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By Robert A. Haney, Stephen J. Gigliotti, James L. Banfield

A series of investigations were made by the Mine Safety and Health Administration to evaluate the performance of various face ventilation systems as part of a program to reduce frictional ignitions of methane and to develop face ventilation systems that could be used with the line brattice more than 10 feet from the face. Tests were conducted in a full-scale laboratory model of a face area. Systems tested included unassisted blowing and exhaust line brattice, diffuser fan and spray fan systems. Systems were evaluated at air quantities ranging from 1.4 to 7.0 m3/s (3,000 to 15,000 cfm), and brattice-to-face distances from 1.5 to 9 meters (5 to 30 feet.). Tests were designed so that systems could be evaluated for the location of the high-point methane concentration in the face area, methane dilution capacity, and face ventilation index. The methane dilution capacity is the total amount of methane a system can dilute to 1.0 volume-percent. The face ventilation index is the efficiency at which the available face air volume is being used.

Jan 1, 1982

Temperatures in the Open-hearth Furnace. By Robert B. Sosman. (Metals Tech. Aug. 1948, T.P. 2435) Steelmaking Direct Oxidation in the Basic Open Hearth Process. By E. R. Hughes and F. G. Norris. (Metals Tech., June 1948, T.P. 2380) With discussion Operation of Oxygen-enriched Open-hearth Furnaces. By J. S. Marsh. (Metals Tech., Aug. 1948, T. P. 2416) With discussion Role of Thermochemical Factors in Basic Open Hearth Production Rate. By T. E. Brower and B. M. Larsen. (Metals Tech., Oct. 1948, T.P. 2451) Structure, Segregation and Solidihcation of Semikilled Steel Ingots. By M. Tenenbaum. (Metals Tech., Sept. 1947, T.P. 2273) With discussion The Origin of Silicate Inclusions in Basic Electric-arc-furnace Steel of Higher Carbon Contents. By Axel Hultgren. (Metals Tech., Aug. 1948, T.P. 2418) A Method for Determining the Origin of Surface Defects in Rolled Steel Products. By C. L. Meyette and V. L. Elliott. (Metals Terh., June 1948, T.P. 2368) With discussion Gases in Steel The Sampling and Analysis of Steel for Hydrogen. By G. Derge, W. Peifer and J. H. Richards. (Metals Tech., June 1948, T.P. 2362) With discussion Apparatus for the Hot-extraction Analysis for Hydrogen in Steel. By C E. Sims and G. .I. Moore. (Metals Tech., June 1948, T.P. 2369) With discussion A Quantitative Experimental Investigation of the Hydrogen and Nitrogen Contents of Steel during Commercial Melting. By C. E. Sims, G. A. Moore and D. W. Williams. (Metals Tech., Feb. 1948, T.P. 2347) With discussion The Effect of Hydrogen on the Ductility of Cast Steels. By C. E. Sims, G. A. Moore and D. W. Williams. (Metals Tech., Sept. 1948, T.P. 2454) Sulphur in Ironmaking Kinetics of the Transfer of Sulphur across a Slag-metal Interface. By Lo-ching Chang and K. Goldman. (Metals Tech., June 1948, T.P. 2367) With discussion Some Correlations between Variables Affecting Sulphur in Blast Furnace Iron. By T. E. Brower and B. M. Larsen. (Metals Tech., Sept. 1948, T.P. 2465) Tracer Study of Sulphur in the Coke Oven. By S. E. Eaton, R. W. Hyde and 11. S. Old. (Metals Tech., Sept. 1948, T.P. 2453) Transformation of Austenite Anisothermal Formation of Bainite and Proeutectoid Constituents in Steels. By Leonard D. Jaffe. (Metals Tech., Dec. 1947, T.P. 2290) With discussion Austenite Transformation Above and Within the Martensite Range. By R. T. Howard, Jr. and M. Cohen. (Metals Tech., Oct. 1947, T.P. 2283) With discussion

Jan 1, 1949

(Members are urged to send in for this column any notes of interest concerning themselves or their fellow-members.) Members and guests who called at Institute headquarters during the period June 10, 1916 to July 10, 1916: Arthur Adams, Miami, Ariz. John M. Lovejoy, New Rochelle, N. Y. J. H. Batcheller, Mattapoisitt, Mass. J. F. Manning, Seoul, Korea. R. S. Bonsib, Low Moor, Va. E. P. Mathewson, Anaconda, Mont. E. L. Booth, New York, N. Y. Edwin W. Mills, Seoul, Korea. C. L. Bryden, Scranton, Pa. Arthur Notman, Bisbee, Ariz. F. Crabtree, Pittsburgh, Pa. L. B. Reifsneider, Daiquiri, Cuba. L. B. Eames, Pueblo, Colo. W. S. Schuyler, Berkeley, Cal. S. J. Gormly, Guayacan, Chile. 0. N. Scott, Toronto, Ont., Canada. Ernest A. Hersam, Berkeley, Cal. Arthur F. Taggart, New Haven, Conn. A. W. Hudson, Douglas, Aria. Warren D. Thompson, Boston, Mass. Chas. W. Johnston, West Norfolk, Va. Thor. Warner, IGngman, Ariz. Rodolphe L. Agassiz has been chosen president of the Calumet & Hecla Mining Co., an office which has been vacant for over a year. Percy E. Barbour, Managing Editor of the Engineering and Mining Journal, resigned his commission as 2d Lieutenant in the Main Coast.

