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By Robert Lowrie

Nine intermetallic compounds were tested in tension at various temperatures. Seven exhibited extensive plastic deformation at elevated temperatures. Correlations of tensile strength and elongation are attempted with melting (decomposition) temperature, valence electron configurations of the component elements, heat of formation, crystal structure, density, and volume decrease accompanying compound formation. A LTHOUGH intermetallic compounds have been -tX known for many years, the study of their mechanical properties, particularly in tension, is just beginning. The problem has been unattractive because of the well-known, erratic behavior of brittle materials tested in tension. The strong influence of surface or internal flaws as stress raisers in non-ductile materials and the effect of eccentricity of loading in superimposing bending stresses on the state of tension in the specimen are extremely difficult to mitigate and impossible to completely eliminate. Thus, tensile properties determined for brittle materials, such as intermetallic compounds at temperatures low in comparison to their melting points, are at best only general guides to the values to be expected in an ideal test of a perfect specimen of the material. It is, nevertheless, surprising that apparently no attempt was made to follow up the pioneer work of Tammann and Dahl1 in this field. Working with crude apparatus, these investigators succeeded in showing unequivocally that at temperatures sufficiently close to their melting points (from 75" to 400°C for the compounds tested) intermetallic compounds did exhibit plasticity. This was indicated by the appearance of slip lines on the surface of the specimen. No observations of strength were made in these tests, which were of a compressive or indentation type. Rossi2 in 1932 attempted to study the physical and mechanical properties of single crystals of a group of intermetallic compounds. However, he was able to prepare only one material, Cu2Z8,, in the form of large, defect-free, single crystals. Thus, he was able to report only the relative fragility of the compounds at room temperature. He reported one compound, Ag,Zn,, to be somewhat plastic at room temperature and Cu,Si to be friable, the latter in agreement with results reported herein. Although test results are available only in classified literature, it has also been announced that MoSi, possesses some ductility at elevated temperatures." In 1948 and 1949 Savitskii and Savitskii and Baron -ublished their work on the hot extrusion of Mg-Zn, Al-Mg, and Cu-Zn compounds. Under the favorable state of stress existing for this process MgZn, MgZn,, MgZn,, ß (Al-Mg), ? (Al-Mg) and 0 (Cu-Zn) could be reduced by amounts up to 90 pct at elevated temperatures. These authors also report that hardnesses of Mg-Zn compounds decrease from room temperature values of about 300 kg per sq mm to 30 to 50 kg per sq mm at 325°C. They found that alloys consisting solely of one Mg-Zn compound were most resistant to softening on heating, mixtures of a compound and eutectic less resistant, and mixtures of two compounds least resistant. The more rapid softening of mixtures of

Jan 1, 1953

By Donald H. McLaughlin

THE primary function of the mining engineer is to find mineral deposits and fuels in the accessible rocks of the earth and to recover them for the vast needs of our complicated civilization. On him has been placed the responsibility for the exploitation of the nation's and world's mineral resources. The degree to which the minerals of the earth have been utilized serves to an extent as a measure of man's material advancement, as well as an index of the relative strength of nations. The natural endowment of lands, varies greatly, but the intellectual energy of a people is revealed by the way in which they take advantage of their heritage of minerals or reach out to less developed regions by exporting their engineering skill as well as capital to secure the raw materials they need.

Jan 2, 1953

By H. Ries

THE stabilization of a gravel road with soil is a method of treatment developed in recent years by the United States Bureau of Public Roads for the purpose of binding the constituents together better, and maintain-ing a more durable surface. The process consists in adding to the gravel or crushed stone and sand, a soil mortar, so-called, of fine sand, silt and clay, mixed in the proper proportions. The coarse gravel and sand supply structural strength and hardness; the fine sand adds embedment support to the coarse sand; the silt acts as a filler to prevent the granular particles from rocking; while the clay serves not only as a binder but also provides pores minute enough to cause connecting moisture films which are supposed to have high cohesive properties1. It will be recognized that the clay is an important ingredient both when wet and dry, and should not show excessive expansion when wet, nor correspondingly high shrinkage in drying, as otherwise there is danger of unseating the nonplastic particles. Such a stabilized road, although an improvement on one with a floating surface, will in course of time be subject to wear, and become dusty when the clay dries out and breaks up. It has been found that if some salts are added to the road mixture they tend to maintain the soil moisture and prevent dustiness of the road or raveling of the road surface. In addition to this, it is claimed that these dissolved salts cause a thinning of the moisture films on the particles, thus permitting greater compaction of the road mixture, and thereby increasing its density. This fact can be proved by noting the increased compaction which a road mixture shows when certain salts are added to the soil water. Since certain chemical substances such as sodium chloride are electro-lytes, the question arises whether they cannot have some effect on. the qualities of the clay in the soil mortar, and perhaps improve them. In view of the fact that certain salts seem to exert a favorable effect on the road mixture it is desirable that they be held in the road soil as long a time as possible.

