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Jan 1, 1943

Jan 1, 1943

By A. G. Spillette, R. L. Nielsen

The purpose of this paper is to further the understanding of reservoir response to hot-water injection by desuribing a two-dimensional, mathematical model of the process. Key assumptions are that no gas phase is present, and that the injected fluid reaches thermal equilibrium instantaneously with the reservoir fluids and sand. The resulting system of three partial differential equations is solved simultaneously through the use of a "leap-frog" application of standard alternating direction implicit methods for the solution of the mass-balance equations and the method of characteristics for solution of the energy-balance equation. The utility of the mathematical model is demonstrated by comparing numerical and analytic temperature distributions for hot-water bank injection and by comparing calculated with observed field behavior. Additional calculations show that hot waterfioding can recover significantly more oil than cold waterflooding, and that a hot-water bank recovers, with less energy input, nearly as much oil us continuous injection. Introduction Consistent field success with hot fluid injection processes requires good reservoir description and a thorough understanding of recovery mechanisms. The latter is fostered by a combination of well designed experimental studies and physically sound mathematical modeling. The purpose of this paper is to further the understanding of reservoir response to hot-water injection by describing a two-dimensional mathematical technique, indicating its validity, and demonstrating its utility for studying the effects of reservoir and operating parameters. Published experimental studies of hot fluid injection processes are few." Even if extensive data were available, two considerations discourage exclusive reliance on laboratory or field work. First, because of the severity of scaling requirements," laboratory results must be interpreted with care. Second, because of the one-shot nature of field experiments — injectivity/productivity tests and pilot floods—results seldom are available over the desired range of operating conditions. These factors emphasize the need for devoting attention to mathematical modeling to complement laboratory and field work. Through the use of mathematical models, scaling uncertainties can be bridged and response can be predicted for unique combinations of reservoir and operating conditions. Numerous mathematical models developed during recent years enable us to calculate temperature distributions, thermal efficiency (or conversely, fraction of heat lost), and oil recovery behavior for hot fluid injection. Ramey" and Spillette' recently have provided reviews of these methods. Most models have concentrated on predicting temperature distributions and thermal efficiency; few have been directed at predicting oil recovery.'."1° Although these techniques are useful for estimating effects of reservoir parameters and operating conditions on process performance, results are limited by the assumptions made and by the methods of coupling independently solved fluid-flow and energy-balance equations. A computer-based method is presented for predicting total reservoir response to hot-water injection that obviates most simplifying assumptions. The model simulates fluid flow and heat transfer in two dimensions within a vertical cross-section spanning the oil sand and adjacent unproductive strata. Known numerical procedures are used to solve the governing partial differential equations. The mathematical model handles the effects of reservoir heterogeneity, gravity, capillarity, relative permeability and temperature-dependent fluid properties. In addition, a wide range of operating conditions can be modeled, including hot-water followed by cold-water injection. Mathematical Description of Hot-Water Injection Key assumptions in the mathematical model for hot-water injection are that (1) no gas phase is present and (2) the injected fluid reaches thermal equilibrium instantaneously with the reservoir fluids and sand. Relative permeability and capillary pressure are assumed independent of temperature. Darcy's law for multiphase fluid flow relates the velocities of the oil and water phases to the phase pressure gradients by the following relations:

Jan 1, 1969

By H. W. Hitzrot

THE new 4800-ton fine-grinding plant at the Hollinger Consolidated Gold Mines property at Timmins, in the Porcupine district of northern Ontario, went into operation in November 1937, and represents the culmination of an experimental program. The plant is a moderately low rectangular building of hollow tile on a steel frame, large enough to house four 7 by 15-ft. ball mills, with a 12 by 27-ft. classifier beside each mill. At one end is space for the addition of another mill and classifier or a mill and classifier for the regrinding of table concentrates. This regrinding is now done in the old grinding department of the main mill building. Also within the new building are the four 6-in. sand pumps for lifting the product from the low-dis- charge ball mills up to the classifier feed launders and the containers and appurtenances of a complete dust-collecting system. Together with the usual overhead crane, these constitute the major units of equipment within the new plant. The location is at the lower end of the main mill buildings toward the old tailings pond, now so neatly leveled off and sodded to rival the very best of our own W.P.A. projects. Close by the new grinding plant is a large dome-shaped structure-the new fine-ore bin designed arid built by Mr. Longmore and the Hollinger milling and engineering staffs. There are four separate automatically loaded inclined belt conveyors leading up from the bottom of the bin to the grinding plant. Each belt is equipped with a recording weightometer, in the grinding building. The whole structure and the machinery within it give the impression of permanence and a carefully integrated design with close attention to details, giving the operators every advantage for consistently good work. The many ideas and opinions behind this achievement were all ably organized and executed by the Hollinger milling and engineering staffs, anti not a few were directly initiated by them. Excellent cooperation was afforded by the Hollinger staff to the engineers helping to conduct the grinding and classification test program. It was the author's privilege

