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By W. R. K. Wu

This bulletin traces the development of high-pressure, coal and tar hydrogenation technology, based on an intensive review of the pertinent literature. The bulletin was written as a part of the Bureau of Mines research program on synthetic liquid fuels. It covers the history and economics of the process; the chemical aspect of hydrogenation of coal, tar, and middle oil; the engineering aspect of converting coal and tar to liquid fuels, principally gasoline; and the equipment for the process. The literature covered includes documents of the United States and British Governments, journals, and other publications. Bureau results in the hydrogenation field are also incorporated.

Jan 1, 1968

The Bibliographic Data Base is the result of a literature search con-ducted as one task of the technology assessment of current and advanced logging techniques, sponsored by the United States Bureau of Mines. After compilation, the bibliography was converted to an automated form for ease of utilization, and to allow for maintaining and updating the data base. The data base covers articles, symposia, books, patents, corporate and government reports, and other literature concerned with some aspect of borehole logging from January 1969 through December 1975. Periodic up-dating will be necessary to keep the data base contents in step with developments in the rapidly advancing field of application of borehole logging to mining. Many bibliographic indexes were scanned for entries relating to the subject of interest, and those entries which were included in our data base contain a reference to the bibliographic index in which they were listed (see Section 2.4.7). With the aid of these indexes, a vast number of publications, including foreign reports and publications, have been scanned for works relevant to borehole logging technology.

Jan 1, 1976

By J. M. Sands

Describes important developments in, four counties, all of which brought in 40° oil. Indications are favorable for the future, although the daily production of the agate decreased 19,000 bbl. during the year 1923. THE state of Kansas had a daily average crude-oil production of about 87,000 bbl. at the beginning of the year. This showed a steady but consistent decline during the 12 months, so that the daily average production at the end of the year was slightly over 68,000 barrels. GREENWOOD COUNTY THE most active development in Kansas during the year was in Green-. wood County, in a line from near Sallyards in T 25-R 9 to east of Madison in T 22-R, 11. The main part of. this development has been in a succession of pools beginning at the south with the Polhamus pool in 34-24-9 and 3 and 4-25-9; Thrall pool in 28, 29, 32 and 33-23-10; Burkett pool in. 13, 23, 24 and 26-23-10; Seeley and Wick pool in 22, 27, 28, 32 and 33-22-11 and 5, 6, 7, and 8-23-11; Frohm pool in 11, 14 and 15-22-11; Madison pool in 31 and 32-21-12 and 6, 22, 12 and 1-22-11. Some of these pools, have two or more sands, locally called Bartlesville and Burgess Sands. They range in. depth from 1850 ft. near Madison to 2450 ft. near Sallyards, the general dip being to the west. The thickness of these sands runs from 20 to 100 ft., the initial production of the wells being 50 to 1000 bbl. of 40-gravity oil or better.

Jan 3, 1924

By A. W. Frolli

This paper, describing the open-cut mining milling, and cyaniding methods and costs at the Yellow Aster gold mine, is one of a series being prepared by the Bureau of Mines on similar practices in the United States. It is presented primarily to show methods and costs of mining and treating low-grade gold ore on a large scale.

Jan 1, 1940

Mr D. Twigg graduated in Metallurgy at the Sheffield Polytechnic, and later obtained a Master of Science degree at the University of Bradford. Mr I.D. Matthews matriculated at Roosevelt High School and joined the No. 1 Parachute Battalion in 1968. He worked in Zimbabwe for 31 years in geological prospecting, civil engineering, and open-pit mining.

