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By D. L. Katz, M. J. Rzasa

The derivations of three methods of computing the static pressure gradients in natural gas wells have been presented to show the assumptions made. Charts were developed from which the pressure gradients may be read when the well-head pressure, the well fluid gravity, depth, and the average well temperature are given. A chart for estimating the well fluid gravity from the condensate content and separator gas gravity is included. The effect of the increased average well temperature after flow on the calculation of the static pressure gradient is discussed. Introduction Reservoir pressures have been calculated from well-head pressures for gas wells for many years. As the pressure measurements become more accurate, the need for a reliable calculation of the static pressure gradient often arises. This paper will develop the several methods for computing the pressure gradient in gas wells and make a comparison between them. The method of calculating static pressure gradients in common use is Eq. I (ref. I) or its counterpart which includes a factor for the deviation of the gas from the ideal gas law. P2 - P1 = P1(e0.0000347GX _ I) Eq. [I] in which P1 = pressure at well head, lb. per sq. in. abs. PP = pressure at bottom of well, Ib. per sq. in. abs. G = gas gravity X = depth of well, ft. An alternate method is to compute the average density of the gas in the well and multiply by the well depth in a manner similar to that used for liquid gradients. Derivation of Formulas A static pressure gradient is a special case of the general fluid-flow equation. Consider a pound of fluid flowing in a vertical column from point I to point 2, Fig. I. By an energy balance for fluid flowing from I to 2: U1 + P1V1 + u12/2g + X1 + q = U2 + P2V2+ u22/2g+X2 +W [2] in which U = internal energy, ft-lb. per lb. P = pressure, lb. per sq. ft. V = volume, cu. ft. per lb. u = average linear velocity, ft. per sec. X = height above datum, fl. q = heat absorbed by fluid, ft-Ib. pcr lb. W = work done by system, ft-lb. per lb. An energy balance on the fluid itself gives: U = ?TdS - ?PdV + etc. [3] in which T = temperature, deg- R- S = entropy, ft-lb. per deg. R. per lb.

Jan 1, 1945

By Harry E. Cross

Kiln Products commissioned a Waelz kiln 4 metres in diameter by 75 metres long, in South West Africa in March, 1969, to recover nine in a form suitable for the production of electrolytic zinc. The raw material consists of a mixture of zinc silicate concentrates and zinc rich tailings purchased from an adjacent zinc mine - the mixture containing 20% to 25% zinc. The chemical composition of the ore is tabulated and the initial test results are described. Due to the comparatively low temperature at which the ore starts softening the kiln has certain unusual features to enable the temperature to be controlled within the necessary limits. A detailed description of the kiln, the starting-up problems and present operating conditions and results are presented.

Jan 1, 1970

By Leonard Grimshaw

DIFFUSION Of carbon from gases into iron has been the object of much research, because of its long recognized importance in carburizing processes, but the direct diffusion of carbon from steel into iron has received relatively little attention. Because of the increasing use of clad metals in industry, direct diffusion from steel into iron is becoming of practical importance. Therefore, the object of this investigation was to study the diffusion of carbon from several different kinds of steel directly into relatively pure iron, realizing that elements in the steels other than carbon might influence the rate of carbon diffusion. The previous work on diffusion of carbon into iron has been consider-able, and includes many reports in foreign languages. This work has recently been well reviewed by Mehl1 and Krynitsky,2 and the reader is referred to their excellent bibliographies.