Jan 1, 1939

By R. Schuhmann

Available thermodynamic data applicable to copper smelting systems are collected and tabulated, and the important gaps are pointed out. A few examples are given of estimations which can be made from the available data. An experimental research program is proposed to supply the thermodynamic data that appear most essential to better quantitative understanding of the chemistry of copper smelting. The proposed program is designed also to shed specific light on the practical problems of slag losses and magnetite behavior. OPPER smelting, from flotation concentrates to V-/ blister copper, is conspicuous among the large scale chemical processes which are conducted with only relatively incomplete knowledge of the physical chemistry involved. For example, no common metallurgy text explains adequately why copper enters the matte phase while iron enters only to the extent that sulphur is left over after satisfying the copper. Explaining this important phenomenon as a manifestation of the greater affinity of sulphur for copper than for iron is unsound because the affinities of copper and iron for sulphur are about the same at smelting temperatures. As will be shown, other affinities are really decisive in the relatively clear-cut separation of copper in the matte. In contrast, thermodynamic studies have contributed much to our understanding of copper refining, zinc oxide reduction, magnesium production, steelmaking, etc. For each of these processes, the important reactions are clearly recognized, and fair to good quantitative values of the free-energy changes and equilibrium constants are available. Such data have proved to be of constantly increasing practical value in process development and improvement. Work in other fields has furnished much thermodynamic data applicable to copper smelting systems. In fact, several promising starts have been made in applying such data to specific smelting problems. Kelleyl made an appraisal of the possibilities of recovering elementary sulphur from low grade matte. His calculations and compilations of thermodynamic data have represented the starting point for much of the work in this field, including the present survey. Huang and Hayward2 nd Aksoy3 used thermodynamic methods in the study of copper losses in reverberatory slags. Peretti4 used thermodynamic data in explaining the chemistry of converting. The recent publications of Darken and Gurry"." and of Darken,' dealing with the iron-oxygen and iron-silicon-oxygen systems, respectively, present equilibrium data that are applicable to copper smelting systems. Also additional data were reported recently on the affinity of sulphur for copper, manganese, and iron8 and on the sulphur pressures of iron-sulphur melts." The survey presented in this paper was made as the basis for planning an experimental program on the thermodynamics of copper smelting. Few researches on the chemistry of copper smelting have been reported in recent years, so that a reappraisal and coordination of old and new data are essential if further work is to take the directions of maximum value. The experimental program is now in progress, and the plan of attack is outlined at the end of this paper. Progressive Oxidation and Desulphurization of Copper-bearing Liquid Phases: The chemical activities of sulphur and oxygen are two of the most important thermodynamic yardsticks to be applied to copper smelting processes. Virtually the entire smelting and refining sequence involves a series of systems characterized by decreasing sulphur activity and increasing oxygen activity. In this section, therefore, an attempt is made to define and explain these activities in terms of equilibrium partial pressures of SO2, s2, and O,. Also, estimates of these quantities are presented, the estimates being based largely on calculations presented in a later section of this paper. The sequence of steps from raw flotation concentrate to fully oxidized copper ready for poling involves progressive and controlled oxidation. Iron is oxidized and enters the slag. Sulphur is oxidized and leaves in the gas. Table I summarizes several important features of this oxidation and desulphurization sequence, starting at the beginning of the matte blow in the converter. The top line gives in order the principal smelting and refining stages up to fully oxidized copper, plus the additional step, not used commercially, of oxidizing all the way to Cu,O. In the second line are shown the principal copper-bearing liquid phases which characterize the process. Through most of the sequence the copper

Jan 1, 1951

By J. C. METCALF

MORE than 80 per cent. of the iron produced in the United States and over 30 per cent. of the world's annual production is obtained in the Lake Superior district. Though iron ore was discovered on the Marquette range in 1844, the poor transportation facilities retarded the development of this region for many years. The structure of the Lake Superior basin is essentially an east-west synclinorium with steep dips on the south side of the lake and considerably flatter ones on the north and west. The Upper Huronian series, which -is the iron-bearing one of the formation, on the south side of the lake dips north from 55' to 80°, and on the north side dips south from 8" to 200. The series has been subjected to local folding and faulting, which have influenced the development of the mining systems used.

