinning mode. Thus for a Type-I mode which is uniquely defined by the rational twinning elements K1 = hi and given by: where the summation convention of the tensor calculus has been adopted. For cubic materials the metrics and reduce to the unit tensors and j so that we have It is clear from these equations that both ki and ui must take on integral values; i.e., Kz, and ql must be rational, if hi and vi are integers, i.e., if K1 and are rational. Thus for cubic materials a Type-I mode must degenerate into a compound mode and the same result also arises for Type-II modes. The apparently irrational habits observed by the authors can thus not be explained in terms of Type-I1 twinning if the classical laws of deformation twinning are to be obeyed. An alternative explanation of the irrational habits is that they may arise from twinning modes with four irrational twinning elements. These modes, which do not obey the classical orientation relationships associated with deformation twinning, have been shown to arise as the result of double twinning processes in magnesium,22 but may also describe a simple shear on an irrational plane in an irrational direction. Indeed double twinning processes in bcc

Jan 1, 1963

By M. Bevis, A. G. Crocker

A. G. Crocker and M. Bevis (Battersea College of Technology)— Richman and Richman and conard17 have recently published the very interesting results of their studies on the plastic deformation of Fe-Ni-C martensites and of an Fe-5 wt pct Be alloy. Other work on the range of Fe-Be alloys containing between 16 and 27 at. pct Be has also been reported by Richman." One of the fascinating features of this work is that the materials investigated deform primarily by means of twinning and that several twinning modes are operative in addition to the well-established (112 ) mode of bcc materials The composition planes of these unusual twins were determined using a single-surface analysis and reported as (0131, "{045)" or "{089)", and "{2,3,10)" or "(127)". (It is now thought1' that the "{0,1,13)" habit reported for the Fe-Ni-C alloys'' is more likely to be near "{127)". Although the full twinning elements of these unusual twinning modes could not be determined directly from the experimental results, the authors attempt to deduce the elements by considering twin intersectionslQ and by using the projection technique of Jaswon and Dove.' The basic assumption of their approach is that the (013) habits are truly rational planes but that the other habits are irrational and merely approximated to by the indices quoted above. They thus deduce that the twinning mode describing the (013) habit is either Type I or compound and that the modes describing the other habits are Type 11. This deduction must however be false as all twinning modes in cubic structures obeying the classical orientation relationships of deformation twinning must be compound. Type-I and Type-I1 modes can occur in all of the other crystal systems (indeed in the triclinic system compound modes are not allowed), but in the cubic system only compound modes can arise. This fact, which does not appear to be well-known, fol- lows immediately from the relations between the four twinning elements defining a twinning mode. Thus for a Type-I mode which is uniquely defined by the rational twinning elements K1 = hi and tj2 = vi (i = 1, 2, 3), the Kz qd 771 elements are given by: where the summation convention of the tensor calculus has been adopted. For cubic materials the metrics cij Iand cij reduce to the unit tensors 6ij and 6ij so that we have It is clear from these equations that both ki and ui must take on integral values; i.e., Kz, and ql must be rational, if hi and vi are integers, i.e., if K1 and 77~ are rational. Thus for cubic materials a Type-I mode must degenerate into a compound mode and the same result also arises for Type-II modes. The apparently irrational habits observed by the authors can thus not be explained in terms of Type-I1 twinning if the classical laws of deformation twinning are to be obeyed. An alternative explanation of the irrational habits is that they may arise from twinning modes with four irrational twinning elements. These modes, which do not obey the classical orientation relationships associated with deformation twinning, have been shown to arise as the result of double twinning processes in magnesium,22 but may also describe a simple shear on an irrational plane in an irrational direction. Indeed double twinning processes in bcc

Jan 1, 1963

By J. Warner, M. J. Marcinkowski, B. Cullen, T. Prevender, J. Mcllwain, T. Carnahan, J. Pahlman, J. Demel, J. Munford

