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By K. Sassa, I. Ito

The dynamic principal stresses induced within rock by an explosion under con fined conditions are analyzed for the case of blasting with one free face by applying the values of measured radial displacement, particle velocity and so on to equations derived from the theory of elasticity. The dynamic stresses on the free face are also calculated from the strain measured by wire strain gauges affixed on the free face. Some results obtained are briefly: 1) The maximum stress on the free face appeared at the intersection between the free face and the burden, and its magnitude was about twice as large as the magnitude of the tangential tensile stress imparted by the incident stress wave within the range related to the breakage by blasting. 2) The maximum value of the compressive stress near the free face was decreased due to the existence of the free face, while that of the tensile stress was increased. 3) At any point near the free face, the directions of the principal stresses in the r? plane using spherical coordinates with the origin at the center of the spherical charge, changed with time except in the direction of the burden. However, at another point near the explosion point where the principal stresses were mainly those stresses caused by the initial longitudinal wave, the directions of the principal stresses coincided with those of the coordinate used. 4) The maximum value of the tensile stress in the F direction was larger than those in the re plane at and near the free face. 5) The tensile stress caused by the Hopkinson effect appeared only near the burden. 6) It is presumed from the results of stress analysis that radial cracks will be produced in the rock mass near an explosion point, but with the approach of the free face, the directions of cracks curve towards a direction parallel to the free face. INTRODUCTION In order to investigate the mechanism of rock breakage by blasting, it is considered to be very im- portant to know how the stresses are generated and distributed within the rock by explosion of a confined charge. As part of a research program concerning the mechanism of rock breakage by blasting, the authors have already published papers on the detonation pressure produced at the inner surface of the charge hole1 and on the behavior of the dynamic stresses within rock caused by an explosion in the case where no free face existed.' In this study the dynamic stresses on and near the free face have been investigated for the case of blasting with one free face. The mechanism of rock breakage in blasting is discussed in the light of these studies.

Jan 1, 1967

By C. C. Harris

The Gaudin-Meloyl equation for the size distribution of fragments resulting from single fracture is where y is the mass fraction of material smaller than size x, and x, and r are parameters to be determined from the experimental data. In physical terms, r is associated with the number of active flaws in a particle of characteristic dimension xo . The special attribute of this equation is its emphasis on the coarse size region of a distribution. There are various procedures2-5 for obtaining the parameters in Eq. 1, but a simple graphical method is awaited. This situation contrasts sharply with that in the cases of the familiar Gates-Gaudin-Schuhmann and Rosin-Rammler equations.6 The purpose of this note is to present a method based on a procedure7 which has been successful in several other applications.8-13

Jan 1, 1967

By N. A. Gjostein

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

Jan 1, 1967

By R. B. Adair, J. S. Browning

The laboratory batch and continuous flotation pilot plant tests demonstrated the technical feasibility of recovering high grade mica concentrates from weathered mica pegmatite ores of Alabama and Georgia. The research indicated that combinations of anionic and cationic collectors may be used effectively for flotation of fine size mica from weathered pegmatite ores. In continuous tests, concentrates containing 98.5% mica were obtained from the Georgia pegmatite ore; the Alabama pegmatite ore concentrates contained 98.4% mica. The recoveries were 91 and 89% respectively. INTRODUCTION The principal uses of fine ground mica are as a filler in wallboard joint cement, as a filler and surface coating for roofing, as an ingredient in paints, and in oil well drilling mud. The mineral has other uses in the manufacture of rubber, wallpaper, plastics, welding rods, electric insulation, house insulation, and textiles, and as an annealing agent in metal treatment. In recent years, more than 99% of the domestic mica produced has been scrap and flake mica (mica which does not meet specifications for sheet mica and is used for producing fine ground mica). There has been a continued increase in mica production for several years, the 1963 production of scrap and flake mica totaling 117,251 tons.1 Ground mica is obtained primarily by crushing and milling pegmatites and schists. To a lesser extent, mica is produced as a byproduct of kaolin washing and feldspar and spodumene flotation operations. The processes used in recovering mica by crushing and milling pegmatites are generally simple, consisting of various combinations of alternate roll crushers and trommel screens that separate the mica and gangue at screen sizes coarser than 6-mesh. As these processes are designed to recover only coarse mica, high losses in the plant rejects are common. Large tonnages of tailings from the crushing and screening plants have been accumulated in a number of areas. Methods for treating such products were developed by the Bureau of Mines in 1941,2 but have not been generally applied. More recently, mica flotation research has been completed and published by the Bureau of Mines.3 These methods required complete removal of 150- to 200-mesh materials from the flotation feed with consequent fine mica losses. Later, the Bureau of. Mines investigated methods for-recovering fine size mica from pegmatite ores after desliming sufficiently to remove clay materials, but not so drastically as to remove the fine sands. This report summarizes the results of these studies. The process developed was effective on pegmatite ores from two locations and should be applicable to the commercial treatment of other mica-bearing pegmatite ores and fine rejects that have been accumulated at various mica-milling operations. DESCRIPTION OF ORES The ores used in the investigation were obtained from the Dixie Mines, Inc., Heflin, Alabama, and the Ruberoid Corporation, Hartwell, Georgia. The sample from Alabama contained muscovite and quartz, with a high percentage of clay, and minor amounts of biotite, kaolin, limonite and tourmaline. The mica in the ore was essentially all minus 4-mesh in size and was free of attached mineral grains. The Georgia sample contained muscovite and quartz, with minor amounts of biotite, kaolin, and limonite. The mica in the ore, which was essentially all minus 4-mesh, was liberated. Petrographic analyses of the two samples are given in Table I. THE ANIONIC-CATIONIC MICA FLOTATION METHOD Previous investigators2,3 have reported that complete desliming of mica ores at 150- to 200-mesh was required prior to flotation with cationic collectors to obtain satisfactory selective separation of the mica from the other mineral components. Numerous tests were made at the Tuscaloosa Metallurgy Research Center to determine if some reagent combination could be used to selectively float finer size mica without complete desliming. The investigation led to development of a process using a simple reagent com-

