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By Harrison Schmitt

During the past decade the writer has studied and mapped certain ore deposits and their structural associations in the states of Chihuahua, Durango, New Mexico and Arizona, and he believes that these deposits, with the exception of the manto-chimney, are representative of the principal types in the area of the states named. In this paper the deposits are described; then generalizations are drawn so far as seems appropriate. Hanover, New Mexico The Hanover, New Mexico, zinc deposits were briefly described by Lindgren and others,' Paige2 and recently in more detail by Schmitt. These, the kind ordinarily called contact metamorphic, border the southern end of an oval area of granodiorite intrusive ¾ mile wide and 2 miles long (Fig. I). The granodiorite has intruded, folded, and metamorphosed sedimentary and igneous rocks, which range in age from pre-Cambrian to Upper Cretaceous. About 90 per cent of the ore has replaced coarse, recrystallized, pure, fossiliferous, lower Mississippian, nonmagnesian limestone (Hanover limestone) 110 ft. thick;4 about 75 per cent of it occurs in the upper 50 ft. of this horizon just below an 18-ft. lower Pennsylvanian shale bed, which lies on a locally inconspicuous unconformity representing upper Mississippian time. The orebodies show five shapes or attitudes, each dependent on a special structural situation: 1. Most of the ore occurs as podlike, thick lenslike or other "three-dimensional" shoots extending from top to bottom of the Hanover limestone and lying adjacent to the outer contact of a silicate zone largely of andradite, which follows the intrusive contact (Figs. 1 and 2).

Jan 1, 1935

By Harrison Schmitt

During the past decade the writer has studied and mapped certain ore deposits and their structural associations in the states of Chihuahua, Durango, New Mexico and Arizona, and he believes that these deposits, with the exception of the manto-chimney, are representative of the principal types in the area of the states named. In this paper the deposits are described; then generalizations are drawn so far as seems appropriate. Hanover, New Mexico The Hanover, New Mexico, zinc deposits were briefly described by Lindgren and others,' Paige2 and recently in more detail by Schmitt. These, the kind ordinarily called contact metamorphic, border the southern end of an oval area of granodiorite intrusive ¾ mile wide and 2 miles long (Fig. I). The granodiorite has intruded, folded, and metamorphosed sedimentary and igneous rocks, which range in age from pre-Cambrian to Upper Cretaceous. About 90 per cent of the ore has replaced coarse, recrystallized, pure, fossiliferous, lower Mississippian, nonmagnesian limestone (Hanover limestone) 110 ft. thick;4 about 75 per cent of it occurs in the upper 50 ft. of this horizon just below an 18-ft. lower Pennsylvanian shale bed, which lies on a locally inconspicuous unconformity representing upper Mississippian time. The orebodies show five shapes or attitudes, each dependent on a special structural situation: 1. Most of the ore occurs as podlike, thick lenslike or other "three-dimensional" shoots extending from top to bottom of the Hanover limestone and lying adjacent to the outer contact of a silicate zone largely of andradite, which follows the intrusive contact (Figs. 1 and 2).

Jan 1, 1935

During the past decade the writer has studied and mapped certain ore deposits and their structural associations in the states of Chihuahua, Durango, New Mexico and Arizona, and he believes that these deposits, with the exception of the manto-chimney, are representative of the principal types in the area of the states named. In this paper the deposits are described; then generalizations are drawn so far as seems appropriate. Hanover, New Mexico The Hanover, New Mexico, zinc deposits were briefly described by Lindgren and others,' Paige2 and recently in more detail by Schmitt. These, the kind ordinarily called contact metamorphic, border the southern end of an oval area of granodiorite intrusive ¾ mile wide and 2 miles long (Fig. I). The granodiorite has intruded, folded, and metamorphosed sedimentary and igneous rocks, which range in age from pre-Cambrian to Upper Cretaceous. About 90 per cent of the ore has replaced coarse, recrystallized, pure, fossiliferous, lower Mississippian, nonmagnesian limestone (Hanover limestone) 110 ft. thick;4 about 75 per cent of it occurs in the upper 50 ft. of this horizon just below an 18-ft. lower Pennsylvanian shale bed, which lies on a locally inconspicuous unconformity representing upper Mississippian time. The orebodies show five shapes or attitudes, each dependent on a special structural situation: 1. Most of the ore occurs as podlike, thick lenslike or other "three-dimensional" shoots extending from top to bottom of the Hanover limestone and lying adjacent to the outer contact of a silicate zone largely of andradite, which follows the intrusive contact (Figs. 1 and 2).