Jan 1, 1936

By W. B. Gogarty

With flow of non-Newtonian fluids in porous media, effective viscosities are needed for use in the Darcy equation. These viscosities depend on the rock parameters and flowing conditions. In this investigation, rheological and flow results were correlated to develop an expression for calculating effective viscosities. Surfactant-stabilized dispersions of water in hydrocarbon were used with consolidated sandstone cores of different permeabilities. The average shear rate in a core was related to the permeability and porosity of the core and the frontal velocity through the core. By using the correlation obtained for determining effective viscosity, experimental and theoretical values were compared for each fluid system by determining average and maximum errors. For the fluid system showing the largest average error, the correlation fit 38 experimental points with an average and maximum percentage error of 4.3 and 14.8, respectively. For the fluid system showing the least error, average and maximum percentage errors of 1.8 and 4.3, respectively, were calculated using 29 experimental points. INTRODUCTION Use of non-Newtonian fluids in the petroleum industry is not new. Fluids of this type have been used for many years as fracturing agents and drilling muds. Recently, attention has focused on the use of high molecular weight polymer solutions for secondary recovery. Results have been reported on studies relating to the flow behavior of polymer solutions in porous media.1-4 Each study gives the viscosity in the Darcy equation as a function of the rheological properties of the fluid, the characteristics of the porous medium and the pressure gradient. The functional forms of the reported expressions differ somewhat in each study. The first three studies used unconsolidated porous media while the fourth used a single consolidated core. Because of the limited information available on the flow of non-Newtonian fluids in porous media, further investigation was undertaken in this area. We selected non-Newtonian fluids that did not contain high molecular weight polymers in order to minimize core plugging. The over-all objective was to gain a better understanding of the flow behavior of non-Newtonian fluids in consolidated porous media. Specifically, our goal was to determine the relationship between the average shear rate in a core and the frontal velocity. Because of this goal, it was necessary to determine the effect of permeability on the shear rate-frontal velocity relationship. We wanted to replace the viscosity in the Darcy equation with an expression relating to the average shear rate in the core and the rheological properties of the non-Newtonian fluid. THEORY For a time-independent, non-Newtonian fluid, the apparent viscosity is a function of the shear rate. This relationship is given by µ = F(v')...........(1) With Eq. 1, a single value of shear rate determines the apparent viscosity at that shear rate. With flow in porous media, a spectrum of shear rates occurs at any average throughput. An average shear rate v' can be used to represent the spectrum of shear rates that exists within the core. By using v' and the rheological data given by Eq. 1, an effective viscosity is determined for the flowing fluid. If v' is the correct average, µe becomes the appropriate viscosity for use in the Darcy equation. Under these conditions, flow rate-pressure drop relationships can be determined for non-Newtonian fluids. HOW the correct average shear rate might be related to the frontal velocity through the core and the characteristics of the porous media will now be considered. Later, the experimental data are presented that indicate the validity of these

By W. H. Yarroll

This paper presents a general discussion of the utility of the statistical technique known as multiple correlation, and gives three specific examples of its application. The first demonstrates the most simple form, or straight-line, multiple correlation. The other two demonstrate multiple correlation analysis in best-fitting third-degree parabolas. With the increasing availability of digital computers, the method becomes entirely feasible where heretofore its use was impractical. The advantages of the method are discussed, and curves are presented which were developed by computerizing the regression equations developed in the examples. The method described in this paper is for use with complex systems, and the examples given are complex metallurgical systems. This subject falls under the general classification of cybernetics, which is defined' as "the science of control and communication, in the animal and the machine." Machine, in this case, can include chemical and physical processes which take place within machines and processing equipment of all kinds. The classical approach to scientific investigation has been the construction of simple models and the changing of variables one at a time. This method is wholly inadequate for obtaining useful information from the complex systems of modern technology including many of our flotation and hydrometallurgical processes. Cybernetics offers the method by which complex systems which have been implemented as an art in the past can now be analyzed with all the discipline of a science. Mathematical techniques for achieving multiple correlation analysis have decided advantages over some of the other statistical methods.2-4 Multiple correlation does not require a series of experiments that have been rigidly planned as do many of the other statistical methods. For this reason, it can be used effectively for interpretation of information from op- erating plants, where planned experiments are impractical, as well as for laboratory experiments. First-degree multiple correlation has been used for many years, and was useful, but limited to linear or nearly linear relationships. The technique described in this paper provides a method for analyzing systems which may be non-linear. This particular technique is multiple correlation analysis in best-fitting third-degree parabolas. It is quite possible that lack of reference to the technique has been due to the overwhelming mass of computations it requires even for relatively simple problems. With the advent of computers, however, its use has become entirely feasible. For the benefit of those who may not be familiar with the subject, it might be well to pause at this point to discuss multiple correlation analysis — what it is and what it achieves. To go back to the old familiar fitting of a set of points with a best-fitting straight line by the least squares procedure, it is conceded that this a good method where there is only one independent variable influencing the dependent variable under consideration, and providing that the relationship is linear. In most fields of investigation, however, there are usually a number of factors exerting important influence, and they frequently bear relationships with the dependent variable other than straight line. Under these conditions, it is easy to see how misleading a simple correlation study might be. Multiple correlation can be used for any number of variables. Within the experience of the writer, this technique has been used to establish regression equations for determination of carbon rate, burden permeability, and production rate on iron blast furnaces, production rate on open hearth steel furnaces, life of molds for steel ingots, rolled steel tensile strength and various defects in rolled products, the performance of ore dressing equipment, and optimization of extractive metallurgical process variables. The discovery of mathematical correlation does not prove, per se, true cause-and-effect relationship, but simply establishes a hypothesis. If the regression equation can be used to make successful predictions of what will happen with future arrays of independent variables, then one can feel reasonably assured that true cause-and-effect relationships have been discovered.

