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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 H. H. Hausner, H. S. Kalish

IN recent years zirconium and beryllium have become of great interest because of their special properties. Zirconium is known for its remarkable ability to absorb the gases oxygen, nitrogen and hydrogen, has extensive use as a getter in electron tubes and has indeed become the primary metal in the manufacture of photoflash bulbs. Beryllium is of interest because it is light metal and as such could supplement aluminum and magnesium in light metal applications. The late development of zirconium ductile at room temperature produced by both the iodide and calcium reduction methods has stimulated frequent articles on this metal in the recent literature. Beryllium is so closely akin to zirconium crystall-ographically that some investigators are of the opinion that beryllium should be ductile at room temperature if it were pure enough. The crystallographic relationship of beryllium and zirconium, the interest created in Be-Zr alloys where the zirconium is believed to function as a remover of solid solution gas in beryllium and thus increase the ductility of the beryllium rich alloy, and the amenability of these metals to powder metallurgy methods stimulated this approach to an investigation of the system Be-Zr. Preliminary work showed that a zirconium compact melted when pressed in contact with a beryllium compact and sintered at 1250°C, without any apparent final bond between the two. A search of the literature revealed nothing pertinent about the Zr-Be system or about any zirconium - beryllium alloys. In 1936 Misch³ vaguely identified the compound ZrBe2 and reported that it has a deformed cubic structure. Two patents," , were issued to Mach-lett Laboratories in 1943 and in 1946 regarding the addition of small amounts of zirconium to beryllium in order to improve the ductility of beryllium so that it may better be used for X ray windows. In considering the alloy formation of beryllium with other metals Raynor thought it unlikely that zirconium would have any solid solubility in beryllium. From this indefinite information nothing could be ascertained about the possible use of Zr-Be alloys or the use of these metals intimately. A brief preliminary study of the system Zr-Be by powder metallurgy methods was undertaken to provide regions for more intense studies of Zr-Be alloys and as a guide to a formal phase diagram determination. The investigation described in the following pages was completed in less than three weeks. The usefulness of this rapid method to facilitate phase diagram studies and new alloy investigations will be shown. Materials and Procedure Zirconium powder was produced from crystal bar stock of high purity supplied by Foote Mineral Co. The crystal bar was converted to hydride at 730°C, crushed, and the hydride decomposed in purified argon at 850°C. 60 pct of the powder passed through a 325 mesh screen, 40 pct of the powder was —140 mesh, +325 mesh and the average particle size of the total was 8 to 12 microns. The beryllium powder was used as re-

Jan 1, 1951

By B. W. Howlett, M. B. Bever, Somnath Misra

The heats oj- formation at 0°C of the compounds AuSn,, AuSn2, AuSn, and the £ phase were measured in a metal -solution calorimeter with liquid tin or a liquid Sn-Bi alloy as solvent. The melting point, heat of fusion, and heat capacities near the melting point of- the compound AuSn in the solid and liquid state were measured in a constant temperature gradient calorimeter. The free energy and entropy of formation of the compound AuSn at its melting point and at 298 °K were calculated from the experimental results and published data. The heats of formation are discussed in relation to the nature of the compounds. The heat capacity below the melting point, heat of fusion, and entropy of fusion of AuSn are interpreted in terms of processes oc-curring before melting. The atomic arrangement in liquid Au-Sn alloys and the bonding in the intermediate phases of. the Au-Sn system are discussed in the light of the measured thermodynamic properties. THE available thermodynamic information on the intermediate phases in the Au-Sn system consists of the heats of formation of the compounds AuSn4, AuSn2, and AuSnly2 and of one composition of the < phase2 besides values of the heat content of the compound AuSn from 0" to 635".&apos; However, the heats of formation refer to different temperatures ringing from 90" to 450°C. Also, the reported error limits of some of the values are large and several inconsistencies are apparent. In the investigation reported here the heats of formation of the compounds AuS-, AuSnz, and AuSn and of three compositions of the < phase were determined for a single reference temperature of 0°C by liquid metal-solution calorimetry. The compound AuSn, which is the only congruently melting intermediate phase in this system, was further investigated in a constant temperature gradient calorimeter by measuring its heat of fusion, melting point, and heat capacity in the solid and liquid states near the melting point. From these data and published free energies of the liquid of composition Au~n,&apos; the free energies of formation of the compound AuSn at the melting point and at 298°K were calculated. The results shed light on the solid-liquid transition of AuSn and on the atomic bonding and state of association of gold and tin in the solid and liquid phases. 1) EXPERIMENTAL PROCEDURES 1.1) Preparation of Samples. Stoichiometric amounts of gold and tin, each 99.99+ pct pure, were melted in evacuated Vycor capsules (12 mm ID). The melts were maintained approximately 150°C above the liquidus for about 12 hr and shaken repeatedly. Samples of the compound AuSn were cooled slowly to room temperature. Melts of the other phases, all of which solidify by peritectic reactions, were transferred to the narrow end (5 mm ID) of the capsule, which was then quenched into iced brine. The solidified samples were annealed in the unopened capsules for 10 days at 30" to 50° C below the respective solidus temperatures. The absence of microsegregation and second phases was confirmed by metallographic examination. At least two batches of each composition were prepared. 1.2) Solution Calorimetry. The heats of formation were determined by liquid metal-solution calorimetry. In this technique, the difference between the heat effects on dissolution in a liquid metal, or alloy bath, of the compound and a mechanical mixture of its annealed components, adjusted for changes in composition of the bath, is the heat of formation of the compound at the temperature from which the samples are added. Details of the equipment and technique have been described."&apos; A tin bath at 300" or 350°C was used with the compounds AuSn,, AuSnz, and AuSn. The high gold content of the £ phase would have caused it to dissolve with an appreciable exothermic heat effect. In order to achieve thermal compensation, the samples were added from 0°C to a bath at 350°C consisting of 66.2 wt pct Bi (99.999+ pct pure), balance Sn (99.99+ pct pure). This solvent gives thermal compensation because gold dissolves exothermically in tin and endothermically in bismuth. The calorimeter was calibrated by adding from 0°C approximately 0.015 g-atom of the solvent.