Jan 1, 1967

By T. F. Bower, M. C. Flemings, H. D. Brody

A series of experiments are reported which show thai reasonable assumptions for analysis of solute redistribution in solidification of castings and ingols illclr(de: negligible undercooling before nuclcation of solid phases, negligible increase of solute in advance of the tips of growing dendrites, complete diffusion within the Liquid oer distances the order, of dentrite arm spacings, platelike dentrite t/o?$holog?.. Qzmli/ali,e and periment is obtained JOY Al-Cu alloys front measurements of amount of nonequilibrium second phase, minimum solute content at the centers dentrites arms (after solidification), and 3) change in minimum solute content in dentrite arms during solidification. In a previous paper' analyses were given describing solute redistribution in dendritic solidification. The analyses were undertaken primarily to permit prediction of "severity of microsegregation" in a casting or ingot after solidification and cooling to room temperature, but can also be used to predict "local fraction solid' as a function of temperature in the solidifying alloy. Numerical results were given for Al-Cu alloys. The aims of this paper are to examine the validity of some of the assumptions of that analysis, and to compare predictions of the theory with experiments. All experiments reported are on Al-Cu alloys, the bulk on Al-4.5 pct Cu alloy. EXPERIMENTS Experiments conducted were on small ingots, 41/2 in. in diam by about 10 in. high. solidified in a controlled thermal environment (i.e., in a resistance-heated, re-circulating air furnace, whose temperature could be controlled to 1°C). In one series of experiments, the ingots were solidified very slowly (solidification time was varied from 8 to 1000 hr) and at constant rate of heat extraction. In a second series of experiments the ingots were solidified ( 'unidirectionally". Fig. 1 is a sketch of the method of making the two different types of ingots. The unidirectionally solidified ingots were fully columnar, and the slowly solidified ingots had equiaxed structures, Fig. 2. In making the slowly solidified ingots, the mold employed was carbon steel, coated with inert refractory. Typically the mold and its environment were heated to 700°C. The molten alloy was then poured into the mold and the temperature of the system equilibrated above the liquidus. The environment of the mold was next cooled with a controller responding to a differential thermocouple that measured the difference between the temperature of the melt and the temperature of the mold environment. The differential thermocouple consisted of one chromel-alumel junction in the melt connected in opposition with a second junction in the furnace. The potential across the differential thermocouple was input to the controller which acted to keep this potential at a set. constant value; hence the temperature difference between the two junctions was maintained nearly constant. Major resistance to heat flow in the above apparatus was between the metal surface and the furnace atmosphere, not in the metal itself. By maintaining a constant temperature difference between the metal and the furnace atmosphere, the controller maintained an essentially constant rate of heat extraction during solidification, regardless of amount of heat released by the metal per unit temperature change. When the metal temperature dropped just below the eutectic temperature. the ingot was removed from the furnace and water-quenched. The unidirectionally solidified ingots were cast in a similar mold to the foregoing except that provision was made to extract heat through the bottom face of the mold by passing air or water through the mold base, Fig. 1. For these experiments, metal and mold temperature were again equilibrated above the liquidus. Temperature of the mold environment was then held

Jan 1, 1967

By B. B. Rath, Hsun Hu

Rates of migration of large-angle boundaries have been studied in zone-refined aluminum crystals, defonned 80 pct by rolling in the (110)[112] orientation at -78°C followed by a recovery anneal at 80°C. Artificially nucleated grains show a marked variation. by an order of magnitude, in their growth rates in different directions. The average activation energy for the migration of all boundaries was found to be about 16,000 cal per mole. The anisotropy of the boundary migration is rationalized on the basis of the boundary structure. It has been observed by Beck and HU,1 Kohara el al,2,3 and Czjzek and Haessner4 that recrystallized grains formed upon annealing Of deformed sing1e crystals of aluminum show anisotropic growth characteristics. Kohara et al. found that single crystals rolled in the (110)[112] orientation, when random nuclei were provided on one side of the crystal by rubbing with emery paper and annealing, developed a sharp recrys-tallization texture on the other side of the crystal upon further annealing. This sharp recrystallization texture consisted of four components, which were related to the deformation texture of the crystal, i.e. (110)[112], by rotations of ±40 deg around each of the two common [ 111] axes' They also noted that recrystallized grains were elongated in directions perpendicular to either of these two common [1111 axes. They attributed this anisotropic growth to the difference in the rate of self-diffusion or diffusion of impurity atoms along the tilt and the twist boundaries. A somewhat similar investigation was conducted by Czjzek and Haessner4 On strained single-crystal sheets Of alum- inum. These authors claimed that the matrix structure of the deformed crystal had a greater effect on the growth anisotropy of the recrystallized grains than did the boundary orientation itself. In the present investigation quantitative measurements of the rate of grain boundary migration in anisotropic growth have been made in zone-refined aluminum (99.9999+pct pure) crystals deformed 80 pct by rolling in the (110) 112] orientation. Crystals of this particular orientation were chosen because of the following desirable features: 1) the crystal does not change its orientation during rolling; 2) the rolling plane contains all the significant crystallographic directions; and 3) when annealed, following deformation, the crystal does not re-crystallize spontaneously but polygonizes to a stable and homogeneous structure. Hence, the initial orientation of the crystal and a constant strain energy in the matrix can be maintained during subsequent grain boundary migration studies. It is essential to keep the driving force constant for the study of boundary mobility.5 EXPERIMENTAL PROCEDURE A cylindrical single crystal of 1 in. diam was grown by the Bridgman method in a high-purity graphite mold. The resistance ratio, R(4.2°K) /R(298°K) , of the grown crystal was approximately 2.0 x 10-4. A number of slices, 1/4 in. thick, were cut from the crystal along the (110) plane and were mechanically and electrolyti-cally polished to remove the strained surface layer. The crystals were then rolled along the [112] direction to 80 pct reduction in thickness at -78°C. To minimize surface friction, the crystals were rolled between two layers of 0.005-in. teflon sheet. Rolling was interrupted, prior to completion, to remove the surface layers and the edges by electropolishing. These and similar precautions in handling the rolled crystals