Jan 1, 1935

During the past decade the writer has studied and mapped certain ore deposits and their structural associations in the states of Chihuahua, Durango, New Mexico and Arizona, and he believes that these deposits, with the exception of the manto-chimney, are representative of the principal types in the area of the states named. In this paper the deposits are described; then generalizations are drawn so far as seems appropriate. Hanover, New Mexico The Hanover, New Mexico, zinc deposits were briefly described by Lindgren and others,' Paige2 and recently in more detail by Schmitt. These, the kind ordinarily called contact metamorphic, border the southern end of an oval area of granodiorite intrusive ¾ mile wide and 2 miles long (Fig. I). The granodiorite has intruded, folded, and metamorphosed sedimentary and igneous rocks, which range in age from pre-Cambrian to Upper Cretaceous. About 90 per cent of the ore has replaced coarse, recrystallized, pure, fossiliferous, lower Mississippian, nonmagnesian limestone (Hanover limestone) 110 ft. thick;4 about 75 per cent of it occurs in the upper 50 ft. of this horizon just below an 18-ft. lower Pennsylvanian shale bed, which lies on a locally inconspicuous unconformity representing upper Mississippian time. The orebodies show five shapes or attitudes, each dependent on a special structural situation: 1. Most of the ore occurs as podlike, thick lenslike or other "three-dimensional" shoots extending from top to bottom of the Hanover limestone and lying adjacent to the outer contact of a silicate zone largely of andradite, which follows the intrusive contact (Figs. 1 and 2).

Jan 1, 1935

By J. W. Rutter, K. T. Aust

Observations are presented of the formation of annealing twins during the growth of a recrystallized grain into a striated, melt-grown crystal of high-purity lead. The formation of an annealing twin resulted in replacement of the original migrating boundary by a large-angle grain boundary of the caincidence-site type or by a near-twin boundary. The results support the Fullman-Fisher theory of annealing twins and demonstrate the usefulness of the coincidence-site model. FULLMAN and Fisher1 have advanced the following theory to account for the formation of annealing twins during grain growth. Whenever a grain A grows into a matrix of grains S1 and S2, a twin A' of grain A may form, as shown in Fig. 1, if the following energetic condition is satisfied: where "E" and "a" refer to the specific interfacial free energy and the area, respectively, of the boundaries indicated by the subscripts. In effect, the twinned grain will persist when the energy of the boundary between the twin(A') and the matrix grain (S, or S,) is less than that of the boundary between the original growing grain (A) and the matrix grain by an amount which exceeds the energy of the coherent twin boundary between A and A'. Experimental observations on the changes in grain boundary free energy accompanying the formation of twins1 are in agreement with the theory outlined in Eq.[l]. Direct observations of the formation of annealing twins at moving grain corners1"3 and the depend-

