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By S. Webster, M. Karmis, C. Haycocks

Mining any seam can seriously affect subsequent operations in coal seams both above and below the one being mined. The effect is often detrimental to the recovery, cost and safety of mining the subsequent seams. This paper describes the ground control mechanisms involved in mining through a passive subsided zone or all actively subsiding trough. Data were extracted from case studies, primarily from the Appalachia region, for construction of empirical models to predict interaction problems that can occur in overlying seams. Inner-burden thickness, innerburden lithology, percentage extraction, lower seam height, time and overburden were analyzed to determine their effect on upper seam damage. Magnitude of upper seam subsidence was incorporated, together with a broad classification of rock types, to predict the type and range of damage that can occur in the upper seam. Results are summarized in graphically and nomogram form for use in. engineering design.

Jan 1, 1984

By G. B. Kasik, George Sachs, George Espey

IT has been reported frequently that the hardness and strength vary over the cross section of cold-worked, particularly cold-drawn, material. Brass rod and wire usually has been found to possess a maximum strength and hardness near the surface.1,2 According to Sachs,1 the center fiber has about the same strength as a wire stretched by the same amount in a tensile-test machine, the strength increasing toward the surface (Fig. I). These differences are particularly large for wire given a small reduction on drawing through a die with a wide opening. However, with increasing reduction and hardness, a tendency to form a thin soft surface skin becomes apparent. On the contrary, copper wire has usually been found to possess a soft surface skin" and it has been reported by Harris3 that during the cold-drawing of hot-rolled wire the surface layer becomes increasingly softer than the core, while the layer of maximum strength moves toward the core, it being found near the surface at first. The increase of strength and hardness from the core to the skin is readily explained by the observation that, in addition to the stretching, the layers of a rod or wire are sheared more the closer they are to the surface.1,6-8 However, the presence of a soft surface layer can be attributed only to an annealing effect. The source of such a softening might be the extremely high temperature that originates from the friction between [ ]

Jan 1, 1941

By R. S. Rickard, B. Ball

INTRODUCTION Pyrite responds to the flotation reagents normally used in sulfide flotation systems. For example, it is well known that xanthates are good collectors for pyrite, and cyanide, sulfide and hydroxides are depressants. The particular response of pyrite to these and other reagents is used to advantage in several areas. By careful control of depressant and collector additions, pyrite can be separated from other sulfides by flotation. This is of obvious importance in base metal sulfide flotation where pyrite depression is often required to produce a marketable grade concentrate. Flotation of pyrite has long been employed in gold ore processing, and it appears that pyrite flotation from coal may become important in the future (1). It is probably a direct consequence of this relative ease of separation, plus the low economic value of pyrite, that detailed investigations on the chemistry of its flotation and depression are relatively limited. Gaudin (2, 3, 4) and others, in the mid-1950's published data on the flotation of pyrite, but detailed or consistent mechanisms were lacking. In 1955, Sutherland and Wark's book (5) was published, in which a large , amount of empirical information, especially earlier work of Wark and Cox, was presented. More recently, in 1968, significant contributions have been made by Fuerstenau et al. (6, 7) and Majima and Takeda (8). These papers introduced electrochemical explanations of the effects observed with xanthate and cyanide ions.

Jan 1, 1976

By Paul Weaver

OF the four papers that comprise this TECHNICAL PUBLICATION, three are case histories of individual geophysical prospects, subsequently tested by drilling. The bibliography of Dr. Barton's published scientific papers† includes investigaions in physiography and surface geological mapping, as well as his geophysical papers, and from this list it is to be observed that he early recognized the place of different types of geophysical prospecting methods in the search for geological structures of economic importance. Moreover, his viewpoint was not merely that the structures should be found, but that the geophysical data should be examined quantitatively to determine the geometry of the structures. In other words, that although these data are insufficient to deduce a unique form for the structure that caused the effects measured in the data, the engineering computations should be carried-out to give as much of a definite configuration to he structure as the data permitted, in order that the testing of the structures could be conducted in the most economical manner and with the idea that the experience so gained could be later incorporated in the study of structures subsequently found. Dr. Barton continually emphasized the quantitative use of geophysical observations, whereas at the time that he began his specialization in geophysics it was considered sufficient to use observations only qualitatively. He, more than any one else, was responsible for -the first volume on geophysical prospecting issued by the Institute in 1929, and his three articles in that volume stressed the quantitative use of geophysical prospecting. The fourth article in this present TECHNICAL PUBLICATION is a further contribution to this branch of geophysical interpretation, and is a supplement to the paper in the 1929 volume, "Calculations in the Interpretation of Observations with .the Eötvös Torsion Balance." From the successful' demonstration by Dr. Barton of the usefulness of quan-

