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By H. A. Lequear, J. D. Lubahn

A sudden change from one constant strain rate to another during a tensile test causes an unusual transient in aluminum alloy 61ST. A sudden change from one constant stress to another during a creep test does not produce an unusual transient in this material. A specially devised test shows that the nature of the previous steady-state conditions, which the sudden change disturbs, is one of the factors affecting the transient behavior. Some of the observations may be explained in terms of strain aging. USUALLY a sudden change during a tensile test from one constant strain rate to another causes a small, abrupt vertical shift from one stress-strain curve to another, parallel one. This behavior is apparently characteristic of all metals at very low temperatures and of many metals for wide ranges of temperature. It is illustrated in Fig. 1 for some early data on 61ST tested at — 195oC, and in Fig. 2 for some recent data on copper at room temperature. The greater accuracy of the results of Fig. 2 over previous ones' is due to the equipment shown in Fig. 3. Three levers apply the bulk of the load, while the changes in the small remainder load are indicated sensitively by a low capacity load scale. Refs. 2 and 3 describe the recording equipment. A test like those in Figs. 1 and 2 provides the information necessary to determine the rate sensitizrity, n,4 of the metal. ( a log s ) ? log s n = ------------------------ ----------------------------= ( a logs e, ? log e logS2-logS1 log S2/S1 log i2 — log e1 log e2/e1 where S equals stress: e is logarithmic strain or natural logarithm of (final gage length/initial gage length);" i is strain rate or de/dt: and n is rate sensitivity, rate of change of log stress with log strain rate at a given strain, or (a log S/a log i),. Normally, the rate sensitivity, n, is positive, which means that an increase in stress causes an increase in rate. However, certain exceptions, attributed to strain aging,5 have been observed. Fig. 2 indicates how rate sensitivity values are derived from the measurements. Table I summarizes the rate sensitivity values derivable from Fig. 1. In contrast to the behavior of copper in Fig. 2, the aluminum alloy 61ST, which strain ages when tested near room temperature, exhibits an unusual transient when the strain rate is suddenly changed,' as shown in Fig. 4. Initially, there is a comparatively sudden vertical shift of the stress-strain curve in a direction corresponding to the rate change, but then the curve gradually shifts back again. The initial shift is not as sudden as might be expected, because the testing machine is unable to achieve the impressed rate change instantaneously, as illustrated in Fig. 2. The behavior shown in Fig. 4 will be referred to as a tensile transient, the word tensile implying that the behavior was observed in a tension type of test. The corresponding test, where the strain rate is maintained constant except for the sudden change, will be called a tensile transient test. A creep transient, by contrast, will be defined as a temporarily abnormal behavior in a creep transient test, where there is a sudden change from one constant load to another.' In Fig. 4, a naive look at the gradually decreasing and then increasing load after a sudden rate incre-

Jan 1, 1957

By R. N. Thurston, E. A. Nesbitt, G. Y. Chin

A general relalionship between the amount of glide shear (due to slip) and the macroscopic shape change has been developed. Since the deformation can be large, finite strain analysis is employed. In this treatnzent, the shape change is expressed by a deformation gradient matrix, F - [axi/aXj1, where X and x refer to the initial and final positions of a particle. This matrix is readily evaluated in terms of the amounl of glide shear, a , and the direction cosines of the slip-plane normal and the slip direction for a single active slip system. In the case of deformation from slip on several systems, the product F(a) of the several deformation gradient matrices is first calculated. Then, by assuming that the final configuration is reached by a long series of small shears of magnitude a, occurring more or less alternately in the several slip sys- IN problems of crystal plasticity, it is often necessary to relate the amount of glide in the operating slip systems to the macroscopic strain components. This relationship is relatively simple when only small strains are considered. In this case the separate strain contributions from several slip systems are additive. Such a procedure is incorrect in the case of large plastic deformation. To the authors' knowledge, no general treatment of the latter problem has appeared in the literature. In specific instances, Mark, Polanyi, and schmid3 have derived the relationship between glide and axial elongation during tensile pulling of a single crystal when only one slip system is active. A similar relationship for duplex slip was worked out by v. Goler and Sachs.4 Taylor and Elam5 have also studied in detail problems of large plastic deformation. Due to uncertainties as to the slip systems at the time, terns, the final deformation gradient matrix can be obtained. Mathematically, the problem is reduced to finding the limit of F(dN as N — m while a — 0 in such a way that the Product Na = 0, a ftnite conslant designatzng the accunzulated amount of shear. It turns out that this limit is simply , where F, is the matrix whose elements are the coefficients of a in the F(a) matix. Application is made of the present treatment to a fcc crystal of Perlrzalloy compressed on the (110) plane and contrained to elongate zn the [112] directzon. In addition, it is shown that one rnay readily obtain from the general analyszs the well-known formulas relating elongation, amount of glide shear, and amount of lattice rotation for crystals deforming by single and double slip under tension. however, they were mainly concerned with proving that slip occurs on {111}(110) systems in fcc metals. The present general treatment arose out of recent investigations of magnetic anisotropy in cold-worked Fe-Ni alloys6 as well as some related problems in strength anisotropy of single crystals.' Detailed application of the general analysis will be provided in the case of a Permalloy single crystal compressed on the (110) plane and constrained to elongate only in the [112] direction. It will be seen that, as expected, the small strain approximation leads to significant errors after moderate straining. It will also be shown that the present general treatment yields the formulas of Mark et al. and of v. Goler and Sachs in those specific cases. GENERAL CONSIDERATIONS Consider a homogeneous deformation in which a material point initially at moves to both positions being referred to the same set of Cartesian axes. Such a deformation can be

