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By R. C. Mahon

THE importance of ground water control in glacial drift overlying mines is widely recognized. Adequate handling of the problem results in considerable saving in overall pumping costs, as the cost of pumping the larger quantity of water under low heads from surface wells is more than offset by the decrease in the quantity of water to be pumped from the mine under high heads. Eliminating or partly reducing seepage of water through the ledge reduces moisture content of the ore, a factor especially important in iron ore mines, where a reduction of 1 pct in moisture effects a very material saving. An important though indeterminate saving is also brought about by the elimination of water in the working places underground. The Homer and Wauseca mines of Hanna Coal & Iron Co. at Iron River, Mich., cover 480 acres. When these mines were started it was possible to operate on only one 40-acre tract, as the depth of water over the remainder of the property was too great to permit operation. Although the average depth of the ground water over the area being mined at that time was less than 50 ft it was necessary to pump 1200 gpm from the mine, the greater part from a depth of 750 ft. The slate footwall and graywacke hanging wall are almost impervious, and it was apparent that seepage into the mine was mainly through the iron formation in which the orebodies were located. Analysis of the water in the iron formation showed it to be of the same character as that in the glacial drift, while the water in both walls was heavily mineralized, also indicating that the water passed much more freely through the iron formation. The first attempt to take off the water above the ledge was by means of drainage drifts driven 15 to 20 ft below the ledge, Fig. 1. Various schemes were used to get the water into these drifts: 1—Holes 15 to 20 ft long were drilled from the back of the drifts to the ledge, but these were difficult to drill and blocked easily. 2—Sections of the drifts were blasted down. This gave a large flow for a time but eventually almost total blockup occurred. 3—Raises 4x4 ft were driven above the drifts to within 8 ft of the

Jan 1, 1955

By G. H. Matheson, J. M. W. Mackenzie

The flotation rate of coal has been studied using a continuous laboratory flotation cell and a multiple exposure photographic technique. The effects of particle size, reagent additions and cell turbulence on the flotation rate of coal have been investigated. The results have been analyzed in terms of current theories of particle bubble encounter and adhesion. The rupture forces which occur during particle bubble encounter have been shown to have an important effect on the flotation rate of coarse coal particles. The flotation of coal is a time dependent process, and in order to obtain a complete understanding of the operation it is necessary to determine the kinetics of the process. In coal flotation, the flotation rate and the associated values of cell productivity in terms of tons per kilowatt-hour and tons per cubic foot of cell volume are of greater importance than in most other mineral flotation operations. The reasons for this are associated with the low unit value of coal and the relatively high cost of coal flotation compared with other coal cleaning processes. An important aspect of coal flotation kinetics is the design of coal flotation cells. The cells used in many coal cleaning operations are often replicas of those used for the treatment of sulfide ores and are not necessarily suitable for the treatment of coal washing pulps, which usually contain a higher percentage of coarse and floatable material than the sulfide pulps for which the cells were designed. This disadvantage of many coal flotation cells has been recognized by Russian engineers who, by the addition of baffles to their subaeration coal flotation cells have increased the cell capacity by 100%. Investigation of the variables which influence flotation kinetics and cell productivity are, therefore, important to the coal industry where flotation is the only accepted method of cleaning the fine (-1/2mm) coal. The kinetics of the flotation process have been investigated in detail by Schumann10 who developed a continuous flotation cell which permitted the study of flotation under steady state conditions. This technique has been used by Gaudin et a1.,6 Brown and Smith and recently by Jowett and Savfi.7 The latter authors have developed a refined mathematical treatment for interpreting the results of continuous laboratory tests. Attempts have also been made to study flotation kinetics using conventional batch testing techniques. The experimental difficulties, however, and the problems of determining the order of the flotation rate process have made this technique of dubious value. A summary of the proposed rate equations for batch testing and the difficulties associated with this technique is given by Brown and Smith. 2 The experimental techniques described above are concerned with the rate of production of froth product. However, several authors, notably Sutherland, 11 Bogdanov1 and Philippoff, 9 have analyzed flotation