Jan 8, 1916

By AIME AIME

COMMITTEES. LOCAL COMMITTEE.-R. C. Crawford, Chairman; Harrison W. Craver, Secretary; Julian Kennedy, Taylor Allderdice, E. W. Pargny, Charles L. Miller, W. H. Rea, S. A. Taylor, M. E. Wadsworth, W. A1. Henderon, A. C. Dinkey, W. L, Jones, E. L. Messier, George Mesta, J. H. Jones, G. H. Riley, S. L. Goodale, D. W. McNaugher. LADIES' COMMITTEE.-Mrs. Taylor Allderdice, Chairman; Mrs. Julian Kennedy, Mr. R. C. Crawford, Mrs. E. M. Herr, Airs. J. W. Marsh, Mrs. T. A. Mellon, Mrs. G. P. Bassett, Jr., Airs. D. M. Clemson, Mr. Charles L. Miller, Mrs. V. L. P. Shriver, Mrs. W. A. Bostwick, Mrs. A. C.. Dinkey, Mrs. A. P. Childs, Jr., Mrs. F. R. Dravo, Mrs. Hermon Griffin, Mrs. W. H. Nimmick, Mrs. F. H. Lloyd, Mrs. S. G. Cooper, Mrs. S. H. Church, Mrs. E. N. Ohl. The Institute Headquarters was established at the Hotel Schenley, where a bureau of information was maintained for the benefit of the visiting members and guests of the party during the time of the meeting. TECHNICAL SESSIONS. The first session, held Tuesday evening, Mar. 1, 1910, in the large lecture hall of the Carnegie Institute, was called to order by Harrison W. Craver, Secretary of the Local Committee. Mr. Craver introduced Dr. John A. Brashear, who extended to the members and guests a hearty welcome to the city of Pittsburg, to which David W. Brunton, President of the Institute, responded. The following papers were presented in oral abstract by the authors: Biographical Notice of Dr. Charles B. Dudley, by Dr. R. W. Raymond, New York, N. Y. Biographical Notice of William Metcalf, by Col. II. P. Bope, Pittsburg, Pa. Development of Hindered Settling Apparatus, by Robert H. Richards, Boston, Mass. (Illustrated by lantern-slides.) A Few Mining Districts in the Argentine Republic, South America, by Z. S. Beyl. (Illustrated by lantern. slides.)

Apr 1, 1910

(The following list contains the names of those members of the Institute of whose connection with military service we have only recently become acquainted; it also includes the names of a few who have recently been promoted or transferred, indicated by a *. A complete list was published in the Year Book, issued as a supplement of the Bulletin for March, 1915.) ADAMS, ARTHUR K., Lieut., Co. 2, E. 0. T. S., Camp Humphreys, Va. AMIDON, CLAUDE E., 11th Training Co., Casual Camp, Camp Cody, N. M *BARBOUR, P. E., Capt., Engineer Corps, U. S. A. *BENHAM, W. M., Master Engr., Headquarters Dept., 115th Engrs. A. E. F., Care Postmaster, N. Y. BICKNELL, H. L., Pvt., Co. D, 27th Engrs., Camp Leach, D. C. *BLANDY, S. H. B., Lieut., Royal Horse Artillery, B. E. F.

Jan 10, 1918

EDWARD W. PARKER,* Philadelphia, Pa. (written discussion ?).-The two papers on coal-mine costs and pride fixing that Mr. Norris has contributed to the Transactions possess as much general interest and are of as much value to the coal-mining industry as any papers that have been presented in recent years. Until recently one of the troubles with the coal business, and especially the bituminous branch of it, has been that because of the lack of a uniform system of cost accounting (many operators, I regret to say, not having had any system at all), the industry as a whole may be said not to have known where it was at. The system adopted by the Federal Trade Commission may not be absolutely perfect but it has accomplished something in that it has compelled a uniform method of reporting and tabulating costs giving results of these compilations which are comparable. The Institute and the coal-mining industry owe a vote of thanks to, and of confidence in, Mr. Norris and his two associates on the Engineers Committee of the Fuel Administration, Messrs. Garnsey and Allport, for the great work they have done in interpreting the results compiled by the Federal Trade Commission, not to speak of the personal sacrifices made by them in giving their services to the government. Those who have read Mr. Norris' paper will probably join me in wishing he had brought out a little more fully the real meaning of the charts so far as they indicate the difference between the cost of producing a ton of anthracite and the price the operators receive for their product. Mr. Norris could have done this more satisfactorily than anyone else. It seems to me that particular attention should be drawn to the fact that, according to these charts, and the tables accompanying them, not less than 25 per cent. of the total output of anthracite, whether "company" or "individual," during the period covered by Mr. Norris' paper,