Jan 1, 1967

By J. S. Aronofsky

The results of polentiometric model studies and numerical computations are described. The purpose of these studies was to determine the influence of the mobility ratio on flooding efficiencies during water encroachment in petroleum reservoirs, in systems of regular well geometry. The direct line drive well pattern having relative spacing distances of one and one-half to one was investigated for water to oil mobility ratios of 10. 1. and 0.1. The results of these studies indicate that the pattern Sweep efficiency i.; very dependent upon the mobility ratio. INTRODUCTION The almost universal occurrence of water in the immediate neighborhood of oil-hearing sands lends considerable emphasis to the desirability of having a rational analysis of water encroachment into petroleum reservoirs. This problem has 1)become increasingly important with the accelerated use of water injection for secondary recovery operations. The water encroachment problem has been studied from both the theoretical and experimental viewpoints by Muskat.' He has formulated, in a precise manner, differential equations to express flow in a water encroachment system, and rigorous analytical solutions have been developed for the linear, radial, and spherical cases.' However, it becomes exceedingly difficult to solve the encroachment problem rigorously for any general two-dimensional system in which the shape of the two-fluid interface is not immediately evident from the geometry of the system. The difficulty lies in the fart that a rigorous analytical solution requires that the shape of the two-fluid interface be known simultaneously with its instantaneous posititon and with the pressure distribution on both sides of the interface. Although this paper concerns the study of the two-fluid system of oil and water. the methods described in the paper are generally applicable to other systems of incompressible and immiscible fluids in which the displacing fluid sweep-the displaced fluid down to a residual value. In each region it is assumed there is only one mobile fluid and its mobility is constant throughout the region. The Same procedure. with minor alteration, is applicable for gas injection systems provided the assumption can be made that both the displaced and displacing gases can be described by steady state formulas. For the particular two-fluid problem considered in this paper, there is a relative permeability. K, and a viscosity. p. associated with the water zone, and a different permeability and viscosity associated with the oil zone. The K/p (mobility value associated with a particular volume element of the porous medium. at any instant of time. will depend upon whether the element is ahead of. or behind the advancing interface. It is assumed that all volume elements ahead of the interface are characterized by the K/p value for oil, while all the elements behind the interface are characterized by the K/p value for water. That is. the K/p value in the oil zone is constant throughout the oil zone. and the K/p value in the water zone is also constant but different from the value in the oil zone. The symbols are defined at the end of the paper. The well pattern chosen for initial study is the direct line drive; the swept-out area at breakthrough was determined by two different methods which are described in the section on theory. These are: 1. Potentiometric analyzer 2. Numerical computation The use of the potentiometric analyzer for studying water flooding problems is adequately described in the literature, particularly for cases where the mobility in the water zone is assumed equal to the mobility in the oil zone." ' 5

Jan 1, 1952

By D. A. Flanagan, B. L. Landrum, P. B. Crawford, B. C. Norwood

Herern is described a heat conduction model which has been developed to predict the pressure distribution within a reservoir being subjected to rrnsteady-state depletion. Although potentiometric models have been widely used to study reservoir pressure distribution, their application is limited to the study of steady-state cases. Electrical analyzers may be used to study unsteady-state phenomena, but their application and simulation have certain limitations. Much of the now accepted theory of unsteady-state fluid flow in porous media has evolved from previous heat conduction knowledge. An analogy between the flow of fluid in an unsymmetrical reservoir and con-duct ion of heat in a similarly shaped unsymmetrical metal plate is made to show adaptability of the hear conduction principle to transient reservoir cases. A description of the model and necessary instrumenrarion is included. Data show influence of well location on pressure distribution during unsteady-state deple[ion. Application of results is made to a hypothetical reservoir and to a reservoir located in an irregular aquifer. INTRODUCTION Development of methods for predicting behavior of petroleum reservoirs has resulted partially from adaptation of electrical and thermal flow concepts to the flow of fluids through porous media. Extensive investigation of electrical and thermal flow problems has resulted in mathematical solutions applicable to many reservoir problems. The relative ease of measuring electrical flow has brought wide acceptance of the use of the potentiometric model to study certain field problems. Potentiometric models are restricted to the study of steady-state conditions because of the instantaneous response of electrical flow to changes in the applied potential. The electrical reservoir analyzer has been one of our most useful instruments for studying certain phases of unsteady-state behavior1. Other than approximation techniques, no method exists for determining pressure distribution in an irregular reservoir during primary depletion. Heat flow, like fluid flow, is inherently transient. The model described here was developed to use this transient nature of heat flow, measurable in the laboratory, to simulate transient flow of fluids in the porous medium of the reservoir above the bubble point. A metal plate shaped like the reservoir to be studied was heated by a "well" source. Temperature increase in the plate is analogous to pressure decline in the field if the field is being depleted, or pressure increase if fluid is being injected. This study is intended to determine the feasibility of using the transient nature of the heat flow to study the transient behavior of fluid flow. It is hoped that this new technique will aid in the understanding of one of the more complex phases of reservoir engineering. THE FLUID FLOW-HEAT CONDUCTION ANALOGY The similarity of the equations which describe the flow of fluids through a porous medium and the conduction of heat through a solid is well known2. Rate of flow of fluids is given by Darcy's law3. while the rate of flow of heat is given by Fourier', (I,, - KA 4T........(2) Combining Eq. 1 with the equation of continuity for a compressible liquid", i.e.,results in Expressing y in terms of the compressibility, i.e., pr = peey ,..........(5) and by expanding the exponential and neglecting higher orders of cp one can obtain

By R. Schuhmann, G. W. Powell

The concept of local equilibrium is examined and, in particular, the applicability of the concept to two-phase binary diffusion couples is discussed. It is concluded that, if binary solid solutions are treated thermodynamically as ternary solutions, vacancies being the third component, then recent experimental observations of nonequilibrium interface compositions (i.e., compositions different from the phase diagram values) are consistent with a state of complete dynamic equilibrium at the interface. CLASSICAL approaches to diffusion and to other irreversible processes often utilize a postulate of "local equilibrium". That is, one assumes even in the presence of gradients, fluxes, and time changes of properties, a) that the Second Law can be formulated locally, and b) that thermodynamic equations of state among intensive properties are identical with those for equilibrium phases. A direct consequence of this assumption, for example, is that one would calculate the total entropy of a nonequilibrium phase simply by integrating the entropy density (eu per unit volume) over the volume of the phase, assuming that entropy density is the same function of energy and particle density as for equilibrium phases. In the study of diffusion and of diffusion-controlled phase transformations, metallurgists take this concept of local equilibrium for granted and utilize it automatically. In fact, experimental evidence of all kinds is overwhelming that "local equilibrium" is a valid limiting law, approached more and more closely as gradients and rates of change approach zero. On the other hand, we have neither experimental nor statistical thermodynamic proof that this principle of "local equilibrium" should remain rigorously valid at high gradients and for rapid processes. Theoretically, in fact, one would expect deviations because interactions between adjacent volume increments of material affect the evaluation of entropy. Also one observes experimentally structural and small energetic differences between equilibrium and nonequilibrium phases. The purpose of this paper is to present a thermodynamic framework for the study and correlation of deviations from strict local equilibrium in isothermal diffusion and related processes. This procedure, in effect, preserves the principle of local equilibrium by thermodynamically assigning the deviations from static equilibrium properties to a defect component. Although this theory is entirely phenomenological, the possibility does exist of correlating the theory with experimental observations of defects under favorable circumstances. The most immediate application appears to be to the equilibria at the interfaces in two-phase binary diffusion couples. A recent pertinent work by Eifert et al.1 has shown that the concentrations of aluminum in the a(fcc) and B(bcc) phases at the 0-8 interface in Cu:Cu-12.5 wt pct A1 diffusion couples are greater than those given by the phase diagram. It is postulated by these authors that the supersaturation of the o phase at the interface provides the driving force for the a-to-B lattice transformation; the excess free energy of the a phase, ?Gaxs, arising from the greater-than-equilibrium aluminum concentration is about 3 cal per g-atom. On the basis of the schematic free energy-composition diagram shown in Fig. 1, Eifert et al. concluded that the thermodynamic situation at the interface is one of the partial equilibrium; that is, = for the more mobile aluminum whereas will be reexamined in the latter part of this paper. THERMODYNAMIC PROPERTIES OF DEFECTS A rigorous analysis of the thermodynamics of defects requires an added degree of freedom in the Phase Rule sense, because the standard formulations of solution thermodynamics (partial molal properties of components, free energy minimization, equality of chemical potentials, and so forth) involve the implicit