Jan 1, 1965

By K. A. Svanstrom, W. R. Opie

Problems associated with deposition of titanium infused chloride baths using TiCl4 as a feed material are reviewed. A potentially workable cell design using Alumdum diaphragms is discussed. Problems inherent to diaphragm-type cells are emphasized and experiments described which led to the development of a cell without a diaphragm. INVESTIGATORS assigned the problem of developing a commercial electrolytic process for making titanium metal have found that they are faced with the difficulty of overtaking rapidly improving magnesium and -sodium reduction processes. The ultimate goal must be a simple process that can be conducted with low-cost raw materials in equipment that is inexpensive to build and operate. This paper deals with some work of a preliminary nature conducted by personnel of the Research Laboratories, National Lead Co., Titanium Division. Many others have reported on the general subject of depositing titanium from fused salt electrolytes. A partial bibliography is attached. PRIMARY CONCEPTS Anyone attempting to deposit titanium metal from fused chloride electrolytes using TiC14 as a source material is faced with at least the following problems: 1) Getting the titanium into solution in the bath. 2) Controlling oxidation and reduction reactions associated with multiple valency of titanium, which result in low electrical efficiency. a) Prevention of dichloride oxidizing to trichloride and trichloride to tetrachloride at the anode. b) Prevention of trichloride from being reduced only to dichloride at the cathode. 3) Prevention of metal formation away from the cathode thru disproportionation of titanium dichloride to satisfy the equilibrium. 3 TiCl2 == 2 TiCl3 Ti [I] 4) Protection of reduced chlorides in the bath from reaction with oxygen from the bath container or air. 5) Removing from the bath the deposited metal formed without allowing it to become contaminated with oxygen or nitrogen. 6) Selecting cell materials of construction which will not contaminate the metal product or cause cell inefficiencies. EARLY EXPERIMENTS The initial attempts made to electrodeposit titanium from fused chloride baths using TiCl4 as a source material indicated that TiCl4 was essentially insoluble in molten chlorides of alkali and alkaline earth metals. If, however, the TiCl4 was introduced close to a nickel cathode some metal could be formed and appreciable quantities of reduced chlorides would be present. These reduced chlorides reacted with any oxygen present in the atmosphere above the bath and would also diffuse quickly to the anode (graphite) where they would react with chlorine and be evolved as TiCl4. The net electrolytic efficiency of such a cell is essentially nil. The TiCl4 evolves from the anode at almost the same rate that it is introduced in the vicinity of the cathode although a small amount of titanium metal can be formed on the walls of the cathodic pipe. It becomes apparent from the operation of such a cell that: metal can be deposited on the cathode, although of small particle size and a nonadherent nature, and when reduced chlorides are present in the electrolyte, TiCl4 can be absorbed, probably by the following reactions: TiCl4 + TiC12 - 2 TiCl3 [21 2 TiCl3 + 2 faradays - 2 TiC12 + C12 [31 DIAPHRAGM CELLS These facts encouraged the development of cells containing diaphragms to prevent migration of reduced chlorides from the cathode area to the anode. Small-scale cells for process development are described by Alpert, Schultz, and Sullivan.20 A larger brick-lined cell incorporating internal heating by passing ac through the bath is shown in