Jan 1, 1921

The Pueblo Viejo Mine, a 7, 250 mtpd (8,000 stpd) gold-silver cyanidation plant built by Rosario Dominicana S. A., was described in Volume I of this monograph. At the time of writing that volume, Pueblo Viejo had not yet gone on-stream and operating data or costs could not be presented. Since that time this information has been obtained and several interesting modifications and an expansion have been made to the plant. Because Pueblo Viejo is the largest open-pit gold mine in the world and one of the world's leading gold-silver operations with production of approximately 31 kg (1,000 oz) gold and 125 to 155 kg (4,000 to 5, 000 oz) silver per day, the authors have updated the previous data and flow sheet. The Dominican Government, which held a 4670 interest in Rosario Dominicana S. A., completed purchase of the mine to gain full control in 1979. Rosario Resources will continue to manage the mine, at least until the end of 1980. Gold was produced at Pueblo Viejo almost 500 years ago with initial production in the year 1505. Rosario Resources became interested in the property in 1969 and found surface oxidation had rendered the upper portion of the ore body amenable to direct cyanide treatment. The treatment of the underlying gold-bearing sulfide zone is still undergoing metallurgical studies. The ore is considered to be a laterite; and because there appeared to be few boulders in the ore zone, only a 400 m (16 in. ) square grizzly was initially installed ahead of the mills when the plant went on-stream in late 1974 at a design capacity of 7,250 mtpd (8,000 stpd). Operation also proved the ore to be harder than was originally anticipated. During 1967 a 1. 25 m by 1. 5 m (48 in. by 60 in. ) jaw crusher was installed to -feed the 1, 000 mt (1, 100 st) mill bin. Minus 200 mm (8 in.) crushed ore is fed directly to two 5.5 m by 1. 8 m (18 ft by 6 ft) semi-autogenous mills re-powered with 750 km (1,000 hp) motors and 50 mm (2 in.) grates. Each mill product is screened at 13 mm (1 /2 in.) by a vibrating screen. Screen oversize from each mill is combined on a single return belt equipped with a magnetic head pulley for grinding ball removal. The non-magnetic oversize is then split into two fractions for return to the primary mills. Originally, a minus 6 mm (1/4 in ) product was made on each screen and fed to a 300 kw (400 hp) 2.6 m by 3. 7 m (8-1/2 ft by 12 ft) regrind mill. During a plant expansion in 1978, an intermediate mill of 746 kw (1,000 hp) was installed to operate in open circuit on the combined primary mill