Jan 1, 1970

By F. F. Craig

A series of both welter and gas puttern Hoods was made in the laboratory to study the oil recovery performances of .such operations. These tests were contlrrctt~tl on consolidated sandstone models, using oil. water, and gas. The model floods were scaled to reprotlrrce field performance under gas arid water five-spot injection. X-ray shadowgraphs permitted observation of the gross fluid movement within the models. A method was developed for applying the mobility ratio concept to water flooding and dispersed gas drives in a five-spot well pattern. The area1 sweep efficiency. tit breakthrough for dispersed gas drives is much higher than previorsly expected, Iying in the range of 50 to 100 per cent. A method is presented for predictitig the water-oil ratio performance of five-spot pattern water flood., in uniform sands. This method is verified experimentally for the cotidition of 120 free gas initially present and for va1ues of gas saturation normally encountered in fields following depletion operations. Prodrrction perfort?zut~cc for pattern gas injection is also predictable by this method. INTRODUCTION In field pattern hater flooding or dispersed gas injection operations, the displacing fluid (water or gas) is injected and oil is produced through wells which are, area-wise. small openings in a large container or rescrwir of oil. As a result, not all of the area between the injection and producing wells is necessarily contacted by the injected fluid by the time it first reaches the producing wells. The question arises in predicting oil recovery. as to what traction of the pattern area involved is contacted by either the injected water or gas due to the relative position of the injection and producing wells. This is the areal sweep efficiency. It is also desirable to know how well arrangement affects the oil production performance. A solution to this problem has been attempted by many means. Mathematical analysis¹,²,³, and electrolytic models', have been used to establish a breakthrough areal sweep efficiency of 73 per cent for a five-spot pattern in which the ability of the oil to flow ahead of the invading fluid is equal to the ability of the invading fluid to flow in the invaded zone. All of these studies simulate only one of many field conditions. Improved studies of areal sweep efficiency at breakthrough were made using the fluid mapper5, poten-tiometric models" and X-ray shadowgraph techniques. In these it was possible to study the effect of variations in mobility of the injected and displaced fluids, and so to cover a wide range of field conditions. The limitation of these studies is that, with these models, it was not possible to simulate the saturation gradient behind the flood front when oil is displaced by gas or water. In the most recent published technical paperS on the subject, a method was presented for predicting the oil recovery performance after breakthrough in a five-spot pattern water flood. The method involved correlations which were obtained experimentally using miscible fluids. One limitation of this work was that a saturation gradient, usually found in immiscible fluid displacement, was absent in these studies. Also the laboratory studies did not cover the situation of a water flood following oil recovery by depletion drive. as is the situation in most field water floods. The tests reported in this paper were made using oil. water, and gas, thus eliminating the simplifications of former studies. Also reported are laboratory studies on

Jan 1, 1956

By S. S. Shen, M. J. Pool, P. J. Spencer

Heats of solution of silver and copper in dilute Ag-Cu-Sn alloys at 720°K have been determined using a liquid metal-solution calorieter. Values of the se2f-interaction coefficient n AgAghave been calculated at constant copper concentrations and n Cu Cuhas been determined at constant silver contents. The reliability of the experimental data is shown by the very good agreement between nCujAg and ij &$; these interaction coefficients have experimental values of -9100 and - 9590 cal per g-atom, respectively. Certain solution models are shown to be inadequate for prediction of solute interaction coefficients in dilute Ag-Cu-Sn alloys. In a previous publication' the results of a thermody-namic study of dilute Ag-Au-Sn alloys were presented. The present work represents the continuation of a program to investigate dilute alloys of the noble metals with tin and in particular is concerned with solute interactions in the Ag-Cu-Sn system. By determination of the magnitude and sign of the various interaction coefficients in dilute alloys it is possible to gain some understanding of the different types of solute-solute and so lute-solvent bonding changes that occur as the solute concentrations are varied. Hence systematic studies of alloys with similar physical characteristics as regards size, structure, electronegativity, and so forth, of their components can contribute a great deal to present theoretical knowledge of solutions. The recent definition of an enthalpy interaction coefficient, 11, by Lupis and Elliott2 is of particular value in calorimetric studies such as the present one: where j and i are solutes and s is the solvent; Si is the relative partial molar enthalpy of component i and x represents the mole fraction of solute or solvent. Values of ?Hi can be obtained directly by solution calorimetry and data for n are thus easily determined, often with a high degree of accuracy. ?Hi is related to the relative partial molar enthalpy at infinite dilution, ?Hi and to the enthalpy interaction coefficients by the expression: ?Hi?Hi + X;nz+ ... [2] The aim of the present work was to determine the self-interaction coefficients n AgAgand 178: in alloys of different compositions and also to establish values for n Agcg| and ncuAg. Since it is a thermodynamic requirement (resulting from the Maxwell-type relationships which can be applied to partial molar properties) that nAgcu and ncuAg should be equal, a further aim of this study was to demonstrate the agreement between experiment and theory. EXPERIMENTAL A description of the liquid metal-solution calorimeter used in this research has already been published,3 and no further details of its construction and operation will therefore be given here. Copper supplied by the American Smelting and Refining Co. was indicated by them as being 99.999 pct pure, and the silver obtained from A. D. Mackay, Inc., was also quoted as being 99.999 pct pure. A solvent bath consisting of between 70 and 80 g of 99.99 pct pure Sn was used for each series of experimental drops. Its weight was accurately determined and the appropriate amounts of copper or silver were added to give alloys of the desired composition. Approximately 0.00125 g-atom additions were used for determinations of the heat of solution of silver in the bath, while, for copper, specimens consisting of approximately 0.0015 g-atom were used. The heat capacity of the bath was determined at regular intervals during a series of drops using tin or tungsten calibration samples. The heats of solution of silver and copper in pure tin were first determined as a function of their concentration in order to establish the self-interaction coefficients 7AgAg and ncucu Alloys containing a constant 0.01, 0.02, 0.03, and 0.04 mole fraction of copper were then used to study 17:: in alloys of different copper content, while alloys of the same mole fractions of silver were used to determine equivalent data for 178: at constant silver concentrations. The composition of the bath was held at the desired copper or silver concentration by making calculated additions of the appropriate solute throughout the experiment. From the limiting values of ?HAg in the constant copper content alloys it was possible to study ?HAg as a function of xCu and hence to determine 42:. A similar analysis of the re, values permitted calculation of nAgcu. Heat content and heat capacity data from Hultgren et al* were used to calculate heat of solution values from the measured heat effects at the experimental temperature of 720°K. RESULTS AND DISCUSSION Determinations of ?HAg. A preliminary investigation of the heat of solution of silver in pure tin at 720°K was first made in order to establish the value of nAgAg before additions of copper were made and also to compare the value of ?HOAg(l) with that obtained in the previous study of Ag-Au-Sn alloys.' Then the heat of solution of silver in Cu-Sn alloys was investigated as a func-

