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By H. W. Seany

Over the years since the initial experiments with underground concreting were made in 1956, attesting to cope with the ground weight and pressure encountered in the development of a large-scale underground block caving system, the use of monolithic concrete linings has grown to include most of the primary development in the, mining area. Although the development cost of concrete linings is higher than either timber or steel-supported openings, the repair and maintenance costs are substantially lower, making concrete the most economical means of ground support. Other advantages are also apparent, in that concrete provides superior fireproofing, better ventilation, and a safer, cleaner working place.

Jan 1, 1965

By M. A. Torcaso, P. Raimondi

The distribution of the oil phase in Berea sandstone resulting from increasing and decreasing the water saturation by imbibition was investigated Three types of distribution were recognized: trapped, normal and lagging. The amount of oil in each of these distributions was determined as a function of saturation by carrying out a miscible displacement in the oil phase under steady-state conditions of saturation. These conditions were maintained by flowing water and oil simultaneously in given ratios and by using a displacing solvent having essentially the same density and viscosity as the oil. A correlation shows the amount of trapped oil at any saturation to be directly proportional to the conventional residual oil saturation Sor The factor of proportionality is related to the fractional permeability to the water phase. Part of the oil which was not trapped was displaced in a piston-like manner (normal part) and part was eluted gradually (lagging part). The observed phenomena are more than of mere academic importance. Oil which is trapped may well provide the fuel essential for forward combustion and thus be beneficial. On the contrary, in tertiary recovery operations, it is this trapped oil which seems to make current techniques uneconomic. INTRODUCTION A typical oilfield may initially contain connate water and oil. After a period of primary production water often enters the field either from surrounding aquifers or from surface injection. During primary production evolution and establishment of a free gas saturation usually occurs. The effect and importance of this third phase is fully recognized. However, this investigation is limited to a two-phase system, one wetting phase (water) and one non-wetting phase (oil). The increase in water content of a water-wet system is termed imbibition. In a relative permeability-saturation diagram such as the one shown in Fig. 1, the initial conditions of the field would be represented by a point below a water saturation of about 35 per cent, i.e., where the imbibition and the drainage curves to the non-wetting phase nearly coincide. When water enters the field the relative permeability to oil decreases along the imbibition curve. At watered-out conditions the relative permeability to the oil becomes zero. At this point a considerable amount of oil. called residual oil, (about 35 per cent in Fig. 1) remains unrecovered. Any attempt to produce this oil will require that its saturation be increased. In Fig. 1 this would mean retracing the imbibition curve upwards. In addition, processes like alcohol and fire flooding, which can be employed at any stage of production, involve the complete displacement of connate water and an increase, or imbibition. of water saturation ahead of the displacing front. Thus, in several types of oil production it is the imbibition-relative permeability curve which rules the flow behavior. For this reason a knowledge of the distribution of the non-wetting phase, as obtained through imbibition, whether "coming down" or "going up" on the imbibition curve, is important.

Jan 1, 1965

By R. W. Stahl

Gas accumulation and dust suspension are the major safety hazards in coal stockpiling and reclaiming operations. This report presents a schedule of safety precautions and plant design features devised by the Bureau of Mines to reduce danger from these and other sources.

Jan 1, 1965

By Frank E. Woolley, Robert D. Pehlke

Jan 1, 1965

By J. M. Stuve

Heat of solution measurements of high-purity neodymium metal and neodymium trichloride (NdCls) in 4.360 molal hydrochloric acid (HCI) were used to determine the standard heat of formation (6EPr) of NdCls? From solution data obtained, the heat of formation of NdCls (c) was computed as -248,970 ±260 cal/mole at 298.150 K.