Jan 1, 1961

By Harrison Schmitt

During the past decade the writer has studied and mapped certain ore deposits and their structural associations in the states of Chihuahua, Durango, New Mexico and Arizona, and he believes that these deposits, with the exception of the manto-chimney, are representative of the principal types in the area of the states named. In this paper the deposits are described; then generalizations are drawn so far as seems appropriate. Hanover, New Mexico The Hanover, New Mexico, zinc deposits were briefly described by Lindgren and others,' Paige2 and recently in more detail by Schmitt. These, the kind ordinarily called contact metamorphic, border the southern end of an oval area of granodiorite intrusive ¾ mile wide and 2 miles long (Fig. I). The granodiorite has intruded, folded, and metamorphosed sedimentary and igneous rocks, which range in age from pre-Cambrian to Upper Cretaceous. About 90 per cent of the ore has replaced coarse, recrystallized, pure, fossiliferous, lower Mississippian, nonmagnesian limestone (Hanover limestone) 110 ft. thick;4 about 75 per cent of it occurs in the upper 50 ft. of this horizon just below an 18-ft. lower Pennsylvanian shale bed, which lies on a locally inconspicuous unconformity representing upper Mississippian time. The orebodies show five shapes or attitudes, each dependent on a special structural situation: 1. Most of the ore occurs as podlike, thick lenslike or other "three-dimensional" shoots extending from top to bottom of the Hanover limestone and lying adjacent to the outer contact of a silicate zone largely of andradite, which follows the intrusive contact (Figs. 1 and 2).

Jan 1, 1935

By F. C. Schora, H. P. Meissner

Iron ore from Cerro Bolivar, Segre', and Sierre Grande was reduced in fluid beds at about SOOT, using gas analyzing 20.5 pct CO, 41 pct Hz, and 38.5 pct N2. Except in the early stages of reduction, the rate of oxygen loss from the bed was directly proportional to the oxygen concentration in the bed, independent of gas composition as long as the gas was reducing, and little affected by temperature. The percentage reduction of the bed solids at any time was independent of particle size. I HE reduction of spheres or cubes of dense iron ore in a slowly moving stream of either pure H, or pure CO has been found to take place at distinct interfaces between well defined layers of iron and the iron oxides.'y4 These interfaces generally penetrate the ore lump in topochemical fashion, remaining parallel to the original contours of the specimen. Thus in the earlier stages of reducing hematite, the specimen's core is Fe,O, surrounded by successive shells of the lower oxides, and finally by an exterior shell of iron. McKewan5 assumed that the rate limiting step occurred at the Fe-FeO interface, with reducing gas penetrating up to this interface through the external porous iron shell, and reduction of the higher oxides within the ore lump occurring by diffusion of iron through the dense FeO shell. He developed an analytical expression based on this model relating the amount of oxygen removed from

Jan 1, 1962

By Henry M. Howe

COLUMBIA UNIVERSITY The Equilibrium Position of A 1.—Some of the most important data on this subject are collected in Table I. Definition of Ae 1.—-Just as we call A 1 of rising temperature Ac 1, and that of falling temperature Ar 1, so we may give the symbol Ae 1 to the equilibrium position of A 1. Preliminary Assumptions.—In deciding what weight to assign the various data, and indeed what data are to count, three assumptions should be made. These are : 1. The corollary from the phase rule, that the temperature of Ae 1 is constant and independent of the carbon content, though, of course, it may be changed by the presence of other elements. 2. That because neither in heating nor in cooling can the transformatioil begin before the temperature reaches Ae 1, though it may be delayed by lag till after the temperature has passed beyond Ae 1, therefore Ae 1 should be at or below the observed beginning of Ac 1 and at or above the observed beginning of Ar 1, and, a fortiori, it should be at or below the observed maximum of Ac 1, and at or above the observed maximum of Ar 1. It may be necessary to take these maxima into consideration in view of the experimental difficulty of detecting these beginnings. 3. Because of the extraordinary degree of lag in the immediate neighborhood of Ae 1, as proved by Brayshaw, little weight should be attached even to the most conclusive evidence that the transformation has not occurred on reaching, or even staying at, a given temperature, because that failure to occur may always be due to lag. Evidence that the transformation has occurred, or has even begun, at a given temperature deserves incomparably greater weight. In other words, the temperature may pass beyond Ae 1 without inducing the ' transformation, but the transformation cannot be induced except by