Jan 1, 1967

By H. G. Warren, E. W. Hough

Correlation of interfacial tension of the methane-n-pentane and methane-n-decane systems was made by Hough and Stegemeier by the use of the Weinaug and Katz equation. The methane-n-heptane and ethylene-n-heptane systems were investigated by the authors. Additional systems taken from the literature were the me thane-propane system by Weinaug. and Katz, the methane-n-butane system by Pennington and Hough, and the n- butane -carbon dioxide system by Brauer and Hough. These systems were analyzed by the Weinaug-Katz equation and the Sugden equation on the IBM 1620 11 computer using a regression analysis program. Parachor and exponent values for each component and system were determined. The experimental work was close to the critical point of the light component in the n-butane-carbon dioxide and ethylene-n-heptane systems, between the critical points of the light and heavy components in the methane-n-pentane, methane-n-heptane and methane-n-decane systems, and close to the critical point of the heavy component in the methane-pmpane and methane-n-butane systems. An empirical formula was developed to find a value of the constant B in the Sugden equation for binary hydrocarbon systems from the parachor values of the two components. Interfacial tension for binary hydrocarbon systems was found to be a direct function of liquid-vapor phase density difference in the same manner as a single-component system. DISCUSSION Interfacial tension may be defined as the measure of the specific free surface energy between two phases having different compositions.1 The interfacial tension (IFT) for a binary system may be predicted for any temperature and pressure if the

Jan 1, 1967

Jan 1, 1967

By J. E. Pavlick, W. W. Mullins, H. W. Paxton

The growth of nitrogen-austenite during nitriding of large-gvained ferrite between 650" and 800°C has been studied as a functimz oJ time and nitrogen potential of the atmosphere for a variety of alloying elements dissolved in the ferrite. Whereas no preferential grain boundary penetration by aistenite takes place in zone-refined iron, the addition of aboit I zot pct oj' V, Ti, Cr. Si, or A1 produces significant protrusion of austenite down former 0-0 boundaries. This group of elernents also produces ragged y-0 interfaces in the a grains which advance more slozuly than those in zone-refined iron. 1 zut pct of Ni, Co, Mn, or Mo dissolved in ferrite leads to essentially smooth 7-a interfaces, which advance at rates very sinzilar to those in zone-refined iron. The reasons for this effect are not clear. Two possible limiting hypotheses, not necessarily exclusive, are discussed. One involves p.referentia1 grain bozindary diffusion of nitrogen. the other the production of a zone of ferrite, stpersatcirated with respect to nitrogen, from which austenite precipitates helerogeneozisly on the a-a gyain boundaries. In many phase transformations which occur by nu-cleation and diffusion-controlled growth, information on the parameters which control the rates of nuclea-tion and of growth is frequently not quantititative. The present work describes a continuation of efforts to obtain quantitative data on growth rates in systems where thermodynamic and kinetic factors are known independently, and thus where comparison with models of the growth process is possible. The work has been conducted on iron-base systems for two reasons. Firstly, there are several interesting transformations in this system, many of which are of practical importance. Secondly, the information on phase diagrams, activities, and diffusion coefficients is more complete in this system than in any other. These data are still inadequate to check all the effects of alloying elements, but at worst it is possible to make estimates and thus examine order-of-magni-tude agreement with proposed models. It will be necessary to do this in the present work. The problem studied was the growth of nitrogen-austenite in from the surface of large-grained columnar crystals of alloyed ferrite exposed to an NHs/Hz atmosphere. Earlier work by Grozier et al.' had suggested that growth of austenite may occur preferentially along grain boundaries of alloyed ferrite, whereas zone-refined (ZR) iron shows no such effect, Fig. 1. Growth of nitrogen-austenite into single crystals of zone-refined ferrite is planar provided sufficient nu-cleation sites for austenite are present, and is controlled by volume diffusion of nitrogen through the

