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By G. L. Fisher, R. Maddin

The rate of self-diffusion in silver single crystals during torsional strain was measured over a wide range of tenperatures and strain rates. The torsional strain was applied in a cyclic manner by reversing the divection of twist aftev a certain fraction of the total strain was reached. Surface roughening was substantially reduced in cyclically strained specimens compared with those strained entirely in one direction. Diffusion coefficients were determined using a special sectioning technique whereby slices could be removed parallel to the surface of a strained torsion specimen. The accuracy of the technique was first determined using roughened specinzens statically diffused to various penetration depths. Simultaneous strain-diffusion experiments were then performed over the temperature range 550' to 800 using strain rates of lo-' to 2.2 x 10' sec-'. The increase in silver self-diffusivity during torsional plastic strain was small. In only one case was the enhancement greater than twice the static value of the diffusion coefficzent. The enhancements increased slightly with decreasing tenzperature and increased with increasing strain rate. A dislocation pipe mechanism of enhancement was found to explain the present results satisfactorily. The magnitude of the enhancements and the tenzperatures at which they were observed suggests that a steady-state dislocation density of 10' to 109 dislocations cm-2 existed during the high-tempevature deformation. The diffusion coefficient in an fcc metal can be increased by 1) an excess concentration of point defects and 2) the rapid movement of diffusing atoms along grain boundaries and dislocations. Plastic deformation may be responsible for enhancements by both of these mechanisms. The results of simultaneous strain-diffusion experiments have caused a controversy over the magnitude of the effect of strain upon diffusion. Experiments reporting large enhancements have been criticized for the manner in which the diffusion coefficient was measured. Several of these experiments have been contradicted by other results obtained in a similar manner. No enhancement was reported by two investigators''' who performed their experiments at high temperatures where strain is expected to have little effect upon diffusion. A recent theoretical analysis3 indicates that strain enhancement by a vacancy mechanism will be small and exist only at low temperatures and rapid strain rates. It is doubtful whether any experiment has yet proven that strain enhancements can occur by an excess vacancy mechanism. In the present research, experiments were performed at extremes of temperature and strain rate in an attempt to measure enhancement of diffusion by strain. Self-diffusion of silver during torsional deformation was chosen since two separate investigations4j5 indicate that at least a small enhancement exists under these conditions. An accurate method of determining the diffusion coefficient, mechanical sectioning, was employed after a technique was devised to apply it to the roughened surface of a strained torsion specimen. First, the accuracy of the technique was determined for different penetrations (2fi). Then diffusion experiments were performed at temperatures between 550" and 800°C at strain rates of 10"" to 10"" per sec. I) EXPERIMENTAL PROCEDURE Preparation of Specimens. The experimental procedure detailing the growth of crystals, their treatment, and the annealing techniques during straining are contained in earlier publications.496 The dimensions and orientations of the torsion specimens are shown in Figs. 1 and 2. licatiin of Torsional Strain. The torsion procedure was changed from that used previously. The specimens were strained in cycles to reduce the gross distortion and surface roughening inherent in twisting to high strains in one direction. For all strains above 0.30, the total surface strain was obtained as follows: the specimen was twisted to 0.10 strain in a clockwise direction; the direction was reversed; the backlash in the torsion apparatus was taken up; and the specimen was twisted in a counterclockwise direction through the initial starting point to 0.20 surface shear strain in the opposite direction. The strain reversal took no more than 1 min to accomplish. The total accumulated surface shear strain was arbitrarily taken as the sum of the 0.10 strain in the clockwise direction plus 0.20 in the counterclockwise direction. Although cyclic torsional strain was beneficial, surface roughening and specimen distortion were not entirely eliminated. The variation in the diameter at various points on the specimen was often much greater than the depth of the diffusion zone. Since serious errors might result if specimens were sectioned in the usual manner, a technique of lathe sectioning was devised to allow sections to be taken parallel to planes of equal concentration.