Jan 1, 1944

By B. S. Butler

Introduction. THE New London copper mine, about 81, miles east of Frederick, Md., was visited by the Writers for a few hours in the spring of 1909 and the following brief notes on ore specimens collected are presented as a contribution to studies in chalcocite ores. For certain data on the structural and areal geology of this portion of Maryland the writers are under obligation to the unpublished notes and maps of Arthur Keith. The detailed study of the ores is the work of B. S. Butler. The deposit here discussed has many similarities to those of the Virginia district of Virginia and North Carolina, which have been described y Graton1 and Laney2, except that in the deposits of the New London mine chalcocite is by far the most important ore mineral, while in the Virginia deposits bornite is commonly-the most important sulphide. In the New London occurrence calcite is the most important gangue mineral.

Jan 7, 1914

By Arthur C. Spencer

The object of the following paper is a description of the Treadwell gold-deposits in their geological aspects. quite apart from any consideration of the economical methods of mining and milling which have been developed and successfully applied

Jan 1, 1905

By L. A. Mekler

The recirculating furnace is primarily a heating apparatus of the convection type in which the heat-absorbing surfaces are heated by a mixture of fresh products of combustion and a portion of the combustion gases that have already given off a part of their heat in their previous passage over the heat-absorbing surfaces. In its basic conception, the recirculating furnace can be considered as a closed thermal system in which the heat-absorbing surfaces are constantly swept by a fixed quantity of products of combustion at a given initial temperature with the gases being constantly returned to the furnace and reheated before they again enter the heating zone. Gases equal in amount to those produced by the fuel burned to reheat the circulating gases are constantly ejected from the system to the stack. The recirculating furnace is the most suitable apparatus for heating by convection where low furnace temperatures must be maintained and where only a small portion of the available heat is taken out of the gases, particularly where the maximum allowable furnace temperature is low and where the final temperature of the gases is only a few hundred degrees below their initial temperature. In such cases, recirculation not only provides a method of reducing the rather high combustion temperatures of the fuel when burned without a large amount of excess air, but, by returning to the furnace the heat content of the gases at their final temperature, recovers a large portion of heat that otherwise would have been lost through the stack. The convection-type oil still is particularly suitable for the application of flue-gas recirculation. In an oil still, the heating of the oil is accomplished by applying to the tube surfaces a given quantity of heat of a certain predetermined quality, usually with the initial temperature of the gases not over 1500" F. as measured by thermocouples placed above the tube bank. To obtain the full benefit of the heating surface of the coil, the final temperature of the gases, after passing over the coil, is kept 200" to 300" higher than the temperature of the incoming oil. This final temperature varies from 500" F. for a topping still with only a slight or no