Jan 1, 1960

By Bunting S. Crocker

PEBBLE grinding at Lake Shore is not a temporary wartime substitute. The tube milling plant, with a 1000 ton per day capacity, grinds a hard siliceous ore to 90 pct - 325 mesh. The plant, prior to using pebbles, was consuming 4.3 lb of 1 1/4-in. grinding balls per ton of ore, which amounted to 785 tons of balls per year. At September 1951 prices, $132.60 per ton, this steel cost amounted to, $104,400 per year, or $0.285 per ton milled. By the Lake Shore method of substituting screened rock for this steel, all of this cost is saved. This is one of the major economies in Lake Shore mill practice. Regardless of the ultimate price of grinding balls, a change, back to steel balls is not considered. The present pebble plant is more flexible than a steel ball plant and equally efficient. For example, if it is desired to change the size of grinding media, the pebble charge in any mill can be changed completely in 4 to 5 days, as against 76 days to change completely a 1 1/4-in. steel ball charge. To change pebble size it is necessary only to change two sets-of screens and clean out the rock feed storage bin. This will take 8 to 10 days as against 3 to 4 months to clean. out the customary supply of grinding balls kept on hand. Also it has not always been &apos; possible to purchase all desired sizes of balls at any price. In an analysis of savings effected by the use of the pebble mills, the flexibility of the Lake Shore grinding plant should be discussed, as it has a direct bearing on these savings. The plant has always used several units to handle tonnage rather than sending all the tonnage through a single unit. This principle may result in using small diameter mills, but no objection to that is seen. At no time has any advantage been found in cost per ton ground in large diameter mills. Both the capacity and the power of any mill varies as the diameter raised to the 2.6th power. Consequently large or small mills are equally efficient, and a plant should be designed to use as many units-or combination of units as is consistent with reasonable operating practice. Mills under 5 ft diam are harder to reline, etc. To define the case at Lake Shore, .2600 tons per day formerly were milled in seven 7x6-ft ball mills and twelve 5x16-ft (and two 6x16-ft) tube mills.* This gave an excellent test plant. and an extremely efficient-one. In this plant the ratio of ball mills to tube mills was 1: 2. When the much cheaper pebble mills were substituted for the tube mills, this. ratio -was changed to one ball mill to four pebble mills to take the greatest possible advantage of the cheaper operating mill, i.e., the pebble mill. This flexibility without loss in efficiency has been an important item in the cost savings. It is interesting to note that the use of pebbles for fine grinding was. proved first in the laboratory in a 12-in. ball mill. In fact, since 1934 all testing on -.8 mesh material has been done in this 12-in. mill. Scope of the Tests A paper on fine grinding at Lake Shore Mines was published in July 1940.1 This paper covered 7 years of intensive research on fine grinding as well as sizing methods and equipment, plant scale grinding tests on 5x16-ft tube mills with and without .grate discharges-both with 1 1/4-in. and 3/4-in. balls, the use of laboratory mills to evaluate plant changes, and several reports on classifiers and classification. In the following July the addendum report&apos; was added in which the idea of series-circuit grinding was introduced, and the results of running five stages of tube mills and bowl classifiers were shown. Since 1940, the ball milling end of the plant has been altered extensively as a result of tests on the use of 3 1/2-in. rods in 7x6-ft mills and the use of the Tyler repulping screen with from 7 to 14 mesh screens. These tests are, lengthy and may be covered in a separate &apos;report later. The scope of this report is confined to ore ground by rod milling and ball milling until it passed through an 8 mesh Tyler Ty-rod screen. The -8 mesh screen undersize then was pumped to a primary bowl classifier in open circuit and the sands .from the bowl sent to the primary pebble mills, see Fig: 1. In the pebble mill circuit the ore is ground to 90 pct -325 mesh (24 pct + 28 microns) In studying the flowsheet, attention should be paid to the efficiency of the classification equipment used. The Tyler repulping screen is an efficient machine on the 8 to 10 mesh separation, and the bowl classifier is equally efficient at the 325 mesh separation. Efficient classification is a necessity for series-circuit stage grinding. The ore is hard siliceous porphyry, 60 pct SiO2, 80 pct insoluble. Its grindability at different. meshes has been shown near the top of &apos;the list in F. C. Bond&apos;s grindability tests&apos; Lake Shore is not shown, but an adjacent-mine with identical ore, Wright-Hargreaves, is. Reasons for the-Changeover Since 1936 grinding balls have been rising steadily in price with no sign of stopping. For a mill that used 4.5 to 5.2 lb of grinding balls for every ton of ore ground this rise represented an alarming increase in grinding costs. In many cases the quality of the grinding balls fell off as the scrap steel became more difficult to obtain. The ratio of tube mills to ball mills increased with the use of the Tyler repulping screen in the ball mill circuit. Originally only 3.0 lb of balls per ton were used in the tube mills, and this

Jan 1, 1952

By Donald A. Brobst

The minerals barite (BaSO4-barium sulfate) and witherite (BaCO3-barium carbonate) are the chief commercial sources of the element barium and its compounds whose many uses are nearly hidden among the technical complexities of modern industrial processes and products. Barite, the major ore mineral, is extremely vital to the petroleum industry which in 1980 consumed at least 90% of the world&apos;s production of 8.8 million tons as a major ingredient of the heavy fluid, called mud, that is circulated in rotary drilling of oil and gas wells. The remaining 10% of the barite production was consumed chiefly in the manufacture of barium chemicals and glass and as a pigment, filler, and extender. Barite occurs throughout much of the world and is available from three major geologic types of deposits-vein and cavity filling, residual, and bedded-in sufficient quantity at competitive prices to meet current demands. The world&apos;s demand for barite is expected to increase, and geologic circumstances are favorable for the discovery of new deposits of commercial value. Witherite is much less common and abundant than barite, although it is more desirable in many ways as a raw material for the production of barium chemicals. The United States has not produced witherite since about 1950; England is currently the chief producer of witherite. End Uses Most of the world&apos;s barite production since 1926 has been used as a weighting agent for the muds circulated in rotary drilling of oil and gas wells. The muds fundamentally are mixtures of water, clay, and barite in different proportions that vary according to local reservoir conditions. Muds with a specific gravity as great as 2.5 are used. The mud is pumped down the hollow drill stem, passes through the bit at the bottom of the hole, and rises to the surface in the space between the drill stem and the wall of the hole. In the course of this circulation the drill bit is cooled, cuttings are removed, the drill stem is lubricated, the walls of the hole are sealed, and the hydrostatic head of the column of weighted fluid helps to confine high oil and gas pressures. The latter feature aids in prevention of gushers, thus reducing both environmental pollution and waste of oil and gas resources as well as conserving the natural reservoir pressure for greater production and rate of recovery of the products contained in the rocks. Barite is particularly well suited for drilling mud because it is clean, easy to handle, soft (nonabrasive), heavy, virtually inert chemically, and relatively inexpensive compared to many other available heavy materials. Barite is used in the manufacture of glass in continuous tanks. The addition of barite homogenizes the melt and gives greater brilliance and clarity to the finished glass. Ground barite, both unbleached and bleached by sulfuric acid, is a common industrial filler, extender, and weighting agent. The rubber industry is a major consumer of barite as a filler. Barite also is added to bristolboard, heavy printing paper, playing cards, rope finishes, brake linings, clutch facings, plastics, and linoleum, to name but a few uses. Bleached barite has long been an extender in white lead paint because of its weight. The low index of refraction of barite, however, makes its ability to cover marks poorer than some other substances, but its low capacity for absorption of oil is a good feature. Off-color or unbleached barite can be used as a filler in colored paints. In the construction industry, some lump barite is used in concrete aggregate to weigh down pipelines buried in marshy areas and to shield nuclear reactors. Because barite absorbs gamma radiation well, its use reduces the amount of expensive lead shielding otherwise