Jan 1, 1981

By P. L. Allsman

A method of analyzing blasting action indicates that major cost savings are possible by revising practice and bringing the classical blasting formulas up to date; difficult problems such as taconite and throw-breakup can be attacked by engineering Denonation pressure — the peak pressure developed by the explosive reaction; "shatter blasting." Average detonation pressure — the average pressure over the time the reaction continues; "heave blasting." Radial presswe — the stress in a radially expanding sphere about the detonation. Corresponds to the diminishing peak pressure. Lateral stress - the stress in a circumferential direction, induced by outward movement of the rock away from the detonation. Limiting stress or Slim— the rock property at which failure will occur in the case at hand; may be tensile or compressive strength, or combinations. Recent developments in explosives technology, following the advent of nuclear explosions, have led to a rather complete understanding of their action. A survey was made for the purpose of uncovering any knowledge which might be applicable in the mining and quarrying industries, the principal users of explosives. Although no revolutionary techniques have become apparent, much basic data pertaining to blasting — fortunately not classified — have been developed by recent research, from which a good general understanding of the process can be derived. It is hoped this explanation of the scientific principles governing explosive action, together with a proposed analysis of blasting practice, will further the development of mining engineering. NATURE OF THE REACTION: The phenomenon of explosion, termed detonation, is in reality a rather complex chemical reaction, and as such is completely explainable by physical and chemical laws. Detonation is characterized by high temperature and pressure, extreme rapidity — often being complete within one microsecond — and most importantly by formation of a shock pulse which accompanies the reaction zone. As with any chemical reaction, there is a critical value of temperature and pressure below which detonation can not occur; this is termed the "critical point". Whereas an explosive substance will decompose slowly at ordinary temperature, with the formation of gases which readily dissipate; at elevated temperature the reaction is considerably speeded. If pressure is suddenly applied at some point in an explosive medium, adiabatic compression results, and the temperature is locally raised. When the temperature becomes high enough the decomposition will be so rapid that the gaseous products do not have time to dissipate, but contribute to a further build-up of pressure. This, in turn, furthers adiabatic temperature rise over a widening area, and with any heat generated by an exothermic reaction, causes a rapid increase in temperature. Both temperature and pressure are spontaneously built up in this manner until the critical point is reached, resulting in detonation. The values of pressure and temperature necessary to create detonation are established by the unusual nature of the process. If temperature alone is raised above the critical point, without sufficient increase in pressure, deflagration or "low-order detonation" occurs. In the true, or "high-order detonation", the shock pulse resulting from the violent decomposition becomes an integral part of the reaction, and itself aids in increasing the detonation

Jan 1, 1961

By N. S. Stoloff, R. G. Davies

A study has been made of the efject oj different dislocation-precipitate interactions upon the temperature dependence of the flow stress of aged Ni-14 at. pct A1 alloy. It is observed that when the dislocations bow between widely spaced (-20004 coherent Ni3Al particles the flow stress decreases with increasing temperature in the normal way. However, when the dislocations cut closely spaced (-5004 particles the flow stress is independent of temperature from -100 to 600°C, due to a balance between softening of the matrix and an increase in strength of the particles with increasing temperature. The retention of strength at high tempera-tures of commercial nickel-base alloys, which are strengthened by the precipitation of a phase based upon Ni3Al, is thought to be due to the unusual strength properties of Ni3Al. The flow stress of Ni3Al increases continuous1y from -196"C to a maximum at -600"C. It is concluded from a series of thermal-mechanical tests that the sevenfold increase in flow stress over this temperature interval is due to a lattice effect and is not diffusion-controlled. The flow stress of precipitation- or dispersion-hardened materials depends on the resistance to dislocation motion within the matrix and the extra energy required for dislocations to bow between or to cut particles. If the dislocations bow between the particles or if the strength of the cut particles is constant with temperature, then the flow stress of the precipitation-hardened alloy must decrease with increasing temperature due at least to the decrease in elastic modulus of the material. There will be softening also from thermally activated cross-slip or climb, offering an additional degree of freedom for dislocations to avoid particles. For example, in the case of nickel containing a dispersion of thoria,' which most probably deforms by dislocations bowing between particles, the flow stress decreases by about 50 pct between 25" and 650°C. In A1-Cu alloys2 aged to produce the 8" precipitate, dislocations cut the particles, and the flow stress decreases by about 20 pct between -269" and 25°C. However, many commercial high-temperature nickel-base alloys, for example Inconel-X and Udimet-700, exhibit little or no decrease in flow stress with increasing temperature up to about 700°C. A characteristic feature of these alloys is that they are strengthened by the precipitation of a phase based upon Ni3A1. Guard and westbrook4 and flinn' have shown that Ni3Al (and alloys in which a third element such as molybdenum or iron is substituted for part of the aluminum) is unusual in that the hardness and flow stress increase with temperature to a maximum at about 600°C. For the flow stress of a precipitation-hardened alloy to be independent of temperature we propose that the particles must be cut by dislocations moving through the matrix and that the strength of the particle must increase with increasing temperature. Theories of precipitation hardening do not take into account the flow stress of the dispersed particles that are cut during deformation; the only dissipative process usually considered7 is the creation of interface within the particle and between the precipitate and matrix. The purpose of the present investigation has been to study in detail the temperature dependence of the flow stress of a nickel-base alloy strengthened by the precipitation of Ni3Al in two structural conditions such that when deformation occurs it does so by dislocations a) bowing between the particles and b) cutting the particles, respectively. A simple binary Ni-14 at. pct A1 alloy was chosen because considerable information is already available for this system concerning phase equilibria and precipitation reactions and rates.' Dislocation-precipitate interactions in the binary alloy should be similar to those in the more complex commercial alloys. In addition, the mechanical and physical properties of NisAl were studied in detail in the hope of elucidating the mechanism by which the strength increases with increasing temperature up to 600°C. EXPERIMENTAL PROCEDURE For the study of the effect of precipitation of Ni3A1 upon the temperature dependence of the flow stress, an alloy containing 14 at. pct A1 was utilized; a Ni-8 at. pct A1 solid-solution alloy was employed as a comparison material. Vacuum-cast ingots were hot-rolled at 1000°C and cylindrical compression samples, 0.20 in. diam by 0.40 in. high, were prepared from the 1/4-in.-diam rod. Specimens were recrystallized and solution-treated at 1000°C for 1/2 hr and then water-quenched. A preliminary study revealed that, when the Ni-14 at. pct A1 alloy was aged for 1 hr at 700°C, significant precipitation hardening was obtained, and that the structure was free from grain boundary discontinuous precipitation; an overaged condition was produced by annealing the aged specimens at 850°C for 1 hr. To circumvent the difficulties involved in the hot rolling and swaging of Ni3A1, compression samples,