Jan 1, 1965

By V. M. Karve, K. K. Majundar, K. V. Viswanathan, J. Y. Somnay

The effect of calcium, magnesium, iron (both ferrous and ferric) and aluminum ions, which are commonly encountered in a typical beryl ore, was studied in the flotation of pure beryl, soda-feldspar and quartz. The vacuumatic flotation technique was employed. With sodium oleate as collector and in the absence of any activator, beryl floated in a pH range of 3 to 7.5, whereas feldspar and quartz did not float at any pH up to 11.5. The pH range of flotation increased in the presence of the ions studied. With calcium and magnesium ions beryl floated from 3 to 11.5 pH and beyond, soda-feldspar floated beyond pH 6 and quartz floated beyond pH 8. Ferrous ion activation was found to be similar to that of calcium and magnesium. Activation by ferric and aluminium ions was found to be complex and the lower and upper critical pH for all the three minerals was around 2 and 10 respectively. These studies indicated the possibility of separation of beryl from feldspar and quartz even in the presence of calcium, magnesium and ferrous ions between pH 4 and 6. Flotation tests on a mixed feed of pure minerals in a 10 g cell revealed that beryl can be selectively floated from feldspar and quartz if ferric ion is reduced to ferrous state or if it is complexed. Beryl occurs mostly in pegmatites, and hence is associated with feldspar, quartz and micas and small amounts of other minerals such as apatite and tourmaline. The separation of beryl from these minerals is difficult because all the silicates accompanying beryl have more or less the same physical properties. Specific gravities of beryl, feldspar and quartz are 2.70, 2.56 and 2.66 respectively. Electrostatic separation has been suggested but no work has been reported. ' The adsorption of sodium tri-decylate tagged with Cl4 on beryl, feldspar and quartz reveal similarity in surface properties. Much work has been reported on the flotation of beryl from ores, either directly or indirectly as a by-product, but little is known about the fundamental aspects of beryl flotation. Kennedy and O'Meara3 laid emphasis on prior cleaning of the mineral surfaces with HF. Mica is removed first by flotation of beryl with oleic acid, around neutral pH. Runke4 introduced calcium hypochlorite conditioning in a final separation stage for activating beryl in a mixed beryl-feldspar concentrate, and after washing to remove the hypochlorite, floated beryl with petroleum sulphonate. The Snedden and Gibbs5 procedure is somewhat similar to that of Kennedy and O'Meara. Emulsified oleic acid is used as collector. Recently Fuerstenau and Bhappu6 studied the flotation of beryl, feldspar and quartz with petroleum sulfonate in the presence of activators and stressed the importance of iron in the flotation of beryl. From the studies conducted in this laboratory, it was found that feldspar and quartz as such do not float with sodium oleate, but in practice selective flotation of beryl from feldspar and quartz in an ore is found to be impossible with sodium oleate as collector. A glance at the chemical analysis of typical beryl ore indicates the presence of several ions like Ca ++, Mg++, Al + + + and Fe+++ in abundance and Ti++++ and Mn++ in traces. Hence, in an attempt to explain the behaviour of feldspar in the beryl flotation, the effect of Ca++, Mg++, Al+++ and Fe+++, which are known as gangue mineral activators7'8 has been investigated. Materials and Methods: Lumps of beryl ore (hand picked) were boiled with 10% sodium hydroxide and washed with distilled water. They were further boiled many times with 10% hydrochloric acid till no positive test for iron was obtained with ammonium thio cyanate. This was followed by thorough flushing with double distilled water. The lumps were crushed in a porcelain mortar and pestle under water. The minus 65 + 100 mesh fraction was used for testing and was always stored under distilled water. Pure feldspar and quartz were similarly prepared and the minus 65 + 100 mesh fractions collected. Inorganic ions tried as activators were ca++, Mg++ , Fe++, Fe ++ and A1 +++ . Calcium nitrate, magnesium chloride, ferrous ammonium sulfate, ferric ammonium sulfate and aluminum nitrate of G.R.E. Merck grade were used. B.D.H. technical grade sodium oleate was used as a collector. The vacuumatic flotation technique developed by Schuhmann and Prakash was used for studying the effect of pH on flotability. 7 The indications given by this work were confirmed by using 10 g miniature cell.'