Jan 1, 1967

By Kurt Kennedy

A method is described by which three elements can be condensed simirltaneously on a common substrate in such a way that the composition varies with position on the substrate. Almost all possible combinations of three solid elements can be formed in a single evaporation. The three elements are heated by magnetically deflected electron beams. The alloys and cornpounds formed by this method generally correspond to those trade by other methods; however, many exceptions exist. Simple symmetric crystallographic phases tend to form in preference to more complex phases. The Nb-Sn. Cr-Fe-Nt, and other systems of alloys made by this method will be discussed. Phases that form very slowly, such as the o phase in Cr-Fe alloys, may be formed rapidly by this method when certain substrate temperatures are used. STUDYING all the mixtures and compounds of two or more elements by the preparation of individual samples forces the investigator to make sampling sufficiently close together so that the properties of the intermediate compositions can be inferred. A completely unknown system will require a dis c our aging ly large number of preparations in order to fully know all its properties. For the purpose of expediting this type of investigation, methods have been devised to prepare samples that have a continuous variation in composition over some predefined area. The code-position of two elements onto suitable substrates has been used to produce alloys or compounds that have variable compositions depending on their positions on the substrates Composition gradients have been formed by depositing a wedge-shaped layer of one element and then depositing a second wedge-shaped layer on top of it such that the total film thickness is kept constant. Concentration equilibrium perpendicular to the surface is then established by annealing.4 This paper describes a method for the simultaneous condensation of three volatile components on a substrate such that there is a regular variation of composition with position on the substrate. The arrangement of the evaporation sources and the substrate is shown schematically in Fig. 1. Materials to be evaporated are placed in three water-cooled crucibles located at the corners of a 10-in. equilateral triangle. Electron beams from cathodes located below the crucibles are bent 180 deg by magnetic fields and focused on the material to be evaporated. The cathodes are connected in parallel to a constant-current 12-kv power supply. The distribution of emission current from each cathode is controlled by filament temperature. When materials that sublime are to be evaporated, the electron beam is deflected by an auxiliary ac magnetic field so that the beam moves over the surface of the evaporating material rather than digging a hole in one spot. The substrate is a 10-in. triangle of 2-mil stainless steel or molybdenum which is stretched against a slightly curved heat sink by a frame as shown in Fig. 2. This frame and heat sink are located so that each corner is directly above an evaporation source. The heat sink has three radiant heaters at each corner that can be separately controlled permitting the

Jan 1, 1967

By G. Beghi, G. Piatti

THE authors examined the problem of the gradual transformation of Al2O3 from the transition phases normally encountered in SAP (r -x-n)1-3 to the stable a phase. This phenomenon is well-known at temperatures above the melting point of aluminum,3"6 whereas in this paper the transformation was studied at temperatures lower than the melting point of the aluminum matrix.

Jan 1, 1967

By Martin H. Stanczyk

In recent, years the demand and consumption of finely ground industrial minerals has substantially increased for such uses as fillers and chemically reactive components. The size, specifications for these types of industrial mineral materials vary to a great extent and depend on the particular end purpose' and on the physical properties of the mineral itself. Size reduction of industrial minerals usually is obtained by conventional crushing and grinding methods. However, some specialized milling techniques have been developed for producing these minerals in extremely fine particle size ranges. During recent years the Bureau of Mines has been investigating an attrition grinding method to produce ultrafine subsieve-size mineral particles. The Bureau developed process, which has been patented,2 comprises the intense agitation of a slurry composed of the material to be ground, a relatively fine granular grinding medium, and a suspending fluid. The process has been shown to be effective for the comminution of kaolin in the particle size range of 2 microns and finer on a batch3 and continuous basis.4,5 This report presents the results of batch tests made to determine the effectiveness of the attrition grinding process for comminuting commercial products of (1) mica, a tough lamellar material, (2) fluorite, a brittle intermediately hard material, and (3) barite, a relatively soft, massive material.