Jan 1, 1983

By C. H. Cheng, C. E. Birchenall

The fundamental problem in the thermodynamics of solid solutions is the determinatiorl or calculation of the activities of the components as a function of temperature and composition. Since the theory of metals is not suficiently developed to allow a priori calculation of these quantities, they must be obtained from experiment. C. Wagner1 has reviewed the literature of this subject for the period before 1940. Although several important and extensive studies have been made in the meantime, the number of systems to which any sort of quantitative information can be assigned is vanish-ingly small. These data have become of great potential importance in studies of the structure of solid solutions2 and intermetallic compounds, the nature of the diffusion process,3,4 and perhaps even the mechanism of mechanical deformation.5 For these reasons, it. seems very worthwhile to extend the experimental data in this field. Although there is little use in duplicating Wagner&apos;s review, attention should be directed to the most recently reported investigations. A brief enumeration of the methods of measurement previously employed also should be valuable. The most direct method is the determination of the partial pressure of the components in the vapor phase in equilibrium with the solution. Both equilibrium and kinetic methods have been tried in metal systems, but almost exclusively on liquid phases. Only in the ease of carbon in iron alloys and in the copper-zinc system have extensive measure- ments been made which include solid phases. When one of the components is an element, such as nitrogen or carbon, which forms compounds which are very volatile and stable at normal temperatures and pressures (CH4, Co2, CO NH3), it is frequently possible to equilibrate mixtures containing these (such as CH4-H2, CO2-CO, NH3-H2) independently with the elernents (C, X) and with the metal (Fe, Ni, etc.). Such measurernents have been made for carbon in iron, iron-silicon, and iron-manganese alloys by Smith6 and in iron and iron-nickel alloys by Toensing.7 Differences between carbon activity values at the same temperature and carbon content when carboil is introduced from CH4-H2 rnixtures or CO-CO. mixtures indicate that the effects of hydrogen and oxygen in the system are not negligible, and one can only hope that the true value lies somewhere between these sets of results, probably nearer the CH4-H2 data since hydrogen is less soluble in iron than oxygen. This is essentially an equilibrium method, although flowing gas is employed. A kirletic method has been employed which consists of sweeping an inert gas (generally hydrogen) over the alloy at a series of rates, condensing the metal vapor out,, and analyzing it. The metal content can be extrapolated to zero flow rate (equilibrium). Wejnarth&apos;s8 work on Cd-Mg and Zn-Mg is a good example of this frequently used method. A variant of this consists of equilibrating a known volume of inert gas with the alloy, sweeping it out quickly, and analyzing for metal. In common with the above method, it has the disadvantage that the "inert" gas is generally somewhat soluble in the alloy. Moreover, the former continuously displaces the system from equilihrium and may give low values if solid diffusion is involved. The dew point method applied by Hargreaves9 to the alpha and beta brasses and by Schneider and Stolll0 to A1-Zn avoids the introduction of another component to the system, but is useful only in systems in which one component is much more volatile than the other. The alloy sealed in one end of an evacuated silica tube is heated to the desired temperature. The temperature of the other end is lowered until droplets of the volatile component condense. When the temperature is raised slightly, the droplets will evaporate. By careful adjustment of temperature, the range between evaporation and condensation can be narrowed appreciably. An independent determination of the vapor pressure of the . pure volatile component is necessary to give the partial pressure over the alloy. This is the method employed here to determine the vapor pressures of zinc and cadmium over their silver alloys up to 34 pct in cadmium and 76 pct in zinc. The former involves only the a solid solution, but the latter covers the a, ß, y, and e fields. In recent determinations, Herbenar, Siebert, and Duffenbarkl1 used the