Jan 1, 1965

By C. A. Queener, W. L. Mitchell

In recent years bismuth telluride has received considerable attention, primarily due to its value as a thermoelectric material. Since there seems to be little dependence of thermoelectric effect upon crystal orientation1 many of those who have previously worked with this material have been unconcerned with knowing its crystallographic angles to any degree of accuracy. However, when one studies deformation modes, lattice stresses, or the aniso-tropy of mechanical properties of a material, knowledge of the interplanar angles and their relationships as depicted in a stereographic projection becomes essential. Lange2 originally published crystallographic data which described the structure of bismuth telluride as rhombohedral with the space group A more recent work by Francombe3 presented data which corroborated and refined the original findings of Lange. In addition, Francombe established that there is no coexistence of rhombohedral and hexagonal lattices in bismuth telluride as was suggested by Vasenin and Konovalov,4 and that the structure can be treated as a pseu do hexagonal structure with an axial ratio, c/a, of 6.95 for convenience of presentation and study. The interplanar angles and standard projections for several unalloyed hexagonal metals have been previously published,5-9 but the present work appears to be unique in that it presents data for a rhombohedral compound in pseudohexagonal form. As a pseudohexagonal structure, this material has an extremely large axial ratio as compared to the usual range of approximately 1.5 to 1.9 for the hexagonal metals. Since the interplanar angles are a function only of c/a, the angular relations between various planes for Bi,Te3 will be grossly different

Jan 1, 1965

By Andrew Allan

[The Thompson Creek Coal and Coke Corporation, a. mall company engaged in producing coal in the Rocky Mountains of Colorado, is currently engaged in a struggle of destiny to increase their production from inclined seam operation to compete with highly mechanized horizontal bed mines. This paper introduces some of the problems encountered it pitch seam mining as they apply to the convention, room and pillar system employed at the present time. Further described is the test work now being conducted to overcome these obstacles with an. attendant increase in productivity. Included in this test work is a mining machine designed especially for pitching seams, an automated longwall, and hydraulic mining of the latter compared with those of conventional work presently employed.]

Jan 1, 1965

By Forrest T. Moyer

INJURY experience in the metal and nonmetal mineral industries during 1964 was better in rates of occurrence but worse in severity rates than in 1963. The frequency rate of injuries per million man-hours was improved at metal mills, nonmetal mines, and sand and gravel operations, and was virtually unchanged at metal mines; however" the rate of occurrence of work injuries at nonmetal mills, stone operations, nonferrous reduction and refining plants, and slag plants was higher than in 1963. The severity rate of injuries during 1964, data for which are presented for the first time in this chapter, was better at metal mills, nonmetal mines, stone operations, and slag plants. However, the severity rate was worse at metal mines, nonmetal mills, sand and gravel plants, and nonferrous smelters.

Jan 1, 1965

By H. J. Beattie

R. L. Stegman and M. R. Achter (U.S. Naval Research Laboratory)—In a study of the surface structures developed in the fatigue of nickel at low strains as a function of temperature, we have obtained similar results.3 As our apparatus permits fatigue tests to be conducted in vacuo, there was no masking of the surface at high temperatures by oxidation so that the structures there could be observed directly. The relatively few broad slip bands observed at room temperature gave way at 300°C to a large number of uniformly distributed and narrower slip bands. At 550°C deformation began to concentrate around the grain boundaries and progressively increased up to 800°C. In addition fatigue strength was observed initially to increase with increasing temperature up to about 600°C due to the effectively increased ductility caused by the dispersal of fatigue damage. The fatigue strength then decreased at higher temperatures as grain boundary cracking dominates. Maria Ronay, W. H. Reimann, and W. A. Wood (authors' reply)— The authors are pleased to note that R. L. Stegman and M. R. Achter reach similar conclusions from their study of surface slip on nickel. However, they would emphasize that their own conclusions are based on what is shown by study of specimens that have been sectioned and that this study also shows that surface slip is not necessarily representative of what happens below the surface.

