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By William G., Pariseau

There are important phenomena in rock and soil mechanics that cannot be explained in terms of theories of homogeneous, isotropic materials. Subsidence of strata about mine openings is an example. In-situ stress measurements in nonisotropic sedimentary, and metamorphic rocks is another. Patterns of joints, faults, fractures, and similar geologic features impart directional mechanical properties to rock masses that are locally isotropic or anisotropic. On the geologic scale, the non-homogeneity of composite rock masses may, in certain instances, be dealt with as homogeneous anisotropy. The mechanics of large rock masses can, therefore, be expected to involve considerations of anisotropy. The source of the anisotropy is not relevant. Once the scale of observation is selected and the material is defined accordingly, the analysis of stress and deformation proceeds without regard to the numerical values of the material constants. There are also important phenomena in rock and soil mechanics that cannot be explained in terms of linear elasticity, theory. For the mechanical description of anisotropic geologic materials capable of de- forming beyond the limit of purely elastic strains, a plasticity theory is required.

Jan 1, 1972

By E. W. Pehrson, J. W. Furness

NONMETALLIC MINERALS, exclusive of fuels, may be divided into three groups: Building materials, fertilizer minerals, and miscellaneous minerals. Building materials, such as sand, gravel, slone, lime, and the ingredients of cement and clay products, occur widely in nature and are thus available near consuming centers at relatively low prices. Cost of transportation over great distances deters any' substantial movement in world trade. On the other hand, fertilizer minerals, such as phosphate rock, potash, nitrates, sulfur, and pyrite, and the miscellaneous nonmetallic minerals, such as long-fiber asbestos, mica, graphite, fluorspar, and china clay, do not have such widespread occurrence and consequently contribute the major part of the world's commerce in such minerals. The U. S. Bureau of Mines has prepared charts showing the inter-

Jan 1, 1936

By J. M. Roberts, D. M. Barnett

The activation energy required to break a pinned dislocation line away from its condensed atmosphere of impurity atoms is calculated as a .function of applied stress, without neglecting line tension. Reasows are presented for not assuming the effect of line tension to be negligible when considering the problem of freeing a small segment of dislocation from an impurity atmosphere. The dislocation is considered to he pinned at each atomic size along its length and the pinning points are assumzed immobile. The development is a refinement of the origznal cottrell-bilby1 theory. The solution is compared to recent approximations developed by cottrell3 and Haasen5 in which line tension con- IN 1949 Cottrell and bilby1 considered the problem of determining the force required to pull a dislocation away from its condensed atmosphere of impurity atoms. They also examined the effect of thermal fluctuations on this force. The dislocation line was pictured as bowing out in a triangular loop under the action of an applied stress, and the activation energy necessary to free the dislocation from its atmosphere was calculated as a function of stress, line energy, and dislocation-solute atom interaction. siderations were neglected. A qualitative explanation of the yielding process in terms of the activation of Frank-Read sources is presented, but the lack of a realistic solution to the dynamic dislocation problem involved prevents an extension of the model at present. A self-consistent correlation between the present calculations and experimental data for delay time associated with yielding and the temperature dependence of the upper yield stress was made. Favorable agreement was noted. It is concluded that extension of the original Cottrell-~ilby' theory which includes line tension effects can just as well describe the yielding process as other approximations3,5 which neglect line tension. Cottrell and Bilby found the form of the activation energy vs stress curves to be almost independent of the line energy and the interaction energy (i.e., these parameters only affected the activation energy U by a scale factor). A check of the theory was accomplished by comparison with the experimental data of McAdam and Mebs2 for the lower yield stress as a function of temperature. cottrell,3 in 1957, attempted to obtain a simple closed-form solution for the activation energy as a function of stress by linearizing the quartic equation relating displacement of the dislocation line and applied stress. It was argued that since the contribution to the line energy/atomic plane of a dislocation is made by the long-range stress field of the dislocation through a term of the type (Gb3/2p)ln A/ro, where

Jan 1, 1963

By W. L., Yerkes

AN interesting study of the application of air-, conditioning to the problem of mine ventilation and cooling can be found on the Witwatersrand in South Africa. Here there are a large number of deep mines in a relatively small area. Due to the nature of the reef, many mines are working at a depth of 6000 ft. and some have gone down to 8000 and 9000 ft. below the surface. At such depths, even in a country geologically as old as Africa, the virgin rock temperature approaches 110°F. The flow of heat from the- rock to the ventilation air is tremendous though the shaft or drift may have been open to ventilation for some years. In addition, there is the heat produced by machinery, lights, and men at work and the heat of adiabatic compression of air introduced into the mine. The difference in atmosphere pressure between the collar of a shaft and a level 6000 ft. below is nearly 3lb. per sq. in., resulting in an increase in heat content of nearly four B.T.U. per pound of air delivered to the mine at surface. Further the exclusive use of wet mining to reduce the incidence of miner?s phthisis increases the latent- heat content of the air.

Jan 1, 1941

By Paul Weir

PRODUCTION METHODS in the bituminous coal mines in the United States are undergoing many changes. Although the primary object of these changes is the production of a better product at a cheaper cost there are other considerations such as the improvement of conditions under which miners live and work. The almost complete unionization of the manual workers in the industry during the past four years has 'brought with it a stabilization of wages on a relatively high basis and of hours of work per day and per week on a relatively low basis. With differentials in wages between producing districts firmly established, and with a nation- wide and uniform application of in-