Jan 1, 1963

By Chu-Phay Yap

This is the second of a series of theoretical papers on the iron-carbon system. The solidus lines obtained as a result of the different methods of investigation fall naturally into three classes; namely, (1) a straight solidus originally suggested by Roozeboom and supported in the main by the work of Carpenter and Keeling, Andrew and Binnie, et al., using the thermal analysis method; (2) a slightly curved solidus obtained by Honda and his associates, using the magnetic and resistance methods: and (3) Gutowsky's solidus obtained by the Heycock and Neville method of quenching at successively higher temperatures. Although the thermodynamic method as shown in the first paper indicates that the straight solidus line is correct, no explanation has ever been advanced to account adequately for the disagreement in the shape and position of the solidus lines obtained. The nature of the solute in austenit.e is theoretically discussed. On the basis of such discussions, the data obtained by Honda and Endo on the change of magnetic susceptibility of steels with respect to temperature were critically subjected to a graphical analysis, which is shown to yield a rational explanation of the curved solidus lines.

Jan 1, 1931

By N. H. Murlenberg, T. M. Drown

It is often a tedious matter to get a solution of pig iron or steel, for the determination of phosphorus, which is absolutely free from silica. Where pig iron rich in silicon is dissolved in hydrochloric or nitric acid in the usual procedure, it is necessary, not only to evaporate the solution to complete dry ness, but to heat the dry residue for some beam in an air-bath to a temperature of about 120° C. The oxide of iron is thus rendered insoluble in nitric acid, and is only slowly dissolved by hydrochloric acid. In the method of determining silicon by nitric and sulphuric acid, described in the Transactions of the Institute, Vol. VII, page 346, arid Vol. VIII, page 508, we obtain in one or two hours a solution of the iron in the form of ferric sulphate entirely free from silica, and containing free sulphuric acid. It occurred to Us that this solution might be made available for the determination of the phosphorus by the molybdate method. The following experiments mere tried with unsatisfactory results. 1st. The iron was precipitated by ammonia, the precipitate filtered, washed, and dissolved in nitric acid. 2d. The iron was precipitated as basic acetate and dissolved in nitric acid. 3d. The solution was neutralized by ammonia, and nitric acid added in small excess. In all these cases the phosphorus obtained by precipitating by ammonium molybdate and magnesia-mixture was too low. The following method was then tried with success. The filtrate from the silica and graphite was evaporated to small bulk and heated in a porcelain dish on a sand-bath. until fumes of sulphuric acid ceased to escape. The dry residue was taken up with dilute nitric acid and the solution precipitated by ammonium molyldate. The phosphorus was weighed as magnesium pyrophosphate. The results were satisfactory. To save time, the original solution of the iron in nitric and sulphuric acids was evaporated to dryness and heated as before until