Jan 1, 1967

Jan 1, 1967

By Raymond L. Orr

Calorimetric measurements have been made of the heats of solution of gold axd indium in a number of liquid tin-rich alloys at a temperature of 705°K. Relative partial molar enthalpies of gold were determined as a function of dilute solute concentrations in the binary Au-Sn system and in the ternary Ag-Au-Sn and Au-In-Sn systems. Relative partial molar enthalpies of indium were determined for dilute solute concentrations in the In-Sn, Ag-In-Sn, and Au-In-Sn systems. Through application of the interaction coefficient concept introduced by Wagner and more recently extended by Lupis and Elliott, ualues have been obtained for the Au-Au, Ag-Au, Au-In, and Ag-In enthalpy interaction coefficients in liquid tin. The results are inte@reted in terms of solute atom distributions through comparisons with the predictions of dilute solution models. INTEREST in the thermodynamic behavior of dilute liquid alloys stems from two primary sources. From a practical viewpoint, it is often of importance to know or to be able to predict the effect that one solute will have on the thermodynamic properties of the other solutes in a multicomponent system. Studies of dilute solutions may also be rewarding from the theoretical point of view. Some of the difficulties arising from the more complex interactions possible in concentrated solutions are avoided, leading to easier interpretations in terms of solutibn models and bonding energies. For example, in a binary alloy the limiting values of the partial molar properties of the solute represent the case for which each solute atom is completely surrounded by atoms of the solvent, and no other interactions are possible. Solute - solute interactions in dilute solutions are conveniently treated by the interaction coefficient concept of ~agner.' Using a Taylor series expansion for the logarithm of the activity coefficient, In yi, of a component, i, in a solution consisting of dilute solutes with atomic fractions xi, xj, xk, and so forth, in a solvent, s, and neglecting the second- and higher-order terms, Wagner obtained the expression: Where Wheyz is the limiting value of yi in the pure solvent, s. The interaction coefficients, e:, e:, and so forth, are defined by: Since yi is related to the excess partial molar Gibbs energy of component i by GfS = RT In yi, E: is re- ferred to as the "Gibbs energy interaction coefficient". Lupis and Elliott~ extended Wagner's treatment to the relative partial molar enthalpy, aHi, and the excess partial molar entropy, qS. They defined the enthalpy interaction coefficient as: and the excess entropy interaction coefficient as: leading to expressions similar to Eq. [I]: The three interaction coefficients are related by? The self-interaction coefficients, E:,qf,and at, represent the effects of interactions between atoms of component i in solvent s; €3, q{, and 03 represent the effects of interactions between i and j atoms in solvent s; and so forth. From the Maxwell-type relationships between partial molar quantities, it may be shown1'2 that e{ = ej, r}\ =tj), and ai - crj. Experimental determination of the interaction coefficients requires extremely precise measurements of the appropriate properties as functions of solute concentrations in very dilute regions. Few such data exist for intermetallic alloys, even for binary systems, because of experimental difficulties. This is especially true with respect to enthalpy data for dilute alloys. Examination of the compilation of data for binary alloys by Hultgren, Orr, Anderson, and ~elle~~ reveals that determination of limiting values of &fii(Xi =0) often requires extrapolations to infinite dilution from xi = 0.05 to 0.10. Direct measurements of the enthalpy interaction coefficient, qi, for multicomponent systems are virtually nonexistent. This quantity is of course subject to direct calorimetric measurement, but its determination must be limited to cases where high experimental precision is possible. The heats of solution of gold and indium in liquid tin can be measured with relatively high precision, which makes determinations of 73 involving these metals as the measured solutes experimentally attractive. This paper presents the results of such determinations of the Au-Au, Ag-Au, Au-In, and Ag-In enthalpy interaction coefficients in liquid tin. MODELS FOR DILUTE-SOLUTION BEHAVIOR Random-Solution Behavior. In the quasi-chemical treatment of solutions, only nearest-neighbor bonds are considered, and a composition independent value

Jan 1, 1967

By D. I. Bardos, Paul A. Beck

The 1100°c isothermal, sections of the V-Fe-Si, V-Co-Si, and V-Ni-Si systems were studied at silicon contents between 0 and 40 at. pct. The single-phase fields in the 30 and 50 at. pct Mn sections of the 1100°C tetrahedron of the V-'Wn-Fe-Si system were also determined. The direction of extension of the elongated O, R, D, and a-Mn Phase fields suggests that the stability of these phases is determined largely by the electron concentration. The peculiar shape of the above ternary a phase fields, as well as of the a phase fields in the V-;Mn-Si and Cr-MTZ-Si systems is accounted for on the assumption that in manganese-(iron-, coball-, nickel-) rich alloys silicon atoms do not exclude d electrons , while in alloys low in the above components they do. This assumption also leads to the expected electronconcentrations for q and ß-Mn phases formed by transition metals with aluminurn. In earlier work it was shown that in ternary alloy systems of transition elements the a a and certain other phases with complex structure, such as the p and R phases,3 form elongated phase fields extending in a direction corresponding to a constant electron concentration. Recently similar behavior was observed in manganese-rich ternary ß-Mn solid solutions with another transition element and with silicon, germanium, or tin,4 confirming earlier indications3 that ß-Mn is also an electron phase. The alloying behavior of silicon in these manganese-rich alloys sug- gested that the four outside electrons of silicon participate in the bonding and that the predominantly d-like bonding electrons are not excluded from the silicon sites. Presumably, some of the normally unoccupied 3d states associated with the silicon atoms are in these alloys lowered to the Fermi level;4 thus silicon behaves as if it, too, were a transition element. The manganese-rich boundary of the a phase in the V-Mn-Si system,4 as well as in the Cr-Mn-Si sys-tem,4,5 extends approximately parallel to the ß-Mn phase boundary, corresponding to the transition ele-mentlike behavior of silicon described above. However, at lower manganese contents (i.e., in the high-vanadium or -chromium region) the a phase field in both ternary systems mentioned extends in a direction roughly perpendicular to that of its manganese-rich boundary, a phenomenon that is apparently inconsistent with the behavior of silicon in the manganese-rich alloys. A similar, although somewhat less pronounced, extension of the a phase occurs also in the high-vanadium (low-iron) region of the V-Fe-Si system at 1175C, but reportedly not in the V-Co-Si or V-Ni-Si systems at the same temperature.5 The present work was undertaken to investigate in more detail the extension of the a phase (as well as of other electron phases that may be present) in the last three systems and to elucidate this phenomenon, which has not been satisfactorily explained previously. EXPERIMENTAL PROCEDURES Most of the alloys were melted in an arc furnace, using a water-cooled copper crucible under helium atmosphere. The transition metals were of better than 99.9 pct purity and the silicon used was 99.98 pct pure. Alloys containing less than 20 pct V were induction-melted in recrystallized alumina crucibles under argon atmosphere.