Jan 1, 1928

By F. W. Jessen, James N. Howell

INTRODUCTION The determination of cloud points has to date been limited to rather transparent oils, visual observation of the formation of a solid phase being the criterion for the standard ASTM D 97-47 method. The need for a quiclc and simple method for determining cloud points under dynamic conditions for opaque crude oils became necessary in a study of fundamental aspects of paraffin deposition from crude oils. PREVIOUS WORK The determination of cloud points in opaque oils by viscosity temperature curves is fairly new, Young' described a method employing the capillary tube principle. No information exists relative to the determination of cloud points of crude or refined oils under dynamic conditions. Shock' noticed that deposition of paraffin from crude oils took place at temperatures at or below the temperature at which a sharp inflection point occurred in the viscosity-temperature curve. This observation indicates a possible correlation between this temperature and the cloud point of the crude oil. Reistle and Vietti1 have reported that when crude oils containing small amounts of asphaltic materials were heated to temperatures sufficiently high to solubilize these materials and immediately cooled the pour point of the crude oil was lowered as much as 70°F. Sachanen\ asribes this effect to the action of colloidal asphaltenes in preventing the formation of the crystalline structure necessary to maintain the oil in a rigid state. At high temperatures, asphaltenes are peptized, and the paraffin crystals formed at these temperatures adsorb the colloidal asphaltenes on their surface thereby hindering further growth of the crystals. Reistle" found, however, that such heating and cooling of crude oils had no effect upon the cloud points. This latter work dealt with a crude oil of fixed composition, and the question immediately arises as to the effect of varying the concentration of asphaltic materials on the cloud point. APPARATUS AND PROCEDURE All viscosity measurements were made with a Bendix Ultra-Viscoson. The Bendix Ultra-Viscoson, which consists of a vibrating probe and an electronic computer. measures viscosity by exciting a thin alloy steel blade on the end of a probe by short electrical pulses in damped oscillation at 28 kilocycles. The blade vibrates longitudinally with an amplilude of less than 55 micron or 20 millionths of an inch. Energy to protlucc this excitation is generated in he computer and transferred to the probe through the connecting cable. The oscillating blade is magnetostric-tive, i.e., it is capable of transforming electrical energy to mechanical energy in the ultrasonic range. Ultrasonic waves are produced in the material surrounding the blade by the oscillating motion of the blade causing layers of the material to slip back and forth over one another at a known frequency. The electronic computer calculates the energy required to produce the sliding motion which is in turn proportional to the viscosity of the material. Actual values of viscosity times density (centi-poise X grams/cc) are indicated on the computer and a continuous D-C signal is provided which is fed into a type 153 Electronic Recorder (manufactured by Brown Instruments Div. of Minneapolis-Honeywell Regulator Co.) The liquid sample container was fabricated from a Lucite cylinder and jacketed by a Luicite water bath. Early experiments using glass and steel sample containers were not satisfactory. since the Ultra-Viscoson was apparently affected by the alterzltion of the magnetic fields surrounding the probe by stresses set LIP in the glass and steel as it cooled. The procedure for determining viscosity-temperature curves was relatively simple. The temperature ot the sample was raised sufficiently high to solubilize all paraffin and asphalts present. After heating, the oil sample was immediately transferred

Jan 1, 1957

By S Bankoff

INCE1 proposed that electrostatic attraction between oppositely charged particles was responsible for slime-coating. Del Giudice2 postulated the metathetic formation of a cementing compound. Wark3 suggested that prevention of slime-coating was related to peptization of the slime. [ ] In the experiments of Table I the technique employed was essentially that of del Giudice, with the difference that the particle was examined under a film of water rather than dry.4 In general, the polished particle was agitated for 2 min. in a pulp consisting of 12.5 grams of the slime (-200 mesh) and 50 c.c. of distilled water, washed in three baths of distilled water, and examined at 220 diameters with the Leitz Ultropak. Observations of Brownian movement were made at 850 diameters with dark-field illumination. Several of these experiments do not jibe with the metathesis theory. According to published solubilities,5,6 the lead salts of the anions in experiments c through g are more insoluble than lead carbonate, there- [ ] fore should prevent the formation of lead carbonate on the galena surface. In experiment i the calcium oxalate, which presumably was on the calcite surfaces, should have permitted the formation of a lead carbonate cement by virtue of its greater solubility. Experiments j through m show that the addition of lime accelerates the deposition of quartz onto a galena surface. The writer is unable to postulate a satisfactory cementing compound, according to the metathesis theory, to explain this effect. These experiments led to the conclusion that the metathetic formation of a cement-