Jan 1, 1882

By J. C. Wilhoit, J. B. Cheatham

Although an oil well is a long cylindrical hole with an irregular bottom, it appears likely that the nature of the stress concentration at the bottom of the hole can be ascertained from an analysis of the stresses around a short cylindrical cavity with rounded comers and smooth bottom. Such a cavity is studied primarily because it leads more readily to a solution to the problem by the use of stress functions. In this paper the stress distribution around a short cylindrical cavity subjected to bit loading, overburden and drilling-fluid pressures is determined by means of an analytical solution which approximately satisfies the boundary conditions of the problem. From this solution the stresses at the corner of the hole are calculated to be about 35 per cent lower than comparable results obtained by photoelastic and relaxation analyses. This difference is apparently due to the large radius of curvature at the corner of the cavity in the present analysis. Since good agreement is obtained between the results of this analysis and the stresses calculated for a similar loading on a semi-infinite elastic solid, it is concluded that the bit action in the region near the center of the hole is not appreciably affected by the presence of the sides of the hole. INTRODUCTION Much has been written concerning drilling "under down-hole conditions" and pertaining to the stress distribution in the rock at the bottom of an oil well.1-5 For example, it is known that identical rocks can be drilled more rapidly at the surface than under subsurface conditions of pressure and stress.6 Information on the behavior of rocks under loading can be obtained from triaxial test data.7-9 From such tests it is found that rocks exhibit brittle failure when the confining pressure and pore pressure are equal, but the mode of failure may change to ductile as the difference between the confining pressure and the pore pressure is increased. Brittle failure implies that there is very little permanent deformation before fracture, whereas ductile failure indicates that permanent deformation takes place before fracture. Some rocks are ductile at differential pressures of 5,000 psi , but other rocks are brittle even at differential pressures of more than 50,000 psi. Cuttings embedded in mud at the bottom of the hole may act as a plastic mass which the bit teeth must penetrate in order to attack the virgin rock below. 10 During drilling, the mud pressure acts as the confing pressure, and in many cases the difference between the mud pressure and the formation pore pressure IS sufficiently low so that the rock most likely falls in a brittle manner. Very little penetratiori by the bit teeth may be required for brittle failure of the rock. For these brittle materials, the elastic stress distribution is of practical interest in determicing the possible effects of a given loading on failure. The penetration of bit teeth into ductile or plastic rock has been analyzed previously ll,12 and will not be considered further in the present work. During actual drilling, many teeth act at various points ovel an irregular hole bottom. In the present analysis a solution is obtained for an idealized problem of determining the elastic stress distribution caused by only one tooth acting alone at the center of a smooth hole bottom. It obviously is not proposed that any driller should put a special one-tooth bit on bottom, but it is hoped that extensions of the simpler problems can eventually lead to a better understanding of more complex actual drilling phenomena. To obtain a solution by the use of stress functions, a short cylindrical cavity with rounded corners and smooth bottom is studied. The solution to this problem should give an insight into the nature of the stress concentration at the bottom of an oil well which is in reality a long cylindrical hole with an irregularr bottom. After selection of the proper curvilinear co-ordinate system, the stress functions are expressed as series of Legendre polynomials. The coefficient of each term in the series is then determined to satisfy the boundary conditions at a finite number of discrete points on the boundary of the cavity with least square error. Results are compared with bottom-hole stresses obtained by photoelastic and relaxation analyses.

By W. R. Wawersik, A. M. Starfield

The classical approach to room-and-pillar mine design in flat-lying, tabular ore bodies limits itself to the special case of an extensive and uniform system of pillars. Each pillar is then assumed to carry the same load, and this load is readily calculated from the extraction ratio e and the weight of the overburden : average pillar stress = [ ] where H is depth below surface, p is average density of overburden, and g is acceleration due to gravity. The average pillar load does not, in this case, depend on the mechanical properties of either the pillars or the surrounding rock mass. The only relevant physical property of the pillars is their compressive strength, (i.e., the maximum load-carrying ability) and the criterion for design is that the average pillar stress should not exceed this strength. The wider the pillar, the greater its strength, and the design of the system is concerned with reconciling this increase in strength to the requirements of roof control so as to optimize extraction.l Any departure from a uniform distribution of pillar loads invalidates the classical approach. Such departures may, for instance, be brought about by: (1) a nonuniform layout of pillars and remnants resulting from selective mining, (2) variations in geology which result in gross changes in the properties of part of the seam or the host rock, (3) deliberate use of abutment support in narrow panels, and (4) the use of yielding pillars for local roof support in conjunction with barrier pillars to carry the overburden load.