Jan 1, 1968

By Roger M. Nendick

The recovery of precious metals from heap leach solutions can be accomplished by two processes: 1. The Carbon Adsorption Process 2. The Merrill-Crowe Zinc Precipitation Process A brief review of the relative process economics is made. Each process presents certain design considerations that must be addressed during the evaluation and engineering design for the project. Discussion is presented on the design criteria for each process.

Jan 1, 1984

By Gerard Matthes

ONLY in recent years has any practical headway been made in the application of aerial photography to geological problems, and up to the present time its principal value to the geologist and mining engineer has been in "areal geology;" i. e., the study of formations as revealed at the surface. The object of this paper is to set forth briefly the principal advantages that may be derived from aerial photographic data in geological work and to serve in a measure as a guide to those who may be con-templating its use. Geophysical prospecting has for object the locating of mineral under the surface. Inasmuch as the geologist's chief complaint in life is a dual one-inability to see under the surface and inability to visualize comprehensively what he does see on top of the ground-geophysical prospecting coupled with aerial photography should do much to lessen his burdens. To what extent aerial photography can be made a useful adjunct to geophysical prospecting remains to be proved, but the inference drawn here is that it holds many alluring possibilities. To avoid disappointments, it should be stated at the outset that to the :geologist or mining engineer an aerial photograph or mosaic is only a tool, the effecient use of which he must set out to master. Upon his skill and ingenuity in applying it to particular problems will depend largely the value of the results that he will obtain. Under the most favorable conditions an aerial mosaic or even a few loose photographs, because of the exceptionally comprehensive oversight which they afford of field data, such as dips and strike observations at isolated outcrops, local indications of faulting, mineral and fossil finds, greatly facilitate study and correlation, save much tedious foot work, and may repay their cost many times. Even so, types of country may be found where the most, skillful use of the best of pictures will produce results so meager as to render the cost of aerial photography entirely unwarranted.

Jan 1, 1928

By Donald Barton

THIS paper outlines a time-saving graphical method of calculation for application to the interpretation of observations with the Eötvös torsion balance. Preliminary to the treatment of this short cut method which has been found practicable, the principal formu-las by which the student of interpretation can calculate the gradient and differential curvature produced by different types of bodies in different types of situa-tions are presented and discussed. It is necessary to split most geologic bodies into a series of simpler ones for which not too complicated formulas are avail-able. The gradient and differential curvature effects are calculated for each of the simple bodies and then summed to the total effect for the whole body. The calculations are considerable in number and, though more tedious than difficult, should be' entrusted to an experienced calculator. Considerable facility in qualitative interpretation can be acquired by the geophysicist from experience and from a thorough study of the types of gradient and differential curvature anomalies produced by the dif-ferent types of possible structural situations. How-ever, semi-quantitative calculations' of the probable structure bring out many relations that are not evident in a simple inspection of torsion balance results ; it throws out as impossible or improbable certain of the alternative structural possibilities that may seem equally probable under simple inspection of the results; it will determine more accurately the position of the crest of the structure; and reduce considerably the un-certainty in the interpretation and it is necessary to intelligent interpretations. The calculation of such cross-sections consists of a trial-and-error calculation of a body that will give gradient and differential curvature effects as closely as possible the same as those observed. From his knowledge of the gradient and differential curvature produced by different types of bodies, the geophysicist sketches a tentative cross-section of the structure as indicated-to him-by the observed results of the torsion balance survey, and the calculator then splits the struc-ture into blocks, and calculates the gradient and differ-ential curvature block by block. If, as rather usual, the calculated .gradient and differential curvature pro-files diverge considerably from, the respective observed ones, it is necessary to add and subtract blocks from the cross-section until a close agreement is obtained .between the calculated and observed profiles. The com-plete calculations have to be gone through for each block that is added or subtracted.

Jan 9, 1928

By J. C. Bayles

It is seldom the privilege of one who contributes to the Transactions of a technical society, to describe a new industry in which, by processes employed for the first time, are attained results of conspicuous value. There are but few such patches of virgin soil worth the tilling, within the area circumscribed by the industries which have experienced a regular and uniform development. New and startling methods in production are often announced as about to be introduced; but, as a rule, they take their place among the " large desires with most uncertain issues," or give new significance to the historic words of an eminent statesman concerning " the bright beginnings and the bitter end of a halcyon and vociferous proceeding." In this paper I shall have the pleasure of briefly describing a new industry which has been established without announcement or proclamation — the manufacture of serviceable pressure pipes of great strength, from strips of steel or iron wound spirally, heated only along the overlapping edges, welded by hammering and finished into tubes of uniform diameter, and of such length as mag be found convenient in handling and transportation. As such tubes are now manufactured on a considerable scale, in a range of sizes which will soon include everything between 4 inches and 30 inches, and as much larger as may be needed, both process and product are likely to be of interest to engineers in all departments of professional work. The raw material of the industry is the ordinary sheet-iron or steel of commerce, of such lengths and widths as it is convenient to roll. The range of the ganges of the metal which can be employed has riot yet been determined. The lightest metal thus far successfully made into pipe is No. 29 iron, and the heaviest a steel gauging somewhere between 12 and 14. Heavier machines are now building which will bend steel .165 of an inch in thickness, or No. 8 of' the Birmingham gauge. Probably No. 20 or No. 22 will be the lightest used in making commercial pipes; hut the experiment with No. 29 was interesting as showing the readiness with which the flame can be controlled. To get a welding heat with such thin

