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Compiled by Mary Ann Gross, Department of Energy. Bruceton. PA. Supplemental data from Coal Age indicated by (*). Reprinted by permission from CoalAge magazine.

Jan 1, 1981

Jan 1, 1947

By J. A. Herbst, R. Mackelprang, J. D. Miller

Droplet size distributions were determined by stabilizing in gelatin and measurement of the distributions by means of computerized image analysis Several variables that affect droplet sizes were studied and the resulting size distributions were modeled via a population balance equation Key parameters in the model were related to the physical properties and operating conditions of the systems examined using a multiple linear approach

Jan 1, 1981

By Russell C., Fleming

FOK, many years the officials of the Magma Copper Co. mine at Superior, Ariz., have had to contend with adverse conditions underground in the form of high rock temperatures, hot water, and high relative humidity. These conditions in the mine have been such that working the mine would have been impossible were it not for the constantly expanding and improved sys- tem of ventilation to produce bearable conditions in the working places. Results that have already been achieved make an interesting study of what can be done along those lines. From the time the mine was first opened in 1910 it has been hot. An idea of the conditions that have persistently been encountered can be obtained from parts of the mine that are not being worked at present or that do not yet have sufficient ventilation. Virgin rock temperatures as determined in drill holes at the faces range from 104° to 116°*. An observation made at the face of No. 5 West footwall drift on the 2800-ft. level.

Jan 1, 1930

By L. Guttman

THE equilibrium diagram of the indium-thallium system was of interest to us in connection with a study of the superconducting properties of metallic solid solutions in progress at this Institute. For this purpose, a series of alloys was prepared covering the range from pure indium to 75 atomic pet TI, and X-ray diffraction patterns were obtained. Roughly speaking, the results indicated a region of continuous decrease in the axial ratio of the face-centered tetragonal structure from the value ca. 1.08 in pure indium to unity at about 23 atomic pct TI. From this concentration to the solubility limit, the structure was face-centered cubic, a form not reported by Hansen.1 At this point we became aware of the work of Valentiner,2 who had found the same structures at room temperature but had not investigated further the relationship between them. To study the transformation f.c.c.??f.c.t., and to clarify the phase diagram, we undertook the work reported in this paper and that which follows." Preparation of Alloys Pure indium and thallium* (both about 99.9 pct, as estimated from spectroscopic analyses) were weighed out in quantities sufficient to prepare 10 to 25 g of alloy of the desired concentration. (Occasionally indium was mixed with a previously pre- pared solution.) The metals were melted over a flame, in an open graphite crucible, stirred with a graphite rod, and poured into a graphite trough. The rough slug was hammered and swaged into a rod of 2 to 3 mm diam, and annealed in a drying oven at about 125°C for 1 to 2 days. Samples were taken from the rod for analysis, as well as for diffraction and other measurements. The thallium was determined by electrometric titration, using a modification of the method of Beale and co-workers.' The precision of analysis was generally about 2 0.2 pct of the thallium content. The rods were sometimes found to vary in thallium content as much as 1.5 pct from end to end, but since analyses were also made close to the segments used in the various studies, the composition was usually known as accurately as the analyses could be made. Where one less significant figure is given, the error is estimated to be ±0.4 pct of the thallium content. X-Ray Diffraction Measurements Three different cameras were used: (1) A 7 cm Debye camera, with oscillating specimen (manufactured by the Picker X-ray Corp., Cleveland, Ohio); (2) a 9 cm diam Debye camera of the type designed by Bradley;" (3) a 10 cm diam symmetrical focusing back-reflection camera (manufactured by Geo. C. Wyland, Ramsay, N. J.). Samples were prepared from the homogenized rods, either by filing under liquid nitrogen, or more often, in the form of wires or foils made by working at room temperature or liquid nitrogen temperature. Sharp patterns were obtained from specimens annealed at room temperature, although higher annealing temperatures were also used (cf. below). Generally, copper radiation was used; a few patterns were obtained with