The following analysis was an outgrowth of a midterm examination given by one of the authors (M.J.M) in a course entitled Metallurgy 541 "Applications of Dislocation Theory'' at Iowa State University. Fig, l(a) shows the three-layer sequence of atoms lying in the (111) plane which characterizes the fully ordered AB3 fcc crystal, i.e., LI2 type. If any two-layer sequence of close-packed planes is constructed from Fig. 16)' the structure would be hcp of the DO,, type. Consider for convenience that the circled atoms lie in the plane of the drawing while those shown square and triangular lie immediately above and below the plane of the drawing, respectively. It has already been shown' that if a Shockley partial dislocation is passed over the plane of the paper, then the square atoms in Fig. 1(a) are displaced from their original positions as shown by the arrows in Fig. l(b). Not only is an intrinsic fault produced but the crystal is simultaneously disordered across the slip plane. In particular, 2AB bonds are converted to 1AA and 1BB bonds when referred to the area outlined by the solid line in Fig. 1. If, on the other hand, a Shockley partial is allowed to pass immediately above and immediately below the plane of the paper so as to displace the atoms in opposite directions as shown in Fig. l(c), an extrinsic fault is producedZ and twice the amount of disorder is introduced into the crystal as compared to the dislocation-produced intrinsic fault, if only broken first-neighbor bonds are counted. If an intrinsic stacking fault is produced by removing a close-packed plane of atoms in Fig. l(a) and displacing the two adjacent planes by 1/3a0[111], no wrong nearest-neighbor bonds are produced. Similarly, if an extra half plane of atoms with the same arrangement as any of those shown in Fig. l(a) is inserted between any two planes in the same figure, then an extrinsic stacking fault is produced in which once again no wrong nearest-neighbor bonds are produced. The latter two faults are bounded by Frank partial dislocations. Since, at least in the alloy CU3AU,3 nearly all of the ordering energy resides in the first nearest-neighbor interactions, intrinsic and extrinsic stacking faults and associated APB's of the Frank type are expected to have significantly lower energy than those of the Shockley type in CusAu in particular and quite likely in L1, and DO19 type alloys in general. Also, because of the higher degree of disorder plus loop interaction

Jan 1, 1968

By J. W. Halley, T. S. Washburn

Rimming steels derive their name from their action during solidification in the molds. As a result of incomplete deoxidation, gas is evolved during freezing, and the metal has a characteristic rolling action. The metal rises along the mold walls and descends in the center of the ingot. This action keeps the top of the ingot open and the advancing rim of solid metal can be seen. The rim grows until the rolling action is insufficient to prevent the top of the ingot from freezing or until the action is stopped by capping the ingot with a heavy plate. The violence of the reaction and its characteristics, such as growth or drop in the molds, are determined by the composition, the furnace practice, and the deoxidation in the ladle and in the molds. Though rimming steels represent a large proportion of the amount of plain carbon steel made, they have received comparatively little attention in the technical literature. The manufacture of rimming steels has been described by Hibbard,1,2 Fleming,3 Pierce4 and Jackson.5 The reactions occurring during rimming have been considered from the theoretical point of view by Chipman and Samarin.? The structure of rimmed-steel ingots has been discussed by Nead and one of the present authors6 Meyer: in studying segregation, investigated the distribution of carbon, sulphur and phosphorus in rimmed-steel ingots by analyzing the rim and core of blooms. In their studies of segregation, the Joint Committee of the Iron and Steel Institute and the British Iron and Steel Federation9 studied distribution in one billet and one ingot of rimmed steel. A detailed study of the distribution throughout the ingot has not been published. The present investigation was undertaken to determine accurately the distribution of carbon, manganese and sulphur in normal rimmed ingots and the general distribution of other common elements present. The study included some work on the effect of pouring conditions and furnace practice on the distribution, though there is still much to be done in this direction. The structure of a rimmed ingot that has been split by dynamiting and a schematic diagram of the zones in the ingot are illustrated in Fig. 1.