Jan 1, 1888

By J. C. Van de Water

In June the supply of M3 army demolition powder being used for mudcapping was depleted and we switched to 4 by 8, 60% Special Quarry Gelatin dynamite. This size cartridge has proved convenient, as a half stick will handle the average boulder. By keeping the gelatin in the paper while cutting it in two, there is little contact with the gelatin and therefore fewer headaches among the powdermen. To further help prevent the headache nuisance the men are furnished with plastic coated gloves. Boulder breaking costs as reported last year were $0.426 using M3. This year, 8180 boulders have been broken with M3 at a cost of $0.472 each and 7479 with 60% Quarry Gelatin at a cost of $0.660 each. This rise in cost is due entirely to the greater cost of the Gelatin as the method has not changed.

Jan 4, 1950

By H. H. Kellogg

Equations representing the standard free energy of formation as a function of temperature, for thirty metallic chlorides, are presented and plotted on a free-energy vs. temperature diagram. The use of these data for calculations on reduction of metallic chlorides, refining of metals with chlorine, and chlorination of metallic oxides and sulphides is illustrated. CHLORINE metallurgy' has attracted metallur- gists for more than a century because the unusual properties of the metallic chlorides—low melting point, high volatility, and ease of formation from the oxides—make possible many useful extractive processes. Interest in chlorine processes is undergoing a renaissance due to present availability of chlorine at relatively low prices, and to recent advances in technology. During the present century there have accumulated a considerable number of reliable values of the thermodynamic constants for the metals and their chlorides. These data permit the calculation of free-energy equations for many metallurgically important reactions. Consideration of free-energy values makes possible certain predictions of the direction and extent of a given reaction, as well as the effect of temperature, pressure, and composition upon the result. Reaction rate, although not predictable from free-energy data, is usually sufficiently great at elevated temperatures that diffusion of the reactants and products to and from the zone of reaction determines the actual rate. Thus, if the free-energy indication is favorable, the chances are good that a high temperature metallurgical reaction will proceed at a reasonable rate, if adequate provision for rapid diffusion has been made. This paper presents standard free-energy equations for a number of metallic chlorides, based on data which are scattered throughout the literature. The equations are presented in a form that simplifies their use, and typical examples are given of the application of free-energy data to metallurgical processes. Free Energy of Reaction The free-energy change (AG) of a reaction is the true measure of the "driving force" of the reaction under a given set of conditions, and this is related to the standard free-energy change (AGO) of the reaction as follows: For the reaction: bB + cC = dD + eE ?G = ?G°+RTln ADd. AEA / ABb. ACc where A, = activity of constituent (i) T = absolute temperature, OK R = gas constant The criterion of a spontaneous reaction from left to right, at constant temperature and pressure, is a negative value for the free-energy change (?G). The standard free energy of the reaction is equal to the free energy of the reaction when all the reactants and products are at unit activity, since under these conditions the second term on the right-hand side of eq 1 is equal to zero. The concept of activity is treated fully in many textbooks on chemical thermodynamics1 and in a recent article by Chipman.2 Briefly, the activity (A,) of a constituent (i) is a measure of the reactivity of this constituent relative to its reactivity in some arbitrary standard state. For liquids and solids the standard state most often used is the pure liquid or solid constituent. Thus the activity of a pure liquid or solid in a metallurgical reaction is equal to unity. Gases under moderate pressure and at elevated temperatures behave very nearly as 'idea1 gases,' and the standard state is chosen as the gas at 1 atm pressure. The activity of an ideal gas is therefore equal to its partial pressure, and this relation is sufficiently exact for real gases in most metallurgical reactions. For a liquid or solid solution there is in general no simple way to express the activity of a constituent as a function of its concentration, and activity must be determined by experiment. A few solutions follow a so-called 'ideal' behavior, and if the pure constituent is chosen as the standard state, the activity of a constituent in an ideal solution becomes equal to its mol fraction. When a reaction reaches a state of thermodynamic equilibrium at constant temperature and pressure, AG becomes equal to zero and eq 1 reduces to: [ADd . AEe ?G°=RTln Abb ¦ Ac c equilibrium [2] The brackets surrounding the activity term are used to emphasize that each of the activities is an activity under equilibrium conditions—not just any arbitrarily assigned value. The bracketed term is the equilibrium constant (K) of the reaction. Eq 2 makes possible the calculation of equilibrium activities for a given reaction, if AGO is known at the desired temperature. The standard free-energy equations presented in this paper were calculated from the fundamental thermodynamic values of enthalpy of formation at 298°K (AH°,), standard entropy at 298°K (So298), heat capacity as a function of temperature (Cp), and enthalpies of transition, fusion, vaporization, and sublimation for the various constituents. Where possible the data reported in the recent "Selected Values of Chemical Thermodynamic Properties," published by the Bureau of Standards," were used. A large number of data came from the publications