Jan 1, 1970

By J Price, M. R. Geer, H. F. Yancey

COAL mine operators recognize coal as an abrasive material, because the wear of drilling, cutting, and conveying equipment is reflected as a cost item for replacement of parts. Similarly, industrial consumers of coal experience abrasive wear on all coal-handling equipment. Operators of pulverized fuel plants are doubtless most keenly aware of the abrasiveness of coal, because under the high contact pressures developed between coal and metal in pulverizers, abrasive wear is increased many fold. Moreover, experience in operating pulverized fuel plants has demonstrated that some coals are much more abrasive than others. Hardgrove' stated that maintenance costs entailed by the wear of grinding elements is often a more important variable than the cost of the power required to pulverize different coals. Craig2 also reports that one coal may cause pulverizer parts to wear several times faster than another. It is apparent, therefore, that those concerned with pulverizing coal could profitably employ a method for estimating the abrasiveness of different coals, just as they utilize standard tests for thermal value, grindability, and ash-fusion temperature to assist in selecting the most suitable and economical coal to use in a particular plant. The objective of this investigation was to develop a test procedure that would be suitable for general use in estimating the abrasiveness of coals. However, few, if any, of the standard tests now used for evaluating the properties of coal are the product of a single investigation or the result of a single investigator's efforts. Rather, in each case, a testing procedure was devised by one investigator, used by others on a wider variety of coals, and finally refined completely as the result of the joint efforts of a number of interested people. Thus, the test procedure for estimating abrasiveness developed in the course of this work may not be refined sufficiently in its present form for general use, but it may serve as the starting point from which an acceptable test procedure can be developed. The method has been used thus far on only about a dozen coals, and there has been no opportunity to attempt a correlation between experimental results and actual plant experience. Only wider use of the procedure by other investigators and correlation with plant experience can determine to what extent the method will have to be modified to render it suitable for general application. Test Method Although the literature contains no record of an attempt to devise a method for estimating the abrasiveness of coal that could be used industrially, several investigators have tested properties of coal that are closely related to its abrasiveness. The abrasiveness of a material generally is considered to be related to its hardness, and hardness tests for coal have been employed by Heywood,' O'Neill," and Mathes. Also, the resistance of coal to abrasion, a property that presumably is related to the abrasiveness of coal, was measured by Heywooda and by Simek, Pulkrabek, and Coufalik.2 11 these investigators tested only individual pieces of coal. Since coal is a heterogeneous material having components of varying properties, tests of this type can yield results having little more than academic interest. Only a test method that utilizes a representative sample of coal can give results that are useful industrially. The abrasion tests used for various other materials have been considered for adaptation to testing the abrasiveness of coal. The tests used for metals,7-9 paving and flooring,'" and rubber," cannot be used because coal is not sufficiently abrasive.~ The present experimental work was begun before World War II and was conducted by three research fellows"'" working under a joint agreement between the University of Washington and the Bureau of Mines. After a great deal of preliminary work with a variety of apparatus and materials, a test procedure was developed which consisted of rotating a test disk 2Yz in. diam in a steel mortar containing the coal sample. The shaft carrying the test disk at the lower end and a 100-lb load on the upper end was free to move vertically. The bed of coal in the mortar was kept fluid by low-pressure air admitted through a port near the bottom of the mortar. Measurable wear on an Armco iron disk could be obtained in this test procedure, but, despite extensive efforts to eliminate them, several major disadvantages remained in this test method. First, with most coals the amount of wear on the iron disk did not exceed a few milligrams. Second, a single type of disk was not applicable for all coals. A smooth iron disk gave satisfactory results with both bituminous and sub-bituminous coals, but hardly any wear with anthracite or coke. A disk having studs or projections gave more satisfactory abrasion losses with anthracite and coke and presented no operating difficulties with free-burning bituminous and sub-bituminous coals. It could not, however, be used with caking coals because these coals formed a

Jan 1, 1952

By J. S. Aronofsky, J. P. Heller

This paper presents a mathematical analysis of the fluid mixing which occurs during flow through porous media. The analysis is based on the well-known diffusion equation with mass transfer term. It is pointed out that the use of this equation is justified by a single general assumption which does not specify any particular mechanism for the mixing process. Formulas are given for tracer fluid concentrations for two different boundary and initial conditions. Calculated numerical values compare closely with some published results of experiments in which no viscosity or density difference existed between displaced and displacing fluids. INTRODUCTION A phenomenological theory of the mixing and diffusion process is presented for the flow in a porous medium of two miscible liquids of equal viscosity and density. This is based on the classical diffusion equation which has been used to explain such processes as Brownian motion and heat conduction. More recently, this same differential equation has been derived (in a manner analogous to the work in this paper) for the problem of heat transfer during fluid flow in porous media.' The purpose of this paper is to show that the available experimental evidence justifies the use of this simple diffusion equation. The recent data of Koch and Slobod' and of von Rosenberg' are used to test this diffusion model by comparing concentration curve shapes and calculating "effective diffusion coefficients". The same differential equation for miscible displacement, as well as some experimental confirmation, has been published in Japan by K. Yuhara,4 and recently in this country by Day.5 Yuhara arrives at his con-clusions through analogy with turbulent diffusion, de- scribing the microscopic velocities in terms of "eddy motion" — although unlike the ordinary eddies of hydraulics. Day proceeds directly from Scheidegger's6 concept of the dispersion of velocities. After a very clear description of Scheidegger's theory, he applies it to calculate the motion first of a drop and then of a thin layer of brine into a bed of sand. For the latter case, Day derives and solves the same differential equation as Eq. 1. In our presentation no detailed assumptions are made as to the mechanism of displacement. In fact, several microscopic processes may well be involved—the only general assumption made is that their cumulative microscopic effect may be described by the addition of a second-order term to the differentirl equation of continuity. DERIVATION OF EQUATIONS Let us consider the displacement in one spatial dimension of Liquid A from a sample of porous media by Liquid B. A and B are assumed completely miscible and of the same viscosity and density. Both fluids are also assumed to be incompressible and it is specified that the total flow is the same for any cross section. It is evident that the rate at which Liquid B would be carried across such a section would be given by the product of the fluid velocity, u, and the concentration, C, of B in the fluid mixture assuming the constancy of u and C over the cross section. Since the volume of Fluid B is conserved, this leads to the one-way wave equation - u ?C/?x = ? ?C/?l where x increases in the direction of u—the "Darcy velocity", Q/A (or velocity flux per unit area), and 9 is the fractional porosity. Consider the case where fluid B is displacing Fluid A and the concentration distribution is represented by a step funcLon (with a vertical discontinuity). The solution of Eq. 1 predicts no mixing