Jan 1, 1937

By R. V. Sara

Determination of the Hf-C phase diagram was conducted primarily by metallographic and X-ray diffraction studies on appropriate alloys. The only intermediate phase observed in this binary system was HfC. This phase was found to be homogeneous between 34.0 and 48.0 at. pct C at 2200°c and between 36.0 and 49.3 at. pct C at 3150°C. The lattice-parameter variation was also determined for HfCI-, compositions prepared at 2200° and 3150°C. The most most refractory composition, with a melting point of 3830°c, was established at 47.5 at. pct C from melting-point data. Solidus temperatures of 2240' and 3150°C occur on the high-kafnium and high-carbon sides of the monocarbide, respectively. The invariant point between HfC and carbon is located at 66.0 at. pct C, whereas the 2240°C solidus corresponds to the peritectic temperature at which hafnium is formed from HfC and hafnium-rick liquid. Hafnium has a melting temperature of 2208°C and is capable of taking carbon into solution to the extent of 10.5 at. pct at this temperature. ALTHOUGH the Hf-C phase diagram has not been previously evaluated experimentally in its entirety, the belief has been that the general configuration would resemble the chemically similar Group rV carbide systems, Ti-C and Zr-c.' These binaries are characterized by a single carbide phase with a simple NaC1-type structure which is maintained over wide compositional ranges. This family of carbides has high thermal stability that increases substantially as the atomic number of the metal component increases. This trend characterizes HfC as one of the highest melting materials. According to Agte and Alterthum,2 the melting point for this monocarbide is 3890°C, a value that has been quoted quite extensively for the past several decades. Recently, in repeating the work of Agte and Alter-thum, Adams and Beall3 determined the melting point of HfC to be 3895°C. A significant departure from the commonly accepted version of the Hf-C system was reported by Avarbe and his coworkers,4 who proposed that there is an extreme stabilization of a hafnium in a narrow field to 2820°C, above which it melts peritectically to form HfC and liquid. Their study was also concerned with the melting temperature of various HfCI-, compositions, but the peak melting point was taken from the work of Agte and Alterthum. Avarbe and his associates were not concerned with the high-carbon region of the system. However, three widely varying temperatures have been reported for the HfC-C solidus by other investigators. Cotter and Kohn5 observed approximately 2800°C; Portnoy et al.' reported 3260°C; and, more recently, Krikorian7 indicated 2915°C. Equally as uncertain is the solidus between hafnium and HfC. As noted above, Avarbe et al. report a peritectic temperature of 2820°C, Krikorian7 measured 2150°C, and Benesovsky and Rudy' estimated 2000°C on their diagram. I) EXPERIMENTAL PROCEDURE The starting materials for this study consisted of reactor-grade hafnium hydride obtained from Fair-mount Chemical Co., Newark, N.J., hafnium carbide supplied by Wah Chang Corp., Albany, Ore., and Union Carbide spectroscopic-grade graphite, SP-1. The graphite analysis indicated impurities at levels of only 0.5 ppm or less. According to the suppliers, the hydride and carbide contained the typical impurities listed in Table I. The samples required for these studies were prepared by dry blending either graphite and hafnium hydride or hafnium hydride and hafnium carbide powders for approximately 5 min in a "Spex Mixer Mill". The latter combination was used only for preparing several samples in the HfC1-, melting-point studies. Small pellets, varying between 3/16

Jan 1, 1965

By Frank J. Tolonen, Nicholas H. Manderfield, Paul Jasberg

EARLY in the study of the low grade iron formations of Michigan, wide variations in their structure and texture became evident. Because of these variations no simple method of concentration is possible, and those portions of the formations that can be exploited profitably under a given stage of metallurgical progress and existing economic conditions must be searched for carefully. Both structure and texture of the formations have an important bearing on their amenability to bene-ficiation. By structure is meant the banding planes of easy fracture, the porosity, and the degree of leaching. Texture, which includes grain sizes, shapes, and degree of interlocking, determines the amount of grinding necessary to liberate the mineral grains. Structure determines the liberation of portions richer in one mineral. Structure and texture may be termed the gross features of the formation. Earliest surveys of the formations were conducted to outline the parts that could be concentrated at % in. (3 mesh). Operators agreed on this size because anything finer required sintering or other agglomeration processes. At 3 mesh only the structural features, as defined above, would be liberated. With suitable ores concentration was easy, as any of the gravity methods could be used. Sink-and-float gave good results, but with this method only limited portions of the iron formations yielded a desilrable product.1,2 n general, the iroa content could be raised to shipping grade, but the silica content remained too high—sometimes 20 pct—instead of 9 or 10 pct. Grinding did not greatly increase the liberation ofsilica until 2010 mesh or finer was reached. To find the reason fpr this T. M. Broderick began micros~opic examin'ations of the formations in 1933.3 Procedure: The purpose of this discussion is to correlate the appearance of typical portions of the iron formations with their amenability to concentration. As liberation is essential before separation becomes possible, much of the work is based on measuring the liberation achieved by crushing and grinding. Both heavy media and magnetic tube tests were used in this work. On the basis of general structural features such as banding, degree of alteration, and leaching, a specimen was selected from each part of the iron formations studied. The specimen represents the gross features of the formation and not necessarily the particular formation quantitatively. One half of the specimen was polished for macro-study, and the remainder was used for analyses to obtain the grades represented by variations appearing in the macrosection. Specimens for microscopic examination were also prepared for each variation in gross appearance. For correlation of microstructure with liberation, the previous work by sink-and-float methods was supplemented by magnetizing roasting followed by magnetic separation. The results show the liberation of silica to be very important at the sizes used, because any silica particle with iron minerals occluded would be held in the concentrate. A magnetizing roast changes the crushing and grinding character of the sample. For partly leached soft samples the change is slight, but with harder types and those in which there is a considerable change in crystal structure of the minerals, the increase in liberation of the iron minerals may be 30 pct more than that of unroasted samples at the same crusheH size. Gogebic Range Iron Formations: The Gogebic Iron Range is located in the extreme western and southern parts of Michigan's Upper Peninsula, extending westward into Wisconsin. Samples for this study were obtained from the Ironwood formation, comprising three chief members—the Plymouth, Norrie, and Ahvil—with several intermediate slates and thick overlying slates. (The slates are not considered in this discussion because grinding finer than present practice is usually required to liberate the iron minerals.) The predominant iron mineral is hematite, about half of which is hydrated to goe-thite. Limonite occurs in some of the partly leached areas, and siderite in parts of the formation.