Jan 1, 1951

By A. B. Dyes

In the operation of a water-driven reservoir, a free gas saturation can he established by maintaining production rates fast enough to cause the reservoir pressure to decline below the bubble point. The benefit of such a procedure on the displacement efficiency of the oil by water is illustrated for two types of sandstone samples from one reservoir. Those rock samples showing the poorest recovery to water drive in the absence of a free gas saturation give the most improvement in the presence of a free gas saturation. Employing one type of reservoir fluid (low .shrinkage) the benefit of evolved gas on oil displacement is calculated at several reservoir pressures below the bubble point. This demonstrates the presence of air optimum pressure for water displace,rnent which is .several hundred pounds per .square inch below the bubble point. Displacement of oil at the optimum pressures results in the removal of 7 to I? per cent more oil than would be obtained by displacement at the bubble point pressure. In some instance. this magnitude of increase may be worthy of consideration in establishing the maximum efficient rate of production from many water-driven fields. INTRODUCTION For many years the belief that the use of gas could be combined with that of water to result in a better recovery operation than the use of either of these phases alone has been prevalent in the oil industry. This is evidenced by the several field trials which have employed the injection of gas and water in combination.1.2.v In most cases the small amount of any additional recovery, in combination with the limited knowledge available on the older reservoirs, has left uncertain the influence of gas on recovery in these earlier attempts to combine the use of gas with water. Research studies in recent years have demonstrated through laboratory. floods the magnitude of the benefit of the presence of gas on the displacement of oil from sandstones by water.5,6,7,8,9,10,11 In addition, studies of the distributions of the phases which are present during the displacement process have developed concepts concerning the mechanism by which this benefit is obtained."." It now remains for the engineer to incorporate these findings into the general technology of reservoir operations. It is the purpose of this paper to illustrate that the production of a water-driven reservoir at pressures below the bubble point is one such operation whereby improved oil displacement efficiency can be obtained as a result of gas evolution. The establishment of a gas saturation by evolution of dissolved gas was one of the techniques used by several investigators in the laboratory studies. The possibility of obtaining the benefit of gas evolution in water-driven reservoirs by producing at pressures less than the bubble point has 3150 been pointed out previously." The desirability of this operation has undoubtedly

Jan 1, 1955

By Will H. Coghill, Fred D. DeVaney, R. G. O’Meara

The size of ball mills in the ore-dressing industry has increased from about 4 ft. in each dimension to 10.5 ft. in diameter by 8 ft. in length. In the cement industry they are as long as 45 ft. Plainly the trend has been toward larger mills. The common belief is that the big mills economize in floor space and first cost, but the advantage with respect to friction has not been clearly defined. In the ball-mill studies at Rolla, Mo., laboratory mills as small as 2 by 2 ft. have been found as efficient in terms of the amount of grinding per unit of net power as mills 6 by 4 or 6 by 12 ft. Therefore, if supremacy can be claimed for the big mills, advantage must come from other sources. The advantage to be considered here is reduced loss by friction or dead load. In the study to determine whether big mills have relatively less loss by friction the commercial catalogs were used for fundamental figures. The dimensions and weights of Table 1 are taken from the catalogs (the last line gives data on a Rolla laboratory mill). The net power—that is, the power expended within the mill for grinding—is calculated by a new formula.' The assumed speeds are each at 70 per cent of their theoretical critical speeds, and the mills are loaded to the center with balls. In other words, they are assumed to be working under analogous conditions and are set for good grinding. In the last column the ratio B: A shows that the larger commercial mills are lighter per unit of net power than the smaller mills, and more of the motor output should therefore go into grinding. The laboratory mill seems to have some advantage over the larger mills; it would be expected to be light because it has no liners.

Jan 1, 1935

By Robert M. Dreyer

During the past two decades, synthetic abrasives have taken over successively greater percentages of the high-grade abrasive market, so that now, with the exception of natural diamonds (discussed in section 3.15.4C of this chapter), the importance of natural high-grade abrasives is negligible. The predominance of synthetic abrasives is indicated in Table 15.4A.1. This shows that the 1968 value of domestically produced synthetic abrasives (excluding synthetic diamonds) was over $80 million, whereas the value of garnet, the largest domestically produced, natural high-grade abrasive, was less -than $2 million. The major synthetic abrasives (other than synthetic diamonds) are: alumina, silicon carbide, boron carbide, tungsten carbide, and metallic oxides, including various iron oxides. A major advantage of synthetic abrasives is that the size and shape of grain can be closely controlled during manufacture. Although Table 15.4A.1 gives the average price of synthetic abrasives, such averages are of somewhat limited value. This is because the actual price varies within wide limits, depending on composition, hardness, size, and shape of grain. In 1968 the approximate total consumption of abrasives in the United States was valued at about $200 million, of which about two-fifths was in the form of synthetic abrasives (other than diamonds), one-third in synthetic diamonds, and the remainder in natural diamonds. Natural abrasive products, such as silica sand, tripoli, and pumice, are important in the low-cost abrasive field. Of the low-cost abrasives, silica sand continues to be the most important, with domestic production of about 300,000 tons at a value of $1.8 million (see Table 15.4A.1). In general, the lower the sales price of the abrasive product, the more limited is the market which can be served from a given production center. Each abrasive has applications for which it is especially useful, but there is a continual struggle among abrasive suppliers to induce substitution of one product for another. Such substitution can be stimulated by changes in method of preparation affecting hardness, shape, and size of grain.