Jan 1, 1965

By D. A. Thomas, M. F. Comerford

Poly crystalline wires of Fe-3.2 wt pct Si were cold-drawn to 31, 66, and 87 pct reductions of area. Mechanical properties and tnicrostructures were studied after recovery and re crystallization. An initial increase in strength during recovery was ascribed to strain aging, and subsequent softening was largely due to polygonization rather than re-crystallization. No unique actioation energies could be determined for the recovery process. Rather, activation energies ranged from 60,600 cal per mole at 10 pct recovery to 83,200 cal per mole when recovery was 50 pct complete. Sites for the nucleation of recrystallization were found to depend on time and temperature. In the early stages of re-crystallization, nucleation occurred in deformation hands. Later, or at high temperatures, recrystal-lized grains were nucleated primarily al grain boundaries. Polygonized structures did not seem to be preferred sites for nucleation. MUCH of the research on deformation, recovery, and recrystallization processes in bcc materials has been performed on single crystals or lightly worked polycrystals. Little study has been devoted to the relation of mechanical properties to micro-structure in polycrystals after severe deformation and subsequent annealing. This paper presents the results of a study of the tensile properties and microstructures of Fe-Si wires drawn varying amounts and annealed at a series of temperatures. EXPERIMENTAL PROCEDURE The experiments were carried out on an alloy of the following composition: 3.2 wt pct Si, 0.08 Mn, 0.016 C, 0.005 0, 0.0002 N, 0.0001 H, 0.008 P, 0.034 S. The material was received as l-in.-sq bars cut longitudinally from a hot-rolled slab provided by the Armco Steel Corp. The bars were forged to 3/8-in. rounds, centerless-ground to 0.250 in., and swaged to '0.108 in. All subsequent reductions were performed by room-temperature wire drawing at the rate of 2 in. per min. Each preliminary draft gave approximately 30 pct reduction of area and was followed by a l-hr anneal at 1010°C in dry hydrogen. Three lots of wire were made with ultimate cold reductions of 31, 66, and 87 pct reduc-

Jan 1, 1965

By S. Zador, C. B. Alcock, K. Sudo

Measurements have been made of the standard free enevgies of formation of the sulfates of cobalt, Cupric copper, nickel, and ferric iron in the temperature range of 750° to 950°C. Dynamic gas-solid techniques have been employed in which oxide-sulfate and basic sulfate mixtures were placed in a stream of gas of controlled SO3 potentials. Thermal analysis and thermogvavimetry were used as detection methods, and it was found THE formation of sulfates during the roasting of sulfide ores is now considered to arise in many cases from the interaction of sulfur trioxide in the gas and the metal oxide which is formed on the sulfide as a first step.' As a preliminary to the investigation of the kinetics of sulfate formation during roasting, measurements have been made of equilibria from which the free energies of formation of cobalt, copper, nickel, and iron sulfates can be that the range of temperatures which could be investigated and the choice of method was largely controlled by the kinetics of these gas-solid reactions. The results are compared with previous results obtained from static measurements with which they agree quite well, and calculations have been made employing themal data to interrelate the present results with those for other sulfates. calculated. The method used has been to expose the solid sulfate (or basic sulfate) to a controlled flowing gas mixture of SO,, 02, and SOs and to observe the temperature of decomposition. The onset of decomposition was detected by thermal analysis or thermogravimetry. EXPERIMENTAL METHODS The thermal-analysis method was similar to that employed by Dewing and Richardson.' The sulfate was dehydrated at 250°C in air, and placed in a small alumina crucible which was held by a quartz ring in the hot zone of a horizontal furnace. The reaction tube of this furnace was made of mullite.