Jan 1, 1958

By S. W. Kennedy, M. Cohen, L. D. Calvert

A high-temperature X-ray diffraction method has been used to study the composition and the kinetics of formation of oxide scales at 800 °C on iron and pure iron-nickel alloys containing 25.6, 75, and 84 pct Ni. This technique has been combined with chemical analysis, and metallographic examination, and determination of weight-gain time curves. The 75 and 84 pct Ni alloys form a three-layer scale consisting of porous NiO next to the metal, a spinel layer, and a -Fe203 on the outside. The 25 pct Ni alloy produces a scale of spinel and Fe,O,, in which, however, traces of FeO and NiO are observed near to the metal. On all the nickel alloys the Fe20, is orieqted with the (107) plane parallel to the surfaces. The exposed surface of the Fe20, is in the form of needles whose axis is perpendicular to the specimen surface. Although the alloys show nonuniform oxidation rates as determined from weight-gain measurements, the X-ray data indicate that the total scale and individml scale layers grow uniformly and parabolically. Deep subscale formation is observed in the 25 pct Ni alloy only. This appeared to be associated with cracking of the scale and penetration of the oxygen along the grain boundaries. ALTHOUGH film formation has been investigated by high-temperature electron-diffraction techniques, for example by Gulbransenl and Hickman,' there have apparently been no investigations of scaling by methods permitting study of the scale during formation at the reaction temperature. Methods involving quenching of scales are based on the working assumption that no significant changes take place on cooling. In general, however, compounds may disproportionate, and the different thermal expansions of constituents may cause disruption of the scale on cooling. In particular, some scales cannot be quenched without spalling. These difficulties are avoided by X-ray diffraction examination at the temperature of formation. High-temperature diffraction procedures also provide a method of determining the kinetics of formation of each phase separately in a multicom-ponent scale. The scaling of binary iron-nickel alloys Containing up to 30 pct Ni at a temperature of 800°C has been studied by Benard and Moreau using cooled specimen~,~ whilst Foley, Druck, and Fryxel14 made an electron-diffraction study of cooled oxide films formed on an iron 42 pci Ni alloy. In the present work the scaling of three iron-nickel alloys containing 25.6, 75, and 84 pct by weight of nickel, at 800°C in oxygen at atmospheric pressure was investigated by X-ray diffraction techniques using a Norelco Geiger-counter diffrac-tometer. The oxidation of iron was investigated for comparison. In addition normal metallographic examinations and chemical and X-ray analyses were made, and weight-gain time curves obtained. EXPERIMENTAL Materials Used—The analyses of the alloys were as follows: Percent by Weight Nickel 25.6 pct 75.4 pct 83.2 pct Aluminum 0.004 None found 0.002 Cobalt — 0.05 0.05 Chromium — — — Silicon — 0.01 None found Carbon All less than 0.05 pct The chemical analysis of the iron was: Al— 0.002 i 0.001 pct, C—0.007 pct, Cr less than 0.001 pct, Cu—0.002 ± 0.001 pct, Mn—0.003 ± 0.001 pct, N—0.0002 pct, 0-0.013 pct, P—less than 0.0002 pct, Pb—not detected, S—0.0017 pct, Si—0.0095 pct, Sn—none detected. This iron was the same as that used to make the alloys and was obtained from the same source-Vacuum Metals Corp. One specimen of pure iron from The British Iron and Steel Research Association was used for preliminary investigation. Specimens were machined to shape from cast rod, polished (the final polish being with 600 Sic paper), degreased in trichlorethylene, washed, and etched. The etching and neutralizing procedure adopted by

Jan 1, 1960

By Warden A. Moller

(Pittsburg Meeting, March, 1910.) THE Fushun coal-field, now being opened up by the South Manchurian Railway Co., is connected with the main line by a branch, 30 miles long, from Sui Chia Tun, 10 miles south of Mukden, the capital of Manchuria. The coal-field, which lies on the southern bank of the Hun river, 25 miles east of Mukden, consists of a long narrow valley,. running east and west between hills composed of granitic and volcanic rocks. At the foot of the northern hills, the Hun river flows westward towards the Liao river, which drains the greater part of South Manchuria. At the foot of the southern hills, resting immediately upon volcanic rocks, and overlain by 20 ft. of alluvial, is a thick layer of Tertiary shales, carrying near the base two coal-seams. In many places the lower of these two seams is in immediate contact with volcanic lauds and basalts, the flows of which were evidently both prior and subsequent to the formation of the coal-seams. This contact has practically destroyed the lower seam for commercial purposes. The value of the field lies in the upper seam, which, for a length of nearly 8 miles, varies from 100 to 130 ft. thick. Of this seam, 85 per cent is good coal. The seam dips to the north conformably with the shales, at angles of from 25° to 30°, and appears to have an uninterrupted dip for about 1.5 miles before being possibly cut o$' by the northern hills. The coal-bearing shales extend east and west for a length of about 20 miles, but towards the east the continuity of the seams is broken by intrusive rocks. The coal is of the sub-bituminous variety, low in ash, bright in appearance, and breaks with a conchoidal fracture. It has the usual qualities of Tertiary coal-quick steam-raising and poor stacking-qualities. Pieces of resin, varying in size from

Apr 1, 1910

By J. S. Kirkaldy, D. H. Weichert, G. R. Purdy

Two-phase diffusion couples have been used to simulate the growth of proeutectoid ferrite in ternary Fe-C-Mn austenites. It has been shown, theoretically and expermentally, that the results fall into two classes: a high-super saturation class in which the major role of manganese additions is to influence the boundary conditions for carbon diffusion; and a low-supersaturation class in which the partition of manganese is required. In the latter case, a drastic inhibition of the reaction rate is to be expected. As an aid to the kinetic analysis, a portion of the iron-rich comer of the Fe-C-Mn constitution diagvam has been determined. The conclusions drawn from this work have a direct bearing on the kinetics of the grain boundary ferrite precipitation reaction and thus yield insight into the manner in which alloying elements can influence the rate of austenite-decomposition reactions. THE role of alloying elements in the austenite-decomposition reactions has provoked considerable interest, since it is apparent that an understanding of this phenomenon will yield insight into the harden-ability problem. In the present investigation, attention is focused upon the proeutectoid-ferrite transformation in the system Fe-C-Mn, and upon the manner in which manganese additions affect the growth rate of ferrite. When hypoeutectoid austenite is supersaturated, the ferrite first formed usually exhibits two distinct types of morphology. At low super saturations, grain boundary layers grow into the austenite grains with an approximately planar interface, and usually possess at least one incoherent phase boundary. At high supersaturations, Widmanstiitten plates appear, which bear an orientation relationship' to the parent austenite. In this case, there is a chance of partial lattice matching along the sides of the plates and an attendant semicoherent interface structure. Purdy and Kirkaldy2 have used a two-phase binary Fe-C diffusion couple to demonstrate that carbon volume diffusion controls the incoherent reaction, while Rouze and rube,' using thermionic-emission microscopy, have shown that the thickening of Widmanstatten ferrite plates is appreciably slower than expected for carbon-diffusion control. This suggests that the plates are bounded by partially coherent, low-mobility interfaces. The redistribution of alloying elements during transformation has been the object of studies by Aaronson4 and owmman,5 who have shown that no alloy partition occurs during ferrite precipitation in the systems Fe-C-Cr and Fe-C-Mo, respectively. More recently, Aaronson et al.6 have shown that some manganese partition occurs at low super-saturations in the system Fe-C-Mn, but that no partition occurs at higher super saturations. Pickle-simer et al.7 observed that no manganese partition occurred during the early stages of the pearlite transformation in a manganese steel, and concluded that volume diffusion of the alloying element is not the rate-deter mining factor. The diffusion coefficients pertinent to this investigation have been measured by Wells, Batz, and Mehl8 (carbon in austenite), R. P. smith9 (carbon in ferrite), Wells and Mehl 10 (manganese in austenite), and Kirkaldy and Purdy11 (diffusion of carbon on a manganese gradient in austenite). Kurdjumov 12 has shown that the diffusivity of substitutional elements in ternary austenites up-quenched from martensite may be greatly enhanced, due, apparently, to the presence of a persistent defect structure. The recent work of Krauss 19 showing high densities of tangled dislocations in reversed Fe-Ni martensite is in agreement with this conception. THEORETICAL Diffusion in ternary or higher-order systems may be described with the aid of Onsager's extenbion of Fick's first law,14 in which the flux of each of the n components is assumed to be a linear function of all concentration gradients:

Jan 1, 1964

By P. Hazebroek, C. S. Mathews, E. E. Allen, H. C. Lefkovits

A rigorous study was made of the behavior of reservoirs composed of horizontal layers, unconnected except at the well and filled with a compressible fluid. The report is presented in two parts. Part I deals with the practical implications of the results obtained; Part 11 contains the mathematical derivation of the solution. The main portion of Part I is concerned with application of the results to reservoirs composed of two layers. Relative rates of depletion of the layers are studied, and it is shown that differential depletion between layers exists in the transient stage of the reservoir, which generally is of an order of magnitude longer than the transient stage in a single-layer reservoir. In the transient stage, the more permeable layer is depleted faster than the less permeable. However, the reservoir approaches a steady-state situation where both layers contribute equally to production. Theoretical build-up curves from such reservoirs are presented, and the influence of a skin effect and flow into casing and tubing are also evaluated. The build-up curves are predicted to have, first, the familiar logarithmic straight-line section and, subsequently, a rising and flattened section. The results found are compared with an extension of an approximate theory, and it is found that this simplified theory is applicable over most of the life of the reservoir. Extensions to reservoirs containing more than two layers are indicated, and examples of the performance and build-up curves for three-layered reservoirs are presented. The theoretical results on build-up curves were applied to field examples of such reservoirs, and satisfactory results were obtained. From the build-up curve, the pemeability-thickness product, the wellbore damage and the static pressure are obtained. However, it apparently is not possible to determine the properties of the individual layers from the combined build-up curve. A large number of reservoirs have been found where the producing formation is composed of two or more layers of differing physical characteristics, such as permeability and porosity, and where also the thicknesses of the layers differ. Since in general a differential depletion should exist between the layers of such reservoirs, it would be advantageous to know the amount of the differential depletion under a given production history. It also would be valuable to know the pressure behavior, because it could be undesirable to produce a reservoir in such a manner that the pressure in one of the layers would have fallen below the bubble point of the oil at a time when another layer might still be virtually undepleted. The determination of static pressures in shut-in wells with slow build-up is another feature of importance in layered reservoirs. If the behavior of the reservoir differs appreciably from the predicted behavior of a single-layer reservoir, the type of analysis for build-up curves suggested for single-layer reservoirs is not applicable. Several authors have treated the problem of finding the pressure and production characteristics of multilayer reservoirs. Horner treated the problem of n layers in an infinite field, the layers being connected only at the well. Tempelaar-Lietz2 has presented an approximate treatment of the characteristics of a bounded reservoir composed of two layers of different permeabilities and equal thicknesses. Homer gave no information on differential depletion between layers, and the treatment of Tempelaar-Lietz was not applicable for prediction of pressure build-up behavior. In addition, it was thought that a more rigorous treatment than the one by Tempelaar-Lietz would be valuable in determining the range of validity of this solution. The present study, therefore, was made of a bounded reservoir composed of two or more layers,

By N. M. Levine, W. M. Fassell

In this laboratory study the problem of aerative conditioning to separate chalcopyrite and pyrite from cobaltite was simply effected with a sulfy-drate collector and pH by proper choice of mixing variables. It was shown that for a given impeller type and geometry, selectivity is governed by a relation between the Froude number and a modified power number multiplied by impeller tank-diameter ratio wherein the power factor is expressed as power intensity or horsepower per unit volume of contained pulp. In applying this approach to other systems, other criteria would be used in place of selectivity. The purpose of this paper is to show how solutions to problems of aerative conditioning of pulps may be enhanced by development of mixing parameters in a given system through application of a fundamental approach to agitation. The term aerative conditioning refers to a combination of processes which include mechanical gas dispersion, gas solution in the liquid phase, transport of dissolved gases and other reactants to the reaction zone, physico-chemico interaction within the liquid phase and/or at the solid surface, and, finally transport of products away from the reaction zone. Important elements of these processes are: 1) Air-Liquid Contact Area: This area limits the rate at which a given gas may dissolve in a given liquid. Thus, an aerative conditioning system should be designed for optimum gas dispersion. 2) Diffusional Factors: Such factors as concentration gradient, diffusion film thickness, and diffusivity may govern the rate at which dissolved constituents are transferred to the zone of interaction at a particle surface and the rate at which reaction products are transported therefrom. Thus, such systems would be designed for maximum turbulence to effect good mixing and to minimize diffusion film thickness. 3) Solids-Turbulent Liquid Contact Time: Sufficient time should be provided for interactions to take place at solid-liquid interfaces. The region of maximum turbulence for mechanical systems being in the impeller zone, it is important that the number of passes through this zone be optimized. This means that a proper balance should be struck be- tween flow and turbulent power to achieve optimum conditioning time. Too high a flow rate and insufficient turbulence may be improper if the reactions are diffusion limited. On the other hand, too much turbulent power and too little time in the reaction zone due to insufficient flow power may also be limiting. 4) Geometry and Impeller Design: The design of the conditioning vessel and the type of impeller employed are important factors in determining the relative distribution between flow and turbulent power and the degree of gas dispersion. Maximization of power input would be to no avail if the distribution between flow and turbulent power were improper or gas dispersion insufficient. 5. Physical Chemistry: The reactions between dissolved gases and solid surfaces may be limiting if gas solubility, activation energies and/or free energies are not favorable. J. H. Rushton, E. W. Costich, and H. J. Everett' have summarized the mechanical elements of the combination of processes listed in a fundamental mixing equation. This equation was derived by dimensional analysis and relates the physical variables for a single impeller, centered in a cylindrical, vertical axis, flat-bottomed tank. It is, where T is tank diameter in feet; H is liquid depth in feet; C is height of impeller off tank bottom in feet; S is pitch of impeller; L is length of impeller blades; W is width of impeller blades; R is number of baffles; D is impeller diameter in feet; Np is the power number, pg/dN3D5; P is power in foot-pounds per second; g is the gravitational constant, feet per second; J is width of baffles; B is number of im-