Jan 1, 1967

By A. D. McMaster, M. L. Gimpl, N. Fuschillo

Low-power, high-speed, radiation-resistant, monolithic thin-film integrated circuits require thin-film resistors of high sheet resistance which are compatible with the processing requirements for monolithic silicon devices. For this purpose the structure and electrical resistance as a function of temperature were investigated for Nichrome-silicon monoxide cermet films on passivated single-crystal silicon substrates. A suitable material was found to be a mixture of 50 vol pct Nichrome-50 vol pct silicon monoxide. This mixture, when evaporated onto 300°C substrates. showed a low temperature coefficient up to 400°C, at both 270 and 1100 ohms per square. Resistors deposited on room-temperature, 300°, and 500°C substrates were heat-treated at 600°C in air for short periods of H- seed, low-power, radiation-re sis tant, monolithic thin-film integrated circuits'-3 require thin-film resistors of high sheet resistance and low temperature coefficients of resistance which are compatible with the processing requirements for monolithic silicon active devices. The present investigation is directed towards the replacement of the Nichrome in the sandwich-type SO2-Nichrome-SiO resistors, currently used for DTL monolithic thin-film integrated circuits, with codeposited Nichrome-SiO cermet resistors. These Nichrome-SiO resistors are provided with an overcoat of SiO and are deposited onto thermally oxidized silicon wafers used in monolithic mi-crocircuit technology. The cermet resistors are shown to provide a lower temperature coefficient of time totaling up to 45 min. Electron nzicrogvaphs and diffraction patterns were taken of the as - deposited and heat-treated films. These results were then compared with electrical-resistance measurements for each condition. The room-temperature and 300°C substrate films showed a large decrease in resistance. The 500°C substrate film remained stable throughout the entire cycle. Electron-microscopy results show that the increased stability after heating to 600°C is largely due to crystallization of the films which begins in the vicinity of 400°C. The slight oxidation of the films when heated in air had a negligible effect on the resistance. The resistance of the film was a function of the substructure. resistance and a more versatile compatibility with silicon monolithic processing. Previous work3, on chromium-SiO coevaporated cermet resistors on glass and ceramic substrates without overcoats of SiO has been reported. For the present application, the thin films should possess the following ideal requirements: a) a temperature coefficient of resistance as near zero as possible up to 300°C; b) have a sheet resistance higher than 200 ohms per sq to conserve space on the chip; c) be easy to evaporate; d) be oxidiation- and radiation-resistant; e) show long-time stability at 100°C; } be stable in N2 atmospheres up to 600°C for short periods of time (5 to 45 min). Requirements a to e are well-known. The last requirement was optional and was due to a mask elimi-