Jan 1, 1937

By J. T. Eash, N. B. Pilling

As a group, the alloys of iron, nickel and carbon are, in application, one of the most versatile of the ferrous alloy family, and while many investigations have been made of their properties and structure only a few attempts have been made to show the microstructural relation over a wide range of composition. It is necessary at once to be clear about the kind of structural relation with which we are concerned. The equilibrium diagram provides quantitative data regarding structural make-up and its variation with temperature, but equilibrium structures often are far different from the technologically significant ones. This is particularly true of steels and cast irons, and some of the most important components of their structure may have no place in the diagram of equilibrium. The fugitive phases that result from transformation are dealt with in a highly detailed and descriptive manner in the S-curves originated by Bain. The present effort lies in a still different field, which is to portray the relation between sweeping changes in composition and in resultant structure, under controlled but nonequilibrium conditions of thermal treatment. The Guillet1 diagram presented in 1903 was the initial attempt at such a correlation and frequent references to this diagram can be found in the literature even though later work has shown it to require considerable modification. Kase2 published in 1925 a diagram that was based upon observations of furnace-cooled melts. At low carbon contents this diagram agreed fairly well with experience in showing pearlite to exist in alloys containing up to 6 per cent nickel, and completely austenitic steels at 24 to 28 per cent nickel. At high carbon contents, however, irons were indicated as being martensitic at around 2 per cent nickel and austenitic at 12 per cent nickel; these interpretations are open to serious question. Based upon experience with steels and cast iron, Wickenden3 suggested a diagram that agreed fairly well with Kase's in the steel range but which presented a wide departure from it in the higher-carbon, high-nickel regions. In its broad picture, the Wickenden diagram is an approach to "practical" structures. [ ] Reference may be made at this point to the efforts of Marshy to construct an iron-nickel-carbon equilibrium diagram by the coordination of scattered data, which are described at length in the monograph cited. None of these preceding attempts has appeared to meet the need for an exposition of the structural sequence that is encoun-

Jan 1, 1942

By G. B. Gould

EVERY mathematical statement of a measure of anything (as distin-guished from a count) is followed by a qualification always implied if not explicity stated--that the statement is only an estimate, which may vary from absolute accuracy within certain limits, according to the accu-racy of the measuring instrument. This basic fact, so obvious to engineers, is not so well understood by many that make use of laboratory coal tests. The tolerances that must be allowed in measurements of coal quality are very important in both their commercial and engineering applica-tions-and the significance of these tolerances depends upon the use made of the laboratory coal test. Only in recent years has there been any intensive study of this ques-tion of tolerances as applied to measurements of coal quality. There is very little in our published literature on the subject, and what has been published is not, readily comprehended by those who sell coal, or buy coal and use it, unless they happen to have made a study of the subject them-selves. There is great need for more widespread understanding of what has been discovered and how it applies to the use of laboratory coal tests. What follows is an attempt to condense into a few pages the results of the major investigations so far reported, and to explain their meaning in simple nontechnical language, with the addition of some recent illustrative experiments.

Jan 1, 1937

By H. W. Weart, D. J. Mack

SINCE the first recognition of eutectic solidification as the simultaneous formation of 2 solids from one liquid,1 many complex structures thus produced have been observed. Despite many attempts to ascertain it, however, the detailed mechanism by which these structures develop remains obscure. In an attempt to clarify the origin of eutectic structures, the study described in this paper was undertaken. The broad objective of the study was to investigate the effect of different solidification conditions on the structure of single eutectic grains. It was expected that the eutectic structure would thereby be isolated for study, but preliminary experiments revealed another structure within each grain. When a literature surveye revealed only 1 previous mention of the subgrain structure,' it was decided to determine the origin of the structure and to study its response to various growth conditions. Before presenting the details of the investigation, it is apropos to distinguish carefully among the 3 structures produced during eutectic solidification. This is especially desirable in view of the apparent confusion existing in the literature concerning the structures in a eutectic specimen. The confusion is due largely to the existence of the subgrain structure noted above which is easily mistaken for the grain structure. In the following paragraphs, an effort is made to distinguish the 3 structures by briefly describing their origin during solidification, even though the results are thereby anticipated slightly. The 3 structures produced during eutectic solidification are the grain structure, the colony structure, and the eutectic structure, each one contained by the one preceding it. The grain structure is analogous to the polycrystalline structure of a metal or inle-phase alloy in that each grain grows from a single nucleus. A somewhat broader interpretation is needed here, however, because of the presence of 2 phases in each grain. Since in most eutec-tics particles of 1 phase are dispersed in a matrix of the other, a grain may be taken to be the region in which the matrix phase is monocrystalline.*