Jan 1, 1950

By E. R. Gilbert, D. E. Munson

Creep of copper under 75 to 1.50 kg per sq cm stresses at temperatures near the melting point was found to he a complex reaction controlled by three mechanisms acting in parallel. In order of appearance with decreasing temperature, the auerage activation energies, Qc , are 168, 79, and 24 kcal per mole. Stress dependence of the minimum creep rate was found to he an exponential for the two high-Qc processes and a power law for the low-Qc, process. Transition of control occurs from one mechanism to another. The relative transition temperature depends upon the applied stress, and the range oiler which the transition occurs depends upon the difference in the activation energies of the mechanisms. The creep behavior at high temperature is explained by the climb of dislocations through thermally or mechanically formed jogs, CREEP in pure fcc metals at temperatures in excess of one half the absolute melting point is normally controlled by dislocation c1imb.1,2 A climb model which seems applicable, according to an extensive analysis of data,3 was derived by Weert-man.4 This model assumes jog-saturated dislocations and predicts an activation energy, Qc, nearly equal to that for self-diffusion, USd. Although the requirement of jog saturation is restrictive, agreement between theory and experiment seems adequate. Many other theoretical treatments, including an early model by Mott,5 include detailed consideration of jog formation as an initial requirement for climb. These models predict activation energies for creep which differ from those of self-diffusion. Seeger6,7 postulates an observed activation energy related to the stacking-fault energy. Thus, Usd <Qc<5Usd + Uj where Uj is the jog-formation energy. Seeger incorporated qualitatively the influence of the relative numbers of thermal and athermal jogs. Expanding this concept, Shoeck8 explicitly states a function based on formation mode and relative numbers of vacancies: e r ci exp {-uf/k T} exp {-Um/k T} [ 1 ] where Uf and Um are energies of vacancy formation and migration, respectively. The concentration of jogs, Cj, depends upon the manner of jog production. For intersection jogs, Cj is not sensitive E. R. GILBERT, Junior Member AIME, formerly with De- to temperature; for thermal jogs, Cj is proportional to exp {—Uj /k T}. Schoeck regards each mode as a distinct mechanism; therefore, the mechanisms may act together.299 The diversity predicted by theory, surprisingly, has not been substantiated by experimental results. A significant investigation must include the extremes in stacking-fault energy. Extensive creep studies of aluminum10 and nickel,11,12 high stacking-fault energy metals, have been made. Comparable studies on a low stacking-fault energy metal, such as copper, have not. It is the purpose of this paper to report the results of an investigation of the creep of copper under conditions which favor thermal jogs. EXPERIMENTAL Cylindrical compression creep specimens (0.240 in. in diameter by 0.400 in. long) were machined from cold-drawn rods of electrolytic tough-pitch copper containing 0.0007 Mg, 0.002 Fe, 0.001 Ni, 0.0005 Ag, Cd < 0.005, and Pb < 0.005 wt pct impurities. Undetected spectrographically was a nominal 0.04 wt pct 0, which occurs as a Cu2O constituent distributed discontinuously at grain boundaries. Vacuum annealing at 900°C for 15 min produced a stable 0.03-mm average grain diameter. Testing was carried out using apparatus similar to that described by sherby,13 modified by enclosing platens and a push rod in a vacuum cylinder. Normally this arrangement resulted in pressures less than 10 Only a slight surface tarnish, less than 0.0005 in. in thickness, occurred during the test. The applied stress, corrected for atmospheric pressure, was maintained within 2 pct of the desired true stress by the addition of lead shot at fixed strain increments. Creep strain was measured with dial gages as a relative displacement of the upper and lower platens; accuracy of measurement was 0.0001 in. Two creep-test methods were used, the differential or cyclic temperature14 and the isothermal, to obtain creep data at stress levels of 150, 100, and 75 kg per sq cm over the temperature range of 620° to 1032°C. Minimum creep rates were used from both test methods; this was considered proper because comparable temperature tests or cycling to the same temperature gave the same creep rate, within experimental error. The cold vacuum test chamber, with the unstressed specimen in place, was heated to temperature by placing a preheated furnace over the chamber. Temperature equilibrium was attained within 30 min. For the cyclic tests, the stress was removed during the 5 to 10 min necessary to effect the temperature change and re-