Jan 4, 1919

Aalde, Kaare, (S'40) Box 827, Socorro, N. M. Aase, Glenn D., (S'40) Engr. Experiment Sta., Univ. of Utah, Salt Lake City, Utah. Abadesco, Enrique A., (S'39) Student. College of Engrg., Univ- of the Philippines, Manila, P. 1. Abbott, John L., (S'40) Met. Engr., Engr. Trainee. Wright Aeronantical Corp., Paterson, N. .J. Abbott, Robert H., (S'42). Agricultural & Mech. College of Texas, College Sta., Tex. Abreu, Ovidio M., (S'38) Dept. of Geol., Compauia Cousulidada de Petroleo, Caracas, Venezuela. Acomb, Allen, (S'41) 3921 Chestnut St., New Or¬ leans, La. Adam, Howard W., (S'41) Montana School of Mines, Butte, Mont. Adams, Charles E., (S'42) Uuiv. of California, Los Angeles, Calif. Adams, Charles W., (S'39) Student, Michigan Col¬ lege of Min. & Tech., Houghton, Mich. Adams, H. Travis, (S'39) 310 South 5th St., Bur¬ bank, Calif. Adams, John W., (S'42) Univ. of Texas, Austin, Tex. Adams, Rob L., (S'40) Lt., B. 0. C. No. 12, Fort Sill, Okla. Adamson, Charles R., (S'41) Uuiv. of Utah, Salt Lake City, Utah.

Jan 1, 1942

By G. R. Speich

The precipitation of the Feab and Fe,Ti Laves phases (MgZn, type, C14) from Fe-Nb and Fe-Ti solid solutions, respectively, has been studied in the temperature range 500" to 800°C using hardness measurements, light and electron microscopy, and X-ray and electron diffraction. The Fe-Nb alloys contained 0.96, 1.67, and 3.80 pct Nb and the Fe-Ti alloys 3.5, 5.8, and 8.8 pct Ti. In both systems only the equilibrium Laves phase is formed, with nucleation occurring at grain boundaries, at dislocations, and in the matrix. No cellular precipitation or transition phases were observed. The precipitation of the Laves phase in a fine dispersion leads to significant hardening in both systems. The hardness of the aged alloys is proportional to the reciprocal of the square root of the interparticle spacing. The maximum solid solubility of titanium in a! iron is 9.0 pct Ti at 1280°C. THE precipitation of the FezNb and FezTi Laves phases (MgZn2 type, C 14) from Fe-Nb and Fe-Ti solid solutions, respectively, has been investigated as part of a continuing study of the mechanisms of precipitation from ferritic binary iron-base alloys. The iron-rich portions of the Fe-Nb and Fe-Ti phase diagrams are shown in Fig. l(a) and l(b). The Fe-Nb diagram is essentially that given by ansen' with the more recent work of Hume-Rothery and Gibson2 added. Goldschmidt3 indicates that the FezNb Laves phase has a solubility extending from 32 to 55 wt pct Nb. The Fe-Ti diagram is also essentially that reported by Hansen.l The recent results of Nishimura and kamei, Murakami, Kimura, and Nishimura,' indicate that the FezTi Laves phase has a solubility extending from 22.5 to 30.5 wt pct Ti. The L/6 + FezTi eutectic temperature of 1298°C indicated by Kornilov and oriskina' has been adopted. The addition of niobium or titanium to iron lowers the 6 — y transformation temperature and raises the y — a! transformation temperature. This results in a closed y field in the Fe-Ti system, but the lower solubility of niobium in a! (6) iron results in a eutec-toid, 6 — y + FezNb, at 1200°C, and a peritectoid, y + FezNb —-a, at 989°C in the Fe-Nb system. The maximum solubility of niobium is reported to be 4.5 wt pct in 6 iron,' 1.0 wt pct in y iron,7 and 1.8 wt pct in a iron.' Some results from the present work indicate that the maximum solubility in a! iron is actually less than 0.96 wt pct Nb. The maximum solubility of titanium in a! (6) iron is somewhat uncertain since the early work of To faute and Butting-haus indicated a value of 6.0 wt pct while later work of Kornilov and Boriskina6 yielded a value of 14.0 wt pct. The present work indicates that the maximum solubility is actually 9.0 wt pct. In both systems the phase in equilibrium with the iron-base solid solutions is a Laves phase (Mg znztype, C14), FezNb or FezTi. Both of these Laves phases have a wide range of Solubility. The precipitation-hardening behavior of Fe-Nb or Fe-Ti alloys has not been studied extensively. Genders and Harrison' reported that binary Fe-Nb alloys hardened upon aging. Peter and Fisher7 studied the mechanical properties of Fe-Nb and Fe-Ti alloys quenched from different phase fields.