Jan 1, 1967

By R. Ebeling, M. F. Ashby

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

Jan 1, 1967

By C. E. Lundin

The Ce-H system was investigated in the temperature range, 573° to 1023°K, and the pressure range, 10-3 to 630 Torr, as a function of 'composition up to 72 at. pct H. Families of isothermal arid isopleth curves were plotted from the pressure-terr~perature-composition relationships. From these curves the solubility relationships were determined for the system. The isopleths are analytically represented by equilibrium dissociation pressure equations. The relative partial molal enthalpzes and entropies of solution of hydvogen in the systerrz were calculated fronz the dissociation pressure equulions and are tabulated. The integral free energies, enthalpies, and entropies of mixing in the Ce-H system were determined from the relative partial quantities and are also tabulated. The standard free energy, enthelpy, and entvopy of reaction of the dihydride phase at kcal per kcal per mole H2, and ?S° = -34. 1 cal per deg mole H2, respectively. The equilibrium dissociation pressure equation in the two-phase region is: UNTIL recently very little was known of the detailed solubility and thermodynamic relationships of the Ce-H system. Two previous investigations1,2 are noteworthy. However, significant discrepancies and omissions exist on analyzing them. The work of Mulford and Holley1 on cerium did not clearly delineate the boundaries of the two-phase region, Cess - CeH2-x. The plateau partial pressures were not thoroughly defined and were considerably displaced in pressure compared to those from the work of Warf and Korst.2 These latter authors concentrated their studies primarily from 823° to 1023°K in the pressure range of 1 to 760 Torr. No data were determined to outline the regions of primary solid solubility and the hydride phase. Also the establishment of the plateau partial pressures was rather limited in scope. In neither work was a treatment conducted of the relative partial molal enthalpies and entropies of solution of hydrogen in the single-phase regions and the integral thermodynamic quantities of mixing throughout the system. Therefore, it was the objective of this research to determine the complete equilibrium solubility relationships and thermodynamic data for the system by pressure-temperature-composition studies. EXPERIMENTAL PROCEDURE The cerium metal for this study was donated by the Reno Metallurgy Research Center of the Bureau of Mines. Total impurity content was 0.13 pct with only 60 ppm O. The metal was checked metallographically and contained only minor amounts of second phase compared to cerium from other sources. Specimen preparation was done in a dry box flushed with argon gas. The surface of a small rectangular piece of cerium (about 0.2 g) was filed with a clean, mill file. Final weighing was done in a tared enclosed vial containing argon gas. The specimen was then loaded quickly into the reaction chamber which was purged several times with high-purity hydrogen gas and then allowed to pump to about 10-6 Torr. The furnace was heated to the reaction temperature and the run started. The equipment used to conduct the hydriding was a Sievert's-type apparatus. Basically it consisted of a source for pure hydrogen, a precision gas-measuring burette, a heated reaction chamber, a McLeod gage, and a mercury manometer. Pure hydrogen was supplied by the thermal decomposition of uranium hydride. The 100-ml precision gas burette was graduated to 0.1-ml divisions and was used to measure the quantity of gas and admit it to the chamber. The reaction chamber was a quartz tube. Prior to each run, the cerium specimen was wrapped in a tungsten foil capsule to prevent reaction of the cerium with the quartz. Control of the temperature was achieved within ±1°K. Pressures in the manometer range were measured to ±0.5 Torr and in the McLeod range (10-3 to 5 Torr) to ±3 pct. The compositions of hydrogen in cerium were calculated in terms of hydrogen to cerium atomic ratio. These compositions were estimated to be ±0.01 H/Ce ratio. The technique used to study the equilibrium pressure-temperature-composition relationships of the Ce-H system was to develop experimentally a family of isothermal curves of composition vs pressure. The range of pressure through which each isotherm was developed was from 10-9 to about 630 Torr in the temperature interval, 573° to 1023°K. RESULTS AND DISCUSSION The hydriding characteristics of cerium are iso-morphous with those of the elements of the light-rare-earth group (lanthanum, cerium, praseodymium, and neodymium) wherein the region from the dihydride to trihydride is continuously single phase.' The structure of this phase is fcc.3 The heavy rare earths form a trihydride,2 which is hcp, separated by a two-phase region from the fcc dihydride phase. The Ce-H system is represented by the family of experimental isotherms in Fig. 1. Due to the small scale required to draw the curves, the experimental points are omitted; however, a total of 240 experimental data points were taken to prepare these curves. The solubility relationships can be deduced therefrom. Three distinct regions of partial pressure and composition can be seen. The region of cerium solid solution is represented by the rapidly rising isotherms in the dilute composition range. In accordance with Gibbs Phase Rule only one solid phase, the cerium solid so-

Jan 1, 1967

By R. N. Stevens

GRAIN boundary sliding plays a part in the high-temperature deformation of polycrystalline solids, and many investigations1-11 have been carried out to determine the deformation contributed by this mechanism. The principal method employed has been to measure one of the components of the grain boundary displacement, see Fig. 1, at a large number of boundaries, and from the mean value so obtained to calculate the elongation contributed by sliding. A formula connecting these mean values and the elongation contributed is evidently required, and many have been derived. They are usually of the form where Egh is the tensile elongation contributed by sliding, is the mean value of the component, x, N is the mean number of grain boundaries intersecting a line of unit length, and K is a dimensionless parameter known as the averaging factor. Table I summarizes the equations used by various investigators. Examination of these shows that their derivations usually involve doubtful assumptions, and are often in serious error. The purpose of this note is to point out that rigorous solutions to the problem of calculating Egb from x have been available in the literature for some years.' Since this is so little known, and also the original derivations do not make some important points clear, it is proposed to rederive the basic equations. These will be extended further, and the conditions in which the extended equations may be applied will be indicated. The mean values of the components of the sliding vector (I, d, and I:, Fig. 1) will depend on the method by which boundaries are sampled in order to make measurements.3,11 Boundaries are usually sampled by marker lines parallel to the stress axis, or lines perpendicular to the stress axis, the measurement being made at the point where the marker line intercepts the boundary. We will denote the mean values determined by these various sampling methods as follows. lT, dT and vT are mean values obtained by making measurements at pointswhere a transverse line intercepts the boundary while lL, dL, and vl, are the mean values from a longitudinal line. The number of boundaries per unit length also may depend on the direction of measurement, and so we define NT and Nl to be the number of boundaries per unit length, after creep, in the transverse and longitudinal directions, respectively.