Jan 1, 1972

By M. P. E. Desvaux, P. Charsley

OLIP-line observations on copper alloys, using the electron microscope, have been made by a number of workers,13 but this work has been confined to a brass. In a CuAl alloys Koppenaal4 and Koppenaal and Fine5 have made observations with the optical microscope and by the use of interferometry. They found that the observed slip step heights inside the Liiders bands accounted for only 42 pet of the total macroscopic strain. The suggestion was put forward that optically unresolvable slip in other parts of the specimen accounted for a major part of the macroscopic strain. This is surprising since it is known from other workers that slip in a brass is inhomogeneous; i.e., large amounts of slip occur on individual {lll) closelys paced than being shared by a large number of closely spaced planes. Furthermore, a brass and a CuAl alloys with high concentration of aluminum exhibit similar deformation characteristics and slip-line patterns. Prior to investigations into the behavior of copper and a CuAl alloys under reversed stresses in tension and compression, some preliminary experiments have yielded results which the authors think resolve this discrepancy, and throw some further light on the behavior of a CuAl in tension. An experiment was carried out on a 10 at. pet CuAl single crystal, of gage length 7.5 cm, diameter 3.1 mm, and orientation shown in Fig. 3 (inset), for the purpose of resolving the above discrepancy. The specimen gage length was electropolished for 10 min in a 50:50 orthophosphoric acid (SG=1.75)-distilled water system, with 2 v across the cell and a current density of 0.5 amp per sq cm. The cathode was made of copper. After a tensile strain of 0.067 ± 0.001, intense slip was observed over a length 2 cm of the gage length whilst the rest of the specimen was relatively undeformed. In the lightly deformed region, slip bands of mean width 20 /x were spaced about 1 mm apart on average. The transition from the heavily slipped region (usually called a Liiders band) to the lightly deformed region was gradual, the slip-band density increasing as the "Liiders band" was approached. In the latter, the slip bands became so close together that, to the naked eye, the specimen appeared to be continously slipped, and the typical microtopography of this region is shown in Fig. 1. Twelve electron micrographs were taken at random from replicas of the Liiders-band region, and the widths of the slip lines were measured. The slip lines account for an over-all tensile deformation of 7.0 ± 0.7 pet, after allowing for the lengths of the un-slipped regions, which is in good agreement with the macroscopic strain. The distribution of slip-line widths was also measured and is shown in Fig. 3. Since Koppenaal could not resolve slip lines with height less than 540A (limit of resolution represented by dashed line), then it was deduced that he could have measured only about 50 pet of the deformation within the 'Liiders Band'. It is concluded, contrary to the suggestion of Koppenaal,5 that virtually all the macroscopic strain is accommodated within the "Luders band" and that there is no need to invoke fine slip distributed uniformly over the gage length.

Jan 1, 1967

By Robert E. Delavault, Harry V. Warren

Circumstances determine whether it is better to make analyses in the field or in a permanent laboratory. The rubeanic acid test described in this article has been designed primarily for field use: it is simple and virtually foolproof, and it requires a minimum of field kit.* It is sensitive, easily detecting 4 ppm of readily extractable copper in a soil. This is by no means a quantitative test, but it is accurate enough to provide a valuable indicator of copper anomalous areas for both prospectors and field geologists. The easiest method for detecting metal deposits that do not produce visible float or stains is to make a simple chemical test for the metal in overlying soil, or in the silt of a stream that may have picked up metal farther upstream.

Jan 11, 1958

By E. J. Roberts, E. B. Fitch

THE mechanism of classification by settling pools is most simply shown in the case of batch sedimentation such as was analyzed by Oden.1 The batch model will be considered, therefore, and it will be shown that the same mechanism applies to continuous operation. Classification in Batch Settling Pools: Consider a beaker or tank of slurry containing particles so dispersed that they can settle independently of one another under the influence of gravity. Originally all particle sizes are uniformly distributed throughout the suspension. All particles start immediately to settle towards the bottom at rates determined by their size, shape, and density—among other factors. Particles reaching the bottom settle out of suspension. After some given time the slurry above the deposited solids is siphoned off or otherwise removed, leaving the deposited solids behind. The deposited solids, together with entrained and any unremoved supernatant slurry, represent the underflow of a classifier. The slurry removed represents the overflow. There is a certain separation, size of particle which during the sedimentation has just time to settle from the top surface of the slurry to the level at which underflow and overflow are parted. All particles with a faster settling rate will have dropped to below this level, no matter where in the beaker they started from originally, and therefore will be absent from the overflow. Particles with a slower settling rate will not reach this level if they started from the top of the slurry, but a portion of them,

Jan 1, 1957

By H. S. Bell

IT SEEMS unnecessary to dwell upon the advantages of the modern pipe still as compared with the older type of distillation equipment used by oil refiners. The relatively low installation cost, coupled with remarkable operating efficiencies of pipe stills, precludes the consideration of other types except in rare instances where some peculiarity of product or plant may have an influence. The question of the actual heat required to distil petroleum is quite involved. We have extensive data on the latent heats of the various hydrocarbons under different conditions of pressure. We also have information regarding the specific heats of various oils and the effect of temperature thereon. Because of the complexity of petroleum and of each fraction, it seems impossible to theoretically analyze the partial-pressure effect of the great number of hydrocarbons upon one another during distillation. If a distillation curve and percentage analysis of any crude or product are available, it is possible to construct a curve with ordinates representing per cent. distilled and B. t. u. per pound or per gallon, or other desired unit. To do so the crude is split into fractions, of 5 or 10 per cent. The boiling point and gravity of each fraction being determined, it is possible to evaluate the heat required. As each fraction is removed, the residue must be raised to a higher temperature and latent heat supplied for the successive fraction. As the calculations progress, the latent heats decrease while the specific heats increase. Such a curve is illustrated by Fig. 1 for a typical 39.9 B° North Texas crude.