Jan 1, 1976

By George F. Comstock

It has been known for many years that the alloy containing 90 per cent. copper and 10 per cent. aluminum can be hardened, like steel, by quenching from a suitable temperature, and that the hardened alloy can be softened again by annealing or drawing the temper. It does not seem to be generally appreciated, however, that the effect of the first slight reheating after quenching is actually increased hardness, the softening effect not taking place until a certain temperature of "drawing" has been exceeded. This paper gives the results of a few experiments on various specimens of cast 10 per cent. aluminum bronze, quenched for maximum hardness, and subsequcntly annealed at different temperatures. The hardness measurements were made with both a scleroscope and a standard Swedish Brinell machine; some peculiarities of the scleroscope test on this material are described. The author is not aware of many previous investigations of the hardness of this alloy when quenched and drawn, but two important papers on the subject should be mentioned. The earliest was by Portevin and Arnou,1 in which it was stated that tempering quenched 10 per cent. aluminum bronze at 400" C. increased the hardness as compared with the quenched untempered alloy and that reheating above that temperature ' was necessary to obtain any softening effect. A later paper was by Seidell and Horvitz,2 who mentioned Portevin and Arnou's work, but did not report any increase in hardness obtained

Jan 1, 1925

By M. R. Tek, K. H. Coats, D. L. Katz

A large number of boundary value problems encountcred in unsteady-state heat transfer, fluid flow through porous media, neutron diffusion and mass transfer involve the solution of a linear, parabolic partial differential equation commonly refcrred to as the diffusivity equation, where U is the dependent potential variable. K is the diffusivity (hydraulic, thermal, neutron, etc.) and 1 is the time variablc. Solutions to Eq. I are available in the literature for a wide variety of initial and houndary conditions. The great majority of these solutions are ohtained for geometric boundaries corresponding to linear. cylindrical or spherical flow models. A typical engineering application where the solution to Eq. 1 is required is the calculation of underground water encroachment across the boundaries of oil or natural gas reservoirs, In this particular area of application, the reservoir boundary is invariably approximated by circular geometry. However. the areal shape of many reservoirs can be better approximated by elliptic rather than circular boundaries. Thus the need for a general method of solving the diffusivity equation in elliptic coordinates arises in this problem as well as in other engineering applications involving elliptic boundaries. The solution to the diffusivity equation usually in volves the Error Function for the linear flow model, Bessel functions for the radial flow model and trigonometric or Legendre functions for the spherical flow model. It is well known that the general solution to the diffusivity equation in elliptic coordinates involves Mathieu functions. The significance of Mathieu functions in the analytical treatment of the diffusivity equation in elliptic coordinates is discussed in the literature However, these references do not providc analytical solutions useful in practical engineering problems. The objectives of this papcr are the development of the equations describing the unsteady-state liquid flow through a porous medium with an elliptic inner boun- dary, the development of a numerical method of solving these equations and, finally, a comparison of the water encroachment quantities calculated from the elliptic flow equation with those calculated from the radial flow equation. While the specific problem treated in this paper relates to unsteady-state liquid flow through a porous medium, the basic equations and computational techniques devcloped will apply equally well to problems occurring in the other areas of engincering interest mentioned previously. The solution given here is limited to a single case in which thc outer boundary encloses an area 100 times that of the inner boundary. DESCRIPTION OF THE FLOW MODEL Fig. 1 shows the flow model upon which the calcu lations presented in this paper are based. The inncr and outer houndaries of the flow model are represented by two confocal ellipses with major and minor axes, respectively, equal to 2a1, 2b1, and 2a, and 26,. The height of the elliptic cylinder flow model is denoted by 17. The following assumptions are employed in the development 01 the equations governing the unsteady-state liquid flow through the described flow model. 1. Uniform porosity and permeability throughout the flow model

By R. S. Burns, J. G. Erskine

The performance of the nine 5.5 m diameter x 6.4 m mills (18 x 21 ft) initially installed at Bougainville Copper Ltd. did not meet the laboratory and pilot plant derived design expectations as measured by Bond Work Index. During the post-commissioning period, inefficient grinding of coarse material resulted in a build-up of large circulating loads and led to reduced throughputs because of pump and cyclone overloading. Installation of larger pumps and cyclones and development of an improved circuit control philosophy alleviated materials handling problems and permitted higher tonnages to be attained. Since 1977, plant throughput has been increased by installation of three additional mills. These are 0.9 m (2.9 ft) longer than the other nine and have a higher capacity. Developments in classification and mill speed-up, together with a finer ball mill feed size and substantial improvements to mill availability (99% in 1982) have further increased plant capacity. There is a continuing emphasis on improving grinding circuit efficiency in terms of throughput/grind. Current development work includes trials of graded ball charges, different liner profiles, and assessment of scalping/regrind proposals.