Jan 1, 1967

By C. H. Stewart, R. A. Fagin

A two-dimensional, three-phasereservoir simulator was programmed for a large memory digital computer. It was designed to provide a practical solution to describing the complex physical relation between the natural forces and the physical properties of a heterogeneous reservoir when subjected to a specific set of conditions. A reservoir study is briefly described to illustrate application of the model. A full volumetric account of three phases (oil, gas and water) is performed simultaneously throughout an integration net representing the reservoir. Absence of one or two of the phases is treated as a special case of the more general situation. Expansion (or contraction) of all phases, including rock expansion, is performed so that the pressure calculation is the general unsteady-state case. To account for the large variations of subsurface elevation encountered in some reseruoirs, and to allow for segregation of the various phases, a gravity head term is included in the basic drive potential. Appropriate fluid and rock properties are used in polynominal surface form (functions of pressure and/or depth) or they can be entered as space variables at each position of the integration net. An unsteady-state water influx calculation, based on the method of van Everdingen and Hurst, l was connected to the boundary of the matrix to simulate aquifers of various sizes. In addition to reservoir calculations, three-phase fluid flow from the producing depth to the wellhead, including provisions for gas lift, was incorporated in the simulator. A workover routine was also built which can automatically switch to a different set of production relations when a gas-oil ratio or water fraction reaches a limit; or it can shut-in the well if prescribed. INTRODUCTION This paper describes a reservoir engineering mathematical simulator used to represent the complex interaction of natural forces and physical properties of a reservoir during natural depletion or with various injection schemes. The simulator, which was programmed for a large memory digital computer, is a two-dimensional calculation which handles three mobile fluid phases simultaneously (oil, gas and water). Basic requisites for the method are individual well production and pressure data, hydrocarbon fluid properties, geological data (producing depth and net sand), capillary pressure data, relative permeability data and permeability and porosity information. Matching the past performance of a combination drive reservoir often has yielded information concerning continuity and the validity of basic data. Detailed predictions of future performance can be made for continuation of current depletion methods (natural depletion) as well as for various types of recovery by gas or water injection. Combination injection cases and pattern studies can also be performed. Workover programs, gas lift and different types of artificial lift programs have been investigated using a technique similar to that described by Kern and Nicholson2 except that conditions of pressure and saturation at the block within which the well is located are used rather than average reservoir conditions. Drilling additional wells to optimize profit was explored, both as to number and location, by placing wells at different spots within the reservoir matrix. Special depletion processes can be examined, such as upstructure drainage and lateral (or strike) waterfloods in thin oil columns. In one case the mathematics of the simulator were modified to calculate the displacement in the vertical plane rather than in the horizontal plane. In this manner specific reservoir problems can be studied, such as coning of gas and/or water around production points, fingering along permeable stringers or, more generally, frontal advances in a heterogeneous section.

Jan 1, 1967

By H. Y. Jennings

An extensive field and laboratory experimental program was carried out to compare the waterflood behavior of carefully preserved soft and unconsolidated cores with measurements on the same cores after extraction. Results obtained from using idealized consolidated and unconsolidated porous media in which wettability could be carefully controlled were contrasted with the preserved core data. The controlled tests on idealized porous media investigated the effect of wettability, flood rate, core length, core permeability and consolidation on the displacement of high viscosity oils. It was concluded from these studies that waterfloods are more favorable when carried out with crude oil in preserved soft and unconsolidated cores than with the same cores after they have been extracted and re-saturated. Waterfloods are usually more favorable when carried out with crude oil in extracted .soft and unconsolidated cores than with refined oil of the .same viscosity in the same cores. The less favorable behavior of extracted soft and unconsolidated cores compared to preserved cores is due to alteration of the core by extraction. Preserved cores saturated with native water and oil should be used for laboratory displacement experiments because they more accurately reflect true reservoir behavior INTRODUCTION The demand for low gravity crude oil created by refinery modernization has focused attention on increasing the production of this viscous crude oil. Billions of barrels are in place in fields that are depleted, or nearly depleted, by primary production mechanisms. Since low gravity reservoirs are relatively recent, geologically, the solid matrix material is usually soft and unconsolidated sand. Such formations are also characterized by a high clay content. Evaluation of sophisticated oil recovery processes with the associated high capital investments has increased the demand for special core analysis tests on material from these soft and unconsolidated sand reservoirs. Data in this paper have resulted from an extensive field and laboratory experimental program. The initial objective vras to provide soft and unconsolidated sand cores for laboratory measurements with as little alteration as possible from their reservoir condition. A secondary objective was to compare the waterflood behavior of these carefully preserved cores with measurements on the same cores after they had been extracted and resaturated. When the comparison showed markedly different behavior the final objective was to attempt to explain the difference by making measurements on idealized porous media free of clay in which initial wettability could be carefully controlled. EXPERIMENTS MATERIALS Core Material The preserved cores used in this study were obtained with as little alteration as possible from their reservoir conditions. Special techniques were developed to satisfy this objective. The cores were cut with native crude whenever the crude had the necessary properties to satisfy the minimum drilling fluid requirements. A pure hydrocarbon chromatographic tracer was added to the crude to provide a simple, safe and inexpensive method to distinguish between oil filtrate and formation oil. Details of the tracer technique used in this study and the procedures used to handle and process the soft, unconsolidated cores have been published.' The core samples were then preserved and packaged at the well site with a dip-applied strippable plastic, or by using a rubber sleeve from a rubber-sleeve core barrel. The final step was to insure that the carefully taken and preserved samples were not altered by processing in the laboratory. Some soft and poorly consolidated sands were carefully shaped in the lab and encased in a protective mounting without disturbing their three-dimensional integrity. Many samples were so poorly consolidated that they literally flowed from the package when the seal was broken. A technique was developed to obtain cylindrical plugs from these samples by using liquid nitrogen as the drilling fluid in a conventional core-drill, drill-press assembly. The idealized porous media consisted of sintered rods of Alundum RA 139, outcrop sandstone identified as Al-hambra sandstone and packs of No. 130 Nevada sand. This sand is 95 per cent 140-200 mesh. (Physical properties of these porous media with those representative of preserved cores are in Table 1.) The natural cores and most of the idealized porous media were 1 1/2-in. in diameter and 3-in. long. The samples used to study the effect of core length were 1 1/2-in. in diameter and 12-in. long. Liquids Water and oil produced from the formations being studied were protected from the atmosphere and collected in carefully cleaned glass or plastic-lined containers. The production was free of chemical additives such as emulsion breakers and corrosion inhibitors. The crude oil was