Jan 1, 1961

By L. S. Darken, H. A. Wriedt

An investigation has been made of nitrogen absorption by the lattice defects in a low-carbon steel afte~ Plastic deformation. Specimens in which defects were distributed by various combinations of cold rolling and vacuum heat treatment were equilibrated with controlled ammonia + hydrogen mixtures at 300° to 450°C to study the relation between the solubility and the thermodynamic activity of nitrogen. The results are interpreted in terms of nitrogen being absorbed upon two different types of defect sites, called A sites and B sites. The concentrations of these sites are calculated for specimens with various histories of straining and annealing; and the thermodynamic relations descrihing the equilibrium distribution of nitrogen among the A, B, and ordinary interstitial sites in ferrite are evaluated as follows: THE generalization that the solute atoms in a solid solution interact with imperfections in the solvent lattice is now universally recognized and the subject of an extensive literature. All types of imperfections—point, line, or surface—exhibit these interactions, but the relative importance of each type depends upon its concentration, the strength of its interaction with the particular solute atom, and whether the interaction is attractive or repulsive. The strength and sign of the interaction vary with the vectorial displacement of the solute atom from the imperfection in the crystal. The concentration of lattice defects increases during plastic deformation and the effect of the imperfections upon the solute atoms is usually perceived only after cold work or irradiation. Two experimental methods have previously been used to observe the effects of interaction between nitrogen atoms and lattice imperfections in a iron. Internal friction, which was first used for this purpose by Dijkstra,1 has been applied more often than the electrical-resistivity method of Cottrell and Churchman.2 The method of the present investigation has not been used before.* Uniform specimens of steel with a metastable defect structure are produced by cold rolling and subsequent heat treatment below the recrystallization temperature. Variations in the defect structure are obtained by varying the amount of strain and the heat-treatment conditions. The specimens are then saturated with nitrogen at moderately elevated temperatures in ammonia + hydrogen mixtures having various thermodynamic activities of nitrogen below saturation with Fe4N. From the nitrogen contents of analyzed samples, the metastable equilibria of interactions between the defects and nitrogen can be established and the concentration of sites for nitrogen atoms in the lattice defects calculated. A steel was used in the present experiments instead of purified iron or iron alloys because the amount of nitrogen absorbed at defects is larger in the steel over a much wider range of experimental conditions and could therefore be measured more accurately. The effect of alloy composition is discussed in Part II of this paper; it is sufficient to say here that impurities and phase heterogeneity in ferritic alloys favor the generation and/or retention of larger defect concentrations during plastic deformation and annealing at 300° to 500°C. MATERIALS AND EXPERIMENTAL PROCEDURE The experimental specimens were prepared from stock of a low-carbon steel, which will be called "X steel" here, with the composition: C, 0.12 pct; Mn, 0.43 pct; P, 0.010 pct; S, 0.034 pct; Si, 0.007 pct; As, 0.086 pct; Cu, 0.022 pct; Ni, 0.009 pct; Cr, 0.003 pct. The stock was all from a single ingot made by the basic open-hearth process, which was hot-rolled to strip 0.080 in. thick.. This hot-rolled strip, given the code designation "XH", was the starting material for preparing a series of cold-rolled sheets. The latter are designated "XC27",

Jan 1, 1965

By K. T. Aust

The relative interfacial energies of symmetrical tilt boundaries in silver of greater than 99.999 pct purity were measured as a function of orientation difference 0 between 9° and 36° about <001>. The results are in good agreement with the dislocation model of the grain boundary. The energy vs H curve may be represented by the Shockley and Read equation in the form Eoe (0.55—In 8). READ&apos; has indicated that an ideal experimental method of testing the predictions of the dislocation theory of the grain boundary would be to measure the interfacial energies of symmetrical tilt boundaries between face-centered-cubic grains that have a common <001> axis, as a function of orientation difference 0. The misfit H should be defined by a rotation of each grain through an angle of H/2 away from the boundary. Such boundaries might be expected, from geometrical considerations, to be made up of a series of edge dislocations, at least for small values of 0. Energy vs H relationships for tin&apos; and lead:&apos; were previously obtained for an asymmetrical tilt boundary separating two grains in which generally only one grain was rotated about a <001> specimen axis through an angle of H away from the boundary, the other grain remaining fixed. It is possible, however, that the boundary atoms in tin and lead may have attained a symmetrical position, in relation to the orientations of the grains on either side of the boundary, during equilibrium annealing. The two sets of measurements on silicon ferrite&apos; were somewhat better suited for comparison with theory, since the boundaries were symmetrical tilt boundaries in which the axis of relative rotation was <110> in the first series and <l00> in the second; but this alloy has a body-centered-cubic structure. Although the grain boundaries in silver" were symmetrically tilted, the axis of relative rotation was not a simple crystallographic direction, and it varied from boundary to boundary. Although the above measurements were in good agreement with the Shockley and Read equation,"&apos;: it appeared desirable to carry out experiments under the ideal conditions specified by Read.&apos; Consequently, the relative energies of symmetrical tilt boundaries in silver between grains that have a common <001> axis were measured. The technique of equilibrating grain boundaries in oriented tricrystals was used rather than the less satisfactory thermal groove method previously employed for silver bicrystals." Experimental Details and Observations The solidification and seeding techniques, described previouslyh for growing tricrystals of controlled orientations, were used to prepare tricrystal specimens from silver of greater than 99.999 pct purity. The silver was obtained from American Platinum Works, Newark, N. J., in the form of poly crystalline rods 10 cm long and 7 mm in diam. These rods were then cold worked by rolling or drawing them into suitably shaped blanks. Single crystal seeds and tricrystals were grown in a high purity graphite boat by means of a movable furnace with globar heating elements. The graphite boat was enclosed in a Vycor tube, which was first evacuated to about l00/u Hg and then filled with a static argon atmosphere. The maximum temperature outside the Vycor tube was 1250°C. A typical tricrystal specimen of silver is shown in Fig. 1. Grains B and C were grown from seed crystals with a <001> specimen axis or longitudinal direction parallel to the direction of growth and with another <001> direction perpendicular to the surface. Each of the two seed crystals was rotated 18" about the <001> specimen axis but in opposite directions away from the boundary. A symmetrical tilt boundary, therefore, separated grains B and C with an orientation difference 8 of 36" about <001>. Grain A in Fig. 1 was grown from the middle seed with a <110> direction parallel to the specimen axis and with a <001> direction inclined at 45&apos; to the surface of the specimen. The interfaces sepa-