Jan 1, 1965

By J. E. Dorn, S. K. Mitra

The low -temperature tensile and creep behaviors of single crystals of copper were evaluated and analyzed in such a manner as to provide an estimate of the separate contributions of short-and long-range stress fields to strain-hardening. Furthermore, the average force-displacement diagram for thermally activated intep-section of two dislocations was estublished. This diagram plus a knowledge of the variation of dislocation spacing and the long-range back stresses with strain permits on accurate prediction of creep rates. The calculated activation energy for intersection under conditions of a constant strain rate increases linearly with the absolute tempevatus-e as required by theory. AN understanding of the detailed mechanisms for strain hardening constitutes one of the principal unsolved problems in dislocation theory. Two major models for strain hardening have been advanced in the past. The one that has received greatest attention assumes that strain hardening arises exclusively from long range interaction stresses between moving dislocations and piled-up arrays of blocked dislocations on the slip planes. This type of interaction was first announced by Taylor&apos; who revealed that the back stress fields due to a simple uniform array of positive and negative dislocations entrapped in the deformed crystal would result in parabolic hardening. Shortly thereafter Andrade and Henderson" demonstrated that the strain hardening of fcc single crystals was not parabolic, as previously thought, and finally it was recognized that a typical stress-strain curve consisted of three successive stages of deformation, niz., the easy glide, Stage I, linear hardening, Stage 11, and the parabolic hardening, Stage 111, ranges. The objections to Taylor&apos;s somewhat na&apos;ive model, which were presented so forcefully by cottrell; were largely removed by the more realistic details incorporated in Mott&apos;s analysis.5 But because Mott&apos;s theory for hardening via long range stress fields gave somewhat analogous results to that of Taylor&apos;s (inasmuch as it also predicted a parabolic rate of strain hardening whereas the observed rate of strain hardening in Stages I and I1 were linear), it was not widely accepted. Major consideration was therefore given to models, such as those which were advanced by Friedel and seegere that were formulated for the ad hoc purpose of yielding linear rates of strain hardening. The second major thought regarding strain hardening is based on the concept that it arises principally from short-range stress fields due to the interactions between intersecting dislocations. Cottrell and stokes7 showed, several years ago, that the constancy of the flow stress ratio at two temperatures regardless of the strain was inconsistent with the concept that strain hardening arose exclusively from long-range back stresses. The argument that strain hardening was primarily due to local interactions of intersecting dislocations was presented in considerable detail by asinski.&apos; Extending Basinski&apos;s method of analysis of the intersection process, Mitra, Os-borne, and dorn recently demonstrated that indeed the strain hardening in aluminum single crystals arises principally from local effects coincident with intersection; however, these conclusions, too, must be modified, as will be shown later in this report. The present investigation, devoted principally to the low-temperature deformation of copper single crystals, was initiated in an attempt to ascertain whether or not the same conclusions arrived at for aluminum also apply to metals, such as copper, which have much wider stacking faults. It was soon observed that the strain hardening in copper could not be attributed exclusively to local effects between intersecting dislocations. Previously no analytical method for arriving at the possible simultaneous contributions of long-range stress fields and localized forces on intersecting dislocations was available; consequently, the separation of these two factors could not be readily accomplished. In the present report a method of estimating the separate contributions of each of these two factors to strain-hardening will be presented. The authors will show that both long-range stress fields of the type contemplated by Seeger and Friedel as well as short-range forces of the type considered by Basinski are responsible for strain hardening in fcc metals at low temperatures. This method of analysis also accounts for, in a satisfactory way, the effect of stress, temperature, and strain on the creep rate under constant stress. Furthermore, in the course of presenting their methods of analysis the authors will also reveal the rather complete agreement of their experimental data with the concepts of the theory for thermally activated intersection of dislocations. INTERSECTION MODEL As shown by seegerl0 the strain rate arising from thermally activated intersection of dislocations is given by

Jan 1, 1962

By J. L. Gillson

THE big mass of anorthosite in the Lake Sanford district and the bodies of titaniferous magnetite that occur in a small area near the south margin of the mass have been described repeatedly, and the puzzling problems of the genesis of the rocks and ores have stimulated the deductive reasoning of geologists for a hundred years. Some of these men have taken a leading part1-15 in describing the anorthosite rock and forming hypotheses concerning its origin; some have contributed most to the study of the ore deposits;&apos;"= and some have made classical Studies3,4,21-27 introducing a basic approach to the problems of the anorthosite rock and genesis of the titaniferous magnetites. Much of the writing on the problems of rock and ore genesis has been based on physical-chemical reasoning rather than on field and microscope observations of the rocks and ores. Most of these geologists conclude that the anorthosite was formed by true magmatic crystallization, involving previous settling or squeezing out of ferromagnesian minerals from the parent magma. The associated gabbro is a separate segregation or later intrusion, and the lighter colored and finer grained facies of the anorthosite is either a chilled border zone of the anorthosite or the result of granulation by crushing of the coarse, dark blue rock of the main mass. This blue rock, called the Marcy type, is named after the higest peak in the range. The finer grained and lighter colored rock is called the White-face, after another mountain appropriately named for a cliff colored by this facies of the anorthosite. In explaining the genesis of the ores the authors have reached no general agreement, but all consider them to be dominantly the result of magmatic processes rather than the result of replacement by pneu-matolytic or hydrothermal processes. However, in the conclusions of two authors, Osborne27 and Ste-phenson," the reader is told positively that the ore minerals were introduced after the wall rock was solid and also that the oxides are later than the silicates. This seems to mean that the ore came in as a later intrusion, like a dike, since Osborne speaks of filter pressing and later injection of a residual magma. Stephenson agrees in general with Osborne but disagrees with his conclusion that ore does not grade into country rock. Singewald22 calls in "mineralizers" to participate in magmatic deposition. Stephenson ends his paper with a statement that replacement was the dominant process for the introduction of ore with anorthosite. Hence both Singewald and Stephenson call on pneumato-lytic or hydrothermal processes to supplement magmatic crystallization from a silicate melt, but they cannot quite bring themselves to state that the orebodies formed in that way. In their conclusions the ores are still magmatic segregations and magmatic injections and—almost as an afterthought— "replacements." According to Bateman18 there was a gravitational accumulation process of the iron silicates and oxides, which were injected later. Rambere explains the ores entirely on physical-chemical theory, as does Evrard.17 Buddington and associates,10 in a paper presented to the Geological Society of America in 1953, believe the facts observed prove that the magnetite-ilmenite formed at magmatic temperatures. The present writer&apos;s conclusions, given here, were first presented in 1947 in Industrial Minerals and Rocks.= Since the papers of Ramberg, Bateman, and Buddington, published after 1947, gave no recognition to those conclusions that differ from their own, the writer has taken an opportunity to restudy the area in the field, and to examine a number of microscopic sections, and now presents the evidence more thoroughly than he had an opportunity to do in the

Jan 1, 1957

Jan 1, 1918

By Theron Wasson

Michigan&apos;s production of 17,301,000 bbl. in 1945, which is in line with previous years, has been maintained by extensions to old fields like Deep River, Adams, Fork, and others. There were a number of new discoveries but, as in the past, these are not given very much importance because enough drilling has not been done to develop their potentialities; however, judging by the past, some of them will develop enough production so that 1946 -will probably be in line with other years. Activities in Michigan were confined to the Basin area of the lower Peninsula, which has been under development since 1925.