Jan 1, 1914

By G. W. Healy

G. W. Healy (union Carbide Metals 0.)-The author's paper is a useful contribution to the store of maps of chemical activities of oxides in multi-component slag systems. It is also a good example of the utility of the Gibbs-Schuhmann technique for calculating activities in a system where that of one of the components has been measured. This paper Koh and Caugherty. This plot is reproduced by alor in X-ray Metallography. Because of this nonlinearity, preparation cf suitable standards and/or correction for absorption and enhancement are essential in microanalysis. However, our objection is not the conclusion that Dr. Aaronson has arrived at nor the technique he has used; but only to the foot-note credited to V. Macres. The level of chromium that he was concerned with (less than 3 pet) is so low that the deviation of uncorrected Cr-curve will be negligible. Besides Dr. Aaronson has used chromium intensity from martensite and set it equal the bulk chromium content of the alloy. Using this chromium-intensity as a reference, he has calculated the amount of chromium in the ferrite. This amounts to the same as using an internal standard. Since the chromium content in austenite and ferrite are almost the same, enhancement due to iron in both will be the same and therefore does not need to be corrected. together with the author's recently published one1 on the CaO-FeO-Fe2O3 system will be most helpful to others learning to apply Schuhmann's method, which merits a far wider application than it has received to date and should greatly aid our understanding of equilibria between metal and oxide phases. As shown by okcen" its use may even be extended to sections of systems with any number of oxides. I have some questions as to the selection of equilibrium constants made by Dr. Turkdogan. He has chosen one for the formation of Fez03 from FeO and oxygen which gives Fea3 activities 50 pct higher

Jan 1, 1963

By R. F. Mehl, J. K. Stanley

THE recrystallization of cold-worked metals is studied ordinarily by determining the temperatures required for complete recrystallization to occur within a given arbitrary time period, usually within 15 min. to 2 hr. The results obtained are conventionally assembled in a three-dimensional diagram relating this temperature to the amount of cold-work (percentage deformation) and the resultant grain size, though sometimes other modes of representation are employed.1 Such three-dimensional diagrams are not complete, for the number of variables exceeds the number represented. The process of recrystallization is characterized by a time-rate, a fact that is not portrayed upon ordinary recrystallization diagrams. It is known that recrystallization consists in the formation of new nuclei and the growth of these nuclei, a process that continues until the matrix is completely consumed and the original set of grains entirely replaced by the new. This knowledge is old.2 Truly heterogeneous reactions invariably proceed by nucleation and growth; the decomposition of eutectoid solid solutions provides an example about which much is known,3 and freezing, originally studied by Tammann, provides the classic example. Although recrystallization is not a heterogeneous reaction within the orthodox meaning of the term, the mechanism of the process is the same. As in eutectoid inversion and freezing, it should be possible to study the rate of isothermal recrystallization as a function of time, and it should also be possible to analyze the isothermal reaction curve into the component rates of nucleation and growth that determine them.* Other methods, not employing the rates of nucleation and growth, have been used to represent the rates of such reactions, but these in general have been artificial and have not led to progress .4,5† The theory of recrystallization is not in advanced state; if recrystallization data were obtained in terms of the rate of isothermal recrystallization, and in terms of the rate of nucleation and the rate of growth of recrystallized grains, and in particular if the temperature coefficients of these rates were measured accurately, an adequate theory should be more readily developed .27 Such an effort requires proper experimental technique, but especially requires suitable methods of mathematical analysis to convert measurements made upon a surface of polish into values for the rate of nucleation and the rate of growth and to combine these into a rate of isothermal recrystallization. These methods are now