Jan 1, 1985

By C. Gravel, A. Fathi, P. Rivard, G. Ballivy, Z. Moradian, M. Quirion

Numerous schemes have been proposed in the past to evaluate the shear strength of rock discontinuities based on in situ and laboratory testing. Due to scale effects, in situ testing is the most reliable way to assess the shear strength parameters. However, practical reasons often impede this kind of testing. This is unfortunate because advances in theoretical rock mechanics are still dependant on qualitative experimental works. This paper presents a mobile high capacity shear apparatus developed for in situ direct shear testing of discontinuities along with testing methodology. The apparatus has the advantage of being simple, although of high capacity, and can be moved to different site locations for other tests. The in situ test was performed on a natural rock outcrop of schist with subvertical schistosity. A concrete block 50 x 50 cm with a base layer of high strength mortar was cast on the rock surface. Prior to the test, the concrete block was lifted and repositioned to have an unbonded joint but with interlocking asperities. The shear load was applied perpendicularly to the schistosity direction. The test was conducted in a constant normal load (CNL) condition. Both normal and shear loads were applied manually. The instrumentation consisted of two load cells for shear and normal loading, eight displacement laser extensometers for shear, normal, and lateral displacements and fourteen acoustic emission sensors for monitoring evolution of asperities’ degradation during the test. The friction angle obtained is 72° for the peak and 58° for the residual. The high values of friction angle indicates that first-order roughness and good interlocking of the joint surfaces can result in high shear strength parameter values in a rock generally regarded to have low values.

Jan 1, 2015

By Amilton Feliciano Castro

In this work, activated carbons (ACs) were prepared using Sewage sludge as starting material. The ACs were pyrolyzed in an inert atmosphere at 550 °C after independent chemical treatment with ZnCl2 or KOH with ratio of 1:1. The materials were used as adsorbents for removal of Cu(II) from aqueous solutions. The adsorbents were characterized using adsorption/desorption nitrogen isotherm, SEM (scanning electron microscopy). The results showed that copper removal could be linked to surface pH and compounds present on the surface of adsorbent. KOH-treated adsorbent has smaller surface area (186 m2 g-1) than ZnCl2-treated adsorbent (192 m2 g-1), however, KOH-treated adsorbent exhibited higher removal of Cu(II). The performance of KOH-treated adsorbent could be attributed to the presence of basic groups on the adsorbent surface. Liu isotherm model gave the best description of the equilibrium data. From the Liu isotherm, the maximum adsorption capacities at 298 K for KOH-treated, ZnCl2-treated and sewage sludge (without inorganic activation) adsorbents are 31.85, 19.79 and 3.513 mg g-1, respectively. The best desorption experiment was obtained using 1.50 mol L-1 of HNO3 as eluent. Recoveries of Cu(II) from Cu(II)-loaded adsorbents are 98.9% (ZnCl2-treated) and 95.5% (KOH-treated.

Aug 17, 2017

By J. Engesser

This paper discusses the effect that water chemistry, and water treatment have on pre-fired pellet quality and bentonite-binding effectiveness. A discussion concerning the effect that water temperature, water chemistry, water treatment, and surface area have on disc filter productivity and filter cake moisture is also included. This report is a summary of the data that were presented in five previous research reports, which are listed as references in this paper.

Jan 1, 2003

By B. Salopek

The greatest part of crushed stone, gravel and sand production is extracted through open pit operations, whereas gravel and sand are also partially extracted from riverbeds. Its obvious that such a mining activity provokes some changes in the configuration and environmental characteristics of the region, in the temporary or permament disapperance of vegetable or animal species and in the creation of noise, dust and waste water. However, the above-mentioned mining operations shouldn not have only negative effects on the landscape and land potential, but they can discover and predetermine the potential of the exploited areas for various communal purposes after exploitation (eg. sports and recreation centers, campsites, resorts, fish-farms, etc.). In this paper, the production of construction aggregates in plants located in the vicinity of Zagreb, the capital of Croatia is presented. The advantages and disadvantages of aggregates? production in urban areas in the spirit of sustainable development are discussed.

Jan 1, 2003

By H. C. Ko

Calorimetric determinations of low-temperature heat capacities and the standard enthalpy of formation were made by the Bureau of Mines for aluminum sulfide, A12S3. The standard entropy (S°), enthalpy of formation (?Hf°), and calculated Gibbs energy of formation (?Gf°) at 298.15 K are 27.93±0.05 call deg-mole, -155.6±0.9 kcal/mole, and -153.0±1.0 kcal/mole, respectively.