Jan 1, 1959

By O. W. Ellis

The question of the influence of gases upon the properties of copper has received the attention of a number of investigators, among whom Sieverts,' Iwase,2 Lobley and Jepson3 stand preeminent. Solubility of Gases in Copper Sieverts and Iwasé concerned themselves with the solubility of a variety of gases in the metal in the solid and liquid states. They determined the absorption coefficients of these gases and in all cases found a sharp change in solubility at the melting point of the metal. In this respect they disagree with Lobley and Jepson, who have based their opinions upon the appearance of small ingots of the metal which had been fused in an atmosphere of one or other of three gases and had then been rapidly cooled, while surrounded by gas, to the freezing point (rate—possibly 30" to 60" C. per sec.). The ingots that had been fused and cooled under nitrogen and carbon monoxide were free from blowholes and it was assumed that these gases were not absorbed in amounts much in excess of those which would dissolve in the solid metal; the ingots similarly treated under hydrogen were full of blowholes and it was assumed in this case that gas was ejected on solidification of the copper. The effect of varying the rate of freezing upon the character of the test ingots was not examined by these investigators; otherwise, it is felt, their views might have been subject to modification. Sieverts' most important contribution is that the solubility of a gas in any metal is proportional to the square root of its pressure or concentration. Knowing then the absorption coefficients of the various gases in copper, it should be possible to determine the analysis of the

Jan 1, 1929

By O. W. Ellis

The question of the influence of gases upon the properties of copper has received the attention of a number of investigators, among whom Sieverts,' Iwase,2 Lobley and Jepson3 stand preeminent. Solubility of Gases in Copper Sieverts and Iwasé concerned themselves with the solubility of a variety of gases in the metal in the solid and liquid states. They determined the absorption coefficients of these gases and in all cases found a sharp change in solubility at the melting point of the metal. In this respect they disagree with Lobley and Jepson, who have based their opinions upon the appearance of small ingots of the metal which had been fused in an atmosphere of one or other of three gases and had then been rapidly cooled, while surrounded by gas, to the freezing point (rate—possibly 30" to 60" C. per sec.). The ingots that had been fused and cooled under nitrogen and carbon monoxide were free from blowholes and it was assumed that these gases were not absorbed in amounts much in excess of those which would dissolve in the solid metal; the ingots similarly treated under hydrogen were full of blowholes and it was assumed in this case that gas was ejected on solidification of the copper. The effect of varying the rate of freezing upon the character of the test ingots was not examined by these investigators; otherwise, it is felt, their views might have been subject to modification. Sieverts' most important contribution is that the solubility of a gas in any metal is proportional to the square root of its pressure or concentration. Knowing then the absorption coefficients of the various gases in copper, it should be possible to determine the analysis of the

Jan 1, 1929

INTRODUCTION IT is 10. years this summer since the first of the contributions which it has been my privilege to make to the working tools of the hydrometallurgist was set at work, but a full description of what has come to be known as "Dorr Machinery" has never been published in the Transactions of the Institute, and it has been suggested to me that an account of the same would prove of interest to members, although most of those engaged in cyaniding and concentration are probably familiar with it. The account which I shall give of the development of the machines must be recognized as being written from the viewpoint mainly of my own local experience and not from that of one who was familiar with the general metallurgical practice throughout the world. Most advances in any art are conceived before the time is ripe for their development and any .invention which comes into general use will usually be found to have been tried out in a crude way and abandoned more than once. If the early experimenter went as far as the Patent Office, his work may serve no other purpose than to prevent the issuance of the broadest patent to those who later may develop a commercial process. The cyanide process in the United States early in 1904 was mainly confined to the leaching of dry crushed ores, both coarse and fine, and sand treatment of tailings from concentration and amalgamation. In the Black' hills some plants were crushing in cyanide solution, leaching sands and handling the slime by the well-known decantation process. Filter pressing, in use for some years in Australia,had been tried in several places in this country and the Moors process had been abandoned at Mercur after' a short run, but was doing good work at the mill of Lindbergh, Dorr & Wilson, at Terry, and being installed at Bodie and the Liberty Bell. A general feeling, however, still existed that, slimes were to be avoided when possible, on account of the losses in treatment and the difficulty of making a good leaching product when they were present in large amounts, especially when the crushing was done in cyanide solution.