Jan 1, 1962

Jan 1, 1967

By Otto H. Henry, Edward L. Badwick

Up to the present time, according to Hansen1 and Haughton,2 the constitution of the bismuth-indium system has not yet been published. The generally accepted value for the melting point of indium, as listed in most scientific journals and textbooks, is 155°C. Recently, however, H. M. Davis3 has determined a new melting point for indium of 257.3°C ± 0.1°C. Since bismuth has been used in preponderance as an alloying element in the majority of low-melting alloys, and indium has been used with considerable success in lowering the melting points of low-melting alloys,4,5 an interest has been developed in the application of these two metals, making a complete knowledge of the constitution of its alloys desirable. In this investigation, the melting point of indium reported by H. M. Davis has been found to be substantially correct. A value of 157.2°C ± 0.5°C was determined. The two eutectic compositions have been placed at 34 and 50 pct bismuth with their respective eutectic temperatures as 72.4'C ± 0.5°C and 90°C ± 0.5°C. The bismuth-indium phase diagram has been determined by thermal and microscopic analysis and is shown in Fig I. THERMAL ANALYSIS Granulated bismuth and indium shot, having a guaranteed purity of 99.99 and 99.95 pct, respectively, were melted in a carbon crucible by means of a laboratory heater. To minimize oxidation of the alloys, a heavy mineral oil (Nujol) having a high flash point was used. A platinum-platinum rhodium thermocouple 0f fine wire encased in a thin-walled Pyrex glass tube, about 1/8 in. in diameter, was connected to a type K potentiometer for temperature measurements. The thermo-couple was calibrated against the melting points of tin, bismuth, and the silver-copper eutectic and the boiling point of water. Since the temperature readings could be reproduced to 0.2°C, and the accuracy of the temperature standards in this range is slightly better than 0.5°C, it seems reasonable to assume that the temperature readings are reliable to approximately 0.5°C. The cooling rate could be controlled by varying the amount of insulation surrounding the crucible. Three or four layers of asbestos paper, 1/16r, in. thick, sufficed to give a cooling rate of from 1° to 2°C per minute. Undercooling was slightly noticeable. This condition was minimized by vigorous stirring, since the advantage of using slower rates was too small to justify the greater expenditure

Jan 1, 1947

By R. W. Vieth, S. A. Bradford

THE orientations of tetragonal tin crystals are commonly examined by either the transmission Laue method or the back-reflection Laue method. The predominant planes and zone axes of the pattern are plotted on a Wulff net and indexed by measuring the angles between planes and directions. The problem of identifying the Laue spots has been approached in several different ways. Nicholas 1 tabulated interplanar angles for ten planes but did not relate the angles to permutation of indices or sign. A table of angles between adjacent planes and of angles between adjacent zones was published by Chandrasekhar and veal.' These tables are very helpful, provided the film shows all the low-order zones that occur within about 20 deg of each other. Frounfelker and Hirthe's compilation3 of angles between the (001) plane and twenty-nine other planes is useful for the indexing, only if the (001) spot can be found on the film. For all but the simplest orientations, however, more information is needed to index the diffraction spots. Standard stereographic projections, such as those published by Bicelli, 4 provide part of the information required. By their nature, these projections show the positions of only a few zone axes. In the tetragonal system many low-order zone axes are not normal to the planes having the same indices. Consequently, planes and directions can have entirely different positions on a stereographic projection. For example, the [011] zone axis is 33 deg from the normal to the (011) plane. The crystallographic orientation usually has to be deduced from a combination of the predominant zone axes and a few low-order planes that appear on the film. In addition to a standard stereographic projection of the planes, a stereographic projection of the directions is needed. Such a projection can be constructed from the angles given in Table I. To provide more information about angles between planes and directions, we have calculated interplanar angles up to (332) and angles between planes and directions up to [332] on an IBM 1620 computer. The angles are differentiated according to permutations of sign and indices. Those doing research on tin single crystals are welcome to request a copy of these tables from the authors.