Jan 1, 1965

By L. J. Gurevich

IN the course of the examination, at the Bureau of Standards, of fusible tin boiler plugs for the Steamboat Inspection Service, it became evident that an investigation should be undertaken to determine the precautions necessary in the manufacture of acceptable plugs. The results of the tests of these plugs show that their manufacture has improved, though at present not all of the plugs tested are satisfactory. Table 1 gives the result of tests of some 1500 plugs from about 100 makers. Records of the tests show that several of the makers were able to produce satisfactory plugs with every pouring. The Steamboat Inspection Service has the following specifications for fusible plugs: "Fusible plugs for use in boilers of steam vessels under the Jurisdiction of the Steamboat Inspection Service shall be made of bronze casing with the bore tapering continuously and openly from end to end, and filled from end to end with tin not less than 99.7 per cent. pure and to contain not more than 0.1 per cent. of lead and not more than 0.1 per cent. of zinc. The small end of the bore may be countersunk not more than 1/32 in. in depth and width, but no recess, thread, or cavity other than this countersink shall be allowed."

Jan 8, 1919

Jan 1, 1950

By Claude Ferquson

MORE men are killed and injured in the metal mines of the United States from falls of rock and ore than from any other cause. Dan Harrington, of the U. S. Bureau of Mines, recently stated that "falls of men and material continue to take about 50 per cent of the lives annually lost in our mines (coal or metal) and this kind of accident is now and has been one of the most difficult to prevent." The fact that comparatively little has recently been written on this important subject for the benefit of the metal miner is the incentive for the present paper. Little will be said that will be new, but I hope to place fresh emphasis on certain well-known' principles' and to reiterate and stress previously stated rules so that the average experienced miner, as well as his buddy who may not be so experienced,' will sit up and take notice. It is not within the scope of this paper to discuss mining methods from the standpoint of safety and the prevention of accidents from falls of rock. It is up to the mine management to select the system of mining best suited to the character of the ore deposit and its wall conditions. This is something that the miner can do little about; although in many mines the management encourages the workmen to make suggestions that will improve existing

Jan 1, 1938

By William M. Bowron

THIRTY years ago, when I stood on the cliff of red fossil iron-ore, on Red mountain, Jefferson county, Ala., I asked what were the geological relations of this remarkable deposit. In reply I was told that it was a limestone colored and saturated by some unknown but wholly external influences, and that at a reasonable distance from the surface the color would disappear. I could find no satisfactory explanation either of the nature of this wonderful external permeating influence, or of the cause of such a ferrous impregnation selecting this one particular bed of limestone, to the exclusion of the higher and lower beds of the same material which are not even stained. I. THE PRESENT THEORY. Referring to this subject, Dana says:' "The clays, clayey sandstones and limestones of the Clinton epoch, through New York and the Appalachians, show that the mud-flats and sand-banks, and hence the shallow seas of the coast region, still continued. . . The beds of argillaceous iron-ore, which spread so widely through New York and some of the other States, south and west, could not have formed in an open sea, for clayey iron-deposits do not form under such circumstances. They are proof of extensive marshes, and, therefore, of land near the sea-level. The fragments of crinoids and shells found in these beds are evidence that they were, in part at least, salt-water marshes, and that the tides sometimes reached them." At first, this explanation seemed satisfactory, but the more I studied the ore the less satisfying the explanation became. 1. In the ore itself I found associated with the small particles of rounded matter (now consisting of iron oxide in which organic structure, if ever present, has become lost, though the