Jan 1, 1928

By H. R. Tunnell

Every one connected with a mine knows that it is hard to keep down the costs of moving ore from the place where it is broken to the shaft or portal. Considered broadly, the subject of handling would cover all work done in a mine, but here it has been limited to handling ore in stopes and drifts, through chutes, and on levels. Good ventilation and a strict enforcement of rules for the prevention of dust safeguard the health of the men and lower transportation costs. Handling ORe in Stopes and Drifts The object of all stoping is to mine ore of good grade at low cost. In Butte, most of the ore is mined, from veins dipping from 60° to the horizontal to those which are vertical, by means of square-set, rill, timbered-rill, and back-filling stopes. When blasted, a part of the rock is carried by gravity to the grizzlies over the chutes, the rest is shoveled. Rock, when broken in a stope, may be deflected by inclined floors or slides toward the top of a chute leading to the level below. Ore broken clean enough to ship should be carried, by the force of its fall, into a chute or.as nearly into that chute as the safety of the stope and the men permits. Ore that requires sorting, about 80 per cent. of all ore mined, is caught on a grizzly and the waste picked out. Waste rock broken in a stope is used to fill that stope and should be blasted into the gob with as little handling as possible. About two-thirds of all the ore mined in Butte comes from square-set stopes; this method was used in nearly all cases until 1912, when the rill method of stoping was introduced in the Tramway mine, of the Anaconda Copper Mining Co. The shoveling and timbering costs in square-set stopes are high when compared with the costs in the rill stopes. All the ore cannot be carried to the chute, in falling from place, unless the chutes are very close together or the distance from the back of the stope to the top of the chute is sufficient to slide all the ore broken. The number of chutes is limited by the tendency of the ground to cave; if carried too close together the stope is weakened. Small stopes, or blocks,

Jan 1, 1923

By H. R. Tunnell

Every one connected with a mine knows that it is hard to keep down the costs of moving ore from the place where it is broken to the shaft or portal. Considered broadly, the subject of handling would cover all work done in a mine, but here it has been limited to handling ore in stopes and drifts, through chutes, and on levels. Good ventilation and a strict enforcement of rules for the prevention of dust safeguard the health of the men and lower transportation costs. Handling ORe in Stopes and Drifts The object of all stoping is to mine ore of good grade at low cost. In Butte, most of the ore is mined, from veins dipping from 60° to the horizontal to those which are vertical, by means of square-set, rill, timbered-rill, and back-filling stopes. When blasted, a part of the rock is carried by gravity to the grizzlies over the chutes, the rest is shoveled. Rock, when broken in a stope, may be deflected by inclined floors or slides toward the top of a chute leading to the level below. Ore broken clean enough to ship should be carried, by the force of its fall, into a chute or.as nearly into that chute as the safety of the stope and the men permits. Ore that requires sorting, about 80 per cent. of all ore mined, is caught on a grizzly and the waste picked out. Waste rock broken in a stope is used to fill that stope and should be blasted into the gob with as little handling as possible. About two-thirds of all the ore mined in Butte comes from square-set stopes; this method was used in nearly all cases until 1912, when the rill method of stoping was introduced in the Tramway mine, of the Anaconda Copper Mining Co. The shoveling and timbering costs in square-set stopes are high when compared with the costs in the rill stopes. All the ore cannot be carried to the chute, in falling from place, unless the chutes are very close together or the distance from the back of the stope to the top of the chute is sufficient to slide all the ore broken. The number of chutes is limited by the tendency of the ground to cave; if carried too close together the stope is weakened. Small stopes, or blocks,

Jan 1, 1923

By Eugene P. Pfleider

Research indicates that the cube diamond is a superior stone for drill bits. It can be oriented to combine a long cutting edge with structural strength and high resistance to wear. Test bits set with preferred orientation give double the bit life at astoundingly low diamond loss in comparison to oriented octahedral diamonds.