Jan 1, 1967

By Richard N. Spencer

Electric-furnace smelting for simultaneous recovery of zinc spelter and lead bullion from complex lead-zinc sinter was investigated. Reduction of lead and zinc was satisfactory. Condensation of lead and zinc vapor to pyrophoric metal powder in a water-cooled, shock-condensing system produced excellent recoveries. Metal-splash condensation to produce zinc spelter was unsatisfactory. Special smelting experiments differentiated the effects of several smelting parameters on zinc metal recovery. The principal cause for unsatisfactory zinc metal recovery was transfer of iron to the condenser and subsequent degradation of zinc in a mixture composed of lead and an iron-zinc intermetallic compound. Limitations of the process were determined. Slag-resistance open-bath electric smelting of complex lead-zinc sinter is not considered feasible.

Jan 1, 1967

By Ronald P. Hollenbeck

This study reviews and discusses the fluorspar industry in the Eastern United States, with emphasis on factors controlling the industry such as production, consumption, uses, and transportation. The greatest potential for increased consumption of fluorspar in the immediate future was found to be in the manufacture of fluorine chemicals and steel. Important factors affecting the future domestic industry include imports and the maintenance of adequate domestic fluorspar reserves. Exploration, commercial deposits, mining and milling, reserves, and new developments in the industry are covered.

Jan 1, 1967

By H. A. Gorrell, S. R. L. Harding

"The potash beds in the Saskatchewan portion of the Williston Basin occur in the upper portion of the Prairie Evaporite formation of the Devonian Elk Point Group. They represent the late stage of a major evaporitic cycle. Two other evaporitic cycles are known in overlying beds, but these apparently never reached the stage of potash salt deposition. The basin in which salt deposition took place extended from the northwestern corner of Alberta southeastward across Saskatchewan into Manitoba, North Dakota and Montana. Deposition of potash salts was apparently restricted to the southeastern portion of the evaporite basin. On a regional basis, five major stratigraphie divisions of the potash-bearing strata have been made. Locally, several of these units may be divided into correlatable sub-units. The potash-bearing strata are separated and overlain by predominantly halite layers of varying thickness. Cross sections show the regional correlation of the potash-rich zones, and maps show the present distribution of the individual potash-bearing zones and the areas of richer development for each zone. The maps tend to substantiate the interpretation of considerable subsurface solution of salt and potash beds."

Jan 1, 1967

By N. A. Gjostein

The formal descnption of the decay of an isolated scratch can be written in terms of an appropriate Fourier integral. With the application of certain approximations, this description leads to the second-moment analysis developed by King and Mullins. It is shown that the second-moment analysis does not adequately describe the behavior of a decaying, isolated scratch, and that it is difficult to obtain internally consistent values of the surface self-diffusion coefficient, D,,from this analysis. This inconsistency arises from contributions of higher-order moments to the decay process. Two new analytical methods, based on the Fourier integval representation of a scratch profile, have been developed for determining values of D, from the decay kinetics of isolated scratches. In the profile-matching method, a given initial profile is resolved into its Fourier components, the components are allowed to decay exponentially over an annealing time interval, At, and finally they are synthesized to form a decayed profile. The predicted profile is adjusted to fit the experimental profile by varying only the parameter, D,At; the contribution from volume diffusion is directly taken into account and the integrals involved in the Fourier analysis are evaluated by numerical integration on an electronic computer. In the kinetic method, the widths, W, of a series of predicted profiles are determined for various volume-diffusion contributions, and the results are plotted in the form W vs DSAt. For a fixed ratio of surface to volume diffusivities, R, these plots are linear; the slope of the lines increases as R decreases. A simi-lar analysis can be performed on the depths of the predicted profiles. In this case, plots of (l/df3 vs D,At are found to be nonlinear. The proper value of Ds is found by superimposing the data for the experimental widths and depths on Plots of this kind and adjusting Ds until a fit is obtained with the line having the appropriate value oj R. An analysis of the slopes of these plots for R —= (surface diffusion only) reveals that they do not give the correct value, 2276, for width tf second-moment standard profile. This finding allows one to modify the second-moment analysis in such a way as to obtain internally consistent values of Ds. ThERE are several processes, involving a flow of matter along a surface, due to gradients in curvature of the surface, that may be used to determine the surface self-diffusion coefficient, Ds. These processes are commonly known as 1) thermal grooving, 2) single and 3) multiple scratch decay, 4) blunting of field-emitter tips, and 5) sintering. In this series of papers, the first three of these processes are examined in detail in an attempt to subject the phenomenological theories governing these processes to a critical test and, furthermore, to make a critical comparison of the values of D, obtained from these techniques. Although the thermal grooving technique has been established'' as a reliable method for determining D, , this has not been the case for the process of scratch flattening. Mullins and coworkers374 have proposed phenomenological laws governing the growth of the width and the decay of the amplitude of an isolated scratch, but only in one study5 has the width-growth law been supported by experimental evidence. In paper I of this series detailed experimental evidence is presented that points up the deficiencies of the second-moment analysis; the origins of these deficiencies are also discussed. Following this development, some new analytical procedures, based on representing the scratch profile by Fourier integrals, are presented as a means of obtaining reliable values of D, from the kinetics of the scratch-flattening process. Further applications of the Fourier integral approach are reported in papers 11' and 111,~ where the method has been useful in interpreting the anisotropy of flattening rates of isolated scratches (paper 11) and in describing the multiple scratch decay process (paper 111). THEORY OF SCRATCH DECAY Following ~ullins" approach we consider an arbitrarily shaped scratch profile, Fig. 6, at some time, t. The profile is designated by a function z(x,t) which can be expressed in terms of a Fourier integral as follows:

Jan 1, 1967

By H. E. Powell

Magnetic susceptibilities were determined by the Bureau of Mines fur 19 cobalt- and nickel-bearing minerals and for a suite for synthetic cobalt-nickel diarsenides analogous to the rammelsbergite and safflorite series. Relations between susceptibility and composition were found to be nonlinear for both impure natural minerals and pure synthetics.

Jan 1, 1967

By A. F. Baker

The Bureau of Mines conducted pressure-drop studies in a 4-foot-diameter simulated blast furnace shaft to compare anthracite metallurgical briquets with coke and formcoke. The test materials were used alone, layered, and in mixed burdens of commercial fuel-to-ore ratios. Anthracite briquets had a higher pressure drop per foot than furnace coke, but they had a lower pressure drop per foot than formcoke. This appears to be due to packing and shape, as well as to particle size. The superficial air velocities at which beds of briquets and furnace coke disrupted were about the same. However, if briquets of the shapes and sizes tested are substituted for furnace coke in commercial metallurgical furnaces, higher blowing pressures will be required to deliver comparable amounts of air. Test burdens with more than 5 percent material smaller than 1/4-inch diameter showed significant increases in resistance to airflow.

Jan 1, 1967

By Robert E. Wood

The compressibility factors, Z, of helium, nitrogen, and helium-nitrogen mixtures in the three-dimensional space of temperature, pressure, and gas composition have been related to the Leiden form of the virial equation of state. The dependency of virial coefficients through the fifth on temperature and gas composition has been established for the temperature range 133.15° to 748.15° K. Compressibility factors, Z, have been computed from the equation of state and tabulated as functions of gas composition, pressure, and temperature. Tabular values of Z are presented for 30.00 through 100.00 percent helium for temperatures from 240° through 700° R for pressures from 14.696 through 3,050 psia and for temperatures from 720° through 1,300° R for pressures from 14.696 through 1,500 psia. Tabular values of Z are presented at increments of 5.00 percent helium and 20° R, and, for pressures greater than 50 psia, at increments of 50 psi.

Jan 1, 1967

By P. R. Jones

A computer program was written for the design of a shell and tube type heat exchanger on a price optimum basis. The program was designed to meet the following requirements: (1) Triangular pitch; (2) single or multiple pass; (3) heating or cooling; and (4) no change in phase. Price optimum design was obtained for four standard tube sizes and standard pitch. Pressure drop both inside and outside were computed and the nearest standard shells having at least the required area were listed. With this information, the estimator can select the heat exchanger best suited for the need. The program was made adaptable to various fluids and to various tube sizes and spacing by reading in much of the required data such as physical properties of the fluids, tube data, and standard shell data in tabular form.

