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By S. P. Goplen, M. Henriksen, T. F. Barron

In the past decade, numerous large scale drilling projects have made use of reverse circulation air lift methods. Reverse air lift pumping can be established by injecting gas into a column of liquid; the subsequently decreased density of the gas-liquid mixture allows atmospheric pressure outside the lift conduit to establish flow. The rate of flow can be controlled by varying the gas to liquid ratio. A typical reverse circulation air lift system is depicted in [Fig. 1]. Allen 1 has described a number of reverse air lift drilling projects. Although cited examples are generally related to large diameter holes, the method has seen use in other applications such as sand dredging, chemical pumping, water well pumping. and continuous coring. One particular benefit obtained with enclosed reverse circulation drilling is elimination of lost circulation. The required air/water ratio for pumping at a given submergence and lift has been established experimentally by Gibbs.2 His data, however, do not reflect sensitivity of flow rate to air/water ratio. Further, in Gibbs' work, air apparently is injec-

Jan 1, 1980

By J. H. Brophy, A. I. Prill

The authors have previously investigated the solid-state activated sintering of tungsten powder with various Ni-Cu additions.' Log shrinkage vs log time plots showed changes in slope from 4 to x at intermediate times during the sintering process. This was attributed to a change in the rate-controlling mass-transport process from solution of tungsten into the tungsten-alloy interface to diffusion of tungsten in this interface. It was postulated that the melting of the activating layer should not affect this transport process. However, the superposition of rearrangement due to the presence of a liquid phase complicates the data analysis. It is the purpose of this note to apply the analysis of Prill, Hayden, and rohy' to account for "rearrangement shrinkage'? in liquid-phase sintering of the W-Ni-Cu system. This results in "solution-precipitation stage" shrinkage plots which were comparable to those obtained in solid-phase activated sintering of the same system. If one assumes total shrinkage to be the sum of rearrangement and solution precipitation, the effects can be isolated easily.2 This results in the general equation:

Jan 1, 1967

By A. D. Rovig, D. W. McGlashan, Donald M. Podobnik

Crystal-chemical and stntctural properties of sulfide minerals are considered. The information gained is to be used to interpret (I ) freshly broken mineral surfaces, (2) modifications of the mineral surfaces, and (3) reactions at the mineral surfaces. From these basic disciplines, concepts with regard to the changes that surfaces undergo, reactions that might take place, the geometry of the interface, the state of different atoms and ions in the interface, and other physical and chemical properties of an interface must be developed, weighed and applied. The authors first deal with these conceptual considerations from which hypotheses are set forth to describe the environ men tal-interfacial relationships for several sulfide minerals. Qualitative and quantitative explanation of par-ticulate solid separations are unknown entities because of the lack of adequate models and mathematical relationships to explain the activity occurring between the solid and liquid phases. It is a transitional region in which it is difficult to ascertain the mechanisms of adsorption of ions, molecules, etc., on mineral surfaces, as well as other secondary reactions which occur in interfacial regions. Thus, in this paper the authors deal with conceptual considerations from which hypotheses are set forth to describe the environmental-interfacial relationships for sulfide minerals. GENERAL CONSIDERATIONS Interfacial Reactions:Interfacial reactions are the cruxes of flotation schemes as well as other processes such as thickening, filtration and hydrometallurgy. However, as noted by Klassen and Mokrousov: 1 "The problems concerning the surfaces of natural minerals, the laws governing simultaneous adsorption from aqueous solution on these surfaces of a whole series of reagents, the laws of the surface reactions and the properties of water layers separating the minerals, are all known to a first approximation only." An investigator has the privilege of postulating methods of solid-liquid interfacial reactions. REACTIONS WITH WATER - Water consists of hydronium (H3 O 4) and hydroxyl (OH-) ions in the ionized state. That this is so forms the basis for the postulated reaction of the hydrated hydrogen ion with net-negative mineral surfaces as depicted in Fig. 1. In this case water is bonded to mineral surfaces through hydrogen-bridge-type bonds - possibly hydrogen bonds. Although bonding of the van der Waal type may be responsible for this reaction, it is most likely that stronger bonds are involved. Once firmly bonded to the surface, the water layer is known to be quite tenacious. It is further speculated that a shear plane exists at some distance (see Fig. 1) away from the mineral surface. Exact location of this plane is not known, but in all probability it will be positioned across a weak bond of the hydrogen-bond type where the surface-attached water is coordinated to the original hydrated hydrogen ion. REACTION WITH METAL IONS - Klassen and Mokrousov ' state: "The presence of an ion in water leads to an immediate formation around that ion of a highly condensed atmosphere of water dipoles and thus to hydration of the ion." The fact is known that multivalent cations are strongly hydrated, usually by six or eight molecules of water, and that anions are not so strongly hydrated. Conceding the fact that thermodynamics, concentration, pH, and physical considerations are of utmost importance in truly explaining a mechanism of metal ions reaction with a hydrated mineral surface, it does seem logical that the mechanism illustrated in Fig. 2 is feasible. In this reaction, the metal ion (M) is coordinated in one dimension - to the mineral-surface hydration layer. Note also that explanation of this reaction requires that the shear plane move to a less stable bond configuration; that is, the shear plane has moved to a position between the metal ion and the other coordinated water molecules which are more free to dissociate. Reactions as depicted in Fig. 2 should cause the formation of an apparent mineral surface which is net-positive. Immediately, it must be noted that measurements of apparent-mineral surfaces serve - within limits - to indicate a degree of ion-surface reaction capability. The major limiting factor he re is one related

Jan 1, 1970

By Evans B. Mayo

This study examines the structural framework of the Southwest for evidence of the four principal trends of lineament tectonics. It attempts to classify their intersections and compares the positions of those trends that appear most favorable with the positions of the presently known mining districts. This is a controversial topic. The author, in presenting his analysis, is aware that the study of lineament tectonics and relation of ore districts to regional structure is complicated by insufficient data and, unavoidably, by personal bias. The development of lineament tectonics has been summarized by Umbgrove.' Early attempts to fit ore districts into the Cordilleran framework were made by Billingsley and Locke, who do not refer to lineament tectonics, although their appoach is similar; they observe that heat and fluids, including the ore-depositing fluids, are most likely to rise at or near intersections of major structures where the crust is fractured, or weakened, to great depth. As a result of studies distributed over the earth-including ocean basins as well as continents— some tectonists recognize four dominant structural trends: 1) northwest; 2) northeast; 3) nearly east-west, or equatorial; and 4) nearly north-south, or meridional. Baker' proposed a theory to account for these trends and Sonder" called their world-wide arrangement the regmatic shear pattern. Moody and Hill proposed a much more complicated shear network which, although fascinating and perhaps ultimately useful, will not be followed here. In a recent review of deformation within the Cordillera, Wisser mentioned the four fundamental directions. The fact that many geologists deny the existence of the regmatic shear pattern implies that the fundamental structures are far from obvious. It may mean, also, that some geologists are not accustomed to examine regional and world maps analytically. The maps require much study, and certain features should be isolated on overlays. Even so, with the present limited knowledge, uncertainties remain. The following analysis is a qualitative experiment, subject to change as information accumulates, and should be supplemented by the western sheet of the Tectonic Map of the United States.' Many have probably gained the impression that the Cordillera of the West is oriented northwest-southeast and from this, unless experience rules otherwise, it is natural to assume that the structure likewise trends northwest-southeast. To an important extent this is true, yet anyone tracing off the western sheet of the Tectonic Map all the recorded north west-southeast structures may be surprised to see what a small part of the entire area they occupy. In southwestern U. S. (Fig. 1) the northwest-southeast structures are mostly restricted to the eastern, southern, and western parts. The eastern margin of the Cordillera from northern Colorado to the International Boundary near El Paso, Tex., is obviously determined by some structure other than northwesterly ones. In eastern Nevada and far southward toward the Gulf of California many mountain ranges, valleys, and faults are meridional. In the Rocky Mts. of Colorado, and at many places in southern Arizona, the crystalline Pre-Cambrian is foliated northeast-southwest. The Uinta Mts. of Utah trend approximately east-west, in much the same way as a broad belt of transverse, west-northwest structures—the Texas lineament of Hill",' and Ransome10 in southern Arizona, southwestern New Mexico, and southern California. It seems, then that there are four regmatic shear directions in the Southwest, but at many places they are discontinuous, and their projections must be inferred. To clarify these trends the four sets have been isolated into two systems: 1) northwest-northeast and 2) east-west-north-south (Figs. 2 and 3). Northwest-Northeast System: A number of prominent northwest-trending zones of structure are easily recognized. They are designated by circled Roman numerals, the northeast-trending structures by circled capital letters. Perhaps no two geologists would agree completely on the positions of all these belts. Names given below are for convenience only, and may be discarded where other names have priority. (I) The Sierra Nevada-Lower California belt contains the Jurassic-Cretaceous granitic massifs of the Sierra Nevada and Lower California. These