Jan 1, 1967

By Wheeler P. Davey

In an article in the General Electric Review, January, 1915, reference was made to the X-ray examination of a steel casting 9/16 in thick. Fig. 1 shows one of the radiographs thus obtained. All these radiographs showed plainly the tool marks on the surface of the casting. All but one showed peculiar markings the shape of which strongly suggested that they were indeed the pictures of holes in the interior. A circular piece, 1 in. in diameter, was punched from the casting at a point where the radiograph shown in Fig. 1 indicated that a blow-hole should be found. (Location of sample shown by circle in Fig. l.) Fig. 2 is a photograph of the end of the punching, showing the hole that was found. Since that article was written it has seemed desirable: (1) to obtain data from which the exposure necessary for any thickness of steel could be at once calculated; (2) to find the thickness of the smallest air inclusion which could be radiographed in a given thickness of steel; (3) to determine in what direction to hope for further progress; and (4) to develop the technique of radiographing metals. In order to gain some preliminary data, several pieces of 1/2-in. (12.5-mm.) boiler plate were obtained, 5 by 7 in. (12.5 by 17.5 cm.) in size. In one of these, holes were drilled in such a way that the axis of each hole was midway between the faces of the steel and parallel to those faces. The diameters of these holes were as follows: Hole number Diameter I.........................................1/4 in. =6.3 mm 2........................................1/8 in. =3.l mm. 3................................... 1/16 in. = 1.6mm. 4....................................... 1/32 in. = 0.8 mm. 5........................................1/64 in. = 0.4 mm. Exposures were made on Seed X-ray plates at 20 in. (50 cm.) distance with Coolidge tube X-117, operated on Scheidel-Western induction coil with mercury turbine break. The X-ray plate was placed on a sheet of 1/8in. (3.1-mm.) lead. The steel was placed above this and a Iead

Jan 1, 1916

By R. W. Armstrong, P. C. Jindal

WE should like to point out that Hu and cline.1 in their study of the recrystallization of titanium, have obtained data which appear very important for accurately determining the dependence of hardness on grain size for this material. It has been proposed2,3 that the macrohardness. H. of a poly crystalline material should depend on its average grain diameter, l. in accordance with the relationship: H =H0 + kHl-1/2 [1] where Ho and kH are experimental constants. This relationship follows from the hardness dependence on yield stress or flow stress4 and. thence. the Hall-Petch stress-grain size relations.5'6 Fig. 1 shows the Diamond Pyramid Hardness. Dph. values vs the reciprocal square root of the average diameter of the recrystallized grains, taken from the titanium data reported by Hu and Cline. The data in this figure give a linear relationship for the hardness over a wider range of grain diameters than anyone has previously measured. The data are not linear, for example. on an I-1 or l-1/3 scale. At the very large grain sizes the data are in reasonable agreement with measurements earlier reported by Holden, Ogden, and Jaffee.7 For the grain sizes smaller than 1 µ, which correspond in Fig. 1 to hardness values greater than 150, the material was reported as not being completely recrystallized and, therefore, these data appear less meaningful as far as the hardness dependence on grain size is concerned. However. it has been suggested by other investigators that deformed materials exhibit strengthening due to an effective grain size refinement even in the unrecrys-tallized condition.8-10 Also. Hu and Cline have shown that a change in texture occurs for titanium during the recrystallization process and. especially. following it. The influence of this texture change on the hardness-grain size relation would be expected to be less than that reflected in the unidirectional stress-strain behavior, even for an hcp material. because of the actual combined stress system which applies for the hardness test. For, at least, certain combined stresses, average values of the orientation factors should still occur in the stress-grain size analysis of a material exhibiting a preferred orientation.' We previously suggested3 that the experimental constants. H0 and kH. from the Meyer hardness-grain size relation should be correlated with the Hall-Petch constants, uoy and ky.5,6 Our recent study" of the Hall-Petch relation and the hardness-grain size results which obtain for a number of polycrystalline materials shows that: The inequality [2] is explained by noting that the hardness should be correlated. perhaps, with the flow stress at some value of strain, as suggested by Dugdale,12 and. also, that the influence of strain on the Hall-Petch relation is to increase uo and not change k very much." Normally. Dph values and Brinell hardness values are nearly equivalent to each other and to the Meyer hardness number. For the case of titanium, then. the inequality [2] may be evaluated using the experimental values of ao = 8.0 kg per sq mm and ky = 1.3 kg per mm3/2 obtained from the experiment of Guard.6,13 Thus, (Ho/uo) = 12 and (kH/k3) = 1.3. This research has been supported at the University of Maryland through the Center of Materials Research by the Advanced Research Projects Agency of the U.S. Government.