Nov 1, 1905

By T. Wasson

The same limitations' that characterized 1931 existed in the old fields of Indiana and Illinois during 1932. Prices remained low. The average for the year for Illinois and southwestern Indiana was $1.032 as against $0.852 for 1931 and $1.616 for 1930. In September a curtailment of production of about 25 per cent became effective and was continued to the end of the year. There were no new discoveries and very little wildcatting was done. Considering the age of the wells, and the number still producing, there were few abandonments. The most outstanding thing about the old fields in these states is their long continued productivity. Illinois The fields along the southeast end of the LaSalle anticline had their peak of 33,686,000 bbl. in 1908. In 1932, with a 25 per cent restriction for 355 months, these fields produced 4,661,000 bb1.l There were 52 new completions (most of them in old territory) and of these 33 were dry, 8 were gas, and 11 were oil wells. The new oil wells had a total initial of 102 bbl., or an average of 9.3 bbl. per well. Nineteen of the new producers were in Crawford County. There were about 200 wells abandoned in the old southeast fields in 1932 as compared to 210 in 1931. The greatest number, 86, were in Lawrence County. To the end of 1932, the four major counties—Clark, Crawford, Lawrence and Wabash—had produced almost 394,000,000 bbl. from 92,160 acres. Better than one-half of this was produced in Lawrence County from 26,240 acres. The Dupo area of Sinclair County had no additions to production although four wells were drilled. On the Jacksonville structure in Morgan County, six gas wells with an average depth of 300 ft. were drilled to sands in the base of the Pennsylvanian. They produced an open-flow total initial of 2,000,000 cu. ft. This gas will be developed further to supply a local market.

Jan 1, 1933

By Eckley B. Coxe

I wish to call the attention of the Institute to a peculiar variety of anthracite which occurs in the Buck Mountain vein at our collieries at Drifton, and in the same and other veins in different localities in the anthracite coal-fields. It is known among the workmen as iron-gray or cast-iron. It has a dull, greasy appearance, as if a piece of ordinary anthracite had been rubbed with a dirty and greasy rag and allowed to dry. It was formerly considered a very impure coal containing a high percentage of ash, and was picked out of the coal and thrown away. But the following analysis of it and of its ash, made by Mr. J. Blodget Britton, of Philadelphia, shows that such is not the case, the percentage of ash not being much higher than that of the ordinary anthracites as they are prepared for market. ANALYSIS OF COAL. Water,.........4.36 Fixed carbon, by difference,.. 84.90 Volatile combustible matter,. . 3 48 Ash,..........7.26 100.00 The carbon proved to some extent to be of the nature of graphite, and slowly combustible. ANALYSIS OF ASH. Silica,.........25.66 Sulphur,........ .17 Alumina,........27.03 Phosphoric acid,.......21 Ferric oxide,.......42.83 Alkali, undetermined matter and Lime,.........1.56 loss,.........60 Magnesia,........1.83 Manganous oxide,......11 100.00 We recently collected a quantity of the substance and made a fire with it, in an ordinary stove, which was kept up several days. We found that it burned with intense heat, and apparently as freely as our other coal does. Mr. Britton is probably right in his view, that the difference in appearance is not due to impurities in the coal, but to the fact that the carbon is in a more or less graphitic form, as many of the standard coals are no purer. I bring this before the Institute as I know that a large quantity of this valuable fuel is thrown away every year, on account of its supposed impurities.

Jan 1, 1879

By L. V. Wade

Abstract-US Bureau of Mines efforts under longwall research programs to develop the capability to predict support requirements for longwall/shortwall support systems are discussed. Ground control studies are being conducted in conjunction with several longwall/shortwall demonstration projects. Geologic, support performance, and strata behavior are being documented on these projects. A hypothesis is presented for the prediction of support requirements.