Jan 10, 1953

By Charles Catlett

THE rapid development of the Portland-cement industry implies that the country is being very carefully searched for material suitable for its manufacture. Such material can be found at a great many places ; but deposits thoroughly satisfactory in chemical composition, and at the same time meeting all the other requirements connected with the economic production and profitable marketing of the product, are exceedingly few, if I may judge from the investigations which I have had to make in a number of States. The raw mixture which by its clinking and grinding forms Portland cement contains approximately 75 per cent. of carbonate of lime. This is found in nature as limestone or marl. The natural rock commonly carries either more than the required percentage of carbonate of lime (in which case it has to be reduced by suitable admixture of clayey ingredients) or less-in which case purer lime carbonate has to be added. The controlling ingredient, therefore, is carbonate of lime, or limestone of the right composition. Among the most serious difficulties is that of finding limestones low enough in magnesia to meet the exacting requirements of certain specifications. All engineers recognize that there is a limit beyond which it is not safe to let the magnesia go; but within that limit there is considerable difference of opinion. Until that difference is finally settled, no one would be willing to invest the large sum of money necessary for a Portland-cement plant, if it were not certain that the usual requirements in this particular could be satisfied. The usual limit in well-established specifications is 5 per cent. of magnesium oxide in the finished cement, but many specifications limit the amount to 3 per cent. These figures

Jan 9, 1907

By Glenn M. Boyce

This paper discusses the results of a laboratory testing pro- gram to determine the validity of hydraulic fracturing stress measurements in salt. Tests were performed on 15 cm diameter samples loaded under hydrostatic stress conditions to determine the influence of time, confining pressure, flow rate, borehole diameter, and packers on breakdown pressure. Tests were also performed in a polyaxial loading frame to determine whether or not hydraulic fracturing could be used to measure non-hydrostatic stresses. The test results indicate that the breakdown pressure is not affected by time delays of up to 64 hours between the application of load and fracturing the rock. Breakdown pressures were found to fall short of predicted elastic values at higher confining pressures for the hydrostatic tests. The ratio of the horizontal stresses in non-hydrostatic tests had no effect on breakdown pressures. Flow rate and borehole diameter variations were found to have a marked effect on breakdown pressures. Shut-in pressure values, which are generally used as an indication of the minimum stress value, exceeded the applied minimum stresses by 10 to 60% depending on the method of determination used. The lack of a relationship between breakdown pressure and horizontal stress ratio may preclude hydraulic fracturing from being used in salt as it is conventionally applied in brittle rocks.

Jan 1, 1984

By J. Spotts McDowell

Preparation and Use.-Magnesite is an important refractory in open-hearth, heating, and electric furnaces for steel-making and in many of those employed in the metallurgy of copper and lead. It is sold in the form of brick, finely ground "furnace magnesite" for brick-laying, and dead-burned grains for making and repairing furnace bottoms. The latter are a mixture of granules varying in size from pieces of about 5/8 in. (1.6 cm.) diameter to very fine but sandy particles. Dead-burned magnesite results from calcining 'the crude or lightly burned mineral at a temperature that will not merely drive off practically all the CO2, but will also cause sintering of the particles. During this process the pieces shrink considerably and become hard, dense, and inert to atmospheric moisture and C02; under-burned material, on the other hand, will hydrate on exposure to the air. A small percentage of ferric oxide seems to be necessary for the production of a satisfactory sinter; from 4.5 to 8 per cent. in the dead-burned grains is considered the most desirable amount. Dolomite has been little used for brick-making in the United States, but it is prepared for use in the granular condition calcined or "double-burned" and is the principal ingredient of several materials offered for sale under various trade names for refractory purposes. Dolomitic refractories are almost wholly confined to the open-hearth and electric furnaces, where they are used for fettling and as substitutes for magnesite. Much more magnesite and dolomite are used for basic open-hearth steel-making than for all other refractory purposes. The hearth of the furnace is usually built up of magnesite brick and dead-burned grain magnesite so laid that the brick base is protected by a working bottom of the granular material. The latter is sintered into place in layers 1 to 2 in. (2.5 to 5 cm.) thick to a total depth of 12 to 18 in. (30 to 45 cm.) at the center of the furnace. After each heat, burned dolomite is thrown against the banks as high as it will stick, and all holes in the bottom are filled. At most plants such holes, at the end of each week, are also