Jan 1, 1951

By N. J. Themelis, A. W. Last

Autogenous grinding, broadly defined as the self-comminution of ore in a cylindrical tumbling mill without using auxiliary grinding media, was first applied in the early 1930s in the so-called Hadsel mills (Hardinge, 1955) as seen in [Fig. 1], mainly used in gold mines on the US West Coast. A number of these mills were built in sizes of 6.1 to 7.3 m (20 to 24 ft) in diameter and 1.5 to 1.8 m (5 to 6 ft) in length but were later abandoned because of operating and maintenance problems. Further development of autogenous grinding led to the Hardinge wet grinding mill, the Aerofall dry grinding mill, and others. A tabulation of all known autogenous and semiautogenous installations around the world was sent recently to the authors by G. J. Kushner of Koppers Metal Processing Division. In the size range of 7.3 to 9.8 m (24 to 32 ft) in diameter, it lists a total of thirty mills used in the processing of copper ores. An additional 120 units are listed in the same size range for the processing of iron ores and other minerals. The largest mills in existence are 11.1-m-diam X 4.6-m-long (36-ft-diam X 15-ft-long) mills in Minnesota, powered by 8950 kW (12,000 hp) motors and used in taconite beneficiation. It is indicative of the phenomenal growth of this technology that none of the above 150 mills was in operation prior to 1964. Grinding rates in autogenous mills are very sensitive to variations in ore breakage characteristics and even with fairly constant ore type can exhibit large fluctuations in throughput. Autogenous grinding also depends on availability of a fraction of the ore to be ground in the form of "competent" rock which can withstand to a certain degree the tumbling and impact action within the mill. If the ore is uniformly "soft", it will soon be crushed into small size particles and further grinding, which depends on the existence of large size rocks in the mill, becomes impossible. This apparently is the case with most copper ores, as discussed by Bachman, Last and Nabbs (1970) who described pilot testing of a large number of ore samples from Kennecott 's Chino Mines. Under circumstances where autogenous grinding is impractical, it is possible to realize most of its benefits by utilizing large grinding balls in place of the "competent" rock and practice what has become known in the mining industry as semiautogenous grinding. In semiautogenous grinding (SAG), a grate discharge tumbling mill is fed the product of a primary crusher or run-of-mine rock. Forged steel or alloy grinding balls, in proportions ranging from 3.10% of the total volume in the mill, are used to complement the self-grinding ability of the ore. Semiautogenous circuits can be either designed for single-stage closed-circuit grinding which produces a final product for recovery processes, or for two-stage operation in which the SAG mill product is fed to a second stage of grinding in a conventional ball mill.

Jan 1, 1981

By T. Vasilos, J. T. Smith

THE mechanism of pressure sintering, or hot pressing, for ceramic materials, has been investigated by several researchers.1-8 Plastic flow has been suggested as the rate-determining mech-anism1,2 while grain boundary sliding3,4 and fragmentation processess have been found controlling in other studies. Vasilos and Spriggs5,6 have reported that pressure sintering occurs by a diffusion-controlled mechanism. For the pressure sintering of metals, investigations with lead7 and with tin6 have not identified the operative mechanism during consolidation of these powders. This note reports the results of a pressure sintering study initiated to determine the mechanism controlling the densification of spherical copper powder. Temperatures of 300°, 400°, 500°, and 600°C at 2500, 5000, 7500, and 10,000 psi pressures were investigated. The copper powder for this study was obtained from Metals Disintegrating Co., Elizabeth, N.J. The minimum purity was reported to be 99.9 pct. The powder size was -325 mesh and a lineal analysis showed the average size to be less than 1 p. An alumina die body and punches were employed. Graphite spacers were placed between the copper powder and the punches before pressing. It was expected that the graphite would form carbon monoxide with any entrapped air and form a reducing atmosphere within the die cavity. This condition was generally realized during pressing although a minor amount of oxidation occurred at 500" and 600°C. The oxide particles were located randomly in the pressed samples and were not considered to influence the densification process. Calibration tests showed the temperature of the copper pellet to be about 20°C less than the die wall temperature, probably resulting from heat losses through the punches. This difference was compensated during the experimental pressing operations. The hot pressing equipment employed for this work has been described by Spriggs et a1.9 and was calibrated with a Baldwin-Lima-Hamilton load cell. Travel of the punches was monitored with a dial indicator showing increments of travel to 0.0005 in. Relative density was calculated at selected time intervals for a known copper weight, punch travel, and die diameter. The accuracy of this calculation was *1 pct. Average grain size after hot pressing was obtained by lineal analysis. Typical densification curves are presented in Fig. 1 and Fig. 2 where relative density is plotted vs log time as a function of applied pressure for the 300" and 600°C pressure sintering temperatures, respectively. The curves for 400" and 500°C were similar to those at 300°C and consequently are not shown. The curves at 300°C as well as 400" and 500°C do not show an end-point or limiting density for a particular applied pressure. At 600°C, a density in excess of 95 pct of theoretical has been reached such that further densification is extremely slow for the 5000, 7500, and 10,000 psi pressures. It is suggested that further densification at these pressure levels may be retarded or prevented by discontinuous grain growth, by entrapped gases, and by other microstructural limitations as described by Cob1e.10 The curve for 2500 psi hot pressing pressure is a straight line over the time interval although a slight change in slope may be occurring at the last time intervals. The plastic flow models,1,2 derived for hot pressing, predict the existence of an end-point (or limiting) density dependent on the yield point of the material at the temperature of interest. The yield stress of copper at a 0.005 strain level has been