Jan 1, 1946

By J. L. Huitt, B. B. McGlothlin, D. K. Lowe

Published correlations for the principal aspects of hydraulic fracturing were combined into a digital computer program to facilitate the study of interrelated variables. The computer program includes individual relationships for fracture width during pumping, fracture area generated, propping agent embedment, flow capacities of propped fractures and transport of propping agents in horizontal fractures. The effects of more than 20 treatment and formation parameters on the predicted results of hydraulic fracturing treatments were studied. The effects of these parameters were determined for (I) fracture width during injection, (2) fracture width after the overburden comes to rest on the propping agents, assumed not to be crushed, (3) generated and propped fracture area, (4) location and concentration of propping agents in the fracture when injection ceases, (5) flow capacities of the various propped sections of the fracture and (6) expected increase in the well productivity. The effects of propping agent, formation and fracturing fluid parameters on well productivity are discussed. The parameters that were found to have the most pronounced effects on hydraulic fracturing treat~nents are injection rate, treatment volume, fracturing fluid coefficient, size and amount of propping agent, spearhead volume, well drainage radius and formation capacity. INTRODUCTION Many correlations have been published for predicting effects of various parameters that are considered in the design of hydraulic fracturing treatments. The Carter equation&apos; can be used to predict generated fracture radius as a function of fracture width, fracturing fluid leakoff and other parameters. Fracture width can be determined by use of the Perkins and Kern correlation&apos; in which the fracture width is related to the fracture radius, fluid injection rate and certain formation and fracturing fluid parameters. Wahl and Lowe et aL4 have reported methods of predicting the location of propping agents in fractures when pumping ceases. The former study is applicable to the case where the ratio of propping agent diameter to fracture width is less than 0.1. The latter is applicable when this ratio is greater than 0.1. These studies showed that the propping agent placement in horizontal-radial fractures depends principally on how the individual particles are transported in the fracture by the carrying fluid. Particle transport in fractures is determined by local fluid velocity in the fracture, fluid and particle properties, and the size of the particle relative to the fracture width. The distribution of propping agents, effective overburden pressure and formation rock strength control the propped fracture width6 by controlling the extent to which the propping agent particles embed into the fracture faces. From the distribution of propping agents and the propped fracture width, fracture flow capacities can be calculated or the various regions of the fracture. The flow capacities and the radial extent of these regions can be combined with reservoir information to predict the productivity increases for fractured wells. In all these studies, the effects of certain treatment and/ or reservoir parameters on one facet of fracturing can be predicted only if other facets which the parameters affect are fixed. For instance, fracture width and radius are interrelated; that is, to calculate the value of one, the value of the other must be known. Also, some parameters influence more than one aspect of fracturing. For example, prop-pant transport is a function of both fracture width and fluid viscosity. but fracture width is itself a function of fluid viscosity. Since these calculations are complex and the parameters interrelated, it is not possible to write an equation with which the over-all effects of treatment parameters can be solved explicitly. For these reasons, the correlations for determining the effects of the parameters which are most significant in hydraulic fracturing treatments have been incorporated into a digital computer program. COMPUTER PROGRAM The program, which was written for an IBM 7094 computer, can be used to predict results of most of the combinations and values for the treatment parameters that are ordinarily considered for fracturing treatments. A spearhead of fracturing fluid and a propping agent-carrying fluid with different fluid properties can be taken into account. Also, the total volumes and relative amounts of the spearhead and carrying fluids can be varied. Two different propping agents (as used in tail-in operations) and a wide range of formation properties and injection rates are considered. The computer program (Fig. 12) consists of several sets of calculations. First, the final flooded fracture radius and average fracture width at the cessation of pumping are calculated. This is done by simultaneous solution of the Perkins and Kern fracture width equation and the Carter equation for flooded fracture radius (equations used in the computer program appear in the Appendix). The next step is to determine local fluid velocity in the fracture as a function of time and radius. Since it is not possible to write this function in closed form expression, a table of velocity values is generated by the program and stored for subsequent use. The time span from the beginning of

Jan 1, 1947

Jan 1, 1930

By W. B. HILLHOUSE

AN excerpt from the Alabama State Mining Law, pertaining to, transporting men&apos; into and out of the mines, reads as follows: "A trip of empty cars may be operated for the purpose of taking employees into and out of the mine, where the distance to and from their work exceeds one mile." The State Mining Department of Alabama includes in its inspection the transportation of men into and out of the mines, also studying and noting improvements, or progress made, that would tend to create a greater assurance of safety in this practice. Everyone is familiar with the original safety methods employed in man-trip transportation, such as passing a rope around the trip of cars, or through the cars, fastened in the conventional manner, and with the usual "clog," commonly called a drag, on the rear end. Also there is a more advanced method of transporting men, such as the double-rope system, which is feasible on slopes used exclusively for this purpose, and is very satisfactory. However, for the past eighteen months; the Republic Steel Corp. and the Tennessee Coal, Iron & Railroad Co. have adopted a practice that shows