Jan 2, 1919

By Stanley L. Lopata, Eric B. Kula

The problem of preferred orientation has been considered in quantitative phase analysis by X-ray diffraction techniques. The average intensity of a diffraction peak can be obtained by integration over the whole pole figure, or by random rotation of the specimen in the X-ray beam, or by a combination of both. For rod or wire, where the pole figure shows rotational symmetry, the intensity is measured along a radius of the pole figure. Where no symmetry is present, rotational symmetry is imparted by rapid rotation of the sheet around its surface normal during measurement. These methods are applied to the determination of aus-tenite in an Fe-31 pct Ni rod and Fe-28 pct Ni sheet. X-RAY diffraction techniques are frequently used for quantitatively determining the relative amounts of two or more phases present in a structure.1,2 Briefly, the method requires a measurement of the intensity of a Bragg reflection for each phase. The method is based on the principle that the intensity of a Bragg reflection, IA, is directly proportional to the volume fraction of the given phase present, CA: T KRACA/2µ [1] where K is a constant independent of the diffracting phase, RA can be calculated and depends on the Bragg angle ? and the particular reflection measured, and µ is the linear absorption coefficient of the mixture.' For a mixture of two phases A and B, IA = RAcA [2] IA/IB=RAcA/Rbcb and CA+ CB = 1 [3] This allows the volume fraction of a phase to be calculated directly from the measured integrated intensities of the two phases present. This method is frequently used for quantitatively determining retained austenite in steels, but can be used for the quantitative determination of in titanium alloys, as well as phases in other alloy systems. The intensities are generally measured by diffracting only from planes whose normals are perpendicular to the specimen surface, with the implicit assumption being made that this intensity is typical of reflections from planes whose normals lie at other angles to the surface. If the specimen contains a texture or preferred orientation of the crys- tallographic planes by virtue of previous mechanical working, however, this measured intensity is correct only if the intensity level fortuitously is one times random. Examination of pole figures for actual rolled sheet shows that the intensity level at the center of the figure is seldom at the random level, and can very easily differ by a factor of five or more, leading to a commensurate error in the calculated amount of the phases. Textures have been commonly found in materials which are cold-rolled or recrystallized after cold rolling. This problem is becoming of greater importance since structural materials in use today, such as the high-strength stainless steels, frequently are further strengthened by cold rolling, and hence contain textures. Although high-strength carbon-containing alloy steels generally do not contain textures, some of the newer thermomechani-cal treatments will impart a texture even in these cases. In the case of hexagonal metals, such as titanium, probably every wrought sample will show some anisotropy. Since the standard X-ray techniques are inapplicable in all these cases, there is a clear need for some method of taking this anisotropy into account. The specific problem is to obtain the integrated intensity of a Bragg reflection for each phase, averaged over all orientations of the sample with respect to the X-ray beam. This can be done either by purely mechanical means or by a mathematical averaging. Mechanically, a small spherical speci-

Jan 1, 1965

By J. A. Herbst, D. W. Fuerstenau

The effect of mill speed and ball load on the dry ball milling of dolomite is examined in the context of the batch grinding model. Observed changes in the parameters of the model are interpreted, as far as possible, in terms of the mechanics of particle motion in the mill. A parameter estimation scheme previously proposed by the authors is shown to provide the basis for a successful simulation of grinding behavior over a wide range of mill speeds and ball loads. Finally, a combination of experimental and simulated results is used to determine the optimum mill speedball load for closed circuit grinding in this mill-material system.