Jan 1, 1958

By H. J. Stehli

Probably the earliest sinter from lead ore was made in the product sinter boxes attached to some hand reverberatory roasters. The ore was drawn from the roaster bed when dead roasted, and then by laborious effort fritted together by rabbling at a high temperature in the sinter box. This was not a true sinter, but was a great improvement over the dusty dead-roasted fine ores. The Huntington-Heberlein pots were the first real advance in the art, and produced some real sinter. They required that the sulphides be preroasted to 5 or 6 per cent sulphur, and the long cycle of operating and deep bed of material used in the pots fostered the formation of densely fused material and fines. This necessitated crushing of the densely fused cake and returning to the next charge large amounts of fines screened out. The Huntington-Heberlein pots made comparatively high lead losses because the deep bed and high internal temperature together favored the volatilization of lead. Lime (CaO) was added to the charges, and this addition constituted the patented feature of the Huntington-Heberlein process. Its sole function we now know was to act as an isolator of the sulphide particles, and any other substance—for instance, iron oxide—of equal fineness performed the same function. The Savelsberg process used limestone instead of burned lime, and in this there was a definite advantage. The converting of CaCO3, to CaO is a highly endothermic reaction, so the lime acted not only as an isolator of sulphide particles but absorbed excess heat and to some extent prevented premature fusion of the sulphides. The Carmichael-Bradford process used gypsum instead of limestone, and had the disadvantage of adding more sulphur to a charge from which it was desired to eliminate sulphur. Here again the gypsum served only as an infusible isolator of sulphide particles. The first Dwight-Lloyd apparatus to sinter lead ores commercially was installed at Perth Amboy in 1907. The fact that lime in any form was necessary to sintering was quickly disproved by making excellent sinter from Bunker Hill and Sullivan table concentrates, silica sand and iron oxide only.

Jan 1, 1937

By A. C. Veatch

THE MIDLANDS of England contain large areas of important oil lands, which, however, will not become of commercial importance for at least 5 years, because the ownership of the oil has become a political issue. In Great Britain, except in certain special areas, all minerals, except for gold and silver, belong to the surface owner. The leasing of minerals on the large estates is a very complicated business, as the family solicitors have many forms and formalities that must be observed. In the case of one of the large estates, the principal revenues of which for several hundred years have been from coal leases, the average time between the agreement on terms for a coal lease and the signing of the same has been 8 years. In 1916, one coal lease on this estate had been pending for 15 years, and was still unsigned, although the important terms had been agreed upon 15 years previously. Under war conditions, and considering the extreme importance that the production of petroleum in England would have had, such delays could not be tolerated. Most of the British landlords, relying on the almost, universal opinion of their own countrymen that there were no commercial deposits of petroleum in Great Britain, were prepared to give all their oil rights to the government, but they feared that such action might establish a precedent with respect to coal. For years the Labor Party and extreme radicals have protested against the payment of royalties to landlords on coal. The government, therefore, introduced a bill taking over all the oil rights and providing for the payment of a small royalty to the landlords, to safeguard the principle of compensation in case the coal mines should ever be nationalized. The provision of this bill, with respect to the payment of royalty to landlords, was defeated by a vote of 44 to 35 in a night session of the House of Commons on Oct. 25, 1917, when most of the members were absent, but when a group of labor members and extreme radicals were present. The resubmission of the point to the House of Commons was prevented by the labor members of the coalition government, who reminded the cabinet that the agreement

Jan 1, 1920

By L. G. E. Bignell, E. A. Hanson, J. O. Lewis

There was a general upward trend of all petroleum activities in Oklahoma during 1933, especially in the last quarter, though the average price for crude oil for the year was below 1932 and overproduction in East Texas demoralized conditions for several months. As the Federal Agencies established under the National Industry Recovery Act began to function conditions in Oklahoma were visibly affected and production of "hot oil" from Oklahoma City field practically ceased. More oil wells were completed, six new fields discovered, extensive geophysical prospecting carried on in many parts of the state, and an increased amount of clean-out and reconditioning work done in older pools during the past year. To increase quantity and rate of recovery of oil many wells producing from limestone formations were treated with hydrochloric acid. The Oklahoma City field had a reported production of 66,984,570 bbl. of oil during 1933, or almost exactly twice the amount reported for 1932. Potential tests and other indicators show that the wells are rapidly approaching the stage where mechanical lift must be applied to all of them, including the wells in the Wilcox sand zone. The major pipe-line companies serving the oil fields of Oklahoma have been anxious to make connections to all wells during 1933 and have indicated a willingness to accept all oil available. The amount offered has been restricted by proration orders, but the state did produce 178,356,-449 bbl. during the year, an increase of about 18.6 per cent over 1932. This increase was practically all due to the greater demand for Oklahoma City oil, as all other pools of any importance showed loss in production or very small gains last year. The U. S. Bureau of Mines' laboratory reports the lubricating distillate content of Oklahoma City crude from Arbuckle and Lower Simpson formations about 17 per cent by volume. East Texas oil is reported to contain about 5.6 per cent lubricating distillates. The desire of the transportation companies to keep their equipment operating at maximum capacity and the need of some refineries for more

Jan 1, 1934

AT THE beginning of February the British Government announced acceptance of the American terms for funding the war debt, the main features-being as follows: Interest rate of 3 per cent. for the first 10 years and then 3 ½ per cent. up to the final extinguishment of the debt at the end of 62 years. The interest from the time since the loans were made to the actual beginning of the funding arrangement to be recomputed at 4 1/4 per cent. instead of the 5 per cent. rate now in effect. Congress ratified the contract respecting the British debt. The ship subsidy bill was relegated to the rear, which is indeed an end to the project. The natural consequence of this will be a liquidation of the Govern-ment's shipping business. The joint committee on the reorganization of Govern-ment departments made its report to the President. In general this seems to offer a well-considered plan for the coordination of Government service. The pro-posals respecting the bureaus that are particularly associated with the mining industry may be subject to criticism. According to the committee's plan, the Geological Survey remains in the Department of the Interior, but the Bureau of Mines and the compilation of the statistics of mineral production are transferred to the Department of Commerce. The Lausanne conference among the European powers came to an end early in February, without any treaty having been signed, owing to the refusal of the Turks to accept the ultimatum of the Allies. Theoreti-cally this left conditions in a state-of war between the Allies and Turkey. However, no actual movements have resulted. The French and Belgians continued to hold the Ruhr district of Westphalia, extending their lines and administration of the region. The Germans adhered to the policy of passive resistance. In the Parliament of Great Britain the French and Belgian policy was plainly declared to be unwise and dangerous. French and Belgian industries, moreover, were troubled by strikes among their own coal miners for higher wages. The Poles and Lithuanians engaged in border war-fare;. the civil war in Ireland continued. The rest of the world was quiet insofar as military operations are concerned.