Jan 8, 1914

By D. J. Weintritt, J. C. Cowan

Methods of studying oilfield mineral .scale deposition in the laboratory do not work for barium sulfate because only small nonadhering crystals ore formed. On the other hand, barium sulfate scale found in down-hole or surface equipment is strongly adhering and may contain very large crystals. Results suggest that most of the difference derives from the extremely low .solubility of barium sulfate. Firm adherence of scale and the consistent development of oriented crystals 100 microns and larger suggest a relationship between scale adherence and crysta1 growth. Data from this study indicate some reasons for barium sulfate's occurring as a deposit in oilfield waters. The unique characteristics as well as the associative properties of barium sulfate scale as related to calcium carbonate and calcium sulfate ere shown. INTRODUCTION The first observed deposition of barium sulfate scale in oilfield production equipment is unknown but probably coincides closely with the beginnings of the oil industry itself. Moore' described barite oolites in some producing wells in the Saratoga field, Tex., in 1914. Currently, positive identification of barium sulfate deposition is recorded in most of the major oil-producing areas of the United States. As efforts continue to identify the composition and functions of the materials found in scale deposits, the geographic and economic importance of the part played by barium sulfate will become even more important. This belief is based on the following Facts. 1. Many oil fields in the U.S. are in or entering their mature phase and the volume of produced water is increasing; thus, the cumulative effects of low-solubility minerals become more significant. 2. Secondary recovery techniques and increased emphasis on waste disposal systems require controlling the behavior of all constituents of water to prevent formation plugging. 3. The more general use of instrumental analysis has reduced the time and improved the accuracy of complete scale and water analysis. 4. Once formed, barium sulfate scale is resistant to present methods of chemical removal; therefore, costly mechanical methods are necessary. Thus, new methods of prevention and control will require specialized chemical techniques and better knowledge of the causes of scaling. Consider the results of some simulated field deposition studies illustrating this need (Fig. 1). The studies utilized a Scale Deposition Test Cell* and each coupon was exposed to 8,000 ml of a 300 me/liter solution of the various types of mineral scale. All tests were conducted at 140F. Only the calcium sulfate and calcium carbonate deposited scale. The solution containing 300 me/liter of barium sulfate exhibited copious amounts of precipitate, but none of the precipitate adhered. The fluids from the effluents were also allowed to impinge on glass slides. Fig. 1 shows the relative adherence of the three types of scale on unetched glass. The barium sulfate failed to deposit in the same manner as the calcium carbonate and calcium sulfate solutions.

By J. J. Thomas, J. H. Nead

This investigation was undertaken to determine, if possible, the relation between static and dynamic tensile tests as measured by the work required to break test specimens slowly, in a tensile testing machine, and rapidly, by means of a falling weight. It was hoped that the investigation would throw some light on the role played by ductility under different rates of application of load. In problems of design, it is usually assumed that the moduli of elasticity of all steels are equal; viz., about 30,000,000. The stress-strain diagram within the elastic limit is a straight line, as shown in Fig. 1, where OA is the curve of a hard steel and OB that of a soft steel. If the modulus of elasticity is constant, as assumed, the slope of the line OC