Jan 1, 1965

By L., Ormsby

DRILLING and blasting practices in the Morenci open pit have undergone considerable modification in recent years. Changes in the character of the ground being mined, modifications of working conditions, and continuous experimentation have been the contributing factors.

Jan 1, 1950

By C. Chamberlain

The Telfer Project, Australia's newest, largest, and most remote gold mine treats 480 kt of ore grading 9.33 g/t derived from open pit mining operations. Coarse gold is recovered by gravity concentration with jigs and further upgraded wing a continuous strake launder table, and by amalgamation. Remaining gold is recovered in a cyanide circuit and incorporates flat bottom air agitators, counter current decantation (CCD) and stellar filters for clarification and precipitate removal. Overall recovery into a bullion averages 98%. The mill incorporates a number of design features that allow for maximum efficiency and security wing a minimum number of operation personnel.

Jan 1, 1983

By Ralph K. Foster

During five underground mine fires which occurred in Arizona during 1980 and 1981, sealing the fire area became necessary. To minimize leakage into the fire area, ventilation control measures were instituted to balance pressure across the bulkheads. Problems en- countered in sealing the fire areas and measures taken to improve these conditions are discussed. The routing of the ventilation and ventilation control to en- sure the workers' safety were also important considerations in reopening the mines. The use of continuous CO monitors is discussed. One important consideration was the condition of the fire, and chromatographic analysis was used to establish this. Graphs comparing the Trickett ratio, carbon monoxide, carbon dioxide, and oxygen concentrations are given. The Trickett ratio was useful but needed to be augmented by the comparison of CO, C02, and 02. Problems with getting good samples from sealed areas and recommended procedures that were developed during these fires are discussed.