Jan 1, 1976

By Martin Bergeron

Producteur d?or de taille intermédiaire Mines Aurizon Ltée Bureau-chef àVancouverMine et projets localisés au Québec2

May 1, 2011

By Christian Bourcier

La méthode d?exploitation traditionnelle de la mine est le chantier chambre-magasin. Cependant, lors de l?exploitation d?un chantier, nous avons été confrontés à un problème de soutirage. Le minerai abattu est resté accroché à l?intérieur du chantier ce qui nous obligea à soutirer environ 200 wagons, représentant 700 tonnes. Suite à l?ampleur de la situation, nous avons décidé de finir l?exploitation du chantier par la méthode sous-niveau long trou retraité. Cette première expérience de récupération de piliers ayant été réalisée avec succès, nous avons décidé de continuer avec deux autres récupérations de piliers afin de pouvoir augmenter notre expertise autant au niveau technique qu?au niveau économique.

Oct 1, 2001

THE Institute assembled in the rooms of the Geographical Society at the Cooper Union, Tuesday evening at 8 P.M. President Raymond called the meeting to order, and introduced Mr. Abram S. Hewitt, who welcomed the Institute to New York. President Raymond, in behalf of the Institute, replied. The President then read the following report of the Council for the past year. The Council respectfully report that the American Institute of Mining Engineers has held four meetings-at Wilkes-Barre, Bethlehem, Troy, and Philadelphia, respectively-all of which have been well attended, and socially and professionally most successful. The proceedings of these meetings having been published in the Engineering and Mining Journal, and sent to all members and associates, are sufficiently well known. Forty-Bur papers, by twenty-six authors, have been read. These papers embrace a wide range of subjects, and prove the practical character of the proceedings of the Institute. The finances are in a satisfactory condition. By the report of the Treasurer it appears that $1290.10 have been received, $519.90 expended, and that $770.20 now remains in the treasury exclusive of fees for 1872. This fund, it is hoped, will be so increased by voluntary subscriptions as to enable us before long to issue a volume of our most important transactions in a permanent form. The Council has made a favorable arrangement with the Scientific Publishing Company, publishing the Engineering and Mining Journal, by which that journal became the organ of the Institute for the first publication of the proceedings, papers, and notices to members. This arrangement it is proposed to continue through the present year unless the Institute shall otherwise direct. I t is not intended to supersede the publication of an annual or occasional volume, but to maintain an interest in the Institute, and to serve the convenience of members while our funds do not permit a more ambitious publication.

By Robert H. Essenhigh

A stirred reactor (SR) combustion system has been developed to gather information on the mechanisms of ignition and flame propagation of coal dust under conditions similar to those found in coal dust explosion flames. The prime scaling variable considered in this study is that of rapid particle heating (between 105 and 106°K/sec) which is accomplished by means of turbulent mixing during combustion. The SR combustors tested in this study have consisted basically of spheres hollowed in the centers of refractory housings. Coal and air mixtures have been injected into the spherical combustion chambers through a single jet, two opposed jets or four opposed jets. The diameters of the jets have ranged from 0.63 to 0.22 cm. The volumes of the combustion chambers have ranged from 1.0 to 0.2 liters. The reactors have been equipped with thermocouples embedded in the combustion chamber wall as well as a thermocouple located in the exhaust gas stream. In the latter versions of the SR, provisions were made for both solid sampling and gas sampling of the reactant stream exiting from the combustion chamber. Experiments have been carried out using pulverized bituminous coal. The coal has been reacted in an SR in mixtures of air and air/nitrogen. These experiments have provided information on the mode of ignition of the coal as well as yielding information on the kinetics of coal pyrolysis through the use of SR theory. Ash tests performed on the reacted samples collected from the SR indicated that the majority of the values of weight loss percentage were between 60 and 70 percent. The percentages of weight loss were relatively unaffected by changes in temperature which varied between 1100 and 1700°K and by changes in residence time which varied between 10 and 20 millisec. Volatile matter tests performed on the samples indicated that the volatile matter left in the char ranged from 3 to 20 percent of the original content. By assuming that all the mass loss was due solely to pyrolysis with no combustion occurring at the particle surface, Q-factors for each test have been calculated. The results of these calculations indicate an average value of Q equal to 1.88. This finding shows that the majority of mass loss can be attributed to pyrolysis. The fact that the extent of reaction varies only slightly over the range of test conditions has been examined in the context of the two component hypothesis of coal constitution. This approach leads to the conclusion that the reaction of the "easily evolved" component VMI is extremely rapid and that the majority of it is removed from the coal in times less than the residence time in the system. This means that the volatile residue remaining in the char can be considered to consist of component II, VMII. If the mass fraction of VMI = 0, then an activation energy of 18.0 kcal is obtained for the pyrolysis reaction. If the mass fraction is assumed to be 0.75, the activation energy increases to 31.2 kcal.