Jan 1, 1985

By R. F. Domagala, M. Hansen, D. J. McPherson

On the basis of metallographic analysis, incipient melting data, thermal analysis work, and X-ray diffraction, phase relationships in the 0 to 50 atomic pct Cr region were carefully resolved. Phase relationships in the 50 to 100 atomic pct region were outlined. A single intermediate phase, ZrCr,, was established in the system. A eutectic and a eutectoid were found in the zirconium-rich region of the system, while a eutectic was located in the chromium-rich region. Limited solubility of chromium in both a and a zirconium was observed. THIS is another in a series of papers on zirconium-base binary phase diagrams based on a program sponsored by the Atomic Energy Commission. The Zr-Sn,' Zr-Si,' and Zr-Mo and Zr-W" systems have already been published. Previous work on the Zr-Cr system includes a partial diagram by Hayes, Roberson, and Davies' and a complete diagram by McQuillan." The phase relationships reported by these authors were determined with magnesium-reduced zirconium, whereas those reported herein are based on iodide metal. Some X-ray work on the intermediate phase in this system was also reported by Hayes et al., as well as by Wallbaum.' Comparisons with these data are made in the appropriate sections. Thermal analysis, metallographic and incipient melting techniques were employed to accurately resolve phase relationships in the 0 to 50 atomic pct Cr region, while the remainder of the diagram is outlined on a basis of cast structures and thermal analysis. A description and analyses of the metals used in the preparation of alloys for this study are included in Table I. A "low-hafnium" zirconium crystal bar (Westinghouse "Grade 3") was used. This material was produced by the decomposition of a volatile iodide onto a hot zirconium filament. The as-received crystal bar was coated with corrosion product from a standard autoclave test by which its grade designation is determined. A sand-blasting and subsequent HF-HNO, pickling treatment was employed to remove this contamination. The bars were cold-rolled to approximately 1/32-in. sheet, pickled again, sheared to 1/4-in. squares, washed with acetone, and stored for use. Ingot chromium metal from National Research Corp. and electrolytic chromium flakes from Johnson, Matthey and Co., Ltd., were available as alloy additions. The ingot chromium was received in granular form. The large granules were sized by crushing, treated for iron removal, rinsed with acetone, and stored. The flakes were broken to approximately 1/8 in. with mortar and pestle, cleaned with acetone, and stored for charging. Experimental Procedure A nonconsumable electrode arc furnace identical to that described by Hansen, Kessler, and McPher-son,' was used in this work. A 400 amp dc welding generator was the source of power. To insure homogeneity, ingots were melted in a water-cooled spun copper crucible, a total of four times without opening the furnace. No difficulties were encountered in the preparation of these binary alloys. Analyzed chromium contents were found to agree very well with the intended content. Melts of pure zirconium were interspersed in the course of preparing the alloys and their hardness was measured to keep a constant check on the melting technique. Vycor and quartz bulbs were used to contain the samples for isothermal annealing treatments. Vycor bulbs were employed for temperatures up to 110O°C, while quartz was used above this temperature. For treatments up to 950°C the bulbs were evacuated before sealing, but for higher temperatures a partial pressure of argon was admitted to the

Jan 1, 1954

By William A. Mitchell

AN X-ray diffraction pattern for "calcined cold precipitated ferric oxide" is reproduced dia-grammatically along with data for other iron oxides by R. C. Mackenzie.1' This pattern, which shows spacings higher than those for any other form of iron oxide, was obtained from material prepared and photographed at several different times over a period of weeks, but later attempts to reproduce the results were unsuccessful, the pattern of hematite being obtained every time.2 In an attempt to solve this problem, the original photographs showing the strange diffraction pattern were examined and a marked similarity to the hematite pattern was noticed, suggesting that the pattern was in fact due to hematite but corresponded to a shorter wavelength of X-rays than the Cu Ka which was assumed to have .been used. The eight strongest lines were provisionally identified with the strongest hematite lines and, by means of the corresponding hematite spacings, the X-ray wavelength was calculated for each line. This gave an almost constant value, with the exception of the innermost line which was somewhat diffuse, and confirmed the presence of hematite. The value obtained, 0.703 ± 0.015Å, corresponds to the molybdenum Ka wavelength. The X-ray tube used was a four-filament demountable tube with a copper target. Other photographs, mostly of soil clays, taken during the same period gave normal patterns of Cu Ka radiation with one exception. This was a calcined soil clay with a high iron content and also showed Mo Ka lines of the hematite structure. The explanation is almost certainly that the copper target was contaminated with molybdenum, but it is not known how this occurred. Specimens of alumino-silicates gave their normal Cu Ka pattern, but as the K absorption edge of iron is a little longer than the Cu Ka wavelength, specimens with a high iron content greatly reduced the intensity of the Cu Ka diffraction lines relative to that of the lines due to the shorter Mo Ka wavelength. The formation of hematite on calcining cold precipitated hydrated ferric oxide3 is thus confirmed. References R. C. Mackenzie: Investigations on Cold-precipi-tated Hydrated Ferric Oxide and its Origin in Clays. Problems of Clay and Laterite Genesis, p. 69, Fig. 4, F. AIME Symposium, St. Louis, Mo. Feb. 19-22, 1951. Published 1952. 'R. C. Mackenzie: Ref. 1. Note added on proof. V. C. Hansen and L. T. Brownmiller: Equilibrium Studies on Alumina and Ferric Oxide and on Combinations of These with Magnesia and Calcium Oxide. American Journal of Science (1928) 5, No. 15, pp. 225-242.