Jan 1, 1938

By J. W. Halley, T. S. Washburn

Rimming steels derive their name from their action during solidification in the molds. As a result of incomplete deoxidation, gas is evolved during freezing, and the metal has a characteristic rolling action. The metal rises along the mold walls and descends in the center of the ingot. This action keeps the top of the ingot open and the advancing rim of solid metal can be seen. The rim grows until the rolling action is insufficient to prevent the top of the ingot from freezing or until the action is stopped by capping the ingot with a heavy plate. The violence of the reaction and its characteristics, such as growth or drop in the molds, are determined by the composition, the furnace practice, and the deoxidation in the ladle and in the molds. Though rimming steels represent a large proportion of the amount of plain carbon steel made, they have received comparatively little attention in the technical literature. The manufacture of rimming steels has been described by Hibbard,1,2 Fleming,3 Pierce4 and Jackson.5 The reactions occurring during rimming have been considered from the theoretical point of view by Chipman and Samarin.? The structure of rimmed-steel ingots has been discussed by Nead and one of the present authors6 Meyer: in studying segregation, investigated the distribution of carbon, sulphur and phosphorus in rimmed-steel ingots by analyzing the rim and core of blooms. In their studies of segregation, the Joint Committee of the Iron and Steel Institute and the British Iron and Steel Federation9 studied distribution in one billet and one ingot of rimmed steel. A detailed study of the distribution throughout the ingot has not been published. The present investigation was undertaken to determine accurately the distribution of carbon, manganese and sulphur in normal rimmed ingots and the general distribution of other common elements present. The study included some work on the effect of pouring conditions and furnace practice on the distribution, though there is still much to be done in this direction. The structure of a rimmed ingot that has been split by dynamiting and a schematic diagram of the zones in the ingot are illustrated in Fig. 1.

Jan 1, 1938

By Thomas Darlington

The obligation of an employer to the State requires certain things of him as matters of good citizenship: for instance, that his workmen shall have a living wage, that child labor shall not be employed, that injuries from accidents shall not make workmen a charge upon the State, and that the laborer's children shall have opportunity for education and to become good and useful citizens. Affairs of this kind are not taken up as philanthropy, for the officials of a corporation or a large manufacturing concern may not feel at liberty to spend the funds of their company as prompted simply by motives of kindliness; but they may spend company money on such matters because it is good business. For years, the poisonous effects of lead, phosphorus, and dust have been emphasized in books on industrial hygiene and their elimination has been urged; but the more important and everyday physiology of the workman himself has been neglected. Part of my object in writing this paper is to show how our knowledge of physiology may be applied to working conditions in everyday life. In the interest of industrial laborers, accident compensation laws have been enacted in 33 States. This has been carried forward rapidly, because it has been shown that it pays both employer and employee. A further step is the recognition of sickness and disablement independent of accidents, not only because of their immediate cost to the worker and to the employer, but because continued efficiency in work and business depends largely upon health. Some measure of the importance of health in industry can be gained by the knowledge that records kept by some companies which now make this the subject of careful inquiry show that the time lost by employees, through illness, is several times as much as that lost as the result of industrial accidents. It is true that accidents frequently result in permanent disability or death, but it is equally true that illness is also a cause of permanent disablement or death. Thus the chief difference is that the loss to the employee through accidents occurring in the course of his employment is now generally recognized as a cost

Jan 1, 1918

By Charles R. Simcoe

The stress-strain curves in the microyield region for various Fe-C solid solutions shown by Davies and Ku are typical examples of parabolic curves defined by the expression a = kEn 111 These data, when replotted on log-log coordinates, as shown in Fig. 9, exhibit three essentially parallel straight lines. It is apparent that carbon increases the flow stresses, but does not affect the exponent n. In other words, the only factor in Eq. [1] affected by in in carbon content is the constant k. As Eq. [1] is written k is the stress at a strain of 1.0. This is unsatisfactory for examining data in the microyield region. Therefore, the equation can be altered to the form: to permit the use of the authors' microyield stress at a strain of 10-6 as k. Extrapolating the curves in Fig. 9 to a strain of 10-6 gives stress values of 2000, 3200, and 5400 psi for 0.008, 0.014, and 0.02 pct C, respectively. These values do not agree exactly with the authors' measured values, but this will not affect the following discussion. The effect of carbon content on the slopes of the stress-strain curves shown in Fig. 2 of the paper by Davies and Ku can be analyzed by differentiating Eq. [2] with respect to strain. Thus: where n is always less than 1.0. Since n is essen- tially constant as a function of carbon content for the data under discussion, the slopes of the stress-strain curves depend only on k and E. If the slopes are examined at various selected Plastic strains. i.e., 10-6, 10-5, and so forth, it follows from Eq. [3] that the dif-ferent slopes for the different carbon contents depend only on the different values of ke=10-6. Thus, the larger ke=10-6, the steeper the linear stress-strain curve will rise with increasing plastic strain. This