Jan 2, 1923

By H. W. Kerr, B. Soutiere

THE possibility of using unidirectionally solidified eutectic alloys as high-strength composite materials has been investigated by several workers. Unidirectionally solidified lamellar and fibrous eutectics have been shown to have good short-time structural stability at temperatures close to the eutectic melting temperature.'-4 Several investigations of both short-time high temperature tensile properties and creep properties of eutectic alloys have been carried out,3-" with promising results. Little work has been reported, however, on the thermal stability of eutectic alloys which have been unidirectionally solidified and subsequently deformed in compression. Since processes such as rolling and grinding introduce compressive stresses, and since the properties depend on the spacing and perfection of the composite structure10,11 this aspect is of definite importance if unidirectionally solidified eutectic alloys are to be considered for commercial use. A Cd-Zn alloy made from 99.999 pct starting materials was cast into a graphite boat and zone levelled12 to obtain a completely lamellar structure at one end of the bar. Sections from this region of the bar were removed, recast into 6.5 mm I.D. Pyrex tubing, and solidified unidirectionally upwards at a rate of 2.8 cm per hr. Specimens were cut from the solidified rods, heated in air at 200°C (0.88 of the eutectic melting temperature) for various lengths of time, and examined metal-lographically. Compression specimens were also cut from the solidified rod carefully machined to a length of & in., and deformed with the compressive axis parallel to the original growth axis to produce a total longitudinal strain of 12 pct. Some of these specimens were examined metallographically; others were heated in air at 200°C for various lengths of time and then examined. Metallographic examination of the deformed specimens showed the two types of deformation previously described; slip lines13 (smoothly bent lamellae) and kinks13,14 (sharply bent lamellae). Very close to the specimen ends there were a large number of deformation bands, but at a distance of about -re- in. the deformation was very localized, as shown in Fig. 1.

Jan 1, 1970

THE strike and dip of bedded formations is readily determined by trigonometry if some marker horizon is intercepted by three holes. If no marker can be identified and if orientation of the cores is unknown, as is the usual case in diamond drilling, the determination still can be made readily by the use of a stereonet if the bearing, inclination, and angle the bedding makes with the core axis is known for each of the three holes. Such determination, valid only if the bedding orientation is fairly uniform within the area drilled, is considered simpler, faster, and more effective than any solution previously published. Method: The steps of this procedure are as follows: 1) Mark north and south poles on tracing paper placed over stereonet.* 2) Plot the three diamond drillholes by drawing a line from the center of the net in the direction of the bearings of the holes. Then rotate the paper until each line, in turn, lies along the equatorial diameter of the net; the end of each line is determined by the inclination of the hole measured in degrees from the periphery toward the center of the net along the equatorial diameter. Fig. 1 illustrates a vertical hole and a hole inclined at —23" due east. 3) With the projection of one diamond drillhole along the equatorial diameter, measure from the end of the hole, to the east and then to the west, a dis- tance in degrees equal to the core axis-bedding plane angle. Find two more points by measuring the same number of degrees north then south along the great circle from the end of the drillhole. Draw a circle, the center somewhere along the direction of the projection of the drillhole, to connect these four points. Draw circles for the other two diamond drillholes in the same manner. See Fig. 1 for two circles representing core axis-bedding plane angles of 35" and 23" and Fig. 2 for these plus a third circle representing a core axis-bedding angle of 42" in a hole bearing S 50 W inclined at —52". 4) Rotate the tracing paper until one great circle on the stereonet is found which is tangent to all three of the circles or parts of circles derived in the previous step. Trace this great circle on the paper and join its ends with a straight line passing through the center of the net. The bearing of this line is the strike of the bedding. In Fig. 2 the bedding strikes N 77 E. 5) Rotate the paper until the strike is along the polar diameter of the net. The dip of the bedding is determined by measuring along the equatorial diameter the distance in degrees from the periphery of the net to the great circle derived in step 4. The dip of plane illustrated in Fig. 2 is 55" to the N 13 W. Fig. 3 indicates the solution for three holes whose bearings and inclinations are N 20 W and —43o, due E and —30°, S 30 W and 23" with core axis-bedding angles of 30°, 50°, and 43" respectively. The bedding (stippled area) strikes N 44 W and dips 70" to the southwest.

Jan 1, 1956

By Frank Woolley, John F. Elliott

The high-temperatzrre solulion calorimeter has been modified and an extension dynamic analysis of i/s transient behavior has provided an improved basis for interpretation of the experimental data. The partial molar heats of mixing, Him, of aluminum, copper, and silicon in the corresponding binary liquid-iron alloys haz,e been measured directly at 1600°C. The resulls in kcal per g-alom are: THE high-temperature1,2 solution calorimeter was planned and designed to obtain directly the partial molar heat of solution of solute elements in a variety of liquid metals that might serve as solvents. Results obtained in the temperature range of 1000° to 1200°C were described in the two earlier publications. However, a long-term goal in the program has been to obtain measurements at 1600°C of the heats of solution of elements in liquid iron. Hence, subsequent to the work last reported,2 and based on the experience of the first two studies, the calorimeter system has been modified and operated at 1600°C to obtain measurements on the Fe-Si, Fe-A1, and Fe-Cu systems. This paper reports the results of the work. THE MODIFIED SYSTEM It was clear from the earlier results that the most precise measurements can be obtained with the high-temperature solution calorimeter when the solution time is less than approximately 30 sec. This can be achieved only when the bath temperature, Tb, is above the melting (liquidus) temperature of the solute material being dropped. A second point of importance is that the refractories used earlier liberated considerable water so that, although the oxygen potential of the atmosphere in the system was satisfactory for work with nickel and copper, it was too high for work with iron, silicon, and so forth. Third, for work at 1550" to 1650°C, an improved temperature-sensing unit is needed. The modified calorimeter in its latest form is shown schematically in Fig. 1. The refractory brick and the Kanthal-Super heating elements which formed the furnace for heating the solute addition have been replaced by a smaller resistance-heated tube furnace which is insulated with bubble-grain alumina. A more elaborate gas purification system was installed to maintain a satisfactorily low oxygen potential in the atmosphere of the calorinieter chamber and of the solute addition furnace. As was the case in the earlier work, at the beginning of a run the calorimeter chamber is evacuated and then filled with purified argon so that a total pressure slightly in excess of 1 atm is maintained during the run. When either of the furnaces within the enclosure attains a red heat, 6 pct H2 is added to the atmosphere. Throughout the run, gas from the calorimeter is circulated through a de-oxidation system at the rate of approximately 5 standard liters per min; the changeover time for the gas within the calorimeter enclosure is approximately 1 hr. The essential stages of the deoxidation system are: a copper furnace at 600°C, a drying tube of anhydrite, and a titanium furnace at 800°C. The oxygen potential of the gas stream in the purification system can be monitored at several points by a stabilized zirconia oxygen cell. This cell is invaluable in detecting the development of leaks in the container vessel and the gas circulating system. The installation of the solute-addition furnace allowed either of two types of temperature-sensing units to be mounted on a water-cooled probe. The first was a small optical device using a silicon diode that was