Jan 1, 1965

By Henry Leidheiser, Melvin C. Jr. Hobson

The rate of formation of the intermetallic compound, indium antimonide, at the interface between iudium and antimony at 100°C is greatly increased when a composite electrode of indium electrode -posited on antimony is made the cathode in an electrolytic cell. The amount of indium antimonide formed during electrolytic treatment at constant potential appeared to he proportional to the square root of time, but the scatter of the data, particularly at long times, makes it impossible to state this conclzlsi1:ely. The rate constant for the electrochemical synthesis was estimated to he 1.5 x 10-12 sq cm per sec. A similar- set of experiments was conducted in the absence of an applied potential but under otherwise similar conditions. The rate constant lor the thermal synthesis was less than 2 x 10-14 sq cm per, sec, at least two orders of magnitude less than obtained during electrolytic treatment. In a series of electrochemical studies it was observed that intermetallic compounds formed on the surface of polarized electrodes.1'2 The possibility of using this technique for the electrochemical preparation of intermetallic compounds was investigated and subsequently applied to the synthesis of the semiconducting III-V compounds. Gallium antimonide, indium arsenide. indium antimonide, and indium bismuthide were successfully formed by electrodepositing the Group III element from a boiling acid solution onto an electrode made of the Group V element. The following kinetic studies were undertaken on indium antimonide to obtain quantitative information on the rate of formation of this representative III-V compound under a potential gradient. EXPERIMENTAL The electrolytic cell for these experiments was a modified, three-neck, round-bottom, 500-ml distillation flask. Sealed into the side of the flask was a Luggin probe which monitored the surface of the working electrode and extended out of the flask to a small reservoir containing a saturated calomel electrode. The counter electrode was platinum. The three electrodes were connected to a Wenking po-tentiostat which maintained a preselected constant potential near the surface of the working electrode with reference to a saturated calomel electrode. All potentials noted in this paper are with reference to a saturated calomel electrode at 45° ± 5°C. The potential and the current were both monitored using Sargent Model MR recorders. The antimony electrodes were cast in graphite molds to form spheres about 15 mm in diameter with a shank 6 mm in diameter and 10 mm long. A heavy copper wire (12B & S gage) was soldered to this shank. Collodion was applied for protection to the shank and the connecting part of the copper lead. A snug-fitting O-ring was slipped over the shank and the electrode was then fitted into a teflon holder such that only the spherical portion was exposed. The electrode surfaces were cleaned and chemically polished prior to assembly and introduction into the electrolyte by etching in a modified CP-4 solution (50 parts glacial acetic acid, 10 parts concentrated nitric acid, 2 parts 48 pct hydrofluoric acid). The electrolyte was 10-2 M In+3 in 1 MH2So4 and its temperature was held constant by refluxing. The reflux condenser was open to the atmosphere and no temperature correction was made for changes in barometric pressure. The indium concentration in the electrolyte was checked from time to time by the analytical method outlined below for the determination of the amount of indium antimonide formed electrochemically. A schematic of the recorded potential is shown in Fig. 1. At point A the antimony electrode was introduced into the cell and the open-circuit potential recorded. At point B the potentiostat, preset at the desired potential, was switched on. It was switched off at point C and the potential fell to the open-circuit value of the electrodeposited indium. The

Jan 1, 1965

By N. E. Hanna

The current Bureau of Mines active list of permissible explosives includes 124 brands. Thirteen are gelatinous and the rest are the more commonly used granular ammonium nitrate type. The list of permissible blasting devices comprises five Cardox models.