Jan 1, 1982

By John D. Roach

DURING an investigation of the yttrium-hydrogen system aimed at producing solid yttrium hydride specimens containing various amounts of hydrogen, it was observed that yttrium containing approximately 2 wt pct H exhibited a tendency to crack and crumble to a powder on standing in air at room temperature. It was also observed that longer hydriding times, at a given temperature, increased this susceptibility to powdering without an increase in hydrogen content, also that moisture in the air is necessary for the observed effects to occur. Even if cracking did not occur, there was a continual formation of a light gray powder on the as-treated surface of the hydrided yttrium and this reaction continues until the entire hydrided piece has been reduced to a powder. Storing the hydrided specimens in the absence of air or removing the surface either by machining or grinding were effective means of preventing this disintegration of hydrided yttrium. In an attempt to determine the reason for this powdering phenomenon, the surfaces of a number of as-hydrided yttrium specimens were examined by X-ray techniques. In all cases the X-ray pattern obtained showed the major phase to be yttrium hydride (YH2) as would be expected since the specimens contained 2 to 2.2 wt pct H. In some cases a trace of yttrium oxide was observed. There was also a third phase present on the surface of these hydrided specimens which could not immediately be identified. This unknown phase was a face-centered cubic material, NaC1-type structure, with a lattice parameter of 4.855 and a calculated density of 5.914 g per cc. Very slight hand polishing of the surface of the hydrided yttrium specimens completely removed both the unknown phase and the traces of oxide so that only the yttrium hydride pattern remained. Based on the X-ray patterns the quantity of the unknown phase on the surface of the hydrided yttrium appeared to be directly related to the susceptibility of the material to powdering. Work at the Denver Research Institute on the yttrium-nitrogen binary system showed that yttrium nitride (YN) is a face-centered cubic material with a lattice parameter of 4.878A and a density of 5.890 g per cc. They also noted that this compound rapidly disintegrated to a powder on standing in air. The unknown pattern observed in the above specimens corresponds very closely to that of the nitride—fcc structure, 4.885 parameter, and density of 5.914 g per cc. The presence of this thin film of nitride on the surface of the hydrided specimens probably accounts for the observed powder formation and crumbling. The nitride reacts with the water vapor in the air (verified by private communication from Dr. C. Huffine, General Electric Co.) to yield yttrium oxide and ammonia. Ammonia is readily detected when hydrided yttrium specimens were allowed to stand in bottled moist air. The powder formed on the surface of the hydrided specimens was shown by X-ray analysis to be yttrium oxide. This reaction appears to occur primarily at the grain boundaries since discrete particles of yttrium hydride separate from the specimens during this powdering process. The reaction of yttrium nitride with water vapor is believed to be as follows: 2YN + 3H2O - Y203 + 2NH3. Despite the fact that this nitride is present only as an extremely thin surface film, if the above reaction is not prevented by removing this film from the surface either by machining or grinding, the reaction continues until the entire hydrided piece has been reduced to a powder. To account for this continuation of the reaction, it is believed that the following reactionalsooccurs: 2YH2 + 2NH3 -2YN + 5H2. The nitride produced by the latter reaction reacts in turn with water vapor. The reaction therefore becomes autocatalytic and continues until the hydride has been consumed and the entire piece reduced to oxide powder. The amount of nitride required to initiate this reaction is quite small and this nitrogen contamination can occur from a number of sources—hydrogen gas employed, minute leak in the hydriding apparatus or even from degassing of the reaction vessel itself. Longer hydriding times increase the possibility of nitrogen contamination and this is especially true when a dynamic gas system is employed in the hydriding process. The production of stable, solid hydrided yttrium is dependent on the complete absence of nitrogen contamination during processing. If such contamination does occur, powdering of the hydrided product can be prevented by removing the nitride from the surface e.g. grinding or by preventing access of air to the pieces e.g. sealing in wax or plastic. The author wishes to express his appreciation to General Electric Co. for sponsoring this research and for permission to publish the results of work under Subcontract AT-93.

Jan 1, 1962

Institute of Metals - Iron and Steel - Mineral Industry - Industrial Minerals Year ?Division - Petroleum Division ? Division - Coal Division - Education Division -Division 1918 W M CORSE 1919 1920 W. H BASSETT 1921 1922 W B PRICE RALPH ARNOLD 1923 E DEGOLYER 1924 G K ELLIOTT 1925 F JULIUS FOHS 1926 PAUL D MERICA 1927 JOHN M LOvEJOY 1928 S SKOWRONSKI A W AMBROSE RALPH H SWEETSER

Jan 1, 1952

By M. G. Nicholas

The influence of deformation, relative movement and surface cleanliness on the strength of room -temperature "interparticle" bonds between copper surfaces has been studied. No bonding resulted when clean surfaces were merely pressed together, even under pressures of 50,000 psi. Bonding resulted, however, when clean surfaces were simultaneously pressed and moved relative to each other, some bonding occurring no matter how small the pressure or relative movement. Exposure of the clean surfaces to various chemicals inhibited bonding, none at all being produced by small relative movements. The size of the movements which first produce bonding between exposed surfaces depends on the nature of the chemical, being less than 0.002 in. for cleansing reagents and greater than 0.004 in. for lubricants, water and hydrogen sulfide. It is concluded from the experimental data that the prime requirement for bonding is the dispersal of surface films such as oxides and adsorbed contaminants. THE formation of interparticle bonds during the room-temperature compaction of powder metallurgy components greatly increases the ease of handling in subsequent production operations prior to sintering. The strength of unsintered compacts follows the same general trends as their density and hardness, but quantitative data are extremely Scarce. Quantitative correlation of the data on the overall strength of a compact with that of the individual interparticle bonds is virtually impossible due to the extremely complex geometry of powder compacts. Qualitatively, however, the strengths of unsintered compacts can be correlated with variations in parameters known to influence the extent of cold bonding, and hence interparticle bonding, such as surface cleanliness, relative movement, and deformation of the mating surfaces. Kuzmic and seelig4 found that contamination of powder particle surfaces with lubricants reduced the strength of unsintered iron and copper compacts. Interparticle shear has been shown to promote bonding by Train and Hersey7 while Gregory has shown that die rotation is beneficial. Eilender and schwalbe6 concluded that most bonding occurred during the early stages of pressing iron powder compacts when interparticle shear is one of the principal processes occurring. mile there can be little doubt that these and other factors, such as particle size and shape, affect the extent of interparticle bonding produced by compaction, evaluation of the influence of individual factors is not easy. Particle deformation and relative movement, for example, occur simultaneously during compaction, making any precise measurement of their relative influences difficult. Because of these and other difficulties encountered in studying interparticle bonding in actual powder compacts, the approach adopted in this study was to