Jan 1, 1959

By Barry D. Lichter, Pierre Sommelet

High-temperature heat contents of InSb, GaSb, and AlSb were measured over the temperature range 400" to 1450°K using a diphenyl ether drop calorimeter. Smoothed ualues of the thermal properties, H$ - H:9s, have been derived and are tabulated at even temperature intervals. The heats of fusion of the three compounds were determined as, respectively, 5707 *100, 7780 * 100, and 9800 5 3011 cal per g-atorn at the determined melting points of 797" l°, 985" * , and 1330" * 5°K. The calculated entropies of fusion are, respectively, 7.16 0.12, 7.90 * 0.11, and 7.37 * 0.23 cal per deg per g-atotn. The heat capacities increase substantially on tnelting in contrast to the behauior of structurally related germanium and silicon. Deriations from the Kopp-Neumann rule are negative for solid compounds and positive for the liquid phases. Previously obsevrrd "post melting" in InSb is confirmed. The high-temperature thermal properties of 111-V compounds are presently not well-established, despite the technical importance of these semiconducting cbmpounds. Uncertainties in available heats of fusion and heat contents have seriously hampered thermo-chemical evaluations' and thermodynamic analyses of phase equilibria2"" in these systems. This paper reports results of high-temperature heat content investigations of InSb, GaSb, and AlSb measured in the range 400" to 1450°K employing a diphenyl ether drop calorimeter. Similar measurements for InAs and GaAs will be reported in a following publication.~ EXPERIMENTAL PROCEDURES Samples. High-purity samples of the compounds InSb and GaSb were supplied in the form of crushed crystal fragments by Dr. Carl Thurmond of the Bell Telephone Laboratories and in the form of single crystals by Dr. A. Strauss of the M.I.T. Lincoln Laboratory. Single-crystal samples of semiconductor-grade AlSb were supplied by Dr. W. P. Allred of the Bell and Howell Research Center. Chemical analyses indicated that all compounds were stoichiometric to *0.1 at. pct, which is within the experimental uncertainties of the analyses. Samples were crushed, weighed, and encapsulated in evacuated, thin-walled, fused silica capsules. The capsules were nearly identical in external shape, 2 cm by 2 cm diam, but varied in weight due to differences in wall thickness. One sample of AlSb was contained in a thin-walled, high-purity alumina cup encapsulated in silica and used for heat content determinations of liquid AlSb. The capsule materials showed no visual evidence of reaction with any of the compounds. The sample and capsule weights are given in Table I. Calorimeter. A Bunsen-type calorimeter, similar in design to a previously described instrument6 but employing diphenyl ether (C6H5)'0 as the calorimetric substance, was used for measurements of heat contents above 300.0°K, the melting point of diphenyl ether. Heat input to the calorimeter caused isothermal melting of diphenyl ether, and the resulting increase in volume was measured by displacement of mercury from the calorimeter into a 200 cm horizontal, calibrated capillary, 1.25 * 0.01 mm diam, or into a weighed beaker. The advantages of diphenyl ether over water have been previously pointed out7 and include: i) an increase by a factor of 3.5 in sensitivity as measured by the ratio of the volume change to the enthalpy change on fusion, ii) the smaller required extrapolation from the melting point to the standard temperature of 298.17"K, and iii) the positive volume change on fusion of diphenyl ether in contrast to the contraction which occurs on fusion of ice. Diphenyl ether was purified by fractional crystallization to 99.95 mol pct as determined from the melting point depression with fraction crystallized. During assembly of the calorimeter, the ether was repeatedly outgassed under high vacuum to remove dissolved air. The calorimeter receiving vessel consisted of an 8-in.-long by 1:-in.-diam copper tube with twelve horizontal 3-in.-diam radiator "fins" for dissipating heat to the surrounding mantle of diphenyl ether. Before forming the mantle the chamber surrounding the receiving vessel contained 3300 cu cm of liquid diphenyl ether above 250 cu cm of mercury which was

Jan 1, 1970

By G. Bruggeman, K. G. Kreider

Grain boundary dij]usion coefficienls were measured in tungsten between 1400° and 2200° C and can be expressed by the equation sq cm per sec This activation energy confirms some eavlier estimates made .from tungsten sintering experiments. Grain boundary diffusion was found to occur in sub-bozrndavies having -misorientations of less than 10 deg. The actiuation energy for this subboundavy diffusion is equal to that for dijjusion in incoherent grain boundaries with in the limits of error. This is shown to be consistent with the dislocation model of Low-angle boundaries wheve diffusion occlcvs along- the dislocation 'YPipes" comprising -tile boundary. RECENT investigations of the sintering of tungsten powders all report activation energies which are considerably less than the activation energy for tungsten volume diffusion. Kothari' reports a value of 100 * 5 kcal per mole, Hayden and Brophy' obtained 90 kcal per mole, and Vasilos and smith3 found 110.7 kcal per mole from their sintering studies. Since most determinations of the activation energy for volume diffu-sion4-' fall between 120 and 160 kcal per mole (the true value seems most likely to be nearer 150 kcal per mole), the conclusion is drawn that the mass transport leading to densification during sintering is accomplished by grain boundary diffusion. This interpretation is consistent with various diffusion models of the sintering process. 10-12 Vasilos and Smith calculate diffusion coefficients from their data which fit the equation D * 1.36 x 10* exp(-llO,700/HD However, no direct measurements of tungsten grain boundary diffusion have been made. Furthermore, considerable disagreement exists between the directly measured values of tungsten volume diffusion.'-' In order to corroborate the inferred results of the sintering experiments concerning grain boundary diffusion and to provide accurate diffusion data essential to the analysis of the kinetics of creep, oxidation, precipitation, and so forth, the present work was undertaken to measure self-diffusion in single-crystal and polycrystalline tungsten between 1400" and 2200°C. It is within this temperature range that tungsten sintering is done, the re crystallization of tungsten occurs, and the widest application of tungsten as a high-temperature material will probably be made. EXPERIMENTAL PROCEDURE Radioactive WlE5 was produced by irradiating tungstic acid in a neutron flux of 1.2 x 1012 neutrons per sq cm per sec for 36 hr. A 2-week waiting period was allowed for the decay of w"~ also produced by the irradiation. (w"~ has a half-life of 24 hr.) The half-life of the remaining isotope was determined to be 75 days confirming the presence of w lE5 and the absence of any undesired radionuclide. Specimens 4 in. in diam and $ in. thick were cut from polycrystalline swaged tungsten rods (recrystal-lized) and from Linde single-crystal rods. Chemical analyses of these materials appear in Table I. Actually upon closer examination, the single-crystal specimens were found to consist of several subgrains separated primarily by tilt boundaries in which the misor-ientation ranged from 3 to 10 deg. Thus, it was possible to measure boundary diffusion coefficients in these low-angle subboundaries as well as in the incoherent boundaries of the polycrystalline specimens. The two faces of each specimen were ground flat and parallel within 0.0001 in. The radioactive tungstic acid was dissolved in concentrated ammonium hydroxide, placed on the ground flat of the specimen, and evaporated to dryness. The oxide was then reduced in hydrogen at 1000°C resulting in a layer of wlE5 approximately 1 p thick. The diffusion anneals were performed in vacuum in a tantalum resistance furnace. Time at temperature ranged from 10 hr at 1400°C to 2 hr at 2200°C. The penetration profile was determined by measuring the residual activity after successive removal of surface layers by grinding on metallographic polishing paper. Extreme care was exercised to insure that sections were always taken normal to the diffusion direction; this was verified repeatedly by checking that front and back surfaces of the specimen remained parallel. The activity was measured with an end-window Geiger-Mueller counter. The sides and edges of the specimen were well-shielded to eliminate possible effects due to surface diffusion. The weight of the