Jan 1, 1935

[ARIZONA Established July 10, 1915 CHARLES R. KUZELL, Chairman GILBERT C. DAVIS, First Vice-Chairman ALBERT MENDELSOHN, Second Vice-Chairman MORRIS G. FOWLER, Secretary-Treasurer Phelps Dodge Corporation, Douglas, Ariz. LYLE M. BARKER P. D. I. HONEYMAN A. T. BARR H. M. LAVENDER T. G. CHAPMAN WALTER C. LAWSON GEORGE M. COLVOCORESSES W. H. LOERPABEL EDWIN H. CRABTREE, JR. CARL F. MILLS WALTER I. GARMS P. M. MOSIER WESLEY P. Goss J. A. RICHARDS 11. C. HENRIE JOSEPH A. WILCOX C. F. WILLIS]

Jan 1, 1946

By Persifor Frazer

IN his “Final Report," Vol. II, part second, p. 763, Prof. Rogers sums up the metalliferous veins of the mesozoic sandstone by remarking that these are not associated with dykes or trap-rock, but are independent metalliferous injections. But singularly enough, in enumerating the different kinds of ores, no mention is made of

Jan 1, 1877

By E. L. Tucker

IN THE metallurgy of precious metals, it has been standard practice for years to use cyanogen compounds, so it was but natural that early investigators in the field of flotation should consider these compounds as possible flotation reagents. In Australian Patent 9508, of 1913, alkali cyanides were described as suitable reagents for the separation of heavy sulfide minerals, the reagents being employed either in an alka-line or neutral circuit. In U. S. Patent 1236501, of 1917, to John M. Tibbet, the use of cyanide in conjunction with soda ash or lime is described. One of the claims of this patent reads, "An improvement in the cyanide process for the treatment of ores comprising, mixing the ore with cyanide solution and oil and alkali: emulsifying the oil in the presence of the ore, the alkali and the cyanide solution, floating a portion of the values in the pulp by producing gas bubbles in the mixture-and removing the values floated." More recently, Sheridan and Griswold, in U. S. Patents 1421585 and 1427235, describe a somewhat similar process and have, successfully introduced it in. the mill of the Timber Butte Milling Co. U. S. Patent 1429544, of 1922, to Stevens, describes the use of double cyanides of copper, zinc, and lead. The success of cyanide as a reagent in the differential flotation of lead and zinc sulfides in highly complex ores is proof that these patents have a solid foundation.. Although the technique of their application to particular ores has been worked out in many cases, no one, so far as is known, has attempted to describe the nature of the action of the cyanide or to determine the ideal conditions for its, application. It was the purpose of the present investigation to gather information on these points. Naturally this would have been an exceedingly ambitious.

Jan 8, 1925

By K. C. Strebig, C. W. Schultz, A. A. Selim

The effect of some organic additives in diamond drilling of quartzite was investigated in the laboratory. The drill was designed to measure the rate of penetration, the thrust, and the torque and to record each as a function of the distance drilled. A statistical plan was followed throughout the investigation and an equation representing the bit performance was derived from the mathematical theory of reliability. The drilling torque was found to increase with the use of additives while the sliding coefficient of friction and the wear coefficient decreased. The energy per unit volume consumed was found to increase with the use of additives. A hypothesis explaining the effects achieved with the additives is given. INTRODUCTION For some time researchers have attempted to increase drilling efficiency by adding certain agents to the flushing medium. Much of this interest is the result of the observations of Rehbinder, Shreiner and Zhigach1 They postulated that "...in processes for the mechanical destruction of solids, a region of increased crack formation is created in the deformed layers adjoining that surface of destruction, forming the predestmction zone. The surrounding medium (for example, a liquid) which wets a given solid will penetrate the embryo microcracks of the predestruc-tion zone. Increasing the molecular affinity of this liquid for the surface of the solid considerably facilitates the deformation and destruction by softening the solid in the zone of increased crack formation. In this manner, the hardness or strength of the deformed body is decreased by the influence of the penetration of the liquid into the predestraction zone." This is known as the "Rehbinder effect". Rehbinder&apos;s work has prompted many investigators to examine the effect of additives on the mechanical destruction of rocks. Engelmann, Terichow and Selim reported that the maximum penetration of the rock by a diamond point in a solution environment was at the isoelectric point of the solution.* Robinson reported that his results did not appear to support the theory of Rehbinder.3 Joris and .McLaren suggested that additives with surface tension lower than water will be more efficient in cooling the diamonds.4 Their effectiveness in removing the fine cuttings from the face of the bit will also improve the efficiency of the system. They reported an improvement in impregnated bit life and penetration rates with the use of soluble oil additives. In contrast, Long and Agnew, drilling with surface set bits, reported that lubricating agents increase bit temperature and wear.5 A significant change was reported6 in the mechanical properties of rock with polar additives. It was concluded that this change in the mechanical properties of the rock in the presence of the additive is due to the rock hydrophilic properties. Ethylene glycol, glycerine and anionic detergent were selected for this investigation because their surface tension is lower than that of water. The surface tension of these additives for the concentrations studied was 42 to 75 percent of the surface tension of water. A low surface tension additive would wet the surface of the diamonds more easily and hence would be more effective in cooling the diamonds. Another characteristic of these low surface tension additives is their effectiveness in removing the cuttings and preventing the flocculation of the formed particles in the drilling process. This article summarizes the results of an investigation performed at the laboratories of USBM, Twin Cities Mining Research Center. The objective of the investigation was to study the over-all effects of some organic additives on the performance of diamond impregnated bits in atmospheric drilling conditions only and not in downhole pressured conditions.

Jan 1, 1970