Jan 1, 1969

By Royal B. Jackman, Carle R. Hayward

Two comprehensive papers have appeared regarding the forms of copper that occur in smelter slags, one by Frank E. Lathe1 and the other by C. G. Maier and G. D. Van Arsdale.2 These authors comment on other published results and draw conclusions from their own investigations. The development of X-ray examination of minerals and improvement in high-power microscopic methods make it possible today to get additional evidence by means that were not available to earlier investigators. The present work was confined to reverberatory slags obtained from five different plants. Some definite conclusions were reached regarding the forms of copper present in these slags. In most cases these agree with some of the findings of Maier and Van Arsdale but new methods of attack were used in the investigation. Conclusions of Previous Investigators Various important conclusions reached by previous investigators are summarized in the following paragraphs, arranged chronologically. William A. Heywood:3 Slag losses increase with grade of matte but with the same grade of matte losses decrease as the acidity of the slag increases. Lewis T. Wright:' Slag losses are only partly due to prills of matte. It is suggested that part of the copper is dissolved in the slag. J. Parke Channing9 A considerable part of the copper enters the slag as silicate or oxide and not as sulfide. C. A. Grabill:6 Slag losses are both physical and chemical. Physical losses, due to poor settling, gas flotation and slight differences in specific gravity, are small under normal conditions. Chemical losses may- be due to formation of oxides or to solution of metals and sulfides. The last is considered the most important. John W. James:' The copper in converter slag is largely the oxide and as such enters the reverberatory slag when converter slag is added to the charge.

Jan 1, 1934

By Edward Keller

Someone some time ago remarked that some chemists still insist on telling us how to determine copper by the electrolytic method. The writer must confess that he believes that everything is not known definitely as yet as to how the exact amount of copper is determined in such material as purest commercial electrolytic copper. Some of us are not yet convinced that the pure copper atom is at all times deposited from an acid solution and that no oxygen or hydrogen will, under certain conditions, accompany it. Difficulties with impurer material are frequent, but erroneous results are not always apparent, since these do not speak so readily for themselves as those in the first case. By this is meant that if a chemist finds 100 per cent. of copper in electrolytic copper it is pretty certain that he perceives the result to be wrong, while if he finds 0.1 per cent. of copper too much in a very impure material he is far more likely to be unconscious of his error. These, in a wide experience, are frequent happenings and the writer has always looked with interest to publications on this subject. In turn, he feels justified in giving to others a few of his own observations. Up to a few years ago there were two methods of electrolytic copper assay in technical use, which had in common, that the amount of copper deposited on the cathode did not exceed 2 g., and they differed in that, for the one a large sample1 (20 to 80 g.) was taken from the general sample by a splitting device, dissolved, and from the solution a small portion (to contain 1 or 2 g. of copper) measured out for the electrolytic deposition; in the other method the copper was determined, generally in 1-g. portions of the separated coarse and fine portions of the sample, all of which passed a 16 or 20-mesh screen, being accomplished by a 40-mesh screen,