Jan 1, 1965

By J. G. Giddings, R. Kobayashi

Residual viscosity, the ViSCOSitY at a given pressure and temperature minus the dilute gas viscosity at the same temperature, has been found to be independent of temperature for pure components and mixtures for simple molecules and light hydrocarbons. The residual viscosities for methane, ethane, propane and four mixtures were correlated as a function of reduced density and molecular weight. INTRODUCTION Earlier efforts in correlating the viscosity of light hydrocarbons and associated gases under pressure, primarily by some form of the corresponding states principle, have been reported elsewhere.7 The formal theory of corresponding states principle for viscosity from non-equilibrium statistical mechanical arguments for simple molecules has been developed by Helfand and Rice.13 The most serious obstacle to the development of a generalized corresponding states representation of viscosity data, even for simple molecules, has been the limited quantity of precise viscosity data of pure components and mixtures over a wide range of pressure and temperature conditions. Viscosity data on light hydrocarbons have recently been contributed by several laboratories.2,6,8,23,25,26 In the study of the viscosity of nitrogen, Michels and Gibson" observed that the viscosities of nitrogen as a function of density gave parallel isotherms. The same behavior has since been reported for other gases.".= The observed behavior indicates that the residual viscosity or the viscosity at a given pressure and temperature minus the dilute gas viscosity at the same temperature is a unique function of the density. Abas-Zade,1 Michels and Botzen,18 and Michels, Bot-Zen, Friedman and Sengers,19 observed similar behavior for thermal conductivity, the residual thermal conductivity being defined in a manner parallel to that of residual viscosity. Thodos and co-workers 4,15,24 applied the residual viscosity concept to the viscosity of pure monatomic and diatomic gases. Ellington and co-workers10,25 made the residual viscosity vs density plots for ethane and propane, but omitted the region below a residual viscosity of 15 micropoise and showed a systematic separation of the ethane isotherms in the low density region. Eakin correlated the residual viscosity of methane, ethane, propane and n-butane empirically as a function of density and molecular weight: Carmichael and Sage6 recently presented ethane residual viscosity vs density values in the gaseous liquid, and near critical regions as a single univariant function of density. Flynn, Hanks, Lemaire and ROSS" have contributed extremely accurate viscosity data to confirm that the residual viscosity concept is essentially correct, but may not be accurate within 0.1 per cent of the viscosity value for the gaseous state- The recent studies by Giddings12 indicate that the residual viscosity of methane, propane and each of four methane-propane mixtures are unique functions of density Over the temperature and the density ranges studied.

Jan 1, 1965

By William D. Klopp

A study was conducted of the tensile and creep properties of are-melted and electron-beam-melted tungsten over the temperature range 2250° to 4140°F. The tensile and creep strengths vary with pain size, the finer -grained materials being stronger. The activation energy for transient creep at 2250° to 3500°F is 95,000 cal per (g)(mole), while that for steady creep at 3300o to 4000°F is 141,000 cal per (g)(mole). At 2875o to 3300°F the apparent activation energy for steady creep decreased with decreasing temperature. It is suggested that cross slip is rate controlling during transient creep, while dislocation climb is rate controlling during steady creep above 3300° F. ALTHOUGH considerable data have been generated on the high-temperature tensile properties of powder-metallurgy tungsten,1 relative few data have been published on the properties of are-melted2 or electron-beam melted tungsten.3 Furthermore, the available data show a fairly large amount of scatter at high temperatures. The effects of structure and purity have not yet been defined, aside from observations that high-purity electron-beam (EB)-melted tungsten3 and single-crystal-plasma-flame tungsten4 are weaker than less pure powder-metallurgy tungsten. The creep behavior of powder-metallurgy tungsten has been studied, but no data are available on the creep behavior of tungsten consolidated by melting. Green5 found that powder-metallurgy tungsten exhibited linear creep at 4082° to 5072°F with an activation energy of 160,000 cal per (g) (mole). The similarity of this activation energy to that of 153,000 cal per (g)(mole) for volume self-diffusion6 suggests that recovery of strain hardening by dislocation climb is rate controlling in this temperature range. In studies at 4800°F, Sutherland and Klopp7 concluded that grain size significantly affected the creep behavior of commercial powder-metallurgy materials. This grain-size effect was suggested by sherby,8 although the opposite relation had been reported for aluminum.' The purpose of the present study was twofold: first, to provide baseline data on high-temperature tensile and creep properties of are-melted and EB-melted tungsten for concurrent tungsten alloy studies, and, second, to determine the phenomenolo-gical effects of structural and purity variables on the high - temperature mechanical properties of tungsten. EXPERIMENTAL The are-melted tungsten materials were prepared by melting sintered 1-1/4-in.-diam electrodes into 2-1/2-in.-diam by 5-in.-long ingots. The are-melting facility has been described previously.' Eight ingots were melted, machined, and hot-extruded at