Jan 1, 1968

By C. Graeme-Barber, R. L. Bell, T. G. Langdon

An analysis is made of the formulas and ,methods used to estimate the contribution of grain boundary sliding to the overall strain of a polycrystal. The errors involved in the approximations and/or ,mistakes in earlier work are assessed quantitatively so as to make possible the critical use of previously published data. SINCE it has been found that, under conditions of very slow creep, the strain due to grain boundary sliding (?gb) may contribute as much as 80 pct of the total creep strain,1,2 it is obviously important to have reliable methods for estimating this grain boundary strain. In two recent papers Stevens3,4 has drawn attention to the pitfalls encountered in assessing ?gb. He criticizes 1) the assumptions made in the derivation of some of the formulas for ?gb, and 2) the indiscriminate averaging procedures used for obtaining the quantities substituted in these formulas. These and further criticisms of earlier work are mostly valid. Unfortunately the only formulas and procedures recommended are either impossible or very difficult to apply in practice. Furthermore no attempt is made to assess the errors involved by the earlier approximations or mistakes, and so it is not possible to make critical use of any of these early dab. The present article attempts to improve on these shortcomings by reference to empirical verification of easily applied formulas whose theoretical derivations involve some otherwise unjustifiable assumptions, and by a quantitative assessment of the errors in previous work. DEFINITIONS First it is necessary to define the terms and symbols to be used. The choice of symbols preferred here is a logical combination and extension of the v introduced by McLean5 and the u by Brunner and rant.' In Fig. 1 the two grains X and Y are displaced by the sliding vector AC. u is the component of sliding resolved along the stress axis, v is that measured perpendicular both to the stress axis and to the specimen surface, and w is that measured perpendicular to the stress axis but in the plane of the surface. Two angles define the orientation of the grain boundary: 8, between the stress axis and the surface trace of the boundary, and +, the internal angle on a longitudinal section cut perpendicular to the surface. In computing the strain resulting from the boundary displacement at all the in- dividual boundaries in a polycrystal the components u, v, or w are sometimes averaged along a longitudinal line (i.e., parallel to the stress axis), sometimes along a transverse line, and sometimes at randomly chosen boundaries. Averages obtained in these three ways are given subscripts 1, t, and r, respectively. Stevens rightly calls attention to the possibility of non-equiaxed grain shapes either at the start or at the end of deformation. In this article all values of numbers of grains per unit length will refer to measurements made before deformation. The subscripts 1 and t will be used for the number of grains per unit length obtained along longitudinal and transverse lines, r for that obtained by averaging along a number of randomly directed lines. FORMULAS FOR ?gb ?gt, as a Function of u. An obvious truth is that cgb can, in principle, be obtained by summation of all the v components at the boundaries intersected by a longitudinal line of known length I, viz.: where nl is the number of grains per unit length, parallel to the stress axis, in the unstrained specimen. There are assumptions in the analytic derivation of Eq. [I] due to Brunner and rant' but ~achinger' arrived at Eq. [la] by a rigorous method. Unfortunately the experimental procedure required by Eq. [ la] proves very difficult as boundary migration tends to obscure the points at which the longitudinal line meets the grain boundary and the errors on such measurements tend to be large, see Fig. 2. For example, on a specimen of Magnox AL 80 at a creep strain of 9.7 pct, 300 measurements of u obtained from the points of intersection of a longitudinal line with the grain boundaries gave ul = 8.95 ± 3.58 pm, or an error of ±40 pct, at the 95 pct confidence limit. These large errors due to migration may be avoided by measuring u from the separation of the segments

Jan 1, 1968

By Pradeep K. Rohatgi, David N. French, Surendar M. Jain, Clyde M. Adams

The effect of solute concentration and diffussivity on dendritic solidification of dilute binary aqueous solutions has been investigated; chlorides of sodium, potassium, lithiurn, and hydrogen were used as solutes. Dendrite spacings were measured in spherical droplets and in unidirectionally solidified specimens. In the droplets, the freezing rate is uniform over the entire specimen and remains constant from the beginning to the end of solidification. In the unidirec-tionally frozen specimens the freezing rate varies within a given volume of liquid during the solidification cycle; in addition, it varies with location uithin the specimen. Mass transport analysis has been used to calculate the supersaturation, AC, supercooling, AT, and transcerse growth velocity, V , of ice dendrites during solidijication from the dendrite spacings measured in the droplels. The ice dendrite spacing in a given solute increases lineary with the solule concentralion at a fixed freezing rate. The ualues of AC, AT, and V increase with an increase in solule concentration. The value of AT in the aqueous solution is of the same order of magnitude as in Al-Cu alloys of the same concentration; the dendrite spacings in Al-Cu alloys also increase with an increase in solute concentralion. For the jamily of aqueozrs solulions incestigaled, the dendrite spacing increases linearly with solute diffusivity at fixed values of concertralion and freezing ,rate. The values of ?C and ?T decrease, whereas the value of V increases with an increase in solule diffusicity. The measured dendrite spacings , L, can be expressed by the relatiun: L = K;(dfa/db) 4 K2C +K3D - K4 where dfs/d? is-change in fraction solid with time (freezing rate), C is solute concentration, D is solute diffusivit K1 = (14 * 4)pmin1'2, K2 = (70 ± 10) pl (moles)- K3 = (24 r 3) . l05 psec (cm)-~. K. = -132 ± 10) 1. FREEZING of solutions is almost always an ehunmix-ing" process because the composition of crystallizing solid generally differs from that of the parent liquid. " Solute concentration and transport are therefore in]portant considerations in solidification of solutions. The influence of these factors on the dendritic solutions produced from metallic solutions is of practical significance since the properties of the solid aggre-gate are often strongly influenced by dendrite spacing.''' Alexander and Fthines3 found that dendrite spac- ings generally increase with solute concentration in several metallic systems. Michael and Bever1 have observed an increase in a aluminum dendrite spacings in dilute A1-Cu alloys. Rohatgi and AdamsJ have reported a linear increase in a aluminum dendrite spacings with increasing copper contents up to 28 pct in A1-Cu alloys. Bolling and Tiller"' have theoretically examined the effects of solute concentration and diffusivity on the growth of cells and dendrites. Their analysis of dendritic growth assumes a steady-state growth and the maximum possible velocity for dendrite propagation. In addition, the quantitative analysis is restricted to dendrites of rotational symmetry and is therefore not directly applicable to the plate-shaped dendrites of ice obtained in the present study. There are practically no experimental observations of the effect of solute diffusivity on dendrite spacings in metallic systems. The reason appears to be the lack of experimental data on solute diffusion coefficients in liquid metallic solutions. The present work is concerned with the effect of solute concentration and diffusivity on dendritic solidification of dilute aqueous solutions: the solutes examined are potassium chloride. sodium chloride, lithium chloride. and hydrogen chloride. There were several reasons for selecting these solutes. The variation of dendrite spacing with freezing rate in these solutiolls is similar to that observed in A1-Cu alloys.8 These aqueous solutions have almost identical phase diagrams at dilute concentrations. Fig. 1. and the diffusion coefficients show very little variation with solute Concentration.9,10 Dendrite spacings were measured as a function of freezing rate. solute concentration. and solute diffusivity. Dendrite spacings were measured in two different types of freezing systems. droplet and unidirectional, respectively. In the droplet freezing system

Jan 1, 1970

By O. C. Holbrook, George G. Bernard

A new theoretical treatment has been obtained for the behavior of pattern waterflood injection wells when closed in. Two cases are treated: Case I where oil and water are assumed to have the same properties, and Case 2 where they arc different. In applying the method, one plots log (p — p,) vs closed-in time, where p is well-bore pressure at any tims and p, is static pressure. The value of p. is determined by trial and error as that value which makes the plot linear at large time. A value for the permeability-thickness product can be determined from the intercept of this linear part, and a value of the skin factor from the injection pressure at time of closing in. Application of the method to data from water floods at three fields seems to give reasonable results. For the case of unit mobility ratio, it is proved that this new method should give the same value for permeability-thickness product as the conventional pressure build-up method. In addition, the new method gives correct values for static pressure, whereas the conventional method does not, often indicating negative static pressures. The new method may be used in cases where the surface pressure persists after closing in as well as in cases where it does not. INTRODUCTION It is of considerable interest and importance to be able to determine the characteristics of the reservoir in an area surrounding a water injection well. Thus, if we can determine early in the life of an injection well that there is a considerable "skin effect", remedial measures can be started before a full-scale pattern flood begins. Similarly, if it can be shown that a gradual buildup of skin effect is occurring with time, measures to free the water of plugging material can be taken. Determination of static pressure in the water-injection well may show that the water is entering a thief zone and not the desired reservoir. Finally, determination of the permeability of the sand around the injection well will allow estimation of the future relation between injection pressure and rate. It should be possible to determine average reservoir permeability, skin effect and static pressure from pressure fall-off data. However, at the time we began work on this subject, it was thought that no adequate theory on which to base such determinations' was available. According to the conventional method which considers the reservoir to be filled with one fluid of small compressibility (see Van Everdingen, Joers2, and Nowak2), shut-in pressure is plotted vs log where is injection time, and At is closed-in time. The physical significance of injection time, may well be questioned in this case, since in a reservoir completely filled with a single fluid (as required by this theory) and with input and output rates equal, the pressure behavior after an initial transient is independent of t,. Attempts by our Tulsa area to use this theory led to negative values of static pressure in most cases. Because of these limitations of the method discussed above, it was decided to attempt to develop a new theory of pressure behavior in water injection wells, one which would apply when there is a gas saturation, as is so often the case in water floods. In the following treatment the assumptions and basic equations are given first, then the method of application of the equations. A complete example is given to clarify details of application. All difficult mathematics has been placed in the appendices so that the reader can follow the text without difficulty. However, if he wishes only to apply the results without knowing the basis for them, he can learn how to do this from reading only the sections entitled "Plotting of Experimental Results" and "Example." ASSUMPTIONS AND BASIC EQUATIONS Statement of Problem It will be assumed that a horizontal layer of constant thickness contains in its pore system a mixture of oil, gas and water. While water is being injected into this pore- system through a well at constant rate, an oil bank is built up, gas being expelled from the space taken by the oil as shown in Fig. 1. The saturations within each

By R. E. Barnes

An overall view of the perlite industry is concisely presented. The geology, mining, milling, processing, and applications of perlite, as well as the present status of the perlite industry are treated. Perlite, in strict petrological usage, describes a specific variety of volcanic glass in which strain, incident to cooling, yielded a concentric structure of fracturing which may be visible either to the naked eye or under a microscope. In commercial usage, the term perlite includes any naturally occurring acidic glass of volcanic origin that will expand when heated to a suitable temperature. The name perlite is a derivation of perlstein which originally defined "certain glassy rocks (hyaloliparites, hyalo-rhyolites) with numerous concentric cracks, from the fancied resemblance of broken out fragments to pearls."1 While perlite has been known to geologists for many years, it was not until 1941, while investigating perlite for use in enamel, that an assayer in Superior, Ariz., noted the unusual expansion characteristics of the ore. Further investigations were delayed until following World War II when many small plants were built and experimentation in the treatment and uses of perlite began. The Perlite Inst. was organized in 1949 to promote the development of the new industry, establish commercial standards through research, and to explore new uses and markets. The Institute, located in New York, represents some 50 producers in the U.S., Canada, Australia, England, France, Germany, Greece, Japan, Mexico, and New Zealand. In 1949, 71,l002 short tons of crude perlite were produced, sold or used by U. S. producers, and this figure increased to 325,0003 short tons by 1959. Such a rate of increase indicates the rapid and continuing growth of the perlite industry. GEOLOGY Perlite ore in its crude form has been found in seven of the mountainous western states, since un-devitrified siliceous volcanic rocks are limited to this section of the U. S. Commercially operated perlite deposits are normally of Eocene and Oli-gocene age.4 These deposits are often several hundred feet thick and may extend over hundreds of acres. In 1959, 13 companies in six states produced crude perlite, although the output in New Mexico comprised 79 pct of the total domestic crude output. Other states in order of their production were: Nevada, Arizona, California, Colorado, and Utah.5 Foreign deposits of perlite which are either producing or under exploration are Australia, Canada, Greece, Hungary,6 Iceland, Ireland, Japan, Mexico, New Zealand, and Sardinia. The ore may exhibit a variety of characteristics depending partially on its water content and eruption history and may range through many shades from black to white. While these characteristics may vary slightly among deposits, perlite ore from a particular source is normally quite uniform. Available chemical analyses of perlites from a large sampling of domestic deposits were recently assembled by the Technical Committee of Perlite Institute and are presented in Table I. While the ranges given do not apply to a particular perlite, they are an indication of the chemical analysis which may be expected from any presently commercially operated deposit. The specific gravity of the perlite ore ranges between 2.2 and 2.4, and its bulk density when crushed and sized is 75 to 90 Ib per cu ft. MINING AND MILLING Perlite ore is quarried from open pits by conventional power equipment, although blasting has been occasionally employed. The rock is then stock-piled until needed. While the milling of perlite may seem a simple process compared to that required for basic metals, or even other nonmetals, the need for accurate control of particle size becomes extremely important in further processing. The first step in this operation is the primary crusher, which is normally a jaw crusher. Following crushing, the material is dried, if necessary, in a rotary dryer and conveyed to a secondary grinder which may be a rod mill, hammer-mill, or cone crusher. However, the crushing characteristics of the perlite, caused by incipient cooling fractures, requires it be removed from the grinding operation once it is reduced to the required size so as to prevent overgrinding. Following the grinding operations, various size screens are used to separate the ore according to particle sizes required for particular uses. Most plants use two or more stages of crushing with perhaps four stages of screening.

Jan 1, 1961

By Lyman Johnson

Single crystals qf copper in "single slip" orientatiorzs have been deformed in compression. During defortnation all of the independent deformation parameters have been measured. These parameters consist of thefive strain components and three components descrihing the lattice rotation. By a finite strain analysis these pararmeters , forrming a deformation gradient martrix, are related to the amounts of slip on each of the twelve slip systems. The results show that the amount of secondary slip is about equal to the amount of primary slip. This is an order of magnitude larger than has been believed previoutsly. ACCORDING to early theory and experiments, when a single crystal of a fcc metal is deformed in tension or compression it should deform by slip on only one slip system until the stress axis reaches a symmetrical orientation.' However. the observation of a large increase in the secondary dislocation density during ..single slip" makes it clear that some slip does occur on secondary systems. Knowledge of the amount and distribution of this secondary slip is essential to a complete understanding of the mechanisms of single-crystal deformation. Ahlers and Haasen 2 and Mitchell and Thornton1 have tried to detect the amount of secondary slip in single crystals of silver and copper, respectively. Each simultaneously measured the angle A, between the tensile axis and the primary slip direction and the length 1 of a gage section of the specimen after incremental amounts of deformation in tension. The measured A, was then compared with the theoretical single slip angle hp. given by sin Ap = j sin . hO where ?o was the initial angle between the tensile axis and the primary slip direction and lo was the initial gage length. In both sets of experiments a small but systematic difference between ?e and ?p was found. This difference must be due to the occurrence of secondary slip. However, as Mitchell and Thornton1 pointed out. nothing quantitative can be said about the amount and distribution of this secondary slip from the measurements that they made. The reason that no quantitative conclusions could be made is because no unique solution for the distribution of slip on the twelve fcc slip systems can be determined from only two measured deformation parameters such as A and 1. There are, in fact, eight independent macroscopic deformation parameters that can be measured when a single crystal undergoes a homogeneous deformation. Physically these can be thought of as the five finite strain components and the three angles describing the crystal lattice rotation. All eight of these parameters were measured by Taylor4,5 for aluminum deformed in tension and compression. At that time the concern was to show that slip occurs on {111 (110) systems in fcc metals, and the mathematics were not available to determine what slip distributions were compatible with the measurements. In this paper the mathematics6,7 are developed that allow the slip distribution to be determined from these measurable macroscopic deformation parameters. The analysis is applied to the measurements of the strain and lattice rotation of copper single crystals deformed in compression. The results show that the amount of secondary slip is an order of magnitude larger than had previously been thought. CRYSTALLOGRAPHIC DESCRIPTION OF A HOMOGENEOUS DEFORMATION The deformation of a solid body can be represented by a transformation matrix F that transforms the un-deformed state into the deformed state. Consider a vector X connecting two material points in the unde-formed material and the vector x connecting the same two material points after deformation, where both vectors are referred to the same set of Cartesian axes. The final vector x is related to the initial vector X by the equation: X = FS. [2] Eq. [2] can be considered as the equation defining F, which is called the deformation gradient matrix. Its components are: If the deformation is homogeneous, the transformation is linear and the components of F are constants. Using subscript notation, if P is the unit vector in the initial direction of a material line, the components of the unit vector p in the direction of the same material line after deformation are given by:

Jan 1, 1970

By I. A. Goddard

INTRODUCTION This paper deals with the development of the sublevel open stoping (SLOS) method in lead orebodies at the Isa Mine of Mount Isa Mines Limited, during the last ten years. Open stoping in different forms has been used at the Isa Mine for many years. Prior to the period under review, stopes were small, pillars were not always recovered, and scrapers extracted the ore. By the end of the sixties, the use of load-haul-dump units was becoming more widespread. Wagner ST5's were the mucking units for the lead cut and fill stopes. Some of the open stopes in 5 orebody above 13 level had 100 kW slushers, but the more southerly stopes were the sites for the introduction of diesel front-end loaders for extraction. In the early seventies, new methods were used in the block of six stopes in 2 and 5 orebodies between 8 level and 13 level and a trial stoping project was undertaken in 7 orebody between 11 level and 13 level to determine possible stope dimensions for the extraction of the Racecourse orebodies below 13 level. By the mid-19701s, stoping was well underway in 5, 7 and 8 orebodies between 13 level and 15 level, using the 'triplet' system, incorporating cemented hydraulic fill to allow greater pillar recovery. As the eighties were entered, development of the Racecourse orebodies below 15 level commenced, as did preparations for 1 orebody in the upper levels of the north end of the mine. In both cases, the pillar recovery method has been changed to reduce the amount of cemented fill required for pillar recovery. GEOLOGY Most of the lead orebodies at Isa Mine lie chiefly to the north of the central shaft complex. They are bedded sulphide deposits in a host rock called Urquhart Shale, which dips at roughly 650 to the west. The main minerals are galena and sphalerite, with the silver mineral, freibergite, being contained in the galena. To the hangingwall of the sequence are the Black Star orebodies (1, 2 and 5) which are relatively wide, pyritic and with low to above average grade lead. The Racecourse orebodies (6 to 16) lie to the footwall, and have a large variation in width, low to high grade lead, and gradation in the lead to zinc ratio from north to south. Stope outlines are often determined by economic or engineering considerations rather than geological. The published extraction reserves are 56 million tonnes of primary ore, containing 150 grams of silver per tonne, 6.4% lead and 6.5% zinc. Traditionally, it has been regarded as lead ore, although the dominant revenue earner varies from time to time. In the Black Star orebodies, the ore and hangingwalls are more competent and open stoping has long been used. The major Racecourse orebodies which have been open stoped are 7 and 8 orebodies. This has been where the orebodies are wider (to the south) and where hangingwall conditions allow. This latter aspect has been greatly influenced by the presence of 'silica dolomite1. This tough, relatively homogeneous, non-bedded rock is, in fact, the host rock for the copper mineralisation at Mount Isa, and provides a competent hangingwall for some of the lead stopes. While the shale's bedding and jointing has a major influence on the ground conditions, there is a major fault system which causes local problems. The principal virgin stress direction is perpendicular to the bedding, but the local stress situation is complicated because of shielding by filled stopes in the hangingwall copper orebodies and because of the interaction between orebodies being extracted to the footwall. Most development on strike is mined with a 'shanty-back’, with the back being as close to normal to the bedding as possible. This is near parallel to most jointing and the principal stress direction. Figure 1 is a plan view of 14 level north, which provides a representative horizontal section through the orebodies. A typical cross section is shown in Figure 2. The narrow, parallel footwall orebodies can be seen to differ from the wider hangingwall orebodies.

Jan 1, 1981

By J. J. Frawley, W. J. Childs

Experiments were carried out to induce grain refinement during solidification by applying vibrational energy (freq 20 kc) to small specimens of bismuth, tin, and bismuth-tin alloys. The results show that if the intensity of the applied sound -field is not great enough to fragment the growing dendrites of a pure metal, no grain refinement is observed and the pain size of the dynamically nucleated specimens is the same as the grain size of a specimen statically supercooled the same amount. Bismuth specimens did not show any grain refinement; whereas, the tin specimens did show grain refinement. This phenomenon is the result of the difference in growth habit between the bismuth and tin dendrites. The bismuth-tin alloys showed grain refinement and, in addition, the segregation pattern was changed. THE solidification process is a change in phase requiring the nucleation of the solid phase from the liquid and the growth of this solid phase at the expense of the liquid phase. Since many physical properties and also the integrity of a casting are dependent on the solidification process, understanding and controlling this process are very important.' A good example in the controlling of a cast structure using heterogeneous nucleation theory is the reduction of grain size in aluminum castings by nucleation catalysis.2 This mechanism of nucleation catalysis has been explained by Turnbull.3 Another technique for grain refinement, which has received much attention but the mechanism has not been fully understood, is to vibrate the solidifying melt. Vibrations can be applied to the melt either by vibrating the mold directly or by introducing a vibrating rod into the melt.4-13 Three mechanisms have been proposed to explain this phenomenon: 1) The mechanical fragmentation of the original dendrites that grew into the melt. These crystals or fragmented dendrites act as new growth sites. 2) The nucleation of new grains in the liquid by the generation of very high pressure pulses caused by cavitation in the liquid. 3) The remelting of the dendrite arms during the solidification process. This mechanism is operative only in alloy systems and would be enhanced by stirring or mechanical vibration. The purpose of this investigation was to determine the mechanism that will increase the number of grains when mechanical energy is introduced into a solidifying melt. APPARATUS The unit used to generate the ultrasonic vibrations was manufactured by the Redford Co., and is similar to the one used in ultrasonic soldering. Fig. 1 is a sketch of the major components used for generating ultrasonic vibrations. The crystal transducer assembly consisted of four lead zirconate ti-tanate piezoelectric crystals in an aluminum holder. An acoustical horn, which was fabricated from stainless steel, was attached to the holder by a set screw. The resonant frequency of this unit was 20,000 cycles per sec. A Pyrex crucible, 4 in. in diam and 4 in. high, was contained in a hole in the top of the horn. The piezoelectric crystals changed volume when excited by an electric signal, thereby generating a sound signal which passed through the horn. The crucible was coupled to the horn by a liquid silicone oil. The purpose of the couplant was to transmit the soundwaves from the horn to the crucible. Without the couplant, much of the sound energy would be lost. The energy transmitted was sufficient at the resonant frequency used, so that acoustical cavitation always occurred in the molten metal. The presence of acoustical cavitation was detected by the characteristic hissing sound emitted from the liquid. EXPERIMENTAL PROCEDURE The influence of ultrasonic vibration on the grain refinement of bismuth, tin, and bismuth-tin alloys was studied. These metals were chosen because of their low melting temperature and the relative ease with which they can be thermally supercooled. The following procedure was used for obtaining large amounts of supercooling. Pure bismuth (99.999+), which was received in bar form, was mechanically broken into pieces small enough to be accommodated in a 50 ml beaker. About 200 to 300 g of bismuth and a few grams of SnCl2 as a flux were placed in the 50 ml beaker and melted by induction heating. The melt was held for 20 min at

Jan 1, 1970

By C. Gatlin, N. E. Garner, A. Podio

Experimental data from single chisel blows on Leuders limestone are presented. A pressure chamber, similar in design to well known microbit drilling chambers, was utilized to impose variorcs stress states on the sample. Confining pressure of zero to 10,000 psi and borehole pressures from zero to 5,000 psi have been used in the studies. Pore pressure was zero and the rock samples dry in all instances. Force-displacement records and visual examination of the craters indicate that the mode of failure depends on both confining and borehole pressure in certain ranges, ranging from brittle, through a transition, to near plastic. The mode of failure is reflected in the observed blow force and energy data, as well as the shape of force-penetration curves. INTRODUCTION A previous paper' presented initial data from the project on which this paper is the second report. While the first paper dealt with impact studies on synthetic rocks, the literature cited there is also pertinent to this paper, but will not be listed again in order to avoid needless repetition. This paper presents experimental data from single chisel impacts on limestone at certain simulated wellbore stress states. Specific variables investigated were combinations of borehole and confining pressure, crater geometry, a narrow range of impact velocity and the forces required to drive the chisel into the specimens under the varying conditions. EXPERIMENTAL PROCEDURE The same basic apparatus described in our earlier paper, except for the pressure vessel, was used in this study. Fig. 1 shows the complete experimental system. Fig. 2 shows details of the pressure cell, which is quite similar to the well known microbit drilling chamber. The confining (overburden) pressure system provides independent pressure control over the sample except for two, 21/4 in. diameter areas located on the sample ends. These two areas provide a pore pressure entrance on the bottom and a striking surface on the top where borehole pressure can be controlled. The ends are isolated from the confining pressure by O-ring seals. The borehole and pore pressures are related through the striking surface; they will be the same unless a seal is deposited on the borehole surface, either a mud cake or some other impermeable membrane. In these studies pore pressure control was not used, as the rocks were dry and unsaturated in all cases. Rock samples were prepared from 4-in. cubes as illustrated by Fig. 3. The circular disks of adhesive vinyl plastic protected the impact surface from the resin coating (Scotchcast No. 2) and were removed just prior to each test. This procedure insured a fresh uncontaminated surface for the impact. Fig. 4 shows the dimensions and loading of the sample, including the concentrations around the "borehole" periphery (O-ring seal). The rock used in this study was Leuders limestone, of Permian age (Leonard), quarried near Leuders, Tex. Geologically, Leuders limestone is a light gray, fossili-ferous limestone (oolitic foraminifera1 biosporite). Its fossil content is 80 to 90 per cent and consists primarily of calcitornellid, ostracods, pelecypods and oolites with the remaining part intraclasts. There are hematite or limo-nite rims on some of the intraclasts. The porosity is approximately 20 per cent, but the permeability is less than 1 md. There is no apparent orientation in the structure. Triaxial tests have been conducted to determine the variation of the physical properties of Leuders limestone in three orthogonal directions', and it is known to be unusually isotropic and uniform. Physical parameters for this rock are: uniaxial compressive strength = 9,700 psi; F = 32 and C = 2,700 psi; where + and C are Coulomb equation values (t = C+u tan +). Impact tests were run under the combinations of confining and borehole pressures shown in Table 1. Samples were dry with atmospheric pore pressure in all cases. Tests, in which elevated borehole pressures were applied, used a single layer of household Saran-Wrap to prevent horehole fluid invasion into the sample. This proved to be simple and reliable. The blunt wedge used in all the tests was 0.75 in. long and had an included angle of 60" with a 0.05-in. flat. In addition, a sharp 60" wedge was used for all confining pressures at zero borehole pressure. The chipper speed

By Richard R. Zupp, David A. Stevenson

An experimental method to determine the carbon activity in various solid solutions was developed. Samples of the solid solutions and an Fe-C reference sample were equilibrated with respect to carbon content by annealing them in a Hz-CHI gas mixture in a closed cell. The carbon content of each sample was determined, and the carbon activity was obtained from the carbon content of' the reference sample and well-established data for the dependence of the carbon activity on the carbon content in Fe-C alloys. The influence of vanadium on the activity of carbon in austenitic Fe-C-V alloys at 1000°C was determined by this technique. A general semiempirical correlation was developed to describe the dependence of the activity coefficient of- carbon on the composition of ternary austenitic iron-base alloys containing interstitial carbon and a substitutional solute. The correlation is particularly useful in predicting the partitioning of- carbon between various alloys. THE influence of substitutional solutes on the activity of interstitial solutes in metallic solid solutions is important in the theory of alloy phases. Solid solutions of particular interest are the fcc austenite phases of ternary Fe-C-Z systems, in which carbon is the interstitial solute and Z represents any substitutional solute. Carbon-activity data are also needed in these solid solutions to solve practical problems; the quantitative treatment of diffusion-controlled transformations' is an examvle. Experimental information is available for ternary austenitic solid solutions containing Mn,2 Si,2 and A16 as the substitutional solute. Because qualitative preliminary studies indicated that vanadium appreciably decreases the carbon activity,14 the present investigation was undertaken to determine the influence of vanadium on the activity of carbon in austenite. Although Flender and ever" measured carbon activity over a range of compositions in the Fe-C-V system, they were primarily interested in determining phase boundaries in the ternary system, so most of their measurements were outside the composition range for stability of single-phase austenite. Petrova and Shvartsman' also made limited measurements of the carbon activity in Fe-C-V alloys. The dependence of the carbon activity on the carbon content of an alloy may be determined by passing COCOz or H2-CH4 gas mixtures of carefully measured composition over the alloys, determining their equilibrium carbon content, and utilizing the relevant equilibrium relationships. smith16 used this technique with both CO-COZ and HZ-CH4 gas mixtures to determine the dependence of carbon activity on carbon content in pure Fe-C alloys. His data, which are in good agreement with those of some previous and subsequent investigators,6'17 but not with those of others,lfl'ao are usually considered to be the most reliable. Although the same method can be applied to Fe-C-Z alloys, it is difficult experimentally, because the appropriate gas mixtures are almost pure CO or Hz. A simpler technique is to simultaneously equilibrate the Fe-C-Z alloys and pure Fe-C alloys with the gas mixtures, and then use Smith's data to determine the carbon activity in the pure Fe-C alloy. A number of investigators have employed this technique. others Have used the partitioning of carbon at the interface of a diffusion couple prepared from an Fe-C alloy and a Fe-C-Z alloy. In the present study, a closed-cell method was developed by which carbon was selectively transferred via a gas medium between pure Fe-C alloys and Fe-C-V alloys which were not in physical contact. A similar method was developed independently by Heckler and winchel14 and used to study the Fe-C-Ni system. EXPERIMENTAL METHOD A schematic diagram of the experimental arrangement is shown in Fig. 1. In a typical experiment, a 5-g Fe-C sample was placed in one compartment of a quartz cell, and a 5-g Fe-V sample was placed in each of the other compartments. The cell was evacuated, outgassed, backfilled with approximately 125 Torr of hydrogen, and sealed. After being placed in a fur-

Jan 1, 1967

By H. L. Hartman

The drop tester has proved an invaluable tool for the investigation of percussion drilling in the laboratory in "slow motion". It has allowed the process of rock penetration by impact to be studied a single blow at a time. In the present work, the relation of cratering to indexing has been determined under conditions simulating those in the bottom of the hole at atmospheric pressure. Indexed blows form craters which are influenced by others adjacent to them. Two unique effects are involved: (1) the provision of additional free faces in proximity to the point of impact and (2) the creation of subsurface damage by the previous blow(s). Both have a pronounced influence on the volume of rock removed per blow, which governs the rate of penetration in actual drilling. The emphasis in this study was placed on determining effects of index distance and impact energy on crater volume when blows were struck on a previorusly "drilled" or damaged surface, a situation most representative of down-hole conditions. The results indicated that (I) the optimum index distance on a damaged surface is greater than on a fresh, undamaged rock surface; (2) the volume of rock broken at optimum index distance is about the same for both surface conditions with die-shaped chisels but tends to be greater on a cratered surface with wedges; (3) the optimum index distance and maximum crater volume are proportional to the energy level; (4) at a given energy level, the volume of rock broken by dies generally exceeds that by wedges; and (5) maximum crater volume varies, approximately, inversely with width of die but is nearly independent of included angle of wedge. INTRODUCTION This is the third of a series l,2 of papers reporting on one phase of a continuing program of drilling research being conducted in the Rock Mechanics Laboratory at The Pennsylvania State U. The phase under consideration is crater geometry — blow energy relations in percussion drilling. While the previous papers have discussed mainly craters produced by single blows, indexed-blow studies are the subject of this paper. The basic mechanism of drilling under study here — that of penetration of a chisel-shaped bit subjected to impact — is the one employed in probably 90 per cent of all rock drilling in mining, percussion drilling. It also forms the fundamental action in nearly all oil well drilling with the so-called rotary (roller-bit) method. Here, the action is more complex, however, and may in actuality comprise rotary-percussion drilling. Certainly, the down-hole air and mud hammer drills, which superimpose percussion on rotation, belong in this latter category. In any event, impact blows constitute one of the principal mechanisms in the vast majority of drilling, mining or petroleum, and it is essential in drilling research to study percussion in all its basic aspects. Percussion drilling can be simulated in the laboratory by means of an impact drop tester. Striking one blow at a time with chisel-shaped bits, the drop tester permits study of most of the parameters in the drilling process except blow frequency and the interrelationship of certain variables. Single-blow craters, the simplest to produce, allow the determination of basic relationships, such as volume vs blow energy; while indexed craters most closely resemble the action in real drilling and provide data for the establishment of optimum operating criteria. Indexed-blow craters are those which are influenced by others in proximity. The simplest case to visualize, and the one studied in detail here, is that in which a given crater is formed adjacent and parallel to a previous crater, such that the second crater breaks into the first. A more complex situation usually exists downhole, where indexing is achieved by rotation of a radial-winged or rolling-cutter bit. But, admittedly, the phenomenon of indexing is more likely to be understood eventually if it is first studied in its simplest form, that related to parallel craters. Limited research has been conducted on indexed blows. The most complete study was that by Simon, 3,4 who proposed universal indexing curves to relate the important variables. His work, however, was conducted entirely with rows of craters formed on a

By Carl Altstetter, Roy Adams

Measurements of enthalpy changes and transformation temperatures me reported for the fcc -hcp marten-sitic transformation in pure cobalt single and multi-variant crystals andpolycrystalline specimens. From these measurements the free-energy difference between the two phases was calculated for both heating and cooling and for repeated cycles through the transformation. For heating of single crystals the average value of enthalpy change was 113 cal per mole but on cooling it was 84 cal per mole. This difference is interpreted in terms of lattice imperfections which are introduced during transformation. A calorimeter suitable for measurement of enthalpy changes of athertnal transformations is described. COBALT exhibits an allotropic phase transformation at around 417°C' where an hcp phase (a = 2.507, c = 4.0686, c/a = 1.6228)~ stable at low temperatures transforms to an fcc phase stable up to 1495°C. The transformation has a hysteresis of about 30°C— the exact magnitude of the hysteresis depending on the number of transformation cycles, grain size, impurity content, and prior treatment.'-6 The athermal character of the transformation and surface relief due to transformation shear indicate that the transformation is martensitic. Pole mechanisms for the transformation have been discussed by Sebilleau and Bibrin, Bilby, Seeger,' and Basinski and Christian. These authors have proposed that the cooling transformation is effected by rotation of a Shockley partial dislocation around a pole dislocation with a screw component of 2a/3(111). Such a rotation would change the stacking of close-packed planes from the abcabc fcc stacking to the ababab hcp stacking sequence. This mechanism would predict a lattice correspondence of {111}fcc~~(0002~cp, have been observed. One would expect the heating transformation to occur similarly, involving dislocation movements on the (0002)hcp. However, a high density of pole dislocations and high dislocation ve- locity are required to account for microscopic observations. Furthermore, the high back stress developed on the Shockley partial dislocation as it rotates toward the sessile dislocation associated with it makes it doubtful that this is in fact the transformation mechanism. A mechanism for spontaneous nucleation of partial dislocations1*l2 seems more reasonable. If a single crystal of cobalt is cycled through the transformation but never heated above 600°C, it will remain single."13 However, if the specimen is heated through the transformation and held for a short time at or above 1000°C before cooling, the cooling transformation usually involves all four {lll}fcc habits, resulting in neighboring orientations of hcp differing by 70.5 deg. This condition is termed multivariance and has been observed by Bibring and sebilleau5 and Nelson and ~ltstetter.' The latter authors used single crystals of cobalt grown in an electron beam zone refiner. They proposed that the strongly directional cooling caused the initial cooling transformation to occur on the {lll)fcc most nearly perpendicular to the temperature gradient. Transformation shear on one set of {lll}fcc planes immobilized dislocations on the other {lll}fcc planes involved in the initial transformation. Since there is only one (0002)hcp plane orientation, the product of subsequent heating transformations could have no more than two variants—the original fcc orientation or its twin. If, however, the specimen was annealed at a high temperature, such as 1000°C, there would be relaxation of dislocations into low-energy configurations, and in the absence of a sharp temperature gradient transformation on all four (111 Ifcc planes could occur. If a dislocation mechanism is responsible for the transformation, the perfection of the lattice should affect the reversibility of the transformation. Mutual constraints of neighboring grains in polycrystalline material would inhibit dislocation movement resulting in increasingly sluggish transformation. Indeed, Nelson and Altstetter found the M, to decrease and the A, to increase in going from single crystals to multi-variant specimens to polycrystals. The effect is enhanced by decreasing the grain size of a solid specimen or a powder.6'14 Data on the free-energy difference necessary to initiate the transformation gives information about the driving force of the transformation. This is an important consideration in the understanding of the transformation mechanism. The free-energy change associated with the transformation of the hcp phase to the fcc phase at some temperature T different from the equi-

Jan 1, 1969

By Brahm Prakash, R. Schuhmann

Chemical conditions for flotation and nonflotation of quartz with oleic acid as collector and barium, calcium, aluminum, iron, and tin as activators were studied using a simple vacuum-flotation technique in glass-stoppered graduates. The detailed study of barium activation led to an interpretation based on ideal Langmuirian chemi-sorption. FLOTATION of quartz is of practical importance as something to be avoided in soap-floating many types of ores. Clean, unactivated quartz is not floated with fatty acids and soaps, such as oleic acid and sodium oleate, in the quantities normally used for flotation. However, data in the literature indicate that almost any multivalent cation will activate quartz if given an opportunity. Thus, a common problem is to prevent activation of quartz by the various inorganic cations inevitably present in flotation pulps. Wark and his coworkers1 have demonstrated the reversibility of the chemical reactions and adsorptions involved in the activation, depression, and collection of the common sulphide minerals. The procedure in much of their work was to bring a mineral surface to equilibrium with solutions of known pH, collector concentration, and activator concentration, and then to test the floatability of the mineral by contact-angle measurement. From the data, graphs were constructed with pH and reagent concentrations as coordinates. These graphs show fields of flotation and fields of nonflotation, separated by narrow transition regions whose locations are shown by so-called contact curves. From the shapes and locations of the contact curves, which roughly separate fields of flotation from fields of nonflotation, a quantitative understanding of the interaction of the reagents with each other and with the minerals often can be deduced. The study of quartz flotation to be described in this paper follows in broad lines the approach of Wark and coworkers. That is, pH, activator concentration, and collector concentration were varied to find equilibrium conditions of flotation and non- flotation, and the results are presented graphically by means of contact curves. However, instead of testing for floatability by measuring the contact angle on a polished surface, a simple vacuum flotation technique was developed and used. Purified oleic acid was the collector and terpineol the frother. Barium activation was studied in some detail, and exploratory studies were made of activation with calcium, aluminum, ferric iron, and stannic tin. Preparation of Materials Quartz: Large lumps of high-grade vein quartz were crushed dry in a cone crusher and rolls. The —20, +28-mesh portion was screened out and used in the subsequent steps. This material was passed through a high-intensity magnetic separator to discard iron, then leached twice with hot concentrated HCl and washed repeatedly with distilled water. The cleaned sand was then wet ground with porcelain balls in a porcelain pebble mill, deslimed repeatedly by settling and decantation to discard —800-mesh material, and again washed with hot HCl followed by distilled water. The resulting stock of quartz was stored under water. Chemical analysis gave 99.8 pct SiO2. Table I gives the size analysis of the quartz used for flotation tests. Calculations from these data, using shape factors given by Gaudin and Hukki9 indicate a specific surface of about 500 cm2 per g. Blank flotation tests in distilled water, and in water with added frother, showed the prepared quartz to be completely nonfloatable and thus indicated the absence of organic contamination. Oleic Acid: The preparation of oleic acid was based on fractional vacuum distillation of methyl oleate2,3 followed by regeneration of oleic acid, and finally fractional crystallization of oleic acid from acetone solutions at low temperatures." The pure oleic acid was stored in a refrigerator. The iodine number of the oleic acid was found to be 90.0 (theoretical 89.93). Oleic acid was used in the form of a dilute water solution of sodium oleate, after preliminary flotation tests showed no effects of form of addition and order of addition of reagents when an adequate conditioning time (that is, 30 min) was provided. Other Reagents: Sodium hydroxide solutions low in carbonate were prepared by first making 1:1

Jan 1, 1951

By Brahm Prakash, R. Schuhmann

Chemical conditions for flotation and nonflotation of quartz with oleic acid as collector and barium, calcium, aluminum, iron, and tin as activators were studied using a simple vacuum-flotation technique in glass-stoppered graduates. The detailed study of barium activation led to an interpretation based on ideal Langmuirian chemi-sorption. FLOTATION of quartz is of practical importance as something to be avoided in soap-floating many types of ores. Clean, unactivated quartz is not floated with fatty acids and soaps, such as oleic acid and sodium oleate, in the quantities normally used for flotation. However, data in the literature indicate that almost any multivalent cation will activate quartz if given an opportunity. Thus, a common problem is to prevent activation of quartz by the various inorganic cations inevitably present in flotation pulps. Wark and his coworkers1 have demonstrated the reversibility of the chemical reactions and adsorptions involved in the activation, depression, and collection of the common sulphide minerals. The procedure in much of their work was to bring a mineral surface to equilibrium with solutions of known pH, collector concentration, and activator concentration, and then to test the floatability of the mineral by contact-angle measurement. From the data, graphs were constructed with pH and reagent concentrations as coordinates. These graphs show fields of flotation and fields of nonflotation, separated by narrow transition regions whose locations are shown by so-called contact curves. From the shapes and locations of the contact curves, which roughly separate fields of flotation from fields of nonflotation, a quantitative understanding of the interaction of the reagents with each other and with the minerals often can be deduced. The study of quartz flotation to be described in this paper follows in broad lines the approach of Wark and coworkers. That is, pH, activator concentration, and collector concentration were varied to find equilibrium conditions of flotation and non- flotation, and the results are presented graphically by means of contact curves. However, instead of testing for floatability by measuring the contact angle on a polished surface, a simple vacuum flotation technique was developed and used. Purified oleic acid was the collector and terpineol the frother. Barium activation was studied in some detail, and exploratory studies were made of activation with calcium, aluminum, ferric iron, and stannic tin. Preparation of Materials Quartz: Large lumps of high-grade vein quartz were crushed dry in a cone crusher and rolls. The —20, +28-mesh portion was screened out and used in the subsequent steps. This material was passed through a high-intensity magnetic separator to discard iron, then leached twice with hot concentrated HCl and washed repeatedly with distilled water. The cleaned sand was then wet ground with porcelain balls in a porcelain pebble mill, deslimed repeatedly by settling and decantation to discard —800-mesh material, and again washed with hot HCl followed by distilled water. The resulting stock of quartz was stored under water. Chemical analysis gave 99.8 pct SiO2. Table I gives the size analysis of the quartz used for flotation tests. Calculations from these data, using shape factors given by Gaudin and Hukki9 indicate a specific surface of about 500 cm2 per g. Blank flotation tests in distilled water, and in water with added frother, showed the prepared quartz to be completely nonfloatable and thus indicated the absence of organic contamination. Oleic Acid: The preparation of oleic acid was based on fractional vacuum distillation of methyl oleate2,3 followed by regeneration of oleic acid, and finally fractional crystallization of oleic acid from acetone solutions at low temperatures." The pure oleic acid was stored in a refrigerator. The iodine number of the oleic acid was found to be 90.0 (theoretical 89.93). Oleic acid was used in the form of a dilute water solution of sodium oleate, after preliminary flotation tests showed no effects of form of addition and order of addition of reagents when an adequate conditioning time (that is, 30 min) was provided. Other Reagents: Sodium hydroxide solutions low in carbonate were prepared by first making 1:1

Jan 1, 1951

By W. M. Robertson

The rate of crack Propagation thvough a solid meta1 in the presence of a liquid metal has been calculated. The crack is assumed to propagate by solution of the solid in the liquid under the influence of an applied stress, with volume diffusion of the dissolved solute through the liquid controlling the propagation. The calculated velocities can be tens of centimeters per second or higher. THE embrittlement of normally ductile solid metals by liquid metals has been the subject of extensive study, as summarized in the book by Rostoker, McCaughey, and arkuus.' In experimental studies of liquid-metal embrittlement it is usually concluded that the observed crack-propagation rates are too high to be accounted for by diffusion processes. Diffusion is considered to be an unimportant factor and various other mechanisms are invoked to account for the experimental observations. The similarities of liquid-metal embrittlement to stress-corrosion cracking, to hydrogen embrittlement of steel, and to low-temperature embrittlement of bcc metals are frequently used as analogies for these mechanisms.1"3 The present paper assesses how rapidly a crack could propagate by a mechanism of volume diffusion through the liquid metal. We assume that the crack propagates by solution of the solid in the liquid at the crack tip under the influence of the applied stress and diffusion of the dissolved solute away from the crack tip. The model uses only macroscopic thermodynamic, kinetic, and elastic concepts. The calculations indicate that this dissolution-diffusion mechanism can give high crack velocities. In some previous treatments4'' of crack propagation in a liquid-metal environment the fundamental step has been the breaking of atomic bonds at the crack tip. The liquid greatly decreases the energy necessary to break these bonds. The present model assumes the crack is filled with liquid metal; the presence of the liquid is essential because diffusion through the liquid is assumed to control the rate of propagation. With proper modification this model could also apply to stress corrosion in a liquid environment. THEORY Consider a crack in a homogeneous elastic continuum, ignoring all the structural details of the solid. This neglects a host of metallurgical details which can be significant in the problem of liquid-metal embrittlement;' but this simple assumption is a useful approach in evaluating the role of diffusion through the liquid. The stress distribution around the crack tip establishes a gradient in the chemical potential at the tip, which causes a diffusion flux through the liquid away from the tip. The solid-liquid interfacial tension works against crack propagation, since propagation requires creation of interfacial area. From these two considerations we derive the diffusion flux, which then yields an expression for the velocity of the crack tip. The concentration of the solute in the liquid, C, is equal to the equilibrium concentration in the presence of an unstressed, flat surface, Co, plus the excess concentration due to the stress, AC(a), plus the excess concentration due to capillarity, AC(y): We calculate AC(o) and AC(y) and then obtain the diffusion flux. Consider (Fig. 1) a long flat crack of length 2L, thickness 2r, and tip radius r, where r remains constant as the crack propagates in the positive x direction. There is no stress ay in the y direction across the flat surfaces of the crack. The magnitude of the stress at the crack tip due to the applied stress, a,, is given by the relation6 ^=^[l-2^] 12] which, for long narrow cracks, becomes The stress increases the chemical potential in proportion to the strain energy.? The excess chemical potential due to the stress, Ap(a), is given by where 52 is the atomic volume of the solid and E the Young's modulus. Inserting Eq. [3] gives Now consider the crack to be filled with a liquid metal. The excess solubility due to stress, hC(a), is given by the excess chemical potential due to capillarity, Ap(y), is given by8 where y is the solid-liquid interfacial energy, and v1 and YZ are the two principal radii of curvature of any surface point. At the crack tip, r1 = -r and vz = m, so TRANSACTIONS OF THE METALLURGICAL SOCIETY OF AIME

Jan 1, 1967