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By J. M. Toguri, H. Flood

The application of the mass action law to the thermodynamic treatment of metal-slag equilibria is discussed. The consideration of the reactions essentially as ionic exchange equilibria is shown to be both an advantage and an aid for the elucidation of the theoretical treatment. This is illustrated by several examples. In general two different methods of application of the mass action law to metal-slag equilibria have been used by different groups of investigators. These could be called the oxide reaction and the ionic reaction approach respectively. At the recent discussion in the metallurgical section of the I.U.P.A.C. Congress in Montreal, 1961,' divergent opinions prevailed regarding the most rational way of applying the mass action law to metal-slag equilibria. This question is of fundamental importance in the treatment and understanding of theoretical chemical metallurgy. Consequently, the following is an attempt to contribute towards its clarification. As an example, the distribution of iron and manganese between molten iron and slag will be considered. I) THE OXIDE EXCHANGE REACTION APPROACH The equilibrium between iron and manganese between molten iron and slag is frequently formulated as an oxide metal exchange reaction as follows:

Jan 1, 1963

By J. D. Lindner, Gene E. Roark

Waterflooding operations in the Langston-Kleiner field. Young County, Tex., are described. Widespread application of formation fracturing has been practiced in both producing and injection wells. Field performance data arc cited which indicate than no detrimental effect on sweep efficiencies and that probable benefits in imectivily have resulted from the fracture treatments. I N T R O D U C I O N This paper is a report on a waterflood operation which is being carried out in the Lanpston-Kleiner field located in Young County, Tex. The oil reservoir aflected by this flood operation occurs in a Strawn sand member at an approximate depth of 3.550 ft subsurl'ace. The operators of' the project are Kleiner Estate. Turncr. Fiske. and West who are hereinafter collectively referred to as the Operators. Although the operation is unusual in several respects, the distinctive feature of this flood has been the widespread application of hydraulic formation fracturing treatments as a means to improve productivity and injectivity of the wells. It shall he the purpose of this paper to present basic information regarding the reservoir characteristics. op- craling practices, and waterflood behavior so that conclusions may be drawn concerning the effects which the fracture treatments have had on the performance of this water flood to datc. DEVELOP MENT Development of the 3,550 ft Strawn sand reservoir occurred during 1951 and 1952. The early development occurred on the Langston and Davis leases which arc in the northern region of the Operators' holdings and the wells were drilled on 20-acre proration units according to the field rules. However, studies of the economics of this program. coupled with the decision to proceed with pressure maintenance by water injection. resulted in the adoption of wider spacing in the later stages of development. This variation in spacing is apparent upon inspection of Fig. I upon which only the 3,550-ft Strawn sand producing and injection wells have been located on the Operators' properties. The development to the north of the operators leases is Ihe Garvey Strawn field and that to the south is the Taylor Strawn field. It wits determined that unitization of the leases to he involved in the waterflood program was not feasihle. Consequently. a system of offset injection wells, or lease line injection wells, was adopted from place to place as required to protect correlative rights in the program. This resulted in a dispersed array of injection and producing wells with relatively close proximity of wells along lease line areas and wider spacing toward

Jan 1, 1956

By Earl Hunner

IT is common knowledge that the iron orebodies of the Mesabi range lie nearly horizontal and are of trough or blanket-like types. These orebodies are from a few feet to several hundred feet thick and vary from a few acres in extent to the size of the largest one, at Hibbing, Minn., which is over 1 mile wide and 3 miles long. They are covered with sand, boulder and clay overburden and occasionally, shallow depths of ledge material, varying in total depth from about 20 to 200 ft. Large areas are not capped with overlying ledge material; the top of the ore lies directly underneath the surface material. Because of the comparatively great tonnage of ore, open-pit mining has made tremendous strides since the first open-pit ore was shipped from this range by the Merritt brothers, from the Mountain iron mine in October, 1892, and along with the great development of open-pit mining on the Mesabi range has gone a tremendous change in the character of equipment used.

Jan 1, 1930

By W. B. Triplett, H. I. Aaronson, G. M. Andes

A detailed morphological study has been made of the pro-eutectoid TiCr, and the eutectoid reactions in a Ti-17.42 pct Cr alloy isothermally transformed at temperatures from 775° through 5561°C. The morphologies of proeute,ctoid TiCr2 were found to be subject to description by the Dube morphological classification system. Grain boundary allotriomo.lphs are the dominant plpoeutectoid morphology throughout the temperature range investigated. lntragranular plates, and especially Widmanstatten sideplates, form only in small numbers. This morphological pattern differs markedly from that of the proeutectoid a reaction in hypoeutectoid Ti-Cr alloys (AIME Trans., 1957, vol. 209, p. 1227; 1958, vol. 212, p. 624), in which plates form prolifically throughout wide ranges of temperature. The eutectoid reaction is nonlamellar in character at 675°C. An increasingly prominent lamellar component develops at lower temperatures. The proeutectoid TiCr 2 and the eutectoid transformations have been studied metallographically in a hypereutectoid titanium-chromium alloy. This investigation was undertaken with the immediate objective of comparing these transformations with their counterparts in hypoeutectoid titanium-chromium alloys, studies of which have been recently completed.1,2 It was also intended, however, to contribute to the general literature on transformations of these types. Especially in the proeutectoid case, this literature is still sufficiently sparse to make difficult the testing of generalizations on the mechanisms of these transformations. TiCr, is the only intermetallic compound in the titanium-chromium system.3-5 The TiCr2 phase field extends to a maximum temperature of 1350°C) and encompasses the approximate composition range of 62 to 68 pct Cr at lower temperatures.3'4 At temperatures below 1000°C, TiCr2 has a MgCu,-type fcc structure, with 24 atoms comprising a unit cell.6,7 Only fragmentary observations on the morphology of proeutectoid TiCr2 have been previously reported. An observation which is of considerable importance with respect to the results obtained during the present investigation was made, however, on anisother-mally transformed alloys with high chromium (48 to 70 pct Cr) contents.3"8 Despite the occurrence of extensive impingement, it is apparent that a substantial proportion of the proeutectoid TiCr, which precipitated in these alloys grew in the form of Widmanstatten plates. Several observations have been made on the eutectoid reaction in hypereutectoid alloys during investigations of the titanium-chromium phase di-

Jan 1, 1961

By Norman Pilling

THE solubilities of a series of experimental alloys covering the range 0 to 100 per cent. Ni, 0 to 30 per cent. Cr have been studied under conditions of complete submersion in several fully aerated acid solutions, and in solutions containing sulfurous acid. In nonoxidizing, hydrogen-discharging acids, if the nickel content is below a certain critical amount, chromium increases the rate of solution and nickel decreases this rate; this critical content of nickel is about 13 per cent. Alloys containing more than this corrode at a constant minimum rate independent of iron, nickel or chromium contents. Austenitic chrome-nickel steels may thus have a resistance to these acids equal to that of nickel-chromium alloys. In nitric acid and in unaerated sulfurous acid rather sharp limits of attack occur which are principally dependent on chromium content. In the former the limit of attack is not related to a particular chromium content but varies continuously with acid concentration. The action of sulfurous acid on these alloys is highly dependent on the presence of small amounts of other substances in solution, and many sulfurous acid mixtures rapidly attack alloys to which the pure acid is wholly inert. The observed effects are. not compatible with Tammann's theory relating corrosion resistance to lattice structure but are believed to be concordant with current views of the electrochemical nature of corrosion.

Jan 1, 1929

By J. J. Rutledge

THE first method of working coal mines in the middle western states, more particularly in Illinois, Indiana and Missouri, was by means of the so-called single-entry method. In this method a single main passageway, or entry, was driven in the coal seam. with no parallel passageways, and from this pas-sageway or entry there were turned at intervals sim-ilar cross-passageways or entries, and from these cross-passageways, if the coal seam worked lay fairly horizontal, rooms were turned right and left. These crude methods of working were followed when the com-panies opening the mines were small and of very limited capital, and when the demand for coal was small and irregular. The principal desire was to produce coal in the short-est possible time and at the cheapest price. The chief evil resulting from such method of working was de-fective ventilation, although there were other serious drawbacks. There were then few or no good mining laws and no restrictions on those operating the coal mines. The hours of labor were long, the wages low, and the miners accordingly worked hard. All the coal was either sheared or undercut with a pick by hand. Very little solid shooting and no machine mining was done. What little air entered the mine, openings was introduced through the entries or. headings and thence conducted through the rooms by means of curtains; in many cases, as the workings became more exten-sive, the number of curtains added so materially to the mine resistance that ventilation was extremely in-efficient. Shots were fired by the miners at any time during the working shift and consequently there was more or less powder smoke or fumes in the mine work-ings all day long. Moreover, the working days were much longer than at present. The fine, dry coal-dust falling from the miners' picks while they were shear-ing or undercutting the coal filled the mine atmosphere and was taken into the lungs of the mine employees.

Jan 2, 1927

By M. R. J. Wyllie

In a recent publication1 wetting phase relative permeability was exvressed as: and it was stated that a similar expression applied, mutatis mutandis, to non-wetting phase relative permeability; i.e., In Equations (1) and (2), Sw and S0 are respectively the wetting and non-wetting phase saturations as a fraction of the pore volume; PC is the capillary pressure; I; the wetting phase electrical resistivity index; IN, the analogous non-wetting

Jan 1, 1951

By M. R. J. Wyllie

In a recent publication1 wetting phase relative permeability was exvressed as: and it was stated that a similar expression applied, mutatis mutandis, to non-wetting phase relative permeability; i.e., In Equations (1) and (2), Sw and S0 are respectively the wetting and non-wetting phase saturations as a fraction of the pore volume; PC is the capillary pressure; I; the wetting phase electrical resistivity index; IN, the analogous non-wetting

Jan 1, 1951

By W. A. James

NATURE endowed the Niagara Frontier with great resources but it was the molding of these resources by the early pioneers that assured its future development. This great industrial district of New York stretches along about fifty miles of shore line on the eastern end of Lake Erie and the Niagara River, embracing the two counties of Erie and Niagara, with the city of Buffalo about in the center. This location at the junction of the eastern end of the Great Lakes and the western boundary of the State, a great focal point of land and water, transportation, guaranteed the development of the Frontier. Although the first white settlers came to this section in 1784, it was not until after the turn of the nineteenth century that real development started. Perhaps the most significant influence in the early days was the completion of the Erie Canal between Buffalo and Albany in 1825. This then monumental achievement gave Buffalo an advantage in the race for the best trade route to the Western

Jan 1, 1938

By Francis S. Kendorski

INTRODUCTION Nuclear waste has been generated since the time of the Curie's and continues to be generated worldwide at an ever-increasing rate as the world will (and should) rely more and more upon fission (and hopefully fusion) for power. Also, the needs for strategic weapons will also generate so-called defense wastes. The largest class of high level nuclear waste (HLW) is spent fuel, the tail end of the nuclear reactor fuel cycle. At present, spent fuel is stored at the reactors producing it or at a few accepting places for away-from-reactor storage. All such storage facilities, as presently constructed, will begin to run out of usable storage space during the next decade or so. Congress enacted and President Reagan signed into law in early 1983 the National Nuclear Waste Policy Act of 1982. This law provides for the permanent isolation of nuclear waste in deep geologic repositories. The Act sets 1998 as the date at which the first repository should be operational. This date is extremely ambitious, and the Department of Energy (DOE), which is charged with the responsibility of constructing and operating repositories, admits that this date will slip by at least a few years. The Act also provides for licensing of repositories by the Nuclear Regulatory Commission (NRC) in a fashion very similar to nuclear power generating reactors. This requirement imposes a very special rigor on the analyses, investigations, designs, construction, and operation of repositories so as to assure the protection of the public and the environment from radioactive contamination. In addition the states and affected Indian Tribes must be consulted, especially concerning siting, and, needless to say, no one wants a HLW repository in their back yard.

Jan 1, 1984

By V. Niemitz

Approximately 30 miles east of Chicago on the southern shores of Lake Michigan stands Bethlehem Steels newest fully integrated steelmaking facility-the billion dollar Burns Harbor plant. The first phase of what will ultimately be the most completely integrated and flexible materials handling system for a steel mill in the western hemisphere is now complete.

Jan 1, 1970

I strongly endorse Mr. Jackson's (Inland Steel Company) oral comment on the authors' paper that, as blast furnace slag is removed from the BOF charge, lime solution may be retarded. After two or three pourings, the blast furnace slag will contain some iron oxide and considerable manganese oxide, and it is hot and possibly still liquid. A few thousand pounds of this slag will speed up the slag development rate considerably and could be considered a good auxiliary flux. Although the removal of blast furnace slag from the BOF charge lowers the total sulfur load by 40 to 50%, we must have a good, quick slag development in the BOF to bring .030 to .035% sulfur hot metal to .020%, a requirement on a high percentage of our steels today. In discussions at off-the-record meetings and one not published at last year's annual meeting as well as discussions with many operators over the past 1-1/2 years, I predicted that the removal of blast furnace slag could slow down lime dissolution and that, if a shop had dissolution problems before, the problem could be quite serious.

Jan 1, 1972

By Hiroshi Oikawa, A. G. Guy

Recent experimental evidence has shown that it is often incorrect to neglect the reactions occurring at an interface with respect to the diffusion reactions. By introducing reaction-rate constants and k for the transfer of components 1 and 2 between the a and b phases, a phenomenological description has been devised for the coupled processes of diffusion and in-terfacial reaction. An illustrative example has been analyzed with the aid of a suitable computer program. The results indicate that for kab values on the order of 10'1 cm per sec and Ð values of about 10¯10 sq cm per sec, the interfacial reactions are significant during the first 10 2 to l0 6 sec of a diffusion experiment. Among the observable effects of the interfacial reactions in this case appear to be the burying Kirkendall markers and an anomaly in the initial shifting of these markers. THE study of diffusion between two phases is especially important because of its direct connection to phase transformations. For example, the transformation of austenite to ferrite involves diffusion in the a and ý phases and also an interfacial reaction (trans formation) at the a/? interface. If ferrite and aus-tenite are the two members in a diffusion couple, the same two reactions occur during the diffusion process. The numerical values obtained for the diffusion coefficients and interfacial-reaction constants from diffusion experiments can then be employed to predict phase-transformation behavior. Refinement of the calculations of phase transformation is also suggested by the present method for treating two-phase diffusion. In the recent paper by Nolfi et al.' only the solute com ponent is considered in the interfacial reaction accompanying a phase transformation. The present analysis demonstrates that both components must be considered. It is generally recognized that reactions of some kind must occur at the interface in a two-phase diffusion couple, but usually it is assumed that the interface reaction occurs so rapidly that its effect on the overall process is unobservable because the slower diffusion process determines the kinetics of the process. However, Seith and Heumann 2 pointed out that effects of the interfacial reaction should always occur in the early stages of diffusion, and recently Eifert et al. 3 have shown that interfacial reactions influence the composition and motion of the interface in a/ß Al-Cu diffusion couples during the entire course of prolonged, high-temperature treatments. A general procedure for handling the combined processes of interfacial reaction and diffusion in a binary, two-phase system is to introduce kinetic coefficients for the interface reactions and to develop the system of equations governing the interlinked processes of diffusion and interface reaction. The resulting equations, although not amenable to solution in closed form, can be usefully manipulated by a digital computer. INTERFACIAL REACTIONS IN TWO-PHASE DIFFUSION Consider the general case of diffusion between two solid solutions, a and ß, which are adjacent phases in a binary system, Fig. 1. Two semiinfinite bars having compositions c1 and c0ß are jointed at x = 0. If concentrations are expressed in volume fraction,4

Jan 1, 1970

By D. M. Hausen

A quantitative x-ray diffraction method has been developed for the analysis of alteration minerals in wallrock. Alteration data are plotted and contoured (analogous to geochemical data). Alteration trends outlined by this technique correlate closely with geochemical anomalies, and in some cases extend well beyond the perimeter of anomalous base metal values. "Monomineralic contouring," applied originally to porphyry-type mineralization, has been extended to other types of mineralization, including volcanogenic massive sulfide deposits. Equipment and techniques used in the quantitative measurement of alteration mineralogy are discussed.

Jan 1, 1980

By William Best

OIL burners, oil furnaces, and methods of installation, have been the subject of many articles, but information concerning oil-burning systems, based upon scientific principles, is still in great demand, especially in the manufacturing districts of our country. Fuel oil, as it is termed (this being the residuum from oil refineries), has for many years been of great service to our manufacturers, and has justified its popularity not only by producing a superior manufactured product, but by turning out approximately 50 per cent. more product than can be made with coal fuel under like conditions. To install a system requiring only an oil-storage tank, a small pump, and an oil-supply main with numerous laterals leading to the various burners, furnaces, boilers, etc., is a comparatively simple matter; and, because fuel oil is very volatile, it is not necessary to heat it, even during the winter months in a very cold climate. Furthermore, only a small amount of power is required to atomize fuel oil, this often being done by a positive pressure blower, or by a mechanical burner. An analysis of fuel oil, together with that of various other liquid fuels, is given in Table I.

Jan 2, 1914

By C. P. Kempter, H. L. Brown

Recently Chang determined heat content values of tantalum monocarbide and tungsten monocarbide from 325" to985°Kand 326" to 912"K, respectively, and, using other published data, made certain solid-state calculations for these two compounds. Chang expressed his Cp values in units of cal per "g-atom alloy" OK. We consider this poor usage since l) tantalum monocarbide and tungsten monocarbide are not alloys, and 2) an atom of an alloy does not exist. However, one may convert his values to units of cal per mole OK by merely doubling them. For TaC he calculated a Nernst-Lindemann parameter of 9.07 x lo-' "g-atom per cal". We have refined the calculation of this parameter and have arrived at a much lower value. Rather than approximating the true coefficient of volume expansion, a,, as three times the true coefficient of linear expansion, a, we calculated u, from the TaCo.99, lattice expansion data of Fries and Wahman.38 At 25°C a, = 14.3 x 10s per OC. The molar volume was calculated to be 13.32 cu cm per mole at 25°C. From the lattice compression data of Champion and Drickamer~' for "TaC,.,," we determined the room-temperature compressibility to be 3.5 x 10-l3 sq cm per dyne by plotting l/Vo (aV/ap) vs applied pressure. (Since the lowest pressure at which Champion and Drickamer reported a relative volume was 20 kbars, one may calculate an approximate compressibility only. Chang calculated a compressibility of 3.175 x 10-l3 sq cm per dyne from the same data.) We also used twice Chang's value of Cp = 4.38 cal per "g-atom alloy" OK for the molar heat capacity at 25°C. From these four values we calculated a Nernst-Lindemann parameter of 5.8 x 10-l4 mole per erg or 2.4 x lo- ' mole per cal, and a Cdil value of 2.3 x 10' ergs per mole OK. In the case of tungsten monocarbide no isothermal compressibility has been reported; however, one may calculate an approximate Nernst-Lindemann parameter by using the adiabatic compressibility reported by Brown, Armstrong, and Kempter." Using the WC lattice expansion data of Mauer and Bolz~l we calculated a, to be 12., x l0-' per OC. The molar volume was calculated to be 12.5 cu cm per mole. We used twice Chang's value of Cp = 4.18 cal per "g-atom alloy" OK for the molar heat capacity at 25°C. From these four values we calculated an approximate Nernst-Lindemann parameter of 2 x lo-' mole per cal, which is much

Jan 1, 1969

By H. H. Rachford, W. P. Schultz

The use of computing machines to solve physical problems has made it imperative to represent physical data in a form computing machines can use. Although curve-fitting is an old and well-practiced art, there still seems to be some interest in questions regarding what methods can be used and why. Even though there are many good references on this subject, it may be of some value to discuss a particular method which has been found to be useful, and to make available the associated tables for its use in the hope that there can be saved a few of the tedious hours necessary to reduce many of the suggested methods to practice. Although a very brief discussion of the mathematical background of the tables is included immediately below, those interested only in their use can skip directly to the section on Use of the Tables. Direct Fit of a Set of Points A frequently encountered problem is: Given data which can be represented by a smooth curve +(x), to find an easy-to-evaluate function F(x), with only a few coefficients, which is a good approximation of +(x) on the interval 0 5 x 5 x,,. Consider F(x) as a linear combination of m + 1 arbitrary, single-valued, continuous, linearly independent functions, f,(x), Ff.r) = a,f,,(x) + a,f,(x) + . . . -+ aifi(x) + If the value of Q(x) is known or can be read from the curve at the points xj: +(x,), +(x,), . . . +(xj) . . . +(x.), and if n = m, then all the coefficients of F(x) can be determined, and F(x,) — +(x,) = 0 for j =. 0, 1, . . . n. This follows from the solution of the set of linear simultaneous equations. +(x<.) = aofu(x,) + aJI(x0) + . . . + a,,f,,(x,) =a, = f,,(x,) + a,f,(x,) + . . . + a,f,,(x,) +(x,,) = a,,f,(x,,) + a,f,(x,) + ... + a,,f.,(x,,) ...........(2) for the coefficients ai. Although the set a, from the solutions of the set of Equations 2 yields an fix) which gives an exact value of $(x,) for the n + 1 points, there is no restraint on ~(xj in the interval xi < x < xj+,. Indeed, if the points +(x,) are not sufficiently smooth, very serious differences may arise between F(x) in the interval and the smooth curve +(x). Least-Squares Fit It has been suggested&apos; that if n is made to exceed m, and the set a, is found to minimize the function the function F(x) is much less sensitive to small errors in +(xi), and usually provides a much better fit to the smooth function +(x). This is known as the best fit in the sense of the least-squares error. To minimize $, set £ = 0,i = 0,1,... iTi,.....(3) The m + 1 equations from Equation 3 are k—n k=n a.^p /,,(a) f,(xt) + a, X A: = 0 k=O k = n k = n k=0 k=0 +(x.) f,(x,),............(4) one equation being obtained for each i = 0, 1, . . . m. Inasmuch as the arbitrary functions f(x) may be evaluated for x,, k = 0, 1, . . . n, and the +(x,) are known values of the curve to be fitted, the simultaneous Equations 4 may be solved for the set a,. Particular Functions Given the functions fi(x) and the set +(xj), the solutions for require evaluating a number of sums of products as well as the solution of an m + 1 order set

Jan 1, 1956

Meeting, Aug. 20, 1913, B te, Montana, at 12.45 p.m.-On, the written request of 27 members of oft Institute residing in Montana, the Montana Local Section was established, and the following Committee was appointed by the President of the Institute to complete the organization : E. P. Mathewson, Chair pan; Frank M. Smith, Vice-Chairman; D. C. Bard, Secre-tary, Montana State School of Mines, Butte, Mont., Oscar Rohn, James L. Bruce. The President reported the appointment of a Committee on Mining Law, the names of whose officers and members are given on page xxxv of this Bulletin, and these appointments were approved. It was voted: That the Committee on dining Law be requested to establish a Sub-Committee on Censorship, a majority of whom shall be lawyers; and, further, that no paper on mining law be recommended for publication to the Committee on Papers and Publications, unless it is previously approved by the Sub-Committee on Censorship of the Committee on Mining Law. The President reported progress in the matter of co-operation between the Institute and the United States Bureau of Mines, through Committees of the Institute. The President reviewed the history of plans for a union or affiliation with the Mining and Metallurgical Society of America, and the following minute was then adopted : " The Board of Directors of the American Institute of Mining Engineers has carefully considered for several months the question of union or affiliation with the Mining and Metallurgical Society of America ; and, while at an earlier time and under other circumstances, such. a union might have been accomplished, yet under present circumstances the Directors of the Institute deem such union inexpedient. "While thanking the Mining and Metallurgical Society of America for its consideration of the matter, we believe that further discussion of the subject will serve no useful end, and we conclude it best that the Society and the Institute continue their useful functions and friendly relations side by side, as heretofore."

Jan 10, 1913

By W. R. Ingalls

The manufacture of zinc oxide directly from the ore is one of the most important contributions that America has made to the metallurgy of zinc. Heretofore, this has been done chiefly for the production of zinc and zinc-lead pigments, and the method has been known as the Wetherill process. While that term may properly be applied to the process for pigment manufacture, it must be recognized that the principles of the process are of far wider application; and that there is going to be wider application in the immediate future is more than an expectation. I have in mind the use of the process as a method of igneous concentration. Igneous concentration is broader in its scope than the Wetherill process, for it may be done in the blast smelting furnace, or in the re-verberatory, or by other means. Igneous concentration is a rather clumsy term, and I prefer to introduce the new generic expression of "zinc burning," which is convenient, readily understood, and precise, for in all cases the zinc oxide is reduced to metallic form, is volatilized and is then burned to zinc oxide, the latter happening, however, after the zinc has been separated from the residue of the ore. As previously indicated, zinc burning may be done either in blast or reverberatory smelting, the gangue of the ore being scorified and drawn off as slag, while other metallic minerals are reduced to matte or metal. Such processes have heretofore been practised on fairly large scales. Thus, F. L. Bartlett smelted zinc ores at Con City, Colo., in specially designed blast furnaces, wherein the smelting column was only about 18 in. high. Such a limitation was necessary in order to prevent zinky accretions in the shaft of the furnace, which in course of time would have interfered with its operation. In running the Bartlett furnaces it was easy to bar them off, indeed, to poke right down into the smelting zone, and keep things going freely. Some iron blast furnaces in Virginia and the spiegeleisen furnaces of the New Jersey Zinc Co. afford other examples of zinc burning in blast-furnace smelting, although in their cases the happening is incidental rather than a primary purpose. Just as zinc may be burned off in a blast furnace, so also may it be done in a reverberatory. Indeed, there is less trouble, in some respects, in a reverberatory, for therewith there is no shaft in which accretions may

Jan 1, 1918

By O. A. Cheadle, F. E. Lane

ThE computer program for arbitrary crystal systems reported by Camp and Clum&apos; has been modified to make it more convenient for hexagonal crystals. The program&apos; uses the Miller indexes (hkl) which can be confusing for hexagonal crystals while the modified program uses the Miller-Bravais indexes with four axes; e.g., the angles between the (110) planes, Fig. 1, are 0 and 90 deg but in the (hkil) system the angles between the (1150) planes are 0 and 60 deg. If a Laue photograph is taken of a crystal oriented with the prismatic planes nearly parallel to the film then the spots on the stereo graphic projection will be from high-index planes. The probable positions of the low-index planes, e.g., (0001) plane, can only be obtained from the intersection of zones and this is not accurate to 1 or 2 deg. The number of planes considered by the program (card 1)&apos; has to be limited to the ones of low index or the program time is excessive but a solution will not be obtained if one of the spots has an index that is not being considered. To overcome this problem the program1 was modified so that if no fit was obtained at *1 deg (card 3) of the tabulated angles then ±2 or ±3 deg was tried. If still no solution was obtained either due to one of the angles not being measured correctly to ±3 deg or because one of the spots was from a high-index plane, then the last spot was discounted and a fit tried for the remaining spots at i1 deg, and so forth. The minimum number of spots that the program will try to fit is five. If the limit on any individual index is 4 (card 1) and (h + k + l + 1) is six then twenty-three planes are considered and there are over 1000 interplanar angles. Many pairs of planes have very similar interplanar angles and with the errors previously mentioned the program will often produce several alternative solutions to a group of spots particularly at ±2 or ±3 deg. However without the program the alternative solutions would probably not have been found. If a large number of spots are used the number of possible fits is reduced. In the example shown in Fig. 2, if only spots which are on the film are used (case 1) the program gives six possible solutions, Table I. However if points 7 and 8 are also used (case 2) the program gives only one fit which also agrees with a standard projection of the crystal. In addition to time-saving the program ensures that a correct solution is obtained since it is unlikely that all the alternatives would have been gound manually; the first would probably be assumed to be the correct solution. The program has been used for zirconium crystals but is equally suitable for other hexagonal materials.

Jan 1, 1969