Jan 1, 1965

By R W. Drybrough

The program to increase production at Sherritt Gordon's Lynn Lake property, which began in 1956, included increasing the rope speed and the horsepower of the ore hoist at the "A" shaft. Because of the limited power sup-ply from the two 7,000-hp. hydroelectric plants, and the ? 3,600 hp. predicted for the combined hoisting requirements of the three production shafts, it was considered desirable to lessen the impact of this type of load on the relatively small power system by equipping all future hoisting arrangements with Ward Leonard direct-current drives. The manually operated 8-by 4-ft. hoist at the "A" shaft had a rope speed of 1000 f.p.m., and was driven by a 385-hp., 380-r.p.m. wound rotor motor with liquid rheostat control. This A.C. drive was replaced by a semi-automatic Ward Leonard direct-current drive with a 515-hp., 566-r.p.m., shunt wound motor, providing a rope speed of 1,500 f.p.m. During several months preceding the con-version, all possible preparations were carried out to keep the changeover period to a minimum, and this resulted in a total shutdown time of twelve days. The capability of the "A" Shaft hoist was increased from 109 tons per hour to 134 tons per hour, and both mechanical and electrical maintenance were reduced considerably. The total cost of the conversion amounted to $130,000. The hoistmen who had been required for the manual A.C. drive were transferred to the new Farley shaft, and the reduction in operating labour costs of the "A" Shaft hoist

Jan 1, 1965

By R. R. Kimpel, L. G. Austin

An equation is derived describing fragment size for single fracture of brittle solids. It contains the equations of earlier workers as special or approximate cases and, in addition, is capable of describing coarse distributions in which a few large particles are produced on fracture. The equation can be fitted well to single fracture experiments where over-breakage is avoided. In 1956 Broadbent and callcottl described a method of analyzing the unit operation of grinding, applicable to homogeneous breakage of brittle materials. In essence, the grinding process was split into two parts: 1) the fractional amount of a given size which is selected for grinding per unit time, 2) the size-weight distribution of the fragments produced by breakage of this certain size (primary breakage distribution function). The theory was formulated using matrix algebra. They attempted an experimental verification of the theory using an assumed primary breakage distribution but the results were not very satisfactory. Austin and Gardner2 showed that this assumed distribution was widely different from experimental values and that it led to the poor agreement of predicted size-weight distributions with experiment found by Broadbent and Callcott. In addition, Austin and Gardner2,3,4 reformulated the original approach in terms of differential equations of grinding and demonstrated that the approach led to a very satisfactory description of the grinding process, providing that the descriptive parameters were measured experimentally. Recent work5 has substantiated these findings and the distribution functions of several materials ground under different conditions in different mills have been determined experimentally. The fraction underweight versus size used by

Jan 1, 1965

By Irving Cadoff, Richard Nolder

An analysis oj a series of samples of single -crystal silicon grown on sapphire shows that ,four distinct orientation relations exist. There are at least thirteen crystallographic planes which serve as substrates ,for epitaxial growth The model which assumes that silicon substitutes for aluminium and bonds with the oxygen atoms of the sapphire to form the first later for subsequent growth can account for the epitaxial geometry in all four cases. Multiplici-ties 01 specific orientations are found which are explained by the symmetry of both the sapphire and silicon crystal structures. It was reported in the previous paper' that single-crystal silicon films can be deposited on single-crystal a A1,03 (sapphire) with a wide variety of orientations. The silicon films, however, were found to deposit in only four different orientation relationships with respect to the sapphire substrate. The X-ray data have been analyzed to determine the plane and direction of atomic fit and an atomic model to account for the epitaxial relationships at the silicon-sapphire interface has been developed. These results are described in the present paper. EXPERIMENTAL The Laue X-ray data described in the previous paper were reduced to stereographic projections in a standard manner. These data were supplemented with X-ray reflection data obtained with -& E and A Full-Circle Goniometer (Electronics and Alloys, Inc.) mounted on a Phillips diffractometer unit. The silicon films were thin enough to result in characteristic reflections from the substrate as well as the silicon. The superimposed stereographic projections were analyzed to determine the orientation relationships. Ambiguities were resolved by referring to constructed models of various lattice planes for both silicon and sapphire. These lattice models were also used to develop the model for atom fit at the interface. DATA AND ANALYSIS 1) Crystal Structures. The crystallography of silico-n, which is of the diamond cubic class with a. = 5.4~, is straightforward. The sapphire structure is more complex and generally difficult to represent in pictorial form. It is of the rhombohedra1 class but usually referred to hexagonal axes. The transformation of indices between these two systems can lead to ambiguities which will have bearing on the analysis presented herein. Therefore, the basis used in this paper is described in the appendix. Referred to the hexagonal system, the parameters of sapphire are co = 12.95.&, a, = 4.75~, c/a = 2.73. All parameters are for room temperature. Figs. 1 and 2 illustrate schematically the hexagonal unit cell model of sapphire used for this analysis. The oxygen atoms are assumed to occupy positions in an idealized hexagonal array on basal planes. Their actual positions are in a slightly distorted hexagonal array. The aluminum-atom positions are scaled to their actual positions in the lattice with respect to the basal layers of oxygen atoms. It was found that an idealized model where the aluminum atoms are assumed to lie exactly at the octahedral interstices of the oxygen lattice, similar to that used by ~ronberg,' was not adequate for this study.