Jan 1, 1941

By Leon Keller, William R. Van Slyke, James Stukel

Two 4-ft wide DSM screens were installed during 1957 in one unit of the two-unit heavy media cy- clone section of the Holman-Cliffs concentrator at Taconite, Minn., following successful laboratory test work on a 1-ft screen. The two screens materially reduced the amount of media sent to the magnetic separator cleaning circuit. Wear life was good and fine size capacity was high. Briefly, the Holman-Cliffs heavy media cyclone plant uses -65 mesh magnetite as media and 10-in. diam., 30º Ni-Hard cyclones as separatory vessels. Feed to the plant averages 130 long tons per hr of -1/8 in. +65 mesh material. The conventional heavy media circuit uses drum or spiral type separatory units and treats +l/8 or 3/16-in. material. The medium is generally -65 mesh ferrosilicon. Ore and media are readily separated by screening at about 6 mesh. At this size, capacity is high and wear and maintenance are not excessive. The heavy media cyclone plant requires an efficient separation between +65 mesh ore and -65 mesh media. To reduce costs, however, the separation was made at a coarser size with the result that the media was un- duly contaminated and it was necessary to clean large tonnages of media and ore in magnetic separators. Due to the high capital cost of these units, their number was kept to a minimum and, consequently, they were overloaded. As a result, the separation between magnetic media and nonmagnetics was not sharp and the magnetite losses were high.

Jan 10, 1958

By Luiz C. Correa da Silva, Robert F. Mehl

An experimental study of the movement of markers in the systems Cu/a-brass, Cu/Sna-solid solution, Cu/Ala-solid solution, Cu/Ni, Cu/Au, Ag/Au, employing many types of markers and a variety of temperatures. Marker movement is confirmed and undoubtedly associated with the manner in which atoms move during diffusion. EVERAL years ago Smigelskas and Kirkendall' •S reported measurements on the interdiffusion of copper and a-brass and on the movement of inert markers placed at the original join. These markers were observed to move toward the a-brass side of the join, and from this it was inferred that zinc diffuses in a-brass more rapidly than copper. Similar results were reported a little earlier for the diffusion of solvents into high polymer solids.' This has attracted much attention, particularly from those interested in the mechanism and the theory of diffusion: Seitz3 has employed it in supporting the vacancy theory of diffusion; from the data Darken4 has calculated separate diffusion coefficients for copper and zinc, developing a "phenomenological" theory of diffusion; and Bardeen5 has employed it in constructing a general theory, including therein the work of Seitz and Darken, as has Le Claire. These matters have recently been reconsidered in a sympo~ium.7 Some reason has existed for questioning the work of Smigelskas and Kirkendall.' Their technique consisted in electroplating copper on a-brass, upon the surface of which Mo-wires had been secured, and then diffusing, measuring the extent of diffusion along the normal to the join, and measuring the marker displacement in the same direction by a comparator determination of the distance between Mo-wires on opposite sides of the electroplated brass sample. It has been suspected that the copper plate might have been porous, and that the original interface might have been an imperfect join, both contributing to the transfer of the volatile zinc by vapor transfer;' it has also been questioned whether the marker movement might not in a measure be a property of the marker itself; etc. These legitimate questions require experimental answers; the present paper offers such answers. Moreover, Smigelskas and Kirkendall studied the effect only in the Cu-Zn system and at one temperature; the attention which the work of Smigelskas and Kirkendall has commanded recommends similar

Jan 1, 1952

By F. M. F. Cazin

Some twenty years ago the author of a book,* by which, for the first time, molecular action was made to account for nearly all phenomena in hydrodynamics, began his preface as follows: " It is contrary to all experience, that any branch of science should suddenly cut short its own line of reasoning, and drop all connection with its past, and yet as quickly re-establish itself on an entirely new basis. It is, therefore, not without justification that this book should be met with caution and even distrust." When the newly-discovered natural facts and laws presented in this paper were, in 1891, first laid before the officers of the American Institute of Mining Engineers, they might have been preceded by a preface to the same effect; and the expression would have found its justification by the actual experience these facts and laws met with. Since then, as the result of their publication in one of the most prominent

Jan 1, 1895

A FEW nights ago while working in the small hours of the morning on a clarion message intended for this page, we repaired to the kitchen for coffee, as is our wont when the solitude of the late hour and the stillness of the night seduce thoughts from the job at hand to reminiscences. The thought occurred, as we slowly dissolved the instant coffee in boiling water, that this modern world of canned, frozen, and dried foods deprives us of some of the subtler and therefore more delightful pleasures of life. We recall the aroma of boiling coffee which greeted us on getting up in the morning before the ease of instant coffee deprived us of the aroma from the old coffees. This line of thinking led us to place the blame on our wife for taking the easy way of making coffee and thereby depriving us of some of our enjoyment. From thinking about our spouse, it is only a short step to thinking about "the boss" or bosses in general.