Jan 1, 1973

By R. D. Reiswig

An increasing amount of high-temperature metall~?~gical research is carried out in resistively heated tube furnaces in which a bare specimen is suspended by a fine wire at the midpoint of the tube. It is shown that the assumption of near-blackbody conditions on the surface of the sample may give rise to errors in optical pyrometry of 50°C or more. A number of papers published in the metallurgical literature in recent years have described the use of high-temperature tube furnaces for heat treatments, melting-point determinations, and other work. Typically, the tube is of a refractory metal with open ends, is heated by the passage of an electric current, and has concentric cylindrical radiation shields outside it. In at least one of these,' the specimen is contained within a crucible having a small hole in its lid through which optical-pyrometer measurements are made under essentially blackbody conditions. In another design,* the specimen is inside a muffle which is concentric with the heater tube and which contains a number of washerlike longitudinal radi- ation shields to reduce axial temperature gradients and to give conditions near the specimen closer to those of a black cavity. Yet another design3 employs a wire specimen coaxial with the heater tube. Blackbody conditions are simulated by passing current from a separate supply through the wire until it "disappears" against the background (the inside of the heater tube) as seen through a radial spy hole in the tube. Good agreement with known melting points is achieved when an optical pyrometer is used under such disappearance conditions as the melting point is approached. That this latter method works so well is due, evidently, to considerations such as those mentioned by Dike4 and others.5-8 A more common method than the above, however, has been the suspension of an uncovered specimen by a fine wire in a resistively heated tube with open ends. A radial spy hole about midway between the ends of the tube permits optical-pyrometer observations on the specimen, the inside of the tube, or both. So observed, the specimen typically appears to differ but little in brightness temperature from the inside of the tube. According to De vos9 the radiation from such a spy hole in an empty tube of reasonable 1ength:diameter ratio (e.g., 10 or greater) should be essentially blackbody radiation. For these reasons, apparently, descriptions of work carried out in such furnaces usually include a statement to the effect that conditions surrounding

Jan 1, 1964

By J. J. Arps

This paper is a study of the effect of temperature on the electrical resistivity of sodium chloride solutions based on the published resistivity and density data in the International Critical Tables. This temperature effect is of considerable importance in quantitative interpretation of electric logs, where it is frequently necessary to correct mud resistivities measured under surface conditions to temperatures existing at the bottom of the bore hole. An empirical approximation formula was developed for this conversion which has proved to be very useful and seems to provide results well within the range of accuracy of the data involved. This approximation formula states: sistivities of sodium chloride solutions at temperatures of t and t degrees Fahrenheit, respectively. INTRODUCTION Research by various investigators during the past 20 years has clarified the physical principles of the phenomena which cause the natural or spontaneous electric potential in rotary drilled bore holes. The basic relationship which is most commonly used reads: in which the SP deflection, as measured from the shale base line, is expressed in millivolts. K is a constant, which appears to vary between 50 and 110; the low value applying to shaly sands, whereas the higher values are more common in carbonate rocks. A good average value for K = 70. for which value there is considerable theoretical justification." In order to calculate the resistivity of the connate water R and to estimate its "equivalent salinity" (as NaCl) from an electric log by means of this SP relationship from a knowledge of the static self potential and of the resistiv- ity of the mud filtrate R it is necessary to first correct the resistivity of the mud filtrate measured under surface conditions to the resistivity of this same mud filtrate in the well bore at a different temperature. In order to make this temperature conversion for the mud filtrate the variation of the electrical resistivity of sodium chloride solutions with temperature is commonly used. Since some discrepancies were found in the charts ordinarily used for this purpose, it was felt desirable to make a new study of this relationship based on the published measurement data. Because of the fundamental nature of these relationships and as an aid to other workers in this field, an attempt has been made in this study to show every step in the calculations. CONDUCTIVITY VS MOL CONCENTRATION The most complete published reference on the temperature relationship of sodium chloride solutions of different concentrations is provided in the International Critical Tables.' The basic measurement data on the electrical conductivity of aqueous sodium chloride solutions, at different temperatures, as given in these tables, are reproduced in Table 1. The electrical conductivity values in this Table 1 are expressed as 10' times the specific conductivity k in ohm-'cm'l per unit of concentration in milligram mols per liter of solution C, or: RESISTIVITY VS MOL CONCENTRATION These conductivity values from Table 1 were first converted to the corresponding electrical resistivity values (R) , expressed in ohm-meters, as is conven-

Jan 1, 1953