Jan 1, 1957

By I. R. Dunlap, R. F. Burdyn, F. D. Patchen

The composition and properties of a new type of cementing mixture are discussed. In these compositions, API Class A or C cements are added to n stable water-in-oil emulsion instead of the crsual water. The cement disperses in the oil phase and remains out of contact with the water under normal conditions of mixing and storage. At higher temperatcrres, such as those encountered down-hole during placement, the emulsion breaks and cement hydration can then proceed. An extremely low filtration rate is obtained; the major part of the filtrate is oil. Thickening times of the mixture may be increased to meet the 18,000-ft casing cementing schedule by varying the amount of emzilsifier. As in conventional Portland cement mixtures, high-temperature strength retrogression can be overcome by addition of silica flour. Results of several field app1ication.r show that mixing presents no diffculty if emulsion blenders are used and the emulsion is prepared beforehand. INTRODUCTION Water-in-oil emulsions., in which oil is the continuous or external phase and in which water exists as discrete droplets, have for some time been used successfully in drilling muds to reduce filtration loss.1,2 Applied to cement slurries, the same results are obtained; i. e., the fluid-loss is greatly reduced. In addition, thickening times may be extended, lower densities and strengths obtained, and water-base borehole fluids more easily displaced without contamination of the cement. A low filtration rate is often a desirable property in oil well cements since loss of fluid increases placement difficulties and may also cause damage to water-sensitive producing formations.&apos; In the casing cementing operation where the cement slurry is pumped into the narrow annulus between open hole and casing, rapid loss of fluid to a porous formation can cause the slurry to thicken and plug the annulus before the desired fill is obtained. Where a casing or a liner is cemented against a productive formation and the well completed through perforations, the fluid lost between the time the cement first contacts the formation and the time a set is obtained may invade the zone past the depth of the perforations. If the sand contains a material which will swell upon contact with cement filtrate, permanent damage may result. Previous methods for reducing the fluid-loss of cements have employed bentonite4 as an additive, usually with a lignosulfonate as a dispersant, or a derivative of some naturally occurring polymeric material such as cellulose ether." Oil emulsion cements have also been proposedv or fluid-loss reduction, but these have been of the oil-in-water type. Bentonite cements have been used most widely and have been successful in reducing incidence of premature setting of cement attributable to loss of water by filtration. It is the purpose of this paper to describe preparation and properties of a water-in-oil emulsion cement and to relate procedures followed and results obtained in several field applications. DESCRIPTION OF SYSTEM AND MECHANISMS A water-in-oil emulsion cement is prepared by adding an API Class A or C cement to a stable water-in-oil emulsion. Fig. 1 is a photomicrograph of this emulsion before addition of cement. Here the droplets are water and the surrounding medium is diesel oil. High emulsion stability is indicated by the small droplet size [1-5 microns], and by their uniformity.&apos; To form a stable water-in-oil emulsion as illustrated, several conditions must be met. A predominantly hydrophobic emulsifier must be present in sufficient concentration to produce a strong interfacial film; initially, the phase volume ratio (the water-to-oil ratio) must be low;

By H. F. Webster, C. G. Dunn

Rolling md annealing procedures are described for developing the (110) preferred orientation in tantalum for use as a thermionic-emission materinl where electrodes of a uniform high work function are needed. The development of a (110) [001] annealing texture is also reported. A preferential growth process due to low (110) gas-metal surface energy is considered in explanation of the observed growth of (110) grains. ThE growth of (110)-oriented grains in thin strips of rolled zone-refined tantalum, previously discussed briefly,&apos; is reported together with more recent information on the formation of a (110)[001.] annealing texture, i.e., one where the [001] direction of each grain lies close to the rolling direction. The development of tantalum sheet with a (110) preferred orientation (position of [001 ] directions unspecified) is of importance as a thermionic-emission material in thermionic-energy converters. Since therm ionic-emission properties of cesium-coated crystals vary over a wide range depending on (hkl) a2-7 a single (hkl) preferred orientation is more useful than either several preferred orientations or none. Furthermore, the (110) preferred orientation yields the highest thermionic-emission density for a cesium coverage of less than a monolayer.5-7 A consideration of the stability of the grain structure needed at high operating temperatures suggests that the preferred orientation itself should be produced by annealing processes. Information on annealing textures in tantalum, however, is rather limited. Pugh and Hibbard 8 obtained (111)[112] and (lll)[112] components in a 1400°C recrystallization texture in 95 pct cold-rolled foil; these components were enhanced on annealing at 2500°C. Muller9 rolled 99.97 Ta to 90 pct reduction in thickness in the final stage and noted only a slight sharpening of the rolling texture, with some intensification of the (111)[112] component upon annealing at 1200°C. The experimental procedure followed in the present work stemmed from the idea of using possible differences in (hkl) surface energies to provide a small driving force for growth of grains having the lowest (hkl) surface energy.l0* This would mean using high-purity tantalum processed into thin sheet form and annealed at high temperatures either in a noncontaminating atmosphere or in one producing additional sample purification. EXPERIMENTAL Zone-Refined Tantalum. National Research Corp. tantalum in the form of 1/8-in.-diam rod and of 99.98 purity (53 ppm 0, 15 ppm N, and 8 ppm C) was zone-melted four times. The traversing speed was 4 mm per min. Such treatment increased the resistance ratio, R293k/R20K , where R293K is the resistance of the specimen at 20°C and R20K the re-resistance at liquid-hydrogen temperature, from a value of 25 for the initial rod to 175 for the zone-refined rod (the increase in the resistance ratio provides a measure of purification11,12). Part of a zone-refined rod was rolled unidirec-tionally to a strip 0.003 in. thick and 0.28 in. wide. Samples were given anneals in the range 1300" to 2100°C using ac conduction heating in an oil-free vacuum system. Recrystallization to small grains appeared to be complete at 1300°C. Large grains were formed at higher temperatures, but these were not entirely strain-free, some grains showing asterism in Laue X-ray patterns and some displaying a range in orientation. Part of the difficulty was caused by thermal expansion of the tantalum strip as it was held between fixed supports. However, in a different arrangement with the tantalum freely suspended in a tantalum can, high-frequency induction heating in vacuo at about l0-6 Torr produced