Jan 1, 1968

By W. D. Robertson, W. L. Phillips Jr.

Stress-strain curves were obtained for single crystals of alpha brass in tension and in direct shear. Specimens were strained various amounts in a given slip direction, unloaded, and immediately strained in a second slip direction 60°, 120°, or 180&apos; from the original slip direction. Crystals strained in tension and direct shear had comparable critical resolved shear stresses and stress-strain curves. The density of slip lines in direct shear and in tension was essentially the same. The stress-strain curves obtained in shear were independent of initial orientation, choice of {111 } slip plane, choice of <110> slip direction, prior annealing temperature, and rate of cooling after annealing. There was no recovery after annealing for 4 hr at room temperature or 200°C; recovery was observed after 4 hr at 400°C. The crystals showed no asterism and mechanical properties were completely recoverable up to 20 pct strain. It was found that there is a barrier to slip in all latent close-packed directions, and that the magnitude of these barriers, evaluated at 3 pct strain, is proportional to prior strain and independent of the choice of latent direction in the {111} plane. The formation of Cottrell-Lomer barriers is discussed as a possible explanation for the hardening of the latent systems. AN idealized concept of plastic deformation indicates that a single crystal should yield at some stress that is dependent on crystal perfection and it should then continue to deform plastically by the process of "easy glide," which is characterized by a linear stress-strain curve and a low coefficient, ds/dE, of work-hardening. Hexagonal metal crystals generally conform to this ideal concept of laminar flow. In face-centered cubic metals the range of easy glide is always restricted in magnitude and it is strongly dependent on orientation, composition, crystal size, shape, surface preparation, and temperature. Since one of the principal differences between the two crystal systems, both of which deform by slip on close-packed planes, is the existence of secondary (latent) slip planes in the face-centered cubic crystals, it has been proposed that the transition from easy glide to turbulent flow, characterized by rapid linear hardening, is due to slip on secondary planes intersecting the primary plane.&apos;-.; However, the characteristic differences between individual face-centered cubic metals remain to be explained; in particular, it is not clear why the range of easy glide should vary so greatly in different metals and alloys similarly oriented for single slip. An investigation and comparison of different metals with respect to latent hardening on the primary slip plane should provide some of the information required to specify the necessary and sufficient conditions governing the transition from easy glide to turbulent flow. But, in order to accomplish this purpose, plastic strain must be produced by simple shear in a chosen plane and in a predetermined direction by some form of directed shear apparatus, the results of which must be correlated with the corresponding tension experiments. Two such experiments have been performed previously with zinc and with aluminum. Edwards, Washburn, and Parker" and Edwards and Washburn7 found that the strain-hardening coefficients in two latent directions in the basal plane of zinc were the same as in the primary direction. However, to initiate and propagate slip in either the [2110] or the [1210] direction, following primary slip in the [1l20] direction, it was necessary to increase the stress above that required to continue slip in the primary direction; when the direction of shear was reversed 180 deg plastic strain began at a much lower stress than that required to initiate slip in the original direction and the stress to propagate slip in the reverse direction was lower than the stress to continue slip in the forward direction, indicating a permanent loss of strain-hardening. Rohm and Kochendorfer observed softening in aluminum for all latent close-packed planes and directions. They also found that the critical resolved shear stress obtained from their direct shear apparatus was 50 pct lower than the value obtained from conventional tension tests, that the stress-strain curve was linear at 50 pct plastic strain, and that slip lines were not visible at strains less than 30 pct. At present it is uncertain whether these diverse results correspond to real differences in work-hardening characteristics of the close-packed planes of aluminum and zinc or to differences in experimental technique. In view of Read&apos;s analysis &apos;" of the stress distribution in the experimental arrangement of Rohm and Kochendorfer, there is some reason to question the significance of the latter results. In order to resolve this problem it is necessary to re-valuate the direct-shear technique and either repeat the previous measurements or investigate a third system. The latter choice seemed most likely to produce significant results with respect to work-hardening, and accordingly, it was decided to examine the hardening characteristics of the latent slip directions in alpha-brass. The choice of alpha-brass was dictated by the fact that easy glide is more extensive in this alloy than in any other face-centered cubic metal or alloy and, presumably, more nearly like the idealized hexagonal system. Experimental Procedure Crystals were made in graphite by the Bridge-man method in the form of cylinders, 11/2 in. diam and 8 to 9 in. long. Material for the crystals was 70/30 brass containing the following impurities:

Jan 1, 1959

By F. D. Wright

Production of a coal preparation plant is governed by many restrictions, such as the tonnage of different products and blends that can be sold within a given period, capacities and output proportions of the cleaning and sizing units, blending proportions, quality specifications, and costs and prices for the various products. Determination of the tonnage of each product and blend that should be made in order to obtain the maximum profit can be difficult unless a systematic method such as linear programming is used. In this paper the basic method of linear programming is described briefly. The Old Ben No. 9 preparation plant is used as an example to illustrate in detail how eqwations can be written to form a linear programming model of a coal preparation plant. Three sample problems, each requiring 56 or more equations and 63 structural variables, were solved with an IBM 650 computer. Linear programming is one of several mathematical tools used for operations research. It has been applied to many fields and has been used by a number of industries either to maximize the profits of certain operations or to minimize costs. P. B. Nalle and L. W. weeks&apos; have described the use of the method by the Riverside Cement Co. to minimize the cost of blending raw materials to make portland cement. Their problem is to obtain at minimum cost a mix with certain specifications from a number of possible materials which have various costs and various amounts of CaO, SiO2, Fe2O3, and other constituents. In a paper on the use of linear programming by the National Coal Board in England, K. B. Williams and K. B. Halley2 describe how the transportation method, a variation of linear programming, is used to minimize the cost of sending 37 grades of coal from 28 mines to seven central washing plants which produce coal for furnace coke and foundry coke. The various coals have different percentages of volatile matter, moisture, sulfur, ash, and phosphorous, so there is considerable choice in how they can be blended to meet the specifications of the two products. The purpose of this paper is to show how linear programming can be used to maximize the profits of a coal washing plant which produces individual final products as well as blends. The Old Ben Corp. furnished assumed sample data from their Old Ben Mine No. 9 preparation plant for this investigation. However, the data that have been used are entirely the author&apos;s responsibility. METHOD OF LINEAR PROGRAMMING Numerous articles and books have been written on the theory and applications of linear programming.3-5 However, since the method has not been widely applied by the mining industry, a brief, nontheo-retical discussion of its basic method seems to be in order. Linear programming (Table I) is used to determine the best possible solution to a number of interdependent activities. It is essentially a method for making systematic selections from a number of possible solutions to determine positively the optimum solution. There may be other equally good solutions but no better ones. Each activity must have linear coefficients and there must be a criterion to judge how good the solution actually is. Linear programming is different from the solution