Jan 1, 1965

By B. Ramaswami, U. F. Kocks, B. Chalmers

This paper describes the tempetrature, solute (gold), and orientalion dependence of the plastic rleforlirnlion of silver single crystals. The virgin flow stress, To, and its temperatutre dependence incrense with increase in solute concentration. el decreases with decrease in temperature below room teiirperature and with increase in solute coucentralion. The dependence of 011 on temperature arid solute sontenl is due to the dependence of Ts on the two variables. An increase in ts, due to either the temperature or the solute conlent, results in a decrease of e11 in crystals of single-slip orientation and an increase of 011 in crystals of' (100) find (111) orientation. is orientation-dependent and at all the temperatures and in all the materials studied. The Leveling off of the engineering stress-strain curve in crystals of (100) 07-ientotion at a stress tl, is associated with extensive cross slib. The temperature and strain -rate dependence of tl are similar to those of indicating that a rate process is the cause 01 this phenomenon. The plastic deformation of silrer crystals of (110) orientation is multiple to that of crystals of single-slip orientation. THE work hardening of fcc crystals has been the subject of intensive investigations in the past 15 years. The effect of orientation, deformation temperature, solutes, second phase or precipitates, strain rate, etc., has been studied in a number of fcc metals.'-5 In spite of the considerable amount of work reported on the dependence of work hardening on the orientation, temperature, and solute concentration, certain aspects of the plastic deformation of fcc crystals have not been clarified. For instance, with the exception of a few investigations,6-8 where crystals of multiple-slip orientations have been studied, almost all the studies have been on crystals of single-slip orientations. Hence, a major portion of this study has been devoted to the dependence of plastic deformation on the multiplicity of slip systems and the enhanced possibility of dislocation interactions resulting from such multiplicity. Further, the abnormally low rate of work hardening observed at large strains at certain temperatures in crystals of the (100) orienta-tion 6-8has not been explained satisfactorily. It is the aim of this study to clarify this aspect of the orientation and temperature dependence of the plastic deformation of fcc single crystals. The work-hardening characteristics of single crystals of aluminum of ( 110) orientation have been studied at room temperatur "'12 and above." They have not been studied at temperatures where the virgin flow stress is dependent on temperature or where, in Seeger's terminology is important. The work hardening of single crystals of (110) orientation is of interest for another reason. As shown in Table I, the dislocation reactions that are possible in the (110) orientation are similar in certain respects to those that are possible in the (100) orientation. Hence, the deformation of single crystals of silver of (110) orientation was studied in the temperature range 100° to 900°K at intervals of 200°K. The effect of solute concentration on the plastic deformation of fcc single crystals of single-slip orientation has been studied by several investiaators.> In all of these investigations—with the exception of Ref. 20—single crystals of identical orientation have not been used, with the result that the orientation dependence of plastic deformation is superimposed on the effect of the solute. In addition, the effect of the solute on the work-hardening characteristics of single crystals of multiple-slip orientations has not been studied by the previous

Jan 1, 1965