Jan 9, 1951

By C. H. Bowen

Industry needs a generally applicable means of defining average grain sire and grain size distribution. Students of sediments have explored this field, employing methods that might also prove useful in engineering problems. Before attempting to solve specific problems it is well to review the derivation of commonly used grade scales and the reasons for their selection. This aspect of the problem seems largely to have been lost, and a review of basic factors may suggest causes for failures in using size analysis data.

Apr 1, 1956

By W. F. Pruden

On June 30, 1960, ground was broken for the construction of the facilities to mine, concentrate, and agglomerate the iron ores of the Atlantic City, Wyo., area which has become known as the "Atlantic City Project." This was a historic occasion for Columbia-Geneva Steel Division of United States Steel Corp. When completed, the installation will be the first integrated iron ore beneficiation plant west of the Mississippi River producing an agglomerated product. This Project, named for a nearby ghost mining town, is located in central Wyoming on the south-east flank of the Wind River Mountains. It is 16 miles north of the South Pass, where the early pioneers who followed the Mormon and Oregon Trails crossed the Continental Divide. White men first penetrated into this area in October, 1812, when Robert Stuart Party brought the returning Astorians through South Pass on route to St. Louis from the Columbia River area. Further interest in the area developed when gold was discovered in the sands of Rock Creek and the towns of Atlantic City and South Pass City were founded.

Jan 5, 1961

By Charles S. Barrett, Robert F. Mehl, Dana W. Smith

The Widmanstatten figures found in the steels have been long recognized and in some aspects carefully studied,' especially as they occur in cast hypoeutectoid alloys. Aside from the practical importance of the structures obtained in the steels by various heat treatments, a study of the characteristics of these figures is interesting because of the rich opportunity the system affords to obtain new data on the mechanism of segregation from solid solutions. This opportunity is twofold: first, by changing composition within the austenite range the proeutectoid precipitate may be changed from that of ferrite to that of cementite, thus offering the same opportunity for changing the type of precipitate while maintaining the same basic lattice as that afforded by the Cu-Zn alloys;2 and second, the eutectoid inversion leads upon drastic quenching to the formation of martensite, a Widman-statten figure of unique interest from the crystallographic viewpoint, particularly in comparison with those formed on slow cooling.3 We have, therefore, two types of structure to study: that formed on slow cooling of hypoeutectoid and hypereutectoid alloys, and that formed on quenching hypoeutectoid, eutectoid, and hypereutectoid alloys. For each of these types of structure we require the crystallographic plane in the mother austenite along which the precipitate forms (we shall see that the precipitates in these alloys are invariably platelike in form), and also the orientation of the precipitate upon this plane. Some of these