Jan 1, 1967

By W. S. Landers

Nine high-volatile bituminous Utah coals were carbonized singly and in blends with low-and medium-volatile bituminous coals. Of the 9 coals, 2 are in commercial use as the base coals in blends that produce industrially accept-able metallurgical coke, while 7 are regarded as weakly coking and are not used commercially in coking blends. The carbonization tests were made in a la-inch diameter, cylindrical retort, using 50-pound charges. Sunnyside coal blended with autogenous char generally produced larger and stronger coke than was yielded by straight Sunnyside coal. The volatile matter of the char and the concentration of the char in the blend appear to be important parameters influencing coke size and strength. A blend of 10 per-cent autogenous char of 7.2-percent volatile matter with Sunnyside coal yielded coke that was larger, stronger, and of higher apparent specific gravity than coke produced from an industrial coke oven blend consisting of 15 percent medium-volatile coal and 85 percent Sunnyside coal.

Jan 1, 1967

Jan 1, 1967

By Forrest T. Moyer

The safety record of the mineral and mineral-fuel mining and processing industries in 1966 was improved slightly for the second consecutive year as indicated by reduced injury-frequency and injury-severity rates. The overall operating activity was higher in 1966, as measured by the increased number of men working and the total man-hours of worktime. Injury Experience.-The rate of occurrence of all disabling work injuries in the mineral industries was 17.38 per million man-hours in 1966. This overall rate comprised frequencies of 0.28 for fatal and 17.10 for nonfatal work injuries, compared with respective rates of 0.28 and 17.26 in 1965. Fatalities totaled 543; 5 more than in 1965. The total of 33.091 nonfatal injuries was 291 higher than in 1965. However, the larger number of disabilities was offset by the increased worktime in 1966. so that the fatality frequency was unchanged and the nonfatal frequency rate decreased from 1965.

Jan 1, 1967

Jan 1, 1967

By Robert H. Merrill

This Bureau of Mines report summarizes the design and tests of a gage that will simultaneously measure the deformation of a borehole along three diameters 60 degrees apart; the measurements are in a single plane normal to the axis of the borehole. The inherent errors in measurement are considered together with the problems associated with the use of the gage in the relatively severe environments in and around mine openings. These problems were treated in the design and tests of the gage and the results establish that the gage can be used to satisfactorily is determine estimates of the stresses in rock.