Jan 1, 1954

By J. Weertman

The paper of Gifkins and Snowden considers the interesting but difficult problem of determining the stress dependence of secondary (steady-state) creep at low stresses. These authors have concluded that at stresses below 250 psi (2 x 107 dynes per sq cm) the secondary creep rate of lead is proportional to the stress (viscous creep) and is not proportional to the stress raised to about a fifth power. The experimental data considered by them were obtained on tests conducted at room temperature and at 50°C. The lowest stress employed was 50 psi (3.5 X 106 dynes per sq cm). The authors pointed out the main difficulty in determining the stress dependence of creep at low stresses. The creep tests must be run for very long lengths of time. However they made no estimates of when an experimental creep rate determination must be rejected because it does not represent a true steady-state or minimum creep rate. In order to be certain that a creep curve is within the steady-state region, the total creep strain should be of the order of 0.1 to 0.2. For a creep test of a year's duration this requirement implies that a secondary creep rate smaller than about 10-3 per hr cannot be measured reliably. The corresponding creep rate for a 10-year test is 10-6 per hr. The creep rates of the tests that were considered by the authors to prove the existence of viscous creep were of the order of or less than 10-6 per hr. One can conclude reasonably that this data does not prove unambiguously that large strain steady-state creep rate of lead is proportional to the stress in the stress range of 50 to 250 psi (3.5 x 106 to 2 X 107 dynes per sq cm). Another technique can be used to obtain the stress dependence at low stress levels. The creep rate is a very sensitive function of temperature. The creep rate can be increased by very large amounts merely by increasing the temperature. We carried out steady-state creep tests on lead single crystals25 at temperatures up to 320°C. We were able to obtain creep rate data down to stresses as low as 35 psi (2.5 x 10' dynes per sq cm). Our smallest creep rate was 8 x 10-5 per hr. Thus we obtained large strain, steady-state creep rates to even lower stresses than were considered by Gifkins and Snowden. No evidence was seen for viscous creep. The creep rate was proportional to the stress raised to about a 4.5 power down to the lowest stresses. Since there is no reason to believe that changing the temperature should change the stress dependence of steady-state creep, we feel that large strain viscous creep does not occur in the stress range quoted by the authors for lead single crystals or large-grain polycrystalline samples of lead. This conclusion does not imply that viscous creep may nat occur in a lower stress range or in the same stress range for fine grain material or at creep strains very much smaller than 0.1. Support by the U.S. Office of Naval Research is acknowledged. Authors' Reply R. C. Gifkins and K. U. Snowden We thank Dr. Weertman for his discussion and although, as we hope to show, we do not agree with his reservations, we do concur in stressing the importance of ensuring that creep rates are reliably obtained. Dr. Weertman appears to be content to accept n = 1 for low stresses with fine-grained material but not for single crystals. We believe our results show that the former result cannot be accepted without also accepting the latter. We will also show that the probable errors in our minimum creep rates are insufficient to alter our conclusions, that the criterion proposed by Dr. Weertman is arbitrarily restrictive and his alternative experimental approach possibly invalid. 1) A principal result of our Fig. 1(a) is that n = 1 for polycrystalline specimens at room temperature and 50°C for stresses below -250 psi. There was evidence that crystal slip and grain boundary sliding contributed approximately equaily to the overall strain in this low-stress regime. This implies that either a) grain boundary sliding controls slip within the grains or b) both grain boundary sliding and crystal slip independently occur according to mechanisms which give n = 1. Alternative a does not seem acceptable, so we were forced to consider b. This led us to reexamine work on bicrystals by Strutt and Gifkins and plot curves Fig. l(b). Previously Strutt et al. (loc. cit.), had merged these points with others using the Zener-Holloman parameter and thus, we now believe, had been led to overlook the behavior where n = 1. Curves C and D in Fig. l(b) did appear to confirm the hypotheses that n = 1 for crystal slip at these low stresses and the sliding curve F was similarly of the expected form. It was comparatively easy to find a quantitative theory to account for n = 1 for sliding and the similarity of curves C and D to curve F (all obtained from the same set of specimens) led us to feel that the single-crystal curves were valid. 2) We believe the secondary creep rates for both the polycrystalline and single-crystal specimens to be in error by factors c2. In Fig. 6 creep curves for polycrystalline specimens of lead(1) and lead(II) are reproduced as curves a and b, respectively, and curve c is for a single crystal at 100 psi. It is clear that, although the attainment of secondary creep rate takes 2 years for a and 150 days for b, thereafter the curve is linear for periods of 7 and -1 year, respectively. The single crystal has a linear portion commencing after 20 and extending to 90 days. Creep extension was measured directly using a traveling microscope reading to 0.01 mm on gage lengths marked on the specimens; the gage lengths

Jan 1, 1968