Jan 1, 1933

By W. W. Vaughn, R. H. Barnett, E. E. Wilson

Soon after the search for uranium ores on the Colorado Plateau began in earnest, thousands of feet of drill core ranging from 1 1/8 to 2 1/8 in. diam became available for study. Although significant advances had been made in the technique of quantitative gamma-ray borehole logging, instrumentation was in the development stage, and complete reliance could not be placed on gamma-ray logs alone to interpret quantitatively the meaning of radioactivity in a drillhole. A method that would be faster than chemical analysis and still give reproducible and reliable results for various drill core sizes was desirable to provide additional information on the enormous footage of drill core being accumulated. A solid phosphor scintillation drill core scanner was designed and constructed. Basically the instrument was developed to measure radiation from a drill core which would not be clearly recorded by a gamma-ray logger using a Geiger tube as the sensitive element. Such data would be beneficial in constructing isorad maps to delineate ore-bearing zones. A calibration in the range 0.01 to 0.1 pct eU.,O, was provided; above 0.1 pct eU3O8 gamma-ray logs were available and were being used to calculate grade and tonnage of ore reserves. The core scanner, however, has been used to estimate equivalent uranium content of ore-grade materials containing as much as 2.2 pct eU3O8 with an accuracy of ± 10 pct, the sample being in the form of a BX drill core. Actually, an apparent calibration of eU3O8 vs counts per unit time is a straight line with a slope that is a function of the sensitive element and the geometry of the counting assembly. A true calibration that will show the expected departure from a straight line is due principally to the random nature of the pulse from a radiation source and the nonlinearity of the electron circuitry. Design and Construction: Three methods of detecting radioactivity were considered and applied in developing the core scanner now in use: 1) the Geiger tube, 2) liquid scintillation phosphors, and 3) solid scintillation phosphors. The desired sensitivity and long-term drift characteristics needed for this operation could be attained only by using solid scintillation phosphors. All three methods are discussed. Before scintillation counters were common, nine beta-gamma sensitive Geiger tubes 7/8 in. diam by 12 in. long were used, arranged to surround the drill core with tube axes parallel to the axis of the core. This arrangement of Geiger tubes was en- closed in a lead shield 1 in. thick, and provision was made to slide a 6-ft length of drill core manually into the counting chamber, one foot at a time. A count for each segment was taken with a scaler while the core remained stationary. The equivalent uranium content of the different sections of drill core could then be estimated with the aid of a calibration curve of counts per unit time vs percent equivalent uranium (eU). In rare cases the effects of the radioactivity concentrated in small areas within the core introduced errors in the readings made with the Geiger tube arrangement owing to the geometry of the measurement. The variability of counting rate due to a localized concentration of radioactivity in a spot in the wall of a drill core is illustrated in Fig. 1. This effect and the inherent low efficiency of the Geiger tube were considered major disadvantages of this counting arrangement. When liquid scintillation phosphors became available the core scanner in Fig. 2 was constructed to make a more accurate measurement of the equivalent uranium content of a sample. This instrument contains about 4 liters of liquid phosphor in a stainless steel coaxial cylinder 1 ft long, with inner and outer walls 0.060 in. and 0.125 in. thick, respectively. Four end-window type photomulti-plier tube with cathodes of 2 in. diam, immersed in the solution at right angles to the axis of the core, were used to observe light flashes in the phosphor. The liquid phosphor offered equal sensitivity to radiation originating at any point in the enclosure and represented geometrically the optimum in design. However, providing a semi-permanent leak-proof seal between the glass envelope of the phototube and the metal walls of the container proved to be a serious problem in constructing the equipment. The most effective seals were especially machined O-rings from sections of large tygon tubing. The tygon took a permanent set owing to cold flow characteristics and in most cases sealed completely. The light absorption characteristics of the liquid phosphor changed gradually with time, and after one month the counting rate had decreased to half the original value. The most sensitive liquid phosphor tested proved to be a solution containing 4 g of 2.5-diphenyloxazole and 0.01 g of 2-(1-naphthy1)-5-phenyloxazole per liter of toluene. With fresh solution in the chamber and with all photomultiplier tubes operating in parallel, the counting rate contributed by any one of the four photomultiplier tubes was about 85 pct of the counting rate from a single tube operated individually. From these observations it was concluded that owing to coincident loss and light attenuation within the liquid phosphor, the apparent sensitivity could not have been materially increased by additional phototubes. However, this approach to core

Jan 1, 1960

By Carl Swartz

FOR many years kettles used in the melting and refining of lead and other nonferrous metals and alloys have been made of cast iron. The logic of this probably lies in the fact that cast iron has been known as a material of construction for vessels of this type much longer than steel, and satisfactory fabrication from it has been more easily accomplished and better understood. As the capacity of lead refineries has increased, it has been only natural to increase the size of kettles. Today kettles of 150 to 250 tons are not uncommon. As the size of the kettles increased and better shapes were designed, the uniformity of material of construction became more important. Records kept over comparatively long periods of time have shown that the length of service of kettles has not been uniform. Many causes contribute to this and the importance of each has not yet been evaluated. Kettle design, kettle setting, method of firing and material of construction have been changed from time to time to obtain better service, but the variation in length of service is still great. A kettle may fail during the first few heats or may last through more than one thousand heats. The purpose of this article is not to present the conclusions of a finished piece of research on kettle manufacture and use, but to present a series of observations made over considerable time in the hope that others will publish data and that all may be correlated into a logical scheme which will result in better service and longer kettle life.