Jan 1, 1942

By W. W. Smeltzer

The linear formation rates of wustite films have been determined over the temperature range 590° to 1030°C using a vacuum microbalance technique. These rates are dependent directly on the partial pressure of carbon dioxide, Activation energies for film and scale formation in carbon dioxide and oxygen atmospheres are equivalent to either the dissociation energies of carbon dioxide and oxygen, or the activation energy for the diffusion of cation vacancies in wustite. Of the metals, iron is the most widely used basic constituent of durable alloys despite its intrinsic property of converting at a relatively rapid rate to the oxides from which it is derived. This property has accounted partially for many investigations on the oxidation of iron at low and high temperatures. Interpretation of the results have been complicated by formation of multilayers containing the various oxide phases. To aid in elucidation of the oxidation kinetics, measurements have been carried out in this investigation on the growth of the wustite surface layer. There are several studies directly related to the objective of this investigation. The growth of multilayer scales has been demonstrated to be diffusion controlled in oxygen at atmospheric pressure over the temperature range 450" to 1200°C by Davies, Simnad, and Birchenall.' To gain an insight into the diffusion mechanism, Himmel, Mehl, and ~irchenall' determined the self-diffusion coefficients of iron in wustite, magnetite, and hematite. These results were used to evaluate the oxidation rates of iron and its oxides, taking as a basis the theoretical parabolic rate equation developed by Wagner., The evaluations were compared to experimental data and were shown to provide essential confirmation of this theory. Fischbeck, Neundeubel, and salzer4 have demonstrated that the oxidation of iron in carbon dioxide and other atmospheres at high temperature obeys a linear relationship. Because the Arrhenius temperature coefficients of the reaction rate constants changed at the A, point they concluded that the passage of iron into the oxide controlled the reaction. This viewpoint has been accepted by Benard and ~albot' to explain the occurrence of linear rates in oxygen before the onset of diffusion-controlled parabolic oxidation. This basic premise of a rate-controlling reaction at the iron/oxide interface has been questioned recently by Hauffe and Pfeiffer.' Since the formation of wustite may follow a linear or parabolic relationship depending on the pressure of the gaseous re-actant, they propose that linear oxidation is determined by a chemisorption reaction while parabolic oxidation is controlled by diffusion. As confirmation of this viewpoint, Hauffe and pfeiffer6 and Pfeiffer and ~aubmeyer' have established that the linear scaling constants of wustite formation at 1000°C in carbon-dioxide or low-pressure oxygen atmospheres

Jan 1, 1961

By Francis Crockard

DURING the past five years we have probably witnessed greater technological advances than in any similar period. Industry and science have steadily marched ahead. The makers of iron and steel products have watched with great interest the development of stream-lined trains, faster and safer airplanes, the entirely new science of air-conditioning and the widespread use of stainless steels. Since 1930, we have witnessed the erection of the world's largest suspension bridge, the largest and fastest ocean liner and the spectacular Boulder Dam, while even greater things are planned in these particular fields. Other indus-tries, too, have been moving ahead rapidly. This advance in a few years has been caused primarily by the fierce competition of the depression. Now, more than ever, is the emphasis placed upon quality and service. Makers of southern merchant pig iron have been no exception and have been confronted with increasingly strict chemical specifications and with much greater stress on physical characteristics than ever before. For example, sulfur in the iron must be held very low, competition demanding that it be in the 0.020's and low 0.030's; silicon content must be held within a very narrow range, and definite requirements of phos-phorus and manganese are an essential part of the specifications. Physical characteristics are becoming of increasingly greater impor-tance. The introduction of triple-skimmed, slow-cooled iron several years ago was the first step in this direction. Now there are a few customers who buy iron by chemical analysis and physical appear-ance, having found that the analysis alone is an insufficient guide to their requirements.

Jan 1, 1935

By Francis Crockard

DURING the past five years we have probably witnessed greater technological advances than in any similar period. Industry and science have steadily marched ahead. The makers of iron and steel products have watched with great interest the development of stream-lined trains, faster and safer airplanes, the entirely new science of air-conditioning and the widespread use of stainless steels. Since 1930, we have witnessed the erection of the world's largest suspension bridge, the largest and fastest ocean liner and the spectacular Boulder Dam, while even greater things are planned in these particular fields. Other indus-tries, too, have been moving ahead rapidly. This advance in a few years has been caused primarily by the fierce competition of the depression. Now, more than ever, is the emphasis placed upon quality and service. Makers of southern merchant pig iron have been no exception and have been confronted with increasingly strict chemical specifications and with much greater stress on physical characteristics than ever before. For example, sulfur in the iron must be held very low, competition demanding that it be in the 0.020's and low 0.030's; silicon content must be held within a very narrow range, and definite requirements of phos-phorus and manganese are an essential part of the specifications. Physical characteristics are becoming of increasingly greater impor-tance. The introduction of triple-skimmed, slow-cooled iron several years ago was the first step in this direction. Now there are a few customers who buy iron by chemical analysis and physical appear-ance, having found that the analysis alone is an insufficient guide to their requirements.