Jan 1, 1964

By M. W. Cox, V. F. Hollister

EXPLORATION for metallic mineral deposits is carried on by those special adaptations of methods which the explorer believes will yield most economically or satisfactorily the particular answer sought. In this project the usual methods of geologic observation, recording, and interpretation, when combined with magnetic geophysical methods and geochemical soil sampling, led to disclosures of appreciable zinc mineralization where none was visible in surface exposure. Since 1945 considerable work has been done with geochemical prospecting methods, chiefly in determining the presence and distribution of various elements existing in minor amounts in rocks, soil, vegetation or waters of mineralized areas. Such work, in which the U. S. Geological Survey has taken the lead, finds a ready place in the field repertoire of the exploration geologist as a supplement, not a substitute, for other methods. The Chollet project was carried out in 1951 by the American Smelting & Refining Co. near its Van Stone mine in northern Stevens County, Wash., in the area shown in Fig. 1. The Van Stone mine is located in the Onion Creek drainage of the Selkirk Mountains, midway between the towns of Colville and Northport, Wash., and some twenty airline miles west of the Metaline mining district. Its zinc-lead orebodies, currently yielding about 1000 tpd of ore, occur as bedding replacement deposits in the middle Cambrian Metaline formation near an intrusive granodiorite contact. The target of exploration at the Chollet prospect was a similar geologic environment along the intrusive contact about 5 miles west of the mine. Geographic Setting The Chollet ground covers a north-facing slope at 3000 to 4000-ft elevation. Second-growth jack pine and tamarack with some hemlock and yellow pine make a thick forest cover. A heavy under-forest of alder, willow, and lesser shrubs occupies the draws, see Fig. 2. Grassy slopes appear at higher elevations. The lower slopes are underlain by a thick blanket of glacial till and alluvium so that outcrops are scarce; however, perhaps 50 pct rock exposure prevails at higher elevations. This part of northern Washington annually receives about 25 in. of precipitation, which largely falls as snow in the winter months. Summers are dry with occasional rainy periods. General Geology The Van Stone mine and the Chollet prospect lie along the southern margin of a westerly extending lobe of the Kaniksu batholith, one of the series of granodioritic masses that are intrusive into Cretaceous and older rocks in northern Washington and southern British Columbia. The margin is composed of complexly deformed Paleozoic sediments ranging in age from the lower Cambrian Maitlen phyllite on the east, through middle Cambrian Metaline formation (limestone and dolomite), to Ordovician Ledbetter slate on the west. In general the formations strike N10 to 50E and dip steeply northwestward, although dip reversals and minor folding occur. This general rock distribution is shown on Fig. 3. In this area the Metaline formation, which is the host rock for mineralization, appears to be of about 4000-ft thickness that can be conveniently divided into the same three units defined by Park and Cannon&apos; for the Metaline area. The basal part consists of 1000 ft of interbedded white limestone, argillaceous limestone, and gray silty argillite. The middle part, approximately 1500 ft thick, consists of fine-grained black, gray, and white dolomite. This unit also contains minor interbedded limestone. The upper part is a gray massive limestone about 1500 ft thick that grades upward into slaty limestone and slate capped locally by a thin black jas-peroidal dolomite which is either the uppermost member of the Metaline formation or the basal member of the overlying Ledbetter (Ordovician)

Jan 1, 1956

By R. H. Frazier, C. H. Lorig, F. W. Boulger

This investigation establishes the effect of ferrite grain size resulting from various heat treatments on the transition temperature of a semikilled steel plate. Different austenitizing temperatures and various cooling rates were used. The ductile-brittle transition temperatures were determined by the Navy tear test and the keyhole Charpy test. THE data presented in this paper deal with quality characteristics of ship-plate material which were investigated in a research project sponsored at Battelle by the Bureau of Ships, Dept. of the Navy. Specifically, the object of this investigation was to establish the effect of ferritic grain size (resulting from various heat treatments) on the so-called transition temperature of ship-plate steel. Transition temperature is not a fixed property of steel. It is derived from a series of static or dynamic tests made at various temperatures and is qualified by specifying the type of test employed as well as the testing criteria. Because in earlier investigations of ship-plate quality1,2 the so-called Navy tear test and standard notched-bar tests (keyhole Charpy) proved to be useful in interpreting instances of brittle behavior of ship plate in service, these tests were used in the investigation reported in this paper. By definition,&apos; in the Navy tear tests the highest temperature at which one or more of four specimens breaks with a brittle fracture (that is, when less than 50 pct of the fracture area has a dull fibrous texture) is termed "transition" temperature. In the Charpy tests, the 12 ft-lb level of energy absorption was used as a criterion indicating the "transition" temperature, although other levels of energy absorption were also used for comparison. Earlier work" on ship-plate steels indicated that the temperature at which ship plate is finished has a very significant effect on its notched-bar properties. Plates rolled in the laboratory, where the finishing temperature can be carefully controlled, showed a 16°F decrease in tear test transition temperature when the finishing temperature was lowered 200°F (from X" to Y°F). The same plates showed a drop of 10°F in the keyhole Charpy transition temperature from the same decrease in finishing temperature. Commercially finished plates&apos; exhibit a similar trend. When the ferrite grain size of the hot-rolled laboratory plates was determined, a close relationship was found between the ferrite grain size and the notched-bar transition temperature." " he indicated relationship between grain size and transition temperature was in agreement with the findings on low carbon steels of Hodge, Manning, and Reichhold&apos; despite the differences in composition of the steels. The cooling rate after rolling varies from one steel plant to another. This variation changes the micro-structure" and appears very likely to affect the notched-bar properties of the steel plates. In the investigation summarized in the present paper, heat treatments simulating finishing practices in the hot rolling of ship plate were used in order to vary the ferritic grain size. It is believed that the indicated relationship between grain size and transition temperatures of the ship-plate material will prove useful in estimating the effect of rolling temperature and of cooling rates from rolling temperatures on the notched-bar properties of semikilled steel plate. Material The semikilled steel plate used in this investigation was a ¾ in. hot-rolled plate from an open hearth heat. Other plates from this heat have been used on many other studies performed for the Ship Structure Committee," "," and the heat has been identified as project steel "A". The chemical composition of the plate1 was 0.25 pct C, 0.49 pct Mn, 0.011 pct P, 0.045 pct S, 0.04 pct Si, and 0.004 pct N.