Jan 1, 1922

By J. H. Nead, J. J. Thomas

This investigation was undertaken to determine, if possible, the relation between static and dynamic tensile tests as measured by the work required to break test specimens slowly, in a tensile testing machine, and rapidly, by means of a falling weight. It was hoped that the investigation would throw some light on the role played by ductility under different rates of application of load. In problems of design, it is usually assumed that the moduli of elasticity of all steels are equal; viz., about 30,000,000. The stress-strain diagram within the elastic limit is a straight line, as shown in Fig. 1, where OA is the curve of a hard steel and OB that of a soft steel. If the modulus of elasticity is constant, as assumed, the slope of the line OC

Jan 1, 1922

By George H. C. Norman

A NUMBER of methods have been developed for the determination of the dust concentration in air, some of which have been reported as very efficient and for research may be more satisfactory than the method about to be described. In practical mine use, however, the accurate research equipment is unwieldy and requires a high degree of technical skill to manipulate it. Also, it gives less general practical information to the operator in the same length of time than the method described here. Moreover, it is doubtful whether at the present stage of affairs the results obtained from the precise methods have any more practical significance than those obtained with simpler and more portable apparatus, which can rapidly give a sufficiently reliable indication of the relative dust hazard. HISTORY OF DUST DETERMINATION IN ONTARIO The first record of mine-dust determination in Ontario is given in an article by Dr. J. H. Elliott,' in which he records a few dust counts made with the Palmer spray apparatus. There were insufficient data from which to draw any definite conclusions or reasonably compare with present-day counts using the konimeter. The first konimeter dust sampling was started in the Porcupine district in 1926, using light-field counting without adhesive and with no sample treatment before counting. A method of semidark-field counting was used from about 1928 to 1931 and dark-field illumination was adopted permanently about December 1931. The konimeter has been continued as the principal means of dust sampling in the mines of Ontario, where South African practice has been adopted because in South Africa most careful study has been given the problem of silicosis, and very complete records of work done there are

Jan 1, 1937

By Wiley C. Buford

Gary Works No. 1 BOP Shop is a three furnace shop which went into operation December, 1965. The heat size is over 200 tons, with a substantial percentage of the production used to feed a Continuous Slab Caster. Vessels are driven by a shaft mounted bull gear and main housing utilizing eight 35 HP flange mounted motors and primary gear reducers. Torque absorption is controlled by two spring actuated torque arms. At 1:00 p.m. on Thursday, August 6, 1970, as "E" furnace was being turned down for a preliminary test, the drive side trunnion bearing failed. The furnace dropped slightly and shifted several inches north in the direction of the drive unit. The decision was made to tap the heat which was done without incident and the vessel uprighted. No attempt was made to completely drain the slag from the vessel, so as to avoid any further damage to the trunnion shaft bearing surface. The bearing failure occurred approximately four years and eight months after start up of the shop. Unfortunately ?M? furnace had gone down for a normal reline two days prior to the bearing failure, leaving the shop with only one operating furnace.

Jan 1, 1972

By H. S. George

On one occasion when it seemed desirable to reveal under the microscope not only the metallic structure of an alloy, but certain small non-metallic inclusions that are ordinarily obliterated by etching, it was discovered that, by partly eclipsing the illuminating pencil of light rays, the residual light was thrown on the object from one side and the structure was brought out in relief. At the same time, the non-metallic inclusions were retained in clear view. In this first demonstration of lighting obliquely through the objective a card was thrust part way into the light beam between the arc iris and the light filter; the shadow of the card on the filter served to locate its position. Next several stiff-paper disks of various diameters were mounted on flexible wires; some plasticine on the other end of the wires made it easy to adjust and maintain a disk at any desired position in the light beam. To facilitate manipulation, an assortment of disks was mounted on a wheel, as shown in Fig. 1. The purpose of partly eclipsing the light beam was discussed in an earlier paper.' There it was pointed out that the usual methods of illuminating opaque objects for microscopic examination lend an unnatural appearance to the view, while the new method, which has been termed conical illumination, revels the true relationship of constituents by simulating natural lighting. In nature, all objects are lighted diffusely, or by light predominating from one direction, or by a combination of diffuse and directed light. Under these conditions, objects appear to have three dimensions—they possess relief. The kind of illumination known to metallographists as vertical or axial results in an unnatural appearance, as a large proportion of the illuminating rays are parallel to the line connecting the eye with the object, a condition almost never met in nature. Microconstituents