Jan 11, 1978

By A. F. Giamei, E. J. Freise

A discussion of the various factors affecting the accuracy of volume fraction determination by the direct comparison X-ray diffraction method is presented. To minimize errors introduced by nonrandomization effects such as preferred orientation and large grain size, as well as errors introduced by statistical effects, an iterative mathematical analysis is introduced. This analysis is applied to all observable diffractio~ spectra from a given specimen by means of computer techniques and is statistically superior to the standard direct comparison technique which utilizes only one or tm sets of intensity spectra. The computer program also presents a graphical interpretation of- the results which enables the investigator to visualize and readily assess the scatter in volume fraction estimates caused by deviations from randomness. Finally, the iterative analysis is applied to experimental data collected from a series of plain carbon steels in both the as-received and spheroidized conditions to determine the volume fraction of cemen-tite present in each case. The results show markedly good agreement with chemical analyses for all spheroidized specimens. In theory, quantitative X-ray diffraction is a power-ful analytical technique for precise determination of the volume fractions of various phases present in a multiphase poly crystalline aggregate. There are two generally used methods; both utilize the fact that the intensity of a diffraction line of a particular phase is a function of volume fraction of that phase present in the aggregate. The more common method is the so-called internal standard technique where a known amount of standard substance is mixed with the aggregate containing the unknown. The resulting ratio of the intensity of a particular diffraction line of the unknown to the intensity of a diffraction line from the standard is used to find the weight fraction of unknown material by reference to the intensity data obtained from a previously prepared set of standards containing the same amount of standard material. The details of this technique are outlined in standard works on X-ray diffraction.' The disadvantages of the technique are that it requires the use of powder specimens and that the powder mixture must be homogeneous near the surface to the maximum effective beam depth. The alternative technique is the direct comparison method in which the ratio of the intensity of a diffraction line of a phase in the aggregate to the intensity of a second-phase diffraction line yields the ratio of the volume fractions of each phase present. This method has been applied most extensively to the determination of the percentage of retained austenite in martensitic steels and to determining the amounts of hcp and fcc allotropic modifications in pure cobalt5 and the amounts of hexagonal and rhombohedra1 modifications in graphite.8 This method is applicable to bulk as well as powder aggregates and is the technique which will be considered in the following text. It is the purpose of the present communication to show that by combining the results of X-ray diffrac-tometry with the use of high-speed digital computers the results of the direct comparison quantitative X-ray analysis technique can be optimized by using all of the data available on a diffraction pattern. THEORETICAL DISCUSSION In optimizing any quantitative X-ray diffraction experiment, the problem of accuracy vs time to collect and analyze the experimental data arises. For any method to be practical, it is required that both experimental and analytical procedures are reasonably short. In most of the previous work performed by the direct comparison method, intensity data from only one or two sets of peaks were used to calculate the volume fraction of phases present in the aggregate. Consequently, rather long-time experimental measurements are required to assure that the intensity data are sufficiently accurate to justify the use of one or two sets of data. By using computer techniques to analyze the experimental data it becomes feasible to use all of the available data on a diffraction pattern. By so doing, the time spent in measuring any one diffraction maxima can be appreciably reduced. Although this results in poor counting statistics for any one maxima, the number of data points available for analysis is greatly increased. Based on the above discussion, it will be assumed that a continuous scanning counter-diffractometer technique will be used to collect intensity data from a two-phase mixture. The integrated intensity of the ith diffraction line from the a phase in the aggregate is given by:'" where is the volume fraction of the a phase, The various quantities in Eq. [la] are angular independent while those in [lb] depend on the hkl spectrum of a particular phase. The meaning of the individual quantities in Eqs. [la] and [lb] are given in Appendix 1. It is convenient at this point to outline briefly the factors which will affect the measured intensity of any one hkl spectrum. a) Extinction effects arise from two independent experimental conditions. Primary extinction arises from a high degree of crystal perfection and results in spectra having lower intensity than predicted by Eq. [I]. Any treatment, such as powdering, which reduces

Jan 1, 1968

Jan 1, 1895

By R. W. Baldwin

On page 309, column 1, the second equation should read: Ma-M1 = dlog_Pa M2-M1 d log P2

Jan 1, 1961