Jan 1, 1967

By R. Ebeling, M. F. Ashby

The paper is in two parts. The first develops the formulae and method needed to calculate the size, nu)nber, spacing, and volume fraction of hard or inert particles in the interior of a specimen from measurernents made on an extraction replica; throughout, the spread of- particle sizes in a single specimen is taken into account, and the extraction efficiency of the replica is considered. A method for testing whether the particles are randotnly distributed in space is described, and the spacing of randomly distributed particles is discussed. The second Part describes the application of the method to copper containing spherical particles of silica; the description includes an estimate of the errors involved, and a comparison of this with alternative methods. All parameters except uolume fraction can be determined satisfactorily, and the method offers advantages over other electron-,rzicroscopic techniques when dealing with hard particles in a softer matrix, or inert particles in a chem-ically less inert matrix. 1 HE experimental measurement of sizes and numbers of discrete particles of a second phase embedded in a matrix material from opaque, plane sections has been considered by many authors, notably by Fullman.' It is assumed that, when the specimen is sectioned, the particles are also sectioned, so that the diameters of the circles of intersection of particles with the plane of the cross section ("surface diameters") are measured. It is difficult to derive the distribution of true particle diameters ("volume diameters") from measurements of the distribution of "surface diameters" on a plane section. The measurement of size and numbers of small second-phase particles by transmission electron microscopy through thin foils of matrix containing the particles has been described by Cahn and ~uttin~' and by ~illiard.~ Because of overlap and the fact that particles which intersect the foil surface may be sectioned whereas those in the bulk of the foil are not, it is again difficult to measure the true distribution of particle sizes. The use of replicas for this sort of measurement has not been analyzed in detail. A replica made from an opaque cross section, thus replicating the circles of intersection of particles with the plane of section, is analyzed by Fullman's method and suffers from the same difficulties. Under certain circumstances, however, extraction replicas can be used, and offer a special advantage in that they make the determination of the true distribution of particle diameters particularly simple. It is the purpose of this paper to describe this extraction replica method. Consider the example of an alloy consisting of SiOz particles, whose mean diameter is about 1000A, dispersed in a copper matrix. When the alloy is sectioned and mechanically polished, the particles are not sectioned, because they are much harder than the matrix, and so will be either left in the surface or pulled out whole, and because the particle size is smaller than the abrasive size of even the finest abrasive. The particles are chemically inert in solutions which chemically etch or electropolish the matrix, so that chemical treatments do not section the particles either. (Experimental measurements of particle shape in this alloy confirm this—truncated particles are never seen.) Small, hard or inert, particles are therefore not sectioned when the specimen is sectioned and polished. An extraction replica taken from this polished surface shows the true "volume" diameter of each extracted particle; the distribution of diameters seen on the replica is the surface distribution of true "volume" diameters, and the volume distribution of true "volume" diameters is easily derived from it. The extraction replica method is not subject to the difficulties associated with sectioning of particles, and avoids the problem of overlap from which the transmission method suffers. The method is well-suited for studying hard particles in a soft matrix. Examples are provided by internally oxidized alloys, oxide-dispersion strengthened metals like T.D. Nickel, and carbides, nitrides, and strong intermetallic compounds in metals. It should be possible to adapt polishing techniques in alloys containing softer but inert particles to avoid sectioning the particles (say by electropolishing or etching). The method is tested and illustrated in Sections 8 and 9 by applying it to a dispersion of spherical SiO2 particles in a copper matrix. I) SYMBOLS Symbols are defined where they first appear in the text. Volume fractions of particles are denoted by the symbol f, particle diameters by x, center-to-center particle spacings by D, and numbers of particles by N. Mean particle diameters and standard deviations about these means are denoted by x and a. Both arithmetic (subscript A) and geometric (subscript G) means are employed. In this paper we measure the distribution of true diameters of particles which touch or pass through a random-plane section of the specimen. We may want to know the distribution of particle diameters in the

Jan 1, 1967

By Adrian J. Mathias

This report presents the results of an investigation of a mine production-scheduling model and a critical path analysis for long-range mine planning. An example is given to illustrate how these techniques might be used to plan long-range development and production scheduling for a large underground mine. The model, based on estimated ore block grades and tonnages, and on designed mine development layout, simulates mining of ore blocks in a sequence necessary to fulfill mill requirements for ore tonnage and grade evaluation within pre-established system restrictions. Simulated production schedules are obtained as output from the model. These production schedules are then incorporated into a critical path analysis to determine the sequence for the long-range development work so as to fulfill the production schedules and thereby meet the ore grade and tonnage requirements of the mill.

Jan 1, 1967

By W. H. Eddy

The Bureau of Mines made small-scale continuous tests and large-scale commercial plant tests of a calcareous fluorspar ore near Cave-In-Rock, Ill., to determine if the application of the lignin-fluoride process of fluorspar flotation would be industrially feasible for treatment of fluorspar ores, and also to compare the lignin-fluoride process with the quebracho process, which is the method currently used for concentrating calcareous fluorspar ores. The small-scale continuous tests yielded fluorspar concentrates analyzing 93.6 percent CaF2 with a recovery of 87.6 percent of the total fluorspar in the ore. In large-scale commercial plant tests, a fluorspar concentrate analyzing 93.3 percent CaF2 with a recovery of 78.0 percent was produced by the quebracho method. About 86.0 percent of the fluorspar was recovered in a metallurgical-grade fluorspar concentrate from the lignin-fluoride circuit which analyzed 89.9 percent CaF2? with a much simpler flowsheet than that in the current commercial application.

Jan 1, 1967