Jan 1, 1956

By U. Andres

U. Andres (The Technion, Haifa, Israel)-The authors are to be congratulated on their research, new and interesting, in a field which, however, the present writer and his assistants have been trying since 1962 to bring to the attention of the scientific and technical world, by means of publications covering several different aspects of this many-sided problem. We announced, in these publications, the results of magneto-hydrostatic (MHD) separation of magnetic and nonmagnetic minerals which we made in magnetic fluids (in paramagnetic solutions and suspensions of magnetic particles) which interact with permanent" and impermanent" inhomogeneous magnetic fields. There is no doubt that the authors have succeeded in creating ferrimagnetic colloids made by dispergation of 10-30 wt % of magnetite in kerosene in the presence of 7-10 vl % oleic acid. It may be judged by [Figs. 3 and 4] that the suspensions represent great stability systems and also "hysteresisless" fluids [(Fig. 5)] which bear witness to the existence of superparamagnetic suspensions. If the viscosity of these colloids is not so high, and the cost of preparing them can be covered, the fluids which have here been received can possibly be of interest to the technology of mineral separation. The potential possibility and technological perspective of similar media is demonstrated in our joint work with G. Bunin18 in 1965. The research carried out on the pushing out of cylinders and spheres from magnetic fluid is impressive; it would, however, have been interesting if the authors had compared their results with those on the pushing out of bodies from magnetic fluids adduced from our work." In my books" there happens to be described an experiment on the pushing out of a sphere in magnetic wedge field, in which the pushing out force of suspension with 5 vl % of magnetite reached 125 g per cc. This testifies to interesting possibilities of these media. Our works&apos; shows also, on the basis of Laplace&apos;s equation the receiving of an interesting distribution of pushing out forces by selection of corresponding configurations of magnetic poles. Objection must be made to the authors&apos; introduction of the term "antigravity force." The direction of this force does not depend on the direction of the gravity force and their opposition, i.e., antigravity is only one particular case. I am in full agreement with the authors&apos; statement that magnetic pushing out forces "can be utilized to separate nonmagnetic objects according to variations in their densities." It is, however, necessary to make only one important addition, which can be found in our research on MHS at the Technion in Haifa, namely, that magnetic fluids in magnetic fields can be utilized in the separation of minerals according to variations in their magnetic susceptibility. The authors&apos; conclusion is especially important considering the fact that in our publications" (including one in English") some designs of MHS separators and some technological results received on MHS-separators have already been described. S. E. Khalafalla and G. W. Reimers (Authors&apos; Reply)We were aware (mostly through Chemical Abstracts of the American Chemical Society) of the use of solutions of paramagnetic salts such as manganous sulfate in agnetohydrodynamic separations by the Russian school headed by G. Bunin."n Professor Andres&apos; contributions to this school are also evident in his application of the ponderomotive forces in an electrolyte placed in electric and magnetic cross-fields to separate coal and other useful minerals." It must be realized, however, that the foregoing research by Bunin et al." involved the use of magnetic fields and field gradients of very large magnitudes, i.e., such that H • grad H - 101 Oe2 per cm. The magnetization of paramagnetic salt solutions range from 0.1 to 0.5 gauss (at fields of a few thousand Oersteds) and never reach saturation. The magnetization of our superparamagnetic ferrofluids ranges from 100 to 500 gauss and reach saturation at fields of a few hundred Oersteds. Hence, to effect the same separation, the quantity "H

Jan 1, 1974

By T. M Morris

THE rate of flotation of solid particles determines the percentage recovery of these particles which can be obtained during a given time interval. It is an established fact that the recovery is greatest in the fine sand size range and falls off on either side of this size range. It is also a fact that the history of the development of concentrating devices has been marked by a desire to recover the small particles: tables were developed to treat material too fine to recover in jigs; flotation recovers material too fine to be recovered on tables. As our ores become more complex and require finer grinding, a greater proportion is in the slow-floating size range. It is therefore of economic importance that the effect of size of particle upon rate of flotation be studied. Many studies have been made along this line. The present investigation attempts to quantify the rate of flotation by means of a rate equation, and then compares the effect of size upon the rate of flotation. It was found that the flotation rate constant increases with increase in diameter of particle in the size range smaller than the optimum size particle. The flotation rate constant decreases with an increase in diameter of particle in the size range coarser than the optimum size particle. This suggested two different actions taking place, and these are discussed. Suggestions for further work in order to improve the flotation rate of both fine and coarse particles are made. The usual method of expressing rate is to plot cumulative percent recovery vs time. If we knew the equation of this kind of curve we could replot it as a straight line, and the slope of the line would be an index of the magnitude of the flotation rate. It is easier to compare straight lines than curves. The basis used for obtaining the equation of the recovery vs time curve is the law of mass action. This law states that the "rate of a chemical reaction is proportional to the &apos;active masses&apos; of the reacting substances present at any given time." This, of course, implies a constant temperature. We can modify this for our use by using the term flotation reaction instead of chemical reaction and the term floatable particle instead of active masses. dC Thus----— kc [1] where C denotes concentration of particles, t denotes time, k denotes a proportionality constant. If the exponent of C is 1, then we have a first order rate reaction. If the exponent of C is 2, then we have a second order rate reaction. For a first order rate reaction, we obtain, after integration, where k is again a proportionality constant and has the dimension of the reciprocal of time. C, is the original concentration or weight or percentage of floatable particles. C, is the concentration or weight or percentage of floatable particles remaining in the flotation cell after time t. If all particles of the mineral to be floated were capable of floating we could take C, as 100 and C, would be 100 - R, where R is the cumulative percentage recovery of mineral at time t. But it is not usual for all of the particles to be capable of floating, because of surface oxidation, etc. Therefore, we must introduce a factor x which is the percentage of un-floatable mineral. Hence the first order equation is It has been proposed by various workers1-&apos; that this equation describes the flotation rate. More recently N. Arbiter4 states that a second order rate equation fits the recovery vs time curve more closely than does a first order rate equation. Morris- as discussed the evidence presented for this statement. It has been concluded that the first

Jan 1, 1953