Jan 1, 1936

By C. Wegert, L. E. Paulson, S. A. Cooley, R. C. Ellman

The Grand Forks Energy Research Center (GFERC) and Commonwealth Edison of Chicago jointly conducted tests in which 400 tons of subbituminous and lignite coals were dried in a commercial scale dryer, oil sprayed and cooled, then shipped from Pekin, Ill., to Grand Forks, N.D., and stockpiled. Cars containing raw coal and dried coal which had not been sprayed, were also transported for comparative purposes. During transit, observations were made of changes in the coals' moisture content, dust losses, and temperature.

Jan 1, 1977

By F. Claisse, R. Angers

Self-diffusion in iron has been measured during rapid a-r transformations using a variant of the Kryukou and Zhukhovitskii diffusion method. The study was performed by thermally cycling iron foils (1 to 6 cpm) through the transformation (=910°C). Some foils have been subjected to over 1000 cycles and some have spent more than 15 pct of their total diffusion time in the process of transformation. The experimental results show that the a-r transformation has no measurable effect on self-diffusion in iron. The study is completed by a quantitative analysis of mechanisms which can affect the diffusion rate during the transformation. The analysis confirms the experimental results. SINCE diffusion is an important factor in many solid-state transformations, it is of interest to study how it is affected by the stresses generated during these transformations. Clinard and Sherby1'2 were the first to make a study along these lines. They measured diffusion coefficients in Fe-FeCoV couples subjected to slow thermal cycling (1.5 cph) through the a-r transformation range. They found an enhancement of diffusion by a factor of about two. The purpose of the present paper is to report measurements of the self-diffusion coefficient of iron during much more rapid thermal cyclings (1 to 6 cpm) through the a-r transformation (-910°C). These more rapid cyclings produce higher strain rates during the transformation and should emphasize any possible influence of transformation upon diffusion. EXPERIMENTAL Iron foils, 25 to 35 µ thick, were cold-rolled from 99.92 pct pure iron and annealed in pure helium for 2 hr at 870°C; the resulting grain diameter was about 150 µ. Specimens 0.5 by 8 cm were cut from the foils and I7e55 was vapor deposited on one of their surfaces. A 38 gage alumel-chrome1 thermocouple was spot welded in the middle of one of the specimen long edges, Fig. 1. Two 38 gage chrome1 wires were also spot welded along the same edge on each side of the thermocouple; they were placed 2.5 cm apart and used for electrical resistance measurements. In order to prevent twisting and crumpling, the specimens were pinched between two quartz plates 0.1 by 1 by 7 cm and the assembly was close fitted into a 1 cm ID quartz tube. Four holes were drilled through the tube to let the 38 gage wires out: these were connected to the recording equipment by means of extension wires. 20-gage nickel wires fixed at both ends of the specimens were used to thermally cycle the foils by Joule heating. The above described device was placed in a 2.7 cm ID quartz tube which in turn was placed in a tubular furnace. Either a pure helium atmosphere or circulating hydrogen was used during the experiments. Specimens were subjected to thermal cycles between a minimum temperature To and a maximum temperature Tm at rates ranging from 1 to 6 cpm. This was obtained by maintaining the furnace at a constant temperature near the minimum temperature To and periodically passing an electric current through the specimen. Cooling was achieved by heat losses to the surroundings. The forms and periods of cycles were varied from one specimen to another; however, each specimen was subjected to one type of cycle only. The temperature and electrical resistance variations of the specimens were recorded as a function of time. The temperature curves were used for diffusion calculations while the electrical resistance curves were used to monitor the transformation and to determine its starting point and its approximate duration. Diffusion was measured by the method developed by Kryukov and zhukhovitskii3 and modified by Angers and Claisse.4,5 In this method a metallic foil is coated on one side with a radioactive isotope and the activity is measured periodically on both sides during the diffusion anneal. The following equation then holds: where: I1 Activity on the surface on which the deposit is made. I, Activity on the opposite surface. t Diffusion time. B Constant. D Diffusion coefficient. d Foil thickness including the deposit. G(t) A function of time; it is a second order correction term which is given graphically in Refs. 4 and 5. The diffusion coefficient D is found by plotting ln[(Il - I2)/(I1 + I,)] -G(t) against t; the resulting slope m leads to an accurate calculation of D through Eq. [2]. The effect of the a-r transformation on diffusion is expressed by the ratio DT/DU where:

Jan 1, 1970

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 B. W. Veal, B. S. Chandrasekhar

THE Laue method of orienting single crystals requires the use of tables of angles between crystal-lographic planes, and between zone axes. Such tables have been published for cubic crystals, and some rhombohedra12 and hexagonal3 crystals. A table of angles between planes in ß-tin has also been published;4 these angles refer to only low-index planes, and are not particularly helpful in the actual indexing of spots on a Laue photograph. Furthermore, it is often useful to know the angles between zones which share a common low-index plane. We have calculated such tables of angles for ß-tin and indium, both between planes in principal zones, and between zones passing through principal planes. The results are given in Tables I and 11. The standard formulas were used, with c/a = 0.54554 for 0-tin, and 1.07586 for indium.

Jan 1, 1962

By H. D. Outmans

The mechanics of filtration are described by a theoretical-empirical nonlinear diffusion equation which, under certain circumstances, may,be linearized and then solved explicitly. For filtration under static conditions linearization leads to a boundary value problem analogous to a heat flow problem with a known explicit solution. The corresponding solution for static filtration is compared with published experimental data. Under dynamic conditions filtration takes place in three successive stages. During each of these the rate of filtration and/or the thickness of the filter cake are different functions of the filtration time. The proposed mechanism explains the observed high resistance of dynamically deposited filter cakes against erosion and also the connection between filtration rate and viscosity of the drilling fluid. Several of the quantities governing dynamic filtration have no counterpart in the static filtration mechanism. The static filtration rate is, therefore, not a reliable measure for the dynamic rate and vice versa. INTRODUCTION Filtration under simulated borehole conditions, i.e.. either from a static suspension or from a suspension flowing parallel to the filter cake (dynamic filtration), has been the subject of several laboratory studies.1-7 This experimental and theoretical work showed that many aspects of the filtration mechanism cannot be explained by an elementary filtration theory based on the assumption that the filter cake is incompressible. For a more satisfactory theory compressibility should be taken into account. This has been done. at least to some extent, in the filtration theory developed for the chemical industry. Surveying the literature (see Ref. 8 for a bibliography) it becomes apparent that, although several properties of filter cakes deposited from many different suspensions have been measured, including compressibility, the filtration equations are essentially empirical in nature. No attempt has been made, for instance, to develop filtration theory along the lines of consolidation theory.12 This theory, upon which a highly successful development in soil mechanics rests, would appear to be an excellent starting point for a filtration theory since the compressibility concept is an essential part of it. As we will use this theory in the following development it is well to state the four assumptions on which it is based: 1. The fluid flow through a compressible porous medium is governed by Darcy's law. 2. The rate of change in fluid content of an element of the porous medium is proportional to the rate of change of solid pressure between the particles. 3. The solid particles are incompressible within the range of pressures considered. 4. The total pressure on a surface normal to the line of flow is equal to the sum of the fluid pressure and the pressure between the particles (solid pressure) at that surface. To calculate the rate of filtration and other quantities of interest it is necessary to know the filter cake compressibility and the permeability as a function of the solid pressure. It has not been possible to calculate these functions from theoretical considerations and they will therefore be introduced in this paper as empirical expressions. Both are determined in a compression cell where the cake is subjected to a mechanical load. Permeability and compressibility are measured after the solid pressure has stabilized, i.e., after the excess fluid pressure has been dissipated and the uniform pressure is transmitted entirely by the solids. The permeability and compressibility thus determined are not the same as during filtration in the borehole, under either static or dynamic conditions, because then, due to frictional drag, the solid pressure and hence also the permeability and compressibility vary along a line normal to the direction of the mean flow and can only be defined locally. DERIVATION OF THE FILTRATION EQUATION FOR COMPRESSIBLE FILTER CAKES As the filter cake in the borehole is thin compared to the radius of the hole the filtration may be considered as linear. Taking the x-axis normal to the wall, with its origin at the formation, we have, according to Darcy's law,