Jan 1, 1978

By Frank M. Monroe, James R. Cost

The solubility of nitrogen in vanadium is determined from 275" to 575°C by measuring the height of the nitrogen internal friction peak of equilibrated V-N alloys. The proportionality constant at 275°C between the internal friction peak height (Q- 1) and the atom percent nitrogen in solution is found to be 0.095 per at. pct for nitrogen concentrations up to 0.8 at. pct. The heat of solution of the nitride in vanadium is 5500 cal per mole. The solubility of nitrogen in the Group V metals is discussed. LITTLE work has been performed on the vanadium-nitrogen terminal solid solution. Hahn1 found the solubility for nitrogen to be very small and reported the existence of a hexagonal phase of composition near that of V2N at the solubility limit. Rostoker and Yamarnoto2 reported the solubility to be at least 3.5 at. pct at the melting point and to be less than this value at 900°C. In addition, they reported from X-ray diffraction studies that nitrogen in solution produces tetragonality in the vanadium lattice. An X-ray study by Schonberg3 has confirmed the results of Hahn but indicated that the tetragonality observed by Rostoker and Yamamoto was due to the presence of oxygen in their specimens. Beatty4 has performed lattice parameter and hardness measurements on terminal solid solutions and found the upper limit of the solubility to be at least 0.66 at. pct N. No measurements have been made of the pressure-temperature-composition relationships (P-T-X) for the terminal solid solution. As a part of a research program on gas-metal equilibrium, an attempt was made to study the P-T-X relationships in the V-N system using both the internal friction and the gas equilibration methods which have been successful with the Nb(Cb)-N and Ta-N systems (see Ref. 5 for a review of this work). Extensive investigation, using the gas equilibration methods, showed this method not to be applicable with vanadium This was presumably due to the gettering action of vanadium sublimed on the walls of the Sieverts apparatus. Thus, the nitrogen pressure relationships with temperature and composition were not obtained. The internal friction methods were, however, found to be applicable, and the temperature-composition relationships are reported in this paper and compared with similar results for the Nb-N6 and Ta-N7 systems. The existence of a Snoek internal friction peak due to nitrogen in solution in vanadium has been clearly demonstrated. 8-10 Powers and Doyle found the peak to be at approximately 275°C for frequencies near 1 cps.8 In a subsequent paper10 they reported the proportionality constant at 275°C between the internal friction peak height (Q-1) and the concentration of ni- trogen in solution (in atom percent) as 0.06 per at. pct. The studies of Stanley and wert9 indicated qualitatively that the height of the Snoek peak decreased with aging at the peak temperature and thus suggested that internal friction methods were suitable for study of the solubility. EXPERIMENTAL METHOD The vanadium for this investigation was of particularly high purity. It was obtained from the Ames Laboratory of the U.S. Atomic Energy Commission, Ames, Iowa in the form of a 1/2-in. diam, three pass zone-refined ingot. The electrical resistivity ratio (p300ºk/p4ºk) was 160. The initial composition was determined as follows: Carbon 200 ppm Oxygen 150 ppm Chromium <50 pprn Iron 125 ppm Silicon <50 ppm Other metallic 100 pprn The initial vanadium ingot was fabricated to 30-mil wire by swaging and wire drawing without the need of intermediate annealing. Lengths of this wire were then further purified (particularly for oxygen) by outgassing at 10-6 torr at 1400°C for 4 hr. The outgassing treatment resulted in specimens with a bamboo grain structure and a lustrous appearance. Desired amounts of nitrogen were added to the outgassed wires in a Sieverts apparatus in which known amounts of nitrogen were equilibrated with the wire at 1300°C. Nitrogen concentrations were produced in the desired range from less than 1 to 10 at. pct N. Monitoring of the partial pressure of nitrogen in the Sieverts apparatus indicated that at 1300°C equilibrium between the nitrogen gas and the vanadium was obtained within 10 min. Relatively rapid cooling from the nitrogen addition temperature was obtained simply by turning off the specimen heating current and cooling to room temperature in the partial pressure of nitrogen. Internal friction measurements of wire specimens were made under forepump vacuum in a torsional pendulum at frequencies near 1 cps. The torsional pendulum was of low thermal inertia and was designed so that specimens could be heated both by a conventional tube furnace and by the joule heating of a separate current through the wire specimen." Use of a static atmosphere of helium gas as a quenching medium made it possible to cut the specimen current, rapidly cool the specimen to the measurement temperature, and make a measurement of the internal friction in less than 1 min. Because of the large solubility of vanadium for nitrogen, the internal friction peak heights were in some cases greater than Q-1 = 0.1. This high damping resulted in an estimated relative uncertainty in the damping measurements of approximately 10 pct. X-ray analyses made to identify the precipitated ni-

Jan 1, 1970

By R. F. Hehemann, R. H. Goodenow

Thermal arrest, hot-stage microscopy, and transtnission electron microscopy techniques have been employed to study the transformations in low-carbon iron and Fe-9 pct Ni alloys. In continuous cooling experiments, each alloy transforms at an essentially constant temperature for cooling rates below the critical rate required for martensite formation. However, high-tenzperature transformation in pure iron takes place by a different mechanism than that in the 9 pct Ni alloys. Pure iron exhibits an equi-a a structure with a low and random dislocation density while the 9 pct Ni alloy exhibits a cell or lathlike substructure analogous to that of low-carbon martensite. This same substructure characterizes upper bainite in higher-carbon inaterials. UNTIL relatively recently, diffusionless transformations have been considered to take place by the same mechanism and have been termed mar-tensitic transformations.l-3 The most characteristic feature2 of this mode of transformation is the shape change produced by a shear deformation and growth of the product phase frequently occurs at an extremely high velocity approaching that of an elastic wave.4&apos;5 A different mechanism of diffusionless transformation was recognized first in Cu-Ga and other copper-base alloys.6,7 From the absence of surface tilting in these alloys, it has been concluded that transformation is not accomplished by the cooperative shear displacements that occur in mar-tensitic reactions. Transformation presumably takes place by the rapid movement of an incoherent interface which is capable of propagating across parent grain boundaries. Although the transformation is diffusionless in the macroscopic sense, advancement of these interfaces is accomplished by an atom by atom rearrangement. Transformations of this type therefore require thermal activation and are generally operative only at high temperature. Although requiring short-range diffusion at the interface, propagation still occurs so rapidly that the reaction cannot be suppressed with normal cooling rates.7 The resulting microstructures exhibit large, irregular-shaped regions of the product phase, which are essentially free of crystallographic features. Consequently, these reactions have been termed massive transformations. Transformation by the massive mechanism has been reported to occur in ferrous systems involving pure iron and binary alloys of iron with nickel, chromium, and silicon by Gilbert and owen.&apos; The Fe-Ni system is of special interest in that the massive transformation was observed in alloys with less than 15 pct Ni while alloys having more than about 28 pct Ni transformed by the conventional mar-tensitic mechanism. By employing cooling rates substantially higher than those used by Gilbert and Owen, Swanson and Parr have been able to suppress the massive transformation in alloys with 0 to 10 pct Ni9 and produce martensite as revealed by surface relief. The massive transformation in the alloys having less than 15 pct Ni was identified by the lack of surface relief and an irregular rather than clearly acicular microstructure.&apos; Speich and Swann, using thin-foil electron microscopy, identified three distinctly different structures10 in quenched binary Fe-Ni alloys. From 0 to 4 pct Ni the structure consisted of blocky grains of a with a low and random dislocation density. Alloys with 4 to 25 pct Ni exhibited a cell structure with a high dislocation density; and at greater than 25 pct Ni the structure consisted of internally twinned plates. The structural change at approximately 4 pct Ni suggests that alloys with low nickel content transform by a different mechanism than those with intermediate nickel contents and the transition from the cellular to the internally twinned structures at approximately 25 pct Ni is analogous to the transition from needles to internally twinned plates that occurs over a narrow range of carbon contents in Fe-C martensites.11,12 Conventional bainitic and martensitic modes of austenite decomposition operate in ternary Fe-C-Ni alloys having less than 10 pct Ni. This investigation was conducted in order to explore the conditions under which the massive, bainitic, and martensitic transformations occur and the relationships between these modes of decomposition.

Jan 1, 1965

By D. R. Wright

"The modest thermal efficiency of the steam turbine cycle essentially determines the heat required and, therefore, the coal consumption and ash production of pulverized-coal-fired powerplants. This paper emphasizes how some properties of coal and its ash can crucially affect the operation of a steam generator and its flue gas cleaning equipment. A brief reference to some siting factors and economics reaffirms the all-pervasive influence of the properties of coal and ash and establishes the importance of a firm supply of cooling water. The economics of scale remains a compelling factor in selecting the size of units, despite disappointing performances by some of the larger units. Environmental considerations suggest that smaller units still have a role to play. IntroductionCoal fuelled one industrial and economic revolution, beginning two hundred year s ago . It was the precursor of competing fuels, notably natural gas, oil and uranium, which eclipsed it in terms of convenience and rate of growth.The turmoil that now exists because of rapidly dwindling supplies of no-longer-cheap oil and the concerns about nuclear energy-justified or unjustified-exacerbated by an operating incident at the Three Mile Island Nuclear Powerplant, prompt speculation for a resurgence of coal, especially where it cangenerate electricity to replace energy from imported oil.The world&apos;s reserves of coal are not inexhaustible, although they are ample for several decades. Of greater import is the fact that the world&apos;s coal reserve s are more widely distributed than its oil reserves, and they appear less convenient as instruments of economic and political persuasion by opportunist powers. The crux is whether or not the world will accept all that a massive, if temporary, return to coal implies.Combustion of pulverized coal in steam generators to pro duce electricity is a 50-year-old, well-understood technique; it is undergoing continuous refinement to meet evolving environmental and economic criteria and is not found wanting. It is certainly the only technique available and technologically advanced enough to replace oil immediately on a large scale. Although it may take a decade to bring a new coal-fired powerplant into service, this delay is a reflection on nontechnical and administrative processes. Capital and operating costs of coal-fired powerplants are significant and subject to inflation, but, because of the accumulated experience in this field, the ability to control costs is better than for those energy processes which are less mature or still in embryo form. More exotic, soft energy systems, touted as the panacea for world energy problems, have still to prove themselves on the scale they are needed and under the stringent climatic and operating conditions coal-fired powerplants have already mastered."

Jan 1, 1980

May 219t, 1872. THE Institute assembled in the rooms of the Geographical Society at the Cooper Union, Tuesday evening at 8 P.M. President Raymond called the meeting to order, and introduced Mr. Abram S. Hewitt, who welcomed the Institute to New York. President Raymond, in behalf of the Institute, replied. The President then read the following report of the Council for the past year. The Council respectfully report that the American Institute of Mining Engineers has held four meetings-at Wilkes-Barre, Bethlehem, Troy, and Philadelphia, respectively-all of which have been well attended, and socially and professionally most successful. The proceedings of these meetings having been published in the Engineering and Mining Journal, and sent to all members and associates, are sufficiently well known. Forty-four papers, by twenty-six authors, have been read. These papers embrace s wide range of subjects, and prove the practical character of the proceedings of the Institute. The finances are in a satisfactory condition. By the report of the Treasurer it appears that $1290.10 have been received, $519.90 expended, and that $770.20 now remains in the treasury exclusive of fees for 1872. This fund, it is hoped, will be so increased by voluntary subscriptions as to enable us before long to issue s volume of our most important transactions in a permanent form. The Council has made a favorable arrangement with the Scientific Publishing Company, publishing the Engineering and Mining Journal, by which that journal became the organ of the Institute for the first publication of the proceedings, papers, and notices to members. This arrangement it is proposed to continue through the present year unless the Institute shall otherwise direct. It is not intended to supersede the publication of an annual or occasional volume, but to maintain an interest in the Institute, and to serve the convenience of members while our funds do not permit s more ambitious publication.

Jan 1, 1873

By John Reilly

The author?s paper at RETC 2007, ?Alternative Contracting Methods? addressed strengths and weaknesses of DBB+DB and introduced Construction Manager/General Contractor (Portland model) and Alliancing (Australian model). Considerable interest in these was expressed by several public agencies at that Conference and at the presentation. The author is assisting the Washington State Department of Transportation (WSDOT) and the Toronto Waterfront Revitalization Corporation (TWRC) with possible implementation of Alliancing. WSDOT is evaluating ways to do this and is considering a delivery methodology, under existing Legislation, based on the CMGC Portland model with incentives and disincentives, moving towards Alliancing. This paper will build on the 2007 paper and update implementation considerations.

Jan 1, 2008

By H. M. Otte, A. L. Esquivel

A new leasl-squares method is Presented for determining lattice parameters of hexagonal or tetragonul structures. The method is adapted for use on electronic computers and involves a reiterative procedure. The correction factor employed raries linearly with the lattice parameter, a (determined from the Brag, angle). In contrast, Cohen&apos;s method and recent modifications of it use a correction factor that varies incersely as the squure of the lattice paramneter, a. While the recent modifications attempt to improve the precision of the extrapolated lattice parameter, a, (or-cu). by stressing the importance of the weighting factor. the present approach emphasizes the need for choosing the correct extrapolation function. A comparison between the present method (the Linear method) and Cohen&apos;s method indicates that the Linear method may be more appropriale in certain cases. through a priori no critertion appears to he available for making a chorce between the methods. The size of hexagonal and tetragonal crystal lattices is determined by two parameters, a, and c,. Although in principle the two lattice parameters can be determined independently from reflections for which h - k = 0 and 1 = 0, respectively, in practice this may be inconvenient (because of the angular positions at which these reflections may occur) or not easily possible (because of low intensity). Furthermore, if a high precision or accuracy is required, the limited number of reflections of this type available, particularly in the high-angle region, is not sufficient for the necessary corrections (mainly due to absorption) to be determined with accuracy. Several methods1-7,11-13 have been proposed employing all reflections, to obtain the optimum values, a. and co, either by a trial and error procedure or a least-squares fit. Of the latter method, cohen&apos;s5 is the best known one since it provides explicit expressions for the optimum a. and c,. However, Cohen&apos;s method is only strictly valid if an extrapolation function is used that varies linearly with l/a2 or lie2 (see Section 3), a requirement that does not appear to be generally appreciated. On the other hand, all the better known and more widely used A recent trial and error method was proposed by Massalski and King8,7 who computed extensive auxiliary tables of axial ratios vs the functions A = [(4/3)(h2 + hk +k2) + l2+(a/c)2] and C = A(c/a)2 used in computing a and c values from the observed Bragg angles. These values of a and c were then plotted against a function which permitted linear extrapolation. As a criteria; for the "optimum" values, Massalski and King rely upon a visual fitting of the line through points representing reflections of low 1-index points to compute the extrapolated value of ao and high 1-index reflections to obtain CO. The successive computations and graphical plotting required to reach the "optimum" value are quite lengthy and tedious even on a desk calculator and no quantitative assurance is obtained of having in fact selected the optimum value.* If the method of Massalski and King is used on an electronic computer, then their published tables become redundant and a least-squares fit becomes a natural selection for the choice of optimum values. Such an approach will be called the Linear method. For work now in progress on the effect of certain physical variables on the lattice parameters of hexagonal crystals, it has become essential to determine the confidence limits of small changes in the lattice parameters. Since extrapolation functions that varied linearly with a and c actually also appeared to vary linearly with l/a2 or l/c2 when tested against published as well as our data, a comparison of Cohen&apos;s method and the Linear method was considered desirable (Sections 3 and 4). For the latter method an electronic computer was required since a reiterative procedure to obtain the optimum ao and co values had to be employed. The purpose of this paper is to describe the principles of the Linear method, illustrate its application, and compare it with Cohen&apos;s method. 1) THE LINEAR METHOD The standard practice in obtaining the lattice parameters in the Debye-Scherrer method is to

Jan 1, 1965