Jan 1, 1963

By Strathmore R. B. Cooke, Iwao Iwasaki, C. S. Chang

The effects of aeration on an aqueous suspension of pyrrhotite were studied and their results correlated with flotation tests using xanthates as collectors. The effects of copper activation and of pH variation were determined and possible mechanisms postulated. PYRRHOTITE has long been considered a gangue mineral to be eliminated as tailing in the treatment of various sulphide ores. However, in recent years the world-wide lack of sulphur resources has called attention to this mineral as a potential source of both sulphur and iron. Its importance as an economic mineral, however, has not been particularly emphasized. For this reason very little is known about its response to flotation, except that it can be depressed easily in alkaline circuit, by long aeration,1,2 addition of oxidizing agents,3 or by starch.' The object of this work was to study the floatabil-ity of pyrrhotite. This includes the effect of oxidation by aeration, of copper activation, and of change in pH. Preparation of the Pyrrhotite Sample: It was desirable that the highest grade of pyrrhotite obtainable be used for this experiment, since the presence of other minerals could affect the surface properties.5 However, no pyrrhotite was available as crystals, and massive deposits of hydrothermal origin commonly contain considerable amounts of chalcopyrite. Pyrrhotite concentrate was, therefore, prepared from a sulphide deposit occurring near Aitkin, Minn. The deposit is of pyrometamorphic nature consistirlg mainly of pyrrhotite and pyrite with graphite, silicates, and carbonates as gangue. The ore, already crushed through 3 mesh when received, was screened at 65 mesh and the undersize discarded. The oversize was crushed through rolls, and then stage-ground dry in an Abbe porcelain mill, the —65 mesh portion being screened out after every 15 min of grinding until all the material passed through this size. The ground product was then concentrated with a drum-type dry magnetic separator. The rougher concentrate was cleaned twice and then demagnetized. The final product was split in a Jones splitter and stored in air-tight bottles. Microscopic examination of the concentrate showed that it was relatively clean and free of pyrite, locked particles, and gangue. By means of the krypton gas adsorption method," the specific surface was determined to be 3000 cm2 per g. The chemical and screen analyses of the final concentrate are given in Tables I and II respectively. It is a well-recognized fact that the oxidation of some sulphide ores during stockpiling, grinding, and conditioning affects their flotation behavior. The problem of oxidation may become serious in the case of pyrrhotite, since this is known to be more easily oxidized than many other sulphides. To ascertain the extent of oxidation, an experiment was carried out by aerating an aqueous suspension of pyrrhotite with air, oxygen, and nitrogen as follows. A 300-g sample of pyrrhotite in 2700 ml of water was agitated and simultaneously aerated in a Fager-gren-type laboratory flotation machine. A Precision wet test meter was connected to the air inlet valve, the flow rate of the gas being kept constant at 0.3 cu ft per min throughout the experiment. Samples of approximately 30 ml each were taken from the cell at 0, 4, 10, 20, 35, 60, and 90 min. After the pH was taken, each sample was filtered and the filtrate was analyzed for total iron and sulphur. The iron was determined colorimetrically by the thioglycolate method using a green filter.' The filtrate was oxidized with bromine to convert all of the soluble sulphur compounds into sulphate and this was determined with a Parr turbidimeter." When aeration tests were made in alkaline circuit, calcium hydroxide or sodium hydroxide was added at regular intervals to maintain a constant pH. A similar procedure was followed in an experiment to determine the abstraction of copper. ion by pyrrhotite. In this case various quantities of cupric chloride were added. The filtrate from each sample taken was analyzed for copper, total iron, and sulphur. The carbamate method with a green filter was used for the copper analysis,' since this method could tolerate a considerable amount of iron in the solution. A pneumatic cell, made from a 350-ml fritted glass Buechner funnel, was used for this experiment. The detail of the assemblage has been described elsewhere." In the present work a stainless steel baffle was inserted in the cell. This baffle overcame the tendency for the coarse pyrrhotite particles to be swirled around the wall of the cell and thus fail to collect in the froth. A 50-g sample of pyrrhotite was added to the cell which contained 260 ml of water. When pretreat-ment of the sample was desired, reagents, such as activator and pH regulator, were then added and the pulp was conditioned for a specified conditioning time. Prior to the addition of the collector approximately 15 ml of the solution were removed for pH measurement and for iron and sulphur analyses. Copper when used as activator was also determined. Collector and frother were then added and the pulp was conditioned for an additional 2 min. Air was admitted to the cell and the froth removed. The separation required from 4 to 6 min, depending on the characteristics of the froth. The float and non-float products were filtered, dried, weighed, and assayed for iron.