By Charles H. Thurman

The data given herein were first included in a paper read before San Francisco Section, A.I.M.E., in October 1940, and are applicable to conditions existing until the gold-dredging industry was temporarily suspended by Order L-208 of the War Production Board in the fall of 1942. There is no doubt that gold dredging will be resumed at some future time, and on a scale equivalent to that of the recent past, but the cost data given herein will be affected to some extent by conditions existing at that time, and by labor rates and prices for materials then prevailing. Dragline vs. Bucket-line Dragline dredges should not be considered for mining large areas of low-grade placer gravel. In such deposits a dragline operator with a 5-cu. yd. dragline would be doing well to maintain an operating cost of 6¢ per cu. yd., while a bucket-line dredge with buckets no smaller than 7 cu. ft. each could be operated for less than 4¢ per cu. yd. By operating costs, I mean only field charges such as direct operating and overhead, which includes pay roll, power or fuel, repairs and maintenance, insurance, land clearing and general expenses, but not including such items as prospecting, depletion, depreciation of equipment, State Franchise Tax, or Federal Income Tax. It is not to be inferred that a dragline dredge cannot make a profit in small low-grade deposits, where the extent of a given property is too small to justify the use of the more costly bucket-line dredge. Consider small deposits of 106 gravel. It is obvious that a deposit of 5,000,000 cu. yd. of such gravel could not be mined profitably with a new 7-cu. ft, bucket-line dredge, costing upward of $250,000, and in operation costs at 4¢ per cu. yd., paying for land or royalties out of earnings; nor could a new combination 5-cu. yd. dragline and washing plant, worth upward of $125,000 and working at 6¢ Per cu. yd., make a profit. These comparisons are made because the hourly capacity of both types of dredges is nearly the same. The bucket-line dredge averages 93 per cent operating time in 24 hr., as against about 80 per cent or less for the dragline dredge. These Percentages of operating time are important factors in making a comparison of this kind- The bucket-line dredge has greater efficiency in cleaning soft bedrock, usually characteristic of dredging deposits, and a 7-cu. ft. bucket-line dredge can be efficient to a total digging depth of 80 ft- (65 ft. below water, 15 ft. above). A 5-cu. Yd. dragline dredge is limited to about 30 ft. of efficient digging depth, 5 ft. of which could be above water. In small areas of gravel not over 30 ft. deep, a 5-cu. yd. dragline dredge could make a profit where a bucket-line dredge could not do so. As an example: compare the dredging of 3,000,000 cu. yd. of 10 gravel 28 ft. deep with bucket line, costin 4¢ Per cu. yd., and with a 5-cu. yd. dragline dredge operating at 6¢ Per cu. yd. Because of small yardage, new equipment is not warranted, therefore we can assume that the dredges of both types are used equip-ment, fully depreciated. Dismantling, mov-

Jan 1, 1946

By R. L. Fleischer, R. S. Davis

BICRYSTAL specimens grown from the melt have been used extensively for investigations of the influence of grain boundaries on plastic deformation. The bicrystals are usually of predetermined orientation prepared by seeded growth from the melt in milled graphite boats. This technique has been described in detail by Chalmers.' Since the direction that the grain boundary follows during growth is affected by both thermal conditions and crystallography, a difficulty arises in maintaining the grain boundary position constant along the length of the specimen. This problem is particularly

Jan 1, 1960