Jan 1, 1914

By L. S. Darken

In the study of reactions occurring in liquid iron, alone or in contact with a liquid oxide or slag phase, it has been found that the experimental data over a limited range of concentration can in some cases be represented satisfactorily by the simple equilibrium expression where (P) denotes the concentration of a product and (R) the concentration of a reactant in the reaction r1R1 + r2R2 + • • • D P lP1 + P 2P2 + • • • Some of the reactions for which it holds are listed in Table 1. For others, however, the simple equation apparently does not hold. This has been attributed to an improper method of expressing concentration (for instance, weight per cent instead of mol fraction); or it has been supposed that the solutions are not ideal in the sense that the activity of a component is not proportional to its true mol fraction. But it may be that the problem has been oversimplified by neglecting some molecular species actually present; that is, by considering only the ostensible simple components and thus leaving out of account possible compound formation. It is the purpose of the present paper to point out how, in a group of related cases, a reasonable consistent assumption relative to the presence of a compound makes it possible to express the experimental data satisfactorily by the simple equilibrium expression when this compound is taken into account, and to bring into harmony data referring to different reactions in liquid iron. There are several a priori reasons for believing that solutions in liquid iron should not deviate far from ideality, provided that the concentration of solute is not too great and is expressed in proper terms. The factors that commonly lead to nonideality in systems at ordinary temperature— as ionization or the occurrence of polar and nonpolar molecules—are presumably less effective in inetal and in slag systems at high temperature. Again, the type of equation commonly used to express the value of

Jan 1, 1940

By L. S. Darken

In the study of reactions occurring in liquid iron, alone or in contact with a liquid oxide or slag phase, it has been found that the experimental data over a limited range of concentration can in some cases be represented satisfactorily by the simple equilibrium expression where (P) denotes the concentration of a product and (R) the concentration of a reactant in the reaction r1R1 + r2R2 + • • • D P lP1 + P 2P2 + • • • Some of the reactions for which it holds are listed in Table 1. For others, however, the simple equation apparently does not hold. This has been attributed to an improper method of expressing concentration (for instance, weight per cent instead of mol fraction); or it has been supposed that the solutions are not ideal in the sense that the activity of a component is not proportional to its true mol fraction. But it may be that the problem has been oversimplified by neglecting some molecular species actually present; that is, by considering only the ostensible simple components and thus leaving out of account possible compound formation. It is the purpose of the present paper to point out how, in a group of related cases, a reasonable consistent assumption relative to the presence of a compound makes it possible to express the experimental data satisfactorily by the simple equilibrium expression when this compound is taken into account, and to bring into harmony data referring to different reactions in liquid iron. There are several a priori reasons for believing that solutions in liquid iron should not deviate far from ideality, provided that the concentration of solute is not too great and is expressed in proper terms. The factors that commonly lead to nonideality in systems at ordinary temperature— as ionization or the occurrence of polar and nonpolar molecules—are presumably less effective in inetal and in slag systems at high temperature. Again, the type of equation commonly used to express the value of

Jan 1, 1940

By A. Ahmadieh, J. E. Dorn, Jack Mitchell

A detailed investigation of the disloccrtion mechanisms controlling prismatic, slip in a solid solutions of magnesium containing up to 15.9 at. pel Li revealed that low-temperature prismatic slip is controlled by the Peicrl's mechanism for all alloy compositions. At higher temperatures slip in the 7.9 at. pet Li alloy was found to follow the diclates of the cross-slip mechanism from basal to prism planes, while the higlier-lilhium alloys exhibited an athermal dejormation process which might be due COARSE-GRAINED polycrystalline aggregates of distilled magnesium exhibit very limited ductility at low temperatures.' The ductility of polycrystalline magnesium, however, is much improved by solid-solution additions in excess of about 8 at. pct to shot-range ordering. The major effect of lithium additions on the low-temperature Shear] stress. for prismatic slip appears to be due to its efftct in lowering the Peierl's stress whereas (1 increase in the shear stress with increased lithium conlent at higher temperatures might he due to short-range order strengthening. Additions rip to 7.9 (at. pel Li appear to have only minor effects on the slackiug-jaidt energy. Li.2 Although the relative amounts of basal slip and twinning are not materially altered by such alloying, a substantial change takes place in the relative amounts of prismatic slip. Whereas prismatic slip is negligible and limited to regions of high stress concentrations in the vicinity of the grain boundaries in pure magnesium, extensive prismatic slip over entire grains occurs in the higher lithium content alloys. Furthermore, as the lithium content is increased above 8 at. pct, the flow stress for polycrystalline aggregates decreases. Comparison of the single-crystal data on pure magnesium for basal slip by Sheely and Nash3 and those for prismatic slip by Flynn, Mote, and Dorn4 indicates that the critical resolved shear stress for prismatic slip is much above that for basal slip.

Jan 1, 1965