Jan 1, 1967

By A. M. Adair

The effect of cathodically charging zone-refined iron with hydrogen and the resultant yield stress-grain size relationship has been investigated by tensile testing at -31°C. The resulting Petch plots (using a least-squares analysis) reveal a significant reduction in the slope and an increase in the intercept for specimens cathodically charged with hydrogen, regardless of whether the hydrogen is present during testing or is removed by evacuation. Other than surface blistering, the major effect of cathodically charging this material is to create occasional grain boundary cracks and thus presumably a large number of free dislocations at grain boundaries. These results are consistent with the hypothesis that the slope of the Petch plot is related to the stress required to activate dislocation sources at or near pain boundaries. While there is no significant effect of the presence of hydrogen on the lower yield stress of this material, the ductility is considerably reduced. After hydrogen removal by evacuation, the ductility recovers substantially and almost complete recovery of ductility is experienced by the smaller grain size specimens. THE influence of hydrogen on the mechanical properties of ferritic materials has received much attention throughout the history of the metallurgy profession. This interest has stemmed from the obvious importance of preventing the catastrophic failure of parts in service, and from the desire to determine what mechanism is responsible for the observed behavior. The various mechanisms proposed for hydrogen em-brittlement have been discussed in detail by Tetel-man,'who concludes that a combination of the applied stress and hydrogen pressure within voids best accounts for the many experimental observations reported. From a quite reasonable correlation of the strain aging and delayed-failure behavior of a variety of materials,2-7 Troiano and coworkers are of the opinion that the delayed-failure mechanism (slow strain rate embrittlement as well) is better explained as a lattice effect; solute elements diffuse to regions of high triaxial stress, form uncondensed atmospheres there, and effect a reduction in the cohesive strength of the lattice. Since hydrogen yield points8,9 have been observed in ferritic materials, and since the hydrogen embrittlement process may be related to strain aging, one further contribution to embrittlement could be hydrogen-dislocation interactions which make crack blunting by plastic deformation a more difficult process. The etch" relationship offers a means of comparing the relative ease of initiating and propagating plastic deformation in metals and alloys. In the present study, this relationship was used to compare the behavior of zone-refined iron in three conditions: uncharged, cathodically charged with hydrogen, and cathodically charged with hydrogen and evacuated. These Petch plots and the observed ductility parameters allowed a separation of the effects of the very presence of hydrogen and the act of cathodically charging hydrogen into this material. MATERIALS AND EXPERIMENTAL PROCEDURE An ingot of zone-refined iron was obtained from Battelle Memorial Institute which contained the following (typical) interstitial impurities in ppm: carbon, 10 * 5; nitrogen, 1; oxygen, 22; hydrogen, 0.9. The ingot was cold-reduced to a 1/2-in.-sq cross section, recrystallized 1 hr at 575°C, and then straight-rolled to a thickness of about 0.105 in. Tensile specimens were milled from the strip having a 1-in. gage length

Jan 1, 1967

By J. C. Uy, A. A. Burr

A quantitative relationship between the allotropic phase boundaries of zirconium-base binary systenzs and the solute metallic valence is shown through an intermediate thermodynamic parameter. A simplified equation relating this parameter to the phase boundaries is briefly reviewed, and data from the literature are used to show the relationship of this parameter to the solute metallic valence. It has been reported that the solute metallic valence can be used as an index of phase stabilization in zirconium-base binary alloys.' It was shown that the algebraic sign of the slopes of the hcp/bcc phase boundaries of zirconium alloys correspond to the algebraic sign of the metallic valence of zirconium minus the metallic valence of the solute, or, in other words, a solute whose metallic valence is higher than that of the solvent tends to stabilize the high-temperature phase while one whose metallic valence is lower than that of the solvent tends to stabilize the low-temperature phase. Further analysis of the zirconium binary systems has revealed a quantitative relationship between the solute metallic valence and the relative slopes of the two-phase allotropic boundaries. This relationship involves a thermodynamic quantity whose significance can be seen in the following section. PHASE-STABILIZATION PARAMETER Let Qb be the difference between the partial molar heats of mixing of a given solute in the two allotropic phases of the solvent which are in equilibrium with each other at a given temperature, thus A relationship between this term Qb and allotropic phase boundaries has been employed by several au-thors'-= in the evaluation of phase diagrams, and can be briefly derived as follows. Referring to Fig. 1, consider the general case of two allotropic phases, each having a small mole fraction (Xa,Xb) of the solute, in equilibrium at temperature T and atmospheric pressure as represented by the reaction. solute in ß phase =solute in a phase If now a reaction occurs such that an infinitesimal amount of the solute is removed from the ß phase and added to the a phase, there would be a partial molar

Jan 1, 1967