Jan 1, 1961

By Frederic L. Kadey

Diatomite is a siliceous, sedimentary rock consisting principally of the fossilized skeletal remains of the diatom, a unicellular aquatic plant related to the algae. Thus, it has been formed by the induration of diatomaceous ooze, and consists mainly of diatomaceous silica, a form or variety of opal which is first formed in the cell walls of the living diatom. Diatomaceous silica is not generally regarded as a synonym or the equivalent for diatomite, although it has been so used at various times. Accurately, diatomaceous silica is the preferred name for the principal mineral component of which the rock, diatomite, is composed. The terms diatomaceous earth and kieselguhr are used as synonymous with diatomite. The designations tripoli, tripolite, infusorial earth, etc., were used at one time but are now obsolete. With the changing nomenclature, these terms that were at one time correct when proposed and used for generations would be considered incorrect if used today in the light of current knowledge. The designation diatomite is reserved for those accumulations of diatomaceous silica that are of sufficient quality, size, and minability to be considered of potential commercial value. Processed diatomite possesses an unusual particulate structure and chemical stability that lends itself to applications not filled by any other form of silica. Foremost among these applications is its use as a filter aid, which accounts for over half of its current consumption. Its unique diatom structure, low bulk density, high absorptive capacity, high surface area, and relatively low abrasion are attributes responsible for its utility as a functional filler and as an extender in paint, paper, rubber, and in plastics; and as an anti-caking agent; thermal insulating material; catalyst carrier; and chromatographic support; polish, abrasive, and pesticide extender to name a few representative applications. The United States is the principal producing country, although diatomite is found in numerous other locations. Geology Composition and Morphology Diatomaceous silica qualifies as a. mineral of organic origin in much the same way that aragonite and collophane do. The silica of the fossilized diatom skeleton closely resembles opal or hydrous silica in composition (SiO2 • nH2O) .4, 12, 203 The silica is of acute biological significance, not only for the cell wall component, but also for the basic life process.45, 51 Without silica, cell development ceases .31 In addition to bound water, varying between 3.5 and 8%, the siliceous skeleton may also contain, in solid solution, or as part of the Si02 complex, small amounts of associated inorganic components-alumina, principally-and lesser amounts of iron, 46, 49, 55 alkaline earths, alkali metals, and other minor constituents.59, 63, 67 Boron is reported to be an essential element for diatom growth .52, 58 Since diatomaceous silica is not pure hydrous silica but contains other intimately associated elements, there is good reason to consider it a distinct type or variety.4 Associated with the diatomaceous silica, and integrated as part of the diatomite, may be variable amounts of organic matter, soluble salts, and particles of rock-forming minerals that were syngenetically deposited or precipitated with the diatom frustules. Sand, clay, carbonate, and volcanic ash are typical common contaminants. Other contaminating minerals may be present, such as feldspar, mica, amphiboles, pyroxenes, rutile, zircon-the result of weathering, then transporting, and subsequent redeposition of surrounding land masses. Commercial diatomite may also contain fragments and particles of

Jan 1, 1983

By P. A. Beck, S. Kohara, M. N. Parthasarathi

IT has been shown1,3 that many observed phenomena related to annealing textures in f.c.c. metals can be adequately accounted for, at least in a qualitative way, by considering the orientation dependence of the boundary mobility, without any hypotheses concerning preferred orientation of nuclei. It was noted1 that this approach is particularly successful in the common cases of primary recrystallization in highly cold-worked polycrys-talline metals, where nuclei occur in great abundance, and that in the other extreme case, where the number of nuclei is very limited, or even only a single crystal is grown, the orientation dependence of boundary mobility has only a small effect, or none at all, on the orientations resulting from annealing. Recently Dunn described examples3-6 where observed secondary recrystallization textures apparently cannot be accounted for on the basis of oriented growth alone, but also require oriented nuclei, or at least the absence of nuclei in certain orientation ranges. In general, the great difficulty in correlating the preferred orientation of recrystallized grains with that of nuclei is inherent in the fact that nuclei are by nature very small, and that they are usually identifiable as "nuclei" only after growth, i.e., after they have already been subject to growth selectivity. An investigation was carried out by Liebmann and Lücke,&apos; and also a very similar one by Graham and Cahn,&apos; to obtain quantitative information on the orientation depend- ence of boundary migration rates in the recrystallization of slightly deformed aluminum single-crystal rods or plates, in which artificially nucleated recrystallized grains of predetermined orientation were grown. Liebmann and Lücke foupd maximum boundary mobility for boundaries across which the misorientation corresponded to a rotation of 40 deg around a common [Ill] axis, in accordance with earlier conclusions.9,1 Also, they confirmed that such an orientation relationship predominates among crystals growing into slightly extended single crystals from presumably random artificial nuclei. On the other hand, Graham and Cahn found no preferred orientation among crystals grown in a similar manner. It is not as yet known how these observations may be reconciled with each other. The view has been expressed in various papers5&apos;10,21 that selective growth based on the orientation dependence of boundary mobility is not in itself sufficient to account for the formation of sharp re-crystallization textures, such as those often observed in highly deformed polycrystalline metals after annealing. The present work was undertaken to ascertain whether or not it is possible to obtain a sharp re-crystallization texture in a case where random nuclei are assuredly present in large numbers. It was previously found1&apos; that high-purity aluminum crystals rolled 80 pct on the (110) plane in the [1T2] direction, when suitable precautions are taken, may be annealed for periods of about 1000 sec at 350°C without recrystallization. It was also found that the reluctance to recrystallize in this case is due to the scarcity of material in sufficiently deviating orientations to serve as nuclei. By using such a matrix,

Jan 1, 1959