Jan 1, 1969

By C. G. Dunn

IDENTIFICATION Of the kinds of orientation relationships that may exist among crystals is an important problem in the metallurgical field. As an aid to its solution standard orientations of several orders of twins would be very useful for rapid analyses to discover high-order as well as low-order twin relationships. Although data have been published that give orientations for three generations of twins, these data are not readily useful in the form presented; i.e., in a stereographic projection with one pole per orientation.1 However, accurate data based on calculations of the positions of all {100} planes for such groups would be very useful when presented in tabular form. Therefore, calculations have been made for a group of four orders of twins and the data are listed in Table 3. Illustrative applications are considered briefly, with the idea of pointing out what may be done with large groups of orientations. METHOD OF COMPUTING ORIENTATION OF A TWIN It is common practice to describe the orientation of a crystal in terms of the positions on a stereographic net of the poles of certain planes of the crystal. A single position on a net may be given it terms of two angle variables, two sets of which appear in the following equations: [Polar NetWalff Net x=rsinOocos4pyx=rcos0. y=rsinB,sin4,ny-rsin0.cos¢,, z=rcos0,,z=rsin0.sin4,,] The three numbers x, y and z determine a length r as well as a direction [(0, 0)] in an X, Y, Z coordinate system. In the present case, r will be set equal to (h2 + k2 +12)1/3, where h, k and 1 are the usual Miller indices for a crystallographic plane, a restriction that facilitates determination of the positions of poles of new planes from those of old or known ones,2 as will become evident later. Furthermore, since twinned lattices have certain planes in common, it is an easy matter to determine the orientation of a twin of a crystal if the orientation of the crystal itself is known. We start therefore with a crystal of known orientation (positions of three {100} poles given) and determine where the cube poles occur in first, second, third and fourth-order twins. Methods for identifying twinned lattices and for making the calculations to find the orientation of a twin have been published.3 4 Reference 4 will be illustrated in the calculation of the orientation of a twin, even though this method differs from the one used by the writer in obtaining the following data on four orders of twins. Consider a crystal S and its twin A1, A1 being one of the four {112} or {III}

Jan 1, 1945

AALL, Christian H.,(M'49), Asst Res Dir Monsanto Chemical Co Anniston, Ala AALSETH, Earl P ,(J,51), Amerada Petr Corp Geological Dept Williston N Dak AAMOT, Olav Crone, (M'29), Met Pacific N W Alloys, Inc , Box 6215, Hillyard P 0 Spokane 14, Wash AARING, Floyd D ,(J'48), Petr Engr P 0 Box 130, Calgary, Alta Canada AARCNSON, Hubert Irving, (S'47), Carnegie Inst of Tech., Pittsburgh, Pa ABADIE, Henry G ,(M'43), Asst to the Sup- of Operations, Long Beach Oil Development Co ,255 So Santa Clara Ave Long Beach, Calif ABBISS, H. J., (A'50), Min. Engr., Buchans Mining Co., Ltd.. Buchans, Newfoundland ABBOTT, Clarence Eugene, (M'04), 901 Insurance Bldg , Raleigh, N C ABBOTT, George, (S'52), Mass Inst of Tech Cambridge, Mass

Jan 1, 1952

By Larry Kaufman

A useful method for estimating the entropy of NaCl type compounds has been developed by combining the Debye theory of specific heat with the Lindemann formula. This method pemnits calculation of the entropy from a knowledge of the atomic weight, atomic volume, and melting point of the compound. Comparison of the calculated and observed entropies of 35 NaCl type compounds over a wide temperature range yields good agreement thus establishing the usefulness of the method. Application of the method to other crystal types is also discussed. KUBASCHEWSKI~ has suggested a useful method of estimating the enthalpy of formation of inter-metallic compounds from a knowledge of the crystal structure, lattice parameter, and heats of sublimation of the component elements. This method is quite valuable in predicting the tendency for compound formation in a given system and is of particular value in considering systems for which no experimental data are available. In order to supplement the enthalpy calculation afforded by Kubschewski's method, it would be of value to be able to estimate the entropy of compounds so that the entropy and free energy of formation could be evaluated. Although a considerable body of such data determined by calorimetric and equilibration techniques exists at present, the difficulty of making such measurements (particularly at high temperatures) and the ever increasing number of new compounds which are of interest make the desirability of such a computational method clear. This paper deals with a method for calculating the entropy of a compound from a knowledge of the atomic weight, atomic volume, and melting point. Since these data are generally easier to determine and therefore more readily available than thermo-dynamic data, they should provide an additional tool in estimating the stability and reactivity of compounds at high temperatures. I) THE ENTROPY OF PURE METALS As a first approximation, the specific heat of a pure metal can be represented by a sum of terms where C,($/tI is the vibrational specific heat calculated on the basis of the Debye theory, lo4 TC, (0/T) is an approximation to the Cp - C, correction. T is the electronic specific heat, and Cp (p) is the magnetic specific heat. Although the Debye theory does not provide a complete description of the vibrational specific heat, i.e., the Debye temperature 0 is not a constant, it does provide a good approximation when used properly. Blackman6'7 has written several reviews on this subject discussing the different values of 0 determined by various methods (specific heat, X-rays, elastic constants, electrical resistivity, and so forth), as well as the observed temperature dependence of 0 with T. In the present case the 0 in Eq. [I] naturally refers to the specific heat 0. The variation of Debye 0 (as determined from specific heat measurements) with temperature is observed to exhibit its most radical behavior at very low temperatures. At higher temperatures the 8 values are observed to become more nearly constant. Blackman6'7 has presented the variation of 0 with temperature for several metals. His tabulation is reproduced in Table I. Reference to Table I shows that above a certain temperature level, 0 remains fairly constant. The value of 0 which is most useful in computing the specific heat, and hence the entropy, is the value of 0 in the range 0/6 « T « 0. In 1910, Lindemann' suggested a relation for estimating Debye 0 values. According to this formula, where V is the atomic volume, T is the melting point in 'K, M is the atomic weight, and CL is a constant. Mott and Jones9 present this formula and state that there is at present no satisfactory theoretical explanation, but that it does have an empirical basis. By using the valuesof 0 in Table I along with known1' values of M, T, and the molar volume VM, where the Lindemann constant can be evaluated. This