Jan 1, 1931

By K. Mukherjee

A quasi-thermodynamic calculation is presented for estirt~ating vacancy Parameters in fcc metals. For fcc metals the equilibrium vacancy concentration at the melting point can be approximated by a constant mole fraction. The Gibbs free energy of formation of the vacancies can then be expressed as a simple function of the absolute melting temperature alone. From this description the formation energy Ef, the vibrational entropy Sv, and the formation volume of a vacancy can be calculated in terms of known thermodynamic parameters. The calculated values are in good agree-rnent with available experimental results. IT appears that many of the physical parameters associated with lattice defects can be empirically related to thermodynamic melting parameters.'-7 Besides the implicit correlations between melting phenomenon and point defects, the melting temperature itself at atmospheric pressure can be used as a reference temperature for the purpose of comparison of vacancy concentrations in a given crystal class. The concentration at the melting point then corresponds to the maximum vacancy super saturation in the crystalline state at a fixed pressure. For pure fcc metals such as Au, Cu, Al, Ag, Pb, and Pt the mole fraction of vacancies at the melting point8 is of the order of 10*"3 to 10"1. The equation expressing the equilibrium vacancy concentration at the melting point contains three parameters: the formation energy, the vibrational entropy, and the absolute melting temperature, see Eq. [2]. Since these three parameters cover a wide range of values8 in the above-mentioned metals, it can be assumed that in other fcc metals, for which no reliable data are available, the mole fraction of vacancies at the melting point most likely lies in the range 10~3 to lO"4. This is then the basis of the calculations described in this article. Within this range the mixing entropy can be linearized and the vibrational entropy, the formation energy, and the vacancy formation volume can be calculated in terms of known thermodynamic constants. 1} LINEARIZATION OF MIXING ENTROPY The Helmholtz free energy of a crystal containing n vacancies at the melting point can be writteng as where Ef, T,, k, and S, are the formation energy of a vacancy, the absolute melting temperature, Boltz-mann's constant, and the vacancy formation entropy, respectively. After applying Stirling's approximation in Eq. [l] and minimizing with respect to n where (n/N), is the equilibrium vacancy concentration in mole fraction at the melting temperature at 1 atm pressure. If instead of setting (6~/6n) = 0 immediately after Stirling's approximation in Eq. [I], the configurational partition function is simplified, then some useful and significant results can be obtained by utilizing the experimental inforrnation After applying Stirling's approximation and rearranging is plotted as a function of (n/N) in Fig. 1. The points, not all of which are shown, are fitted by a straight line substituting from Eq. [5] into Eq. [I] and minimizing with respect to n combining Eqs. [6] and [2] It must be emphasized that Eq. [7] is only a crude approximation based on an oversimplified model of

Jan 1, 1967

By J. D. Meakin

The self-diffusion coefficients of ß tin have been deterttlltled using a plating and sectioning technique. The principal diffusivities pavallel and perpendicu1ar to the "c" axis are given by the Arrhenius relations Dc = 8.2 exp (-25,600/RT) sq cnl per sec and Da = 1.4 exp (-23,300/RT) sq cm) per sec. The results are discussed in terms of a vacancy mecharism of diffusion. In conjunction with an investigation of diffusion in dilute indium-tin alloys we have reexamined self-diffusion in tin single crystals. The published self-diffusion coefficients of tin, eensham') have always appeared anomalous in comparison to diffusion data for other metals and do not correlate with parameters derived from creep tests.' In addition to the necessity of confirming the self-diffusion values for use in analyzing the alloy work, self-diffusion in an anisotropic lattice is of considerable fundamental interest and confirmation of the published data seemed worthwhile. For a crystal with an axis of symmetry three-fold or higher the diffusivity at an angle 6 to the axis is given by D? = (Da - Do) sin2?+ Do [1] where Da and Do are the principal diffusivities perpendicular and parallel to the axis. For a particular diffusion mechanism, again in a crystal of axial symmetry, these principal diffusivities are [2] Do - ? ?i2 COS?i In these expressions ?i is the displacement undergone by the ith atom and 8, is the angle this displacement makes with the symmetry axis. In this, as

Jan 1, 1961