Jan 1, 1924

By F. C. NINNIS

AT THE Belmont mill, the pregnant solution is de¬livered to a 30 by 10-ft. tank, from which it is pumped to three Merrill clarifying presses of the sluice-bar type, whence it flows through the meter to the precipitation supply tank. ?The solution for precipitation is pumped by a 10 by 10-in. Aldrich triplex pump and delivered through a 6-in. line to the forty-eight triangular frame Merrill presses at the head of the mill. Zinc dust is fed in at the pump suction and the solution precipitated to 0.01 to 0.02 oz. silver. The solution flowing from the presses is tested at 1-hr. intervals with sodium sulfide. All solution is precipitated to the same value; 4J tons of solution are precipitated for each ton of ore treated and the presses are cleaned every 15 days. The product from the presses' is dumped into steel cars having steam-jacketed bottoms, in which they are dried until the moisture content is between 15 and 17 per cent. when 8. per cent. of soda and .3 per cent. of borax are added and the contents thoroughly mixed. In the case of special clean-ups, the precipitate is tested and the flux is added to meet the requirements.

Jan 1, 1921

By William E. Ford, Edward Salisbury Dana

Normal phosphoric acid is H3P04, and consequently normal phosphates have the formulas R3PO4, R3(P04)2 and RPO4, and similarly for the arsenates, etc. Only a comparatively small number of species conform to this simple formula. Most species contain more than one metallic element, and in the prominent Apatite Group the radical (CaF), (CaCI) or (PbCI) enters; in in the Wagnerite Group we have similarly (RF) or (ROH).

Jan 1, 1922

By H. V. Flagg

OPERATION of a modern steel plant presents a curious anomaly. Large-scale operations, in which large volumes or heavy weights of materials are involved, are not usually subject to close control or narrow specifications. On the other hand, operations that call for a high degree of precision are usually carried out under carefully controlled conditions with delicate, precise machinery and tools, and production is made secondary to quality. In a modern steel mill both extremes are taken as a matter of course. A strip mill making auto-body sheets must supply its customers with sheets that all come within a tolerance of plus or minus 0.003 in. in gauge at any point from side to side or end to end, and without blemishes either of color or surface. Sheets that were considered par excellence as recently as ten years ago could not even find a market today. Such exacting requirements have made necessary a nicety of control that approaches the watchmaker's art. Notwithstanding this necessity for precision, the scale of operation is stupendous.

Jan 1, 1940

By Virgil R. D. Kirkham

NoRth America has for many years led the world in phosphate production, but with development of African deposits and their marketing conditions with respect to European countries, this leadership will shortly pass to Africa. Algeria, Egypt, Tunis, and Morocco have large phosphate reserves and a correspondingly large production because of easy mining and a ready European market, which was developed during the war. An increase in home consumption is destined to develop for the eastern American fields, and the countries of the Pacific will provide a market for the western producers. New processes indicate a decrease in fertilizer costs, which will encourage a more widespread domestic use and assure better marketing conditions. The African deposits, although benefited by a water haul, have the disadvantage of being isolated from a source of acid so that the crude rock is shipped from Africa to its destination, whereas in the United States the chief product shipped is acidulated rock or various types of superphosphatic fertilizers, The principal types of phosphate deposits used in the manufacture of fertilizers are guanos, apatite, phosphatic marl, phosphatic limestone, phosphatic shale, and phosphate rock which is also known as phosphorite. Some of these deposits are found on each of the continents; Table 1 gives their occurrence, age, location, character, extent, etc. Most of the information found in this table represents a compilation of information published elsewhere in a different form and widely scattered.

Jan 1, 1925

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