Search Documents

By R. Schuhmann

D. W. Fuerstenau (Associate Professor of Metallurgy, Dept. of Mineral Technology, University of California, Berkeley, Calif.) In his excellent paper, Dr. Schuhmann has proposed a mechanism for conlrninution which can be utilized to explain a number of phenomena which have been observed in the size reduction of solids. The difference between the product obtained from a ball mill and from a rod mill can readily be explained by Dr. Schuhmann's hypothesis. Consider that the size distribution of the product from each comminution event is given by y; - 100 (x/ki) (1) where Yi is the cumulative percent finer than size x, ki is the size modulus, and is the distribution modulus for the single comminution event. The total product from a cornminution operation will be the summation of the products from all of the individual cornrninution events. If the size moduli from the various comminution events range from kl to kn , the size distribution of the total product will be a straight line on a log-log plot only to a particle size equal to k ,. Considering 100 volurnes of feed, the value of y for x equal to kl is Riven by where y is the cumulative percent finer than size kj, z is the number of comminution events of kind i, and vi is the volume of each particle crushed. y=z1 qv1+z2 qv2 (k1/k2) +.............zn qvn (k1/kn) (3) F or particle sizes greater than k1 7 e. 6. x = k3, the value of y will be given by k3 A y = z1 qv1 + z2bv2 + Z3uV3 + zn zn qvn (k3/kn)(4) Only when x is equal to k, will y equal 100. 'Thus, the total product from a comminution operation will be a straight line on a log-log plot strictly up to a particle size equal to kl and above that size the line will curve so that y will equal 100 for the coarsest particle or k, (see Fig. 1). The actual shape of the size of distribution curve will depend upon the relative number of conmninution events of different kinds. In the case of ball milling, the ratio kn/kl may be pite large and there will be considerable deviation at the coarse sizes in a Schuhmann plot. kIowever, the grinding action in a rod mill is such that fine particles are protected from the rods by the coarse particles. Consequently, kn/kl will be quite small and the product from a rod mill will give a straight line Schuhmann plot almost to y equal 100%. In his paper, Dr. Schuhmann also has presented a very straightforward definition of grindability derived from the basic energy equation E = Ak-a (5) where E is the energy required to comminute a material to a size modulus of k and A is a constant. According to Dr. Schuhmann, the grindability of a material is the volume of material comminuted finer than unit size per unit of energy expended, this being 1/A. For comparison of grindabilities at any size two numbers are required, both = and 1/A, and anyone tabulating grindabilities should give both of these numbers. Concerning the experimental determination of grindabilities, if the material being comminuted possesses distinct cleavage, the energy re quired for comminution is given by E = Ak-(a-y) (6) where y is small number less than = . Because of cleavage, less energy will be required for comminution. To be certain that cleavage does not affect the gindability of the material being tested, it is suggested that the method used by Dr. Charles for determining grindability be used to ascertain if the deviation exponent y is zero or finite. R. Schuhmann, Jr. (Author's Reply) Dr. Fuerstenau's interesting comparison of rod milling and ball milling

Jan 1, 1961

By F. H. Ellinger

A BRIEF description of the thermal expansion characteristics and of the four known crystal structures among the six allotropes of plutonium has been covered in a summarizing report on plu- tonium by E. R. Jette.' A detailed description of the crystal structure and thermal expansion of y plutonium has been published.' The present paper deals with the crystal structure of d plutonium, and with the thermal expansion of 6, 6' and € plutonium, as determined by X-ray diffraction methods. The X-ray diffraction patterns were taken in Uni-cam high temperature powder cameras using fil-

Jan 1, 1957

By Bennett Bates

A PAPER presented in South Africa' during 1925 by H. A. White gave a formula to express the efficiency of classification. The formula was originally developed by H. W. Newton of The Dorr Co. The derivation of this formula is as follows: Where E = Over-all efficiency of classifier Eu = Efficiency with respect to sand discharge Eo = Efficiency with respect to overflow I = Tons feed to classifier (input) 0 = Tons overflow U = Tons sands (underflow) i = Fraction of oversize in classifier feed o = Fraction of oversize in overflow u = Fraction of oversize in sands

Jan 5, 1927

1-Iron and Steel JOHN A MATHEWS, Chairman RALPH H SWEETER, Vice-Chairman WILLIAM CAMPBELL, Vice-Chairman MAX ROESLER, Secretary Iron Ore CHARLES B MURRAY, Chairman R C ALLEN W O HOTCHKISS MAX ROESLER ERNEST F BURCHARD WILLIAM KELLY DWIGHT E WOODBRIDGE M M DUNCAN CHARLES F RAND CARL ZAPFFE C T FAIRBAIRN THOMAS T READ Blast Furnace WALTER MATHESIUS, Chairman WILLIAM H BLAUVELT P KINNEY C SNELLING ROBINSON A J BOYNTON DORSEY A LYON H SWEETSEP D T CROXTON RICHARD MCCAFFERY R J WYSOR THOMAS L JOSEPH CHARLES P PERIN

Jan 1, 1923

"Located on Missouri River 16 miles N. E. from Helena, 67 miles from Butte and 18 miles below Canyon