Jan 1, 1955

By W. A. Backofen, D. Lee

The deformation of textured sheet of titanium and several of its all-a (hcp) alloys was investigated with two kinds of experiments: tension testing along different directions in the plane of the sheet, and combined-stress loading along the principal axes of anisotropy (the rolling and transverse directions). Texture and plastic anisotropy were evaluated with pole figures and by measurement, as a function of orientation, of the tensile transverse-strain ratio, or R parameter. The results as a whole can be rationalized qualitatively with the present understanding of deformation mechanisms in titanium. Quantitative agreement between the orientation dependence of tensile yield strength and the Predictions of continuum ANISOTROPY in the properties of engineering materials is more the rule than the exception because anisotropy in structure is so common, and the one generally follows the other. Two broad categories of structural anisotropy are represented by mechanical fibering and crystallographic texture. The former is important in many aspects of fracture.' The latter has more significance for yielding and plastic deformation, theory, using the R measurements, was relatively poor. However, in tension-tension quadrants of the yield-locus diagrams, the difference between theory and experiment was hardly more than 10 pct. The maximum texture-hardening effect was found in a 4Al-1/4O2 alloy to be nearly 50 pct. In the compression-compression quadrant, {1012} deformation twinning prevented the locus from expanding much beyond the Position predicted for isotropic material. With increasing temperature the trend in R was downwards, approaching unity (isotropy) near the a-transus temperature; an accompanying development was large amounts of neck-free extension. which are of special concern in this paper. The tendency has been to view crystallographic texture more as a liability or curio than as an asset. The prominent exception is found in silicon-ferrite sheet for power-transformer cores, which is processed to develop a new optimum texture for high electrical efficiency. Yet it should be possible to find other examples, involving other kinds of properties. More specifically, there is good analytical reason to expect improved combined-stress yielding resistance in suitably textured material,2,3 and it has now been shown by experiment that texture hardening or softening is a potentially useful phenomenon in certain engineering devices and processes.'-I To date, work has included measurements of the transverse (width to thickness) strain ratios in the

Jan 1, 1967

By E. A. Anderson

THE copper-zinc phase equilibrium diagram has been the sub-ject of many investigations. Until recently, however, the boundary of the terminal solid solution of copper in zinc (eta) has not been thoroughly investigated. This paper reports determinations of the solid solubility of copper in zinc at temperatures from 100° to 400° C., the course of the liquidus and solidus for the eta solid solution and determinations of the peritectic temperature and peritectic point for the reaction between epsilon and the melt to form eta. The liquidus of the eta phase was determined by thermal analysis and the solidus by the microscopical examination of specimens quenched from temperatures above and below the solidus. The temperature of the peritectic horizontal was obtained by thermal analysis and the com-position at the peritectic point was determined by extrapolation of the solid solubility boundary of the eta phase to the peritectic horizontal. The solid solubility boundary of the eta solid solution was investigated very carefully. Particular care was used to achieve equilibrium in the alloys at each temperature selected. The X-ray, electrical con-ductivity and microscopical methods were used in determining the solid solubility limits. The X-ray method measures the changes in the solvent lattice with increasing solute content and in this manner locates the composition of the alloy at which no further change in the solvent lattice takes place, the limit of solid solubility. The method of electrical conductivity measures the conductivity of the alloys of a graded series of compositions, whereby the solubility limit is indicated by a discontinuity in the conductivity-

Jan 1, 1934

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 Cyril Smith

IN the study of the structure or the properties of a series of alloys or nonmetallic compounds, it is often advantageous to express the com-position not as percentage by weight, according to which the material is always made up and analyzed, but as the atomic percentage of the two constituents. The conversion from the one to the other is repre-sented by the formulas: 100A 100x Y x 100 ? x/A A [1] A+ B x + A/B(100-x) X _ 100yA 100y [2] yA+(100-y)B or y+A(100-y) where x and y are the weight and atomic percentages respectively of the element of atomic weight A, and (100 - x) and (100 - y) are the per-centages by weight and by atoms respectively of the element of atomic weight B. While calculations according to these formulas are simple, they are' time consuming if several conversions have to be made. In 1931 Water-man' constructed a nomograph for performing the conversion, but this did not permit an accuracy greater than about 1 per cent to be obtained in the neighborhood of 50 per cent. Olander2 has proposed a graphic method simpler than Waterman's and one that gives a uniform precision throughout the entire scale. The possible accuracy is about 0.5 per cent of the whole, depending on the size and accuracy of the coordinate paper used. Recently, Hermann3 has described a slide rule for making the calculations. These devices make use of the simple rearranged equation:

Jan 1, 1933

By Cyril Smith

IN the study of the structure or the properties of a series of alloys or nonmetallic compounds, it is often advantageous to express the com-position not as percentage by weight, according to which the material is always made up and analyzed, but as the atomic percentage of the two constituents. The conversion from the one to the other is repre-sented by the formulas: 100A 100x or 1 x/A+100-x/B B(100-x) _ 100yA 100y [2] X. yA + (100 - y)B or y (100 - y) where x and y are the weight and atomic percentages respectively of the element of atomic weight A, and (100 - x) and (100 - y) are the per-centages by weight and by atoms respectively of the element of atomic weight B. While calculations according to these formulas are simple, they are time consuming if several conversions have to be made. In 1931 Water-man1 constructed a nomograph for performing the conversion, but this did not permit an accuracy greater than about 1 per cent to be obtained in the neighborhood of 50 per cent. Ölander2 has proposed a graphic method simpler than Waterman's and one that gives a uniform precision throughout the entire scale. The possible accuracy is about 0.5 per cent of the whole, depending on the size and accuracy of the coordinate paper used. Recently, Hermann3 has described a slide rule for making the calculations. These devices make use of the simple rearranged equation

Jan 1, 1933

By J. B. Cheatham

The influence of friction on the force required for an idealized bit tooth to penetrate a "plastic" rock is analyzed. The rock is assumed to obey the Coulomb-Mobr yield criterion and the tooth is represented by a two-dimensional sharp wedge. At the tooth-rock interface the stress field not only satisfies the yield condition but also is such that the ratio of the shearing stress to the normal stress is equal to the coefficient of friction. The solution relates the force on the tooth to the depth of penetration, the tooth angle, the coefficient of friction between the rock and bit tooth and the angle of internal friction and compressive strength of the rock. INTRODUCTION Most rocks are brittle at atmospheric pressure but exhibit ductility and increased strength as the confining pressure is increased. In a previous analysisl the force required for a bit tooth to penetrate a rigid-plastic rock was computed for two limiting conditions: (1) a perfectly lubricated tooth-rock interface which should correspond to a lower limit for the penetrating force, and (2) a perfectly rough interface which should provide an upper limit. Experimental results2 for rock indentation under confining pressure have confirmed that the analysis generally predicts upper and lower limits for the penetrating force as a function of rock properties and tooth angle. The present analysis extends the previous work to account for the friction between the rock and the tooth. ANALYSIS The force required for incipient plastic flow of an idealized model of a rock under a bit tooth is computed subjected to the following assumptions. BIT TOOTH 1. sharp two-dimensional wedge (end effects neglected) 2. rigid tooth (elastic deformation of tooth neglected) 3. displacement of tooth is normal to rock surface 4. friction exists between tooth and rock ROCK 1. semi-infinite, isotropic and homogeneous 2. rigid-plastic (elastic deformation of rock neglected) 3. non-work hardening (horizontal stress-strain curve) 4. Coulomb yield condition* (linear Mohr envelope) 5. smooth, flat surface According to the Mohr theory of failure it is assumed that failure occurs when the state of stress is such that the Mohr stress circle becomes tangent to an experimentally determined envelope. The Mohr failure curve is frequent1y approximated by a straight line and referred to as the Coulomb-Mohr failure criterion. If the rock is under sufficient pressure to be ductile we can use the linear envelope as a yield condition. The Coulomb-Mohr yield criterion is illustrated by Fig. 1 and is expressed by the following equation:l