Jan 1, 1962

By C. C. Hatch, C. R. Larsen, A. L. Mular

INTRODUCTION As part of a general project to simulate a concentrator, the Brenda Mines Limited secondary crushing plant, located near Peachland, B. C., was sampled during the summer/winter of 1975 and during the summer of 1978 to develop a digital crushing plant simulator specific to the Brenda operation. The purpose of this simulator was to study the influence of manipulable process variables on important responses, to permit study of alternative circuit configurations if desired and to perform off-line optimization. This chapter describes the methodology employed to develop the simulator (1,2) along with typical applications thereof. SECONDARY CRUSHING PLANT FLOWSHEET Figure 1 is a schematic diagram of the Brenda Mines Ltd. secondary crushing plant circuit. The 41,000 tonne coarse ore stockpile(a) is -17.8 cm oversize (3B belt) from two 2.4 m x 6.1 m double deck vibrating screens (not shown). The screens are fed by 2 conveyor belts operated in series with two 198 cm apron feeders that handle discharge from a 152 cm x 226 cm primary gyratory crusher(520 KW). The primary crusher (not shown) treats up to 2725 tonne/hr of run of mine ore. Minus 1.9 cm undersize from the primary screens (#19 belt), referred to as the primary fines, joins secondary screen undersize (#18 belt) for conveyance to fine ore bins (not shown). Feed from the coarse ore stockpile is transferred by means of vibrating feeders and two 120 cm conveyors (#6 and #7) to transfer belts #8 and #9 (Figure 1). The belts feed two secondary 2.1 m standard heavy duty cone crushers (bl and b2). Each crusher is equipped with a modified coarse mantle liner and a standard coarse bowl liner. Mantle throw is 9.2 cm; nominal close side set is 3.2 cm. Crusher .countershafts (443 rpm) are driven by single 260 KW synchronous motors (710 rpm). Discharge from the secondary cone crushers joins discharge from four 2.1 m tertiary heavy duty shorthead cone crushers (fl, f2, f3 and f4). With the exception of the cavity (modified medium mantle liner and standard coarse bowl liner; close side set is nominal .84 cm) and motor (224 KW), these machines are similar to the secondary crushers. The combined discharge is transferred from a 183 cm conveyor to #14 belt which empties into a 1452 tonne secondary screen surge bin (c). Vibrating feeders beneath the bins feed five 2.4 m x 6.1 m double deck vibrating screens (dl, d2, d3, d4 and d5) sloped at 200 from the horizontal. The upper decks are punched plates with 2.7 cm x 7.6 cm slots. Lower decks are woven wire (1.27 cm diameter) sections with

Jan 1, 1982

Jan 1, 1968

By W. A. Tiller

The conventional techniques1 for determining the liquidus and solidus surfaces of an alloy system containing more than two components are extremely tedious to use and do not provide a complete picture of the equilibrium relations between solid and liquid alloys. These techniques are unable to yield "tie-line" information concerning solid and liquid phase equilibrium, a very important parameter in the solidification description of the liquid alloy and a very necessary parameter in the preparation of "zone-levelled" alloy crystals. The tie-line in a polycomponent system is analogous to the partition coefficient, k, in a binary system, it gives the composition of the solid, Cs, in equilibrium with a liquid of composition CL. That is, CS = kCL, where CL = [CO, c1,...Cn] denotes the concentrations of the n + 1 constituents, and k = [ko, kb ,...kon] denotes the gross partition coefficient for the elements between the two phases; thus, k is the tie-line in this system. To provide complete information concerning the two-phase equilibrium in a polycomponent system it is necessary to know both the liquidus surface and the gross partition coefficient. From these two the solidus surface is obtainable. The conventional techniques are unable to provide this information in other than a binary system so we must look elsewhere. In recent years considerable insight has been gained into the correct description of the liquid-solid transformation, 2,3 and controlled solidification experiments may now be designed to both facilitate and enhance equilibrium diagram studies. In the present paper consideration is given to two methods for obtaining the liquidus surface and the tie-lines in polycomponent systems. The methods to be described below deal with the solidification of an n + 1 constituent liquid alloy of initial composition [co, Co ,...Con], where the superscripts refer to the elements present and the Oth element is considered as the solvent in which the n solutes are dissolved. The general assumptions made in the treatment are the following: (i) the solid and the liquid at their interface are in equilibrium during the growth of the solid phase, (ii) there is no diffusion in the solid phase, and (iii) the liquid phase is completely mixed and is therefore homogeneous in concentration. METHOD I In this section a general experimental method will be described which, in principle, is capable of giving an exact description of the liquidus surface and tie-lines. Consider the unidirectional solidification of the liquid alloy specimens L cm in length (freezing either horizontally or vertically). Allow the sample to be frozen very slowly from one end, as indicated in Fig. 1, with complete mixing in the liquid, and then analyze the solid bar to determine its chemical constitution as a function of position, x, along the bar. Let Fig. 2 represent a possible distribution of the ith constituent along the bar. At the point x' the concentration of the ith constituent is C1/5(x'), and the average concentration of the rest of the bar between x' and L is given by C:(X' - L) where [ A(x) c1s(x)dx c1/s(x'-L) = f A(x) dx x * and A(X) is the cross-sectional area at x. In a similar manner. all the Cf(x' - L) may be determined. Thus, the gross artition coefficient k for liquid of composition [Cs(x - L),...Cs(X' - L)] is given by -ko= CUs')/Cos(x' - L)" k0 = csn{x')/cs(x'- L) During the freezing of a charge of length L, the liquid composition may vary over a wide segment of the phase diagram and the gross partition coefficient over this segment of the phase diagram may be determined from one, bar. Fig. 3 illustrates the magnitude of Cs(g)/C,' as a function of the fraction g of the bar which has Solidified.2 We can see that the concentration in the bar will vary over a range of about 15 wt pct for C,' = 10 wt pct and k0 = 0.5. It appears that 4 or 5 specimens would be adequate to study a simple binary eutectic phase diagram.

Jan 1, 1960

By W. F. Hosford

A series of aluminum single crystals was subjected to axially symmetric flow by drawing through dies. The orientation dependence of the drawing stress, which indicates the resistance to this type of flow, compares reasonably with predictions of Taylor and of Bishop and Hill. Measured lattice rotations likewise are generally consistent with theory. The most successful analyses of the plastic behavior of polycrystalline metal and its relationship to single crystal behavior are those of Taylor1-3 and of Bishop and Hill.4-6 The purpose of this paper is to provide a critical test of some of the basic assumptions involved in these theories. Both treatments apply to fcc metals and assume the shape change of each grain in a polycrystal to be the same as that of the polycrystal as a whole. Thus for a randomly oriented polycrystal extended under uni-axial tension each grain is assumed to undergo axially symmetric flow. dey = dez = -1/2dex, deyZ = dezx = dexy = 0 [l] where x, y, and z are a set of orthogonal axes, x being the tensile axis. Although [011.] oriented grains in bcc and fcc metals may depart markedly from this ideal behavior,7,8 the assumption is probably quite reasonable for most grains. Under a uniaxial tensile stress, ox, the work dW per unit volume expended in producing an increment of axial strain dex is, dW=oxdex [21 Since this work is expended in slip, dw =STi dyi 131 where Ti and yi are the shear stress and shear strain on the active slip systems. In both analyses Ti is taken to be the same on all slip systems, and dependent only on the total prior shear strain on all systems, so dw = Tdy [41 where t is the shear stress required for slip and y is the sum of the shear strain yi on all slip systems. Combining 121 and [4] and defining M = oX/T The ratio M is a generalized Schmid factor. It relates the tensile stress required for axially symmetric flow, ox, to the basic shear stress, 7, and it also expresses the ratio of crystallographic strain, y, to the tensile strain, Ex It depends only on the orientation of the crystal. Taylor evaluated M for various orientations by finding the least value of dy/dEx which could satisfy the shape change. Bishop and Hill, on the other hand, found M by considering the relative work (1/T)dW/dEx expended by stress states which could activate enough slip systems to produce the shape changes. The results of both methods appear to be equivalent, although certain omissions were made in Taylor's original work. The orientation dependence of M, calculated by the second method,9 is shown in Fig. 1. Taylor used the average 2= 3.06 for all possible orientations to predict the tensile stress-strain curve (oxvs Ex) for a random polycrystal from the shear stress-strain curve (t vs y) of a single crystal. Changes in M from lattice rotation were neglected so points on the ox vs ex curve were simply taken at ox = 3.06t and e = y/3.06 from corresponding points on the t vs y curve. Recent extension of the analyses of Taylor and of Bishop and Hill to crystallographically textured metals has been used to relate plastic anisotropy to textures, and to predict the potential texture hardening that could result from texture control.9 Unfortunately there have been relatively few experimental tests of the underlying theory. Taylor found that the tensile stress-strain curve of polycrystalline aluminum did agree reasonably well with that predicted from a single-crystal T-y curve. Had the single crystal undergone easy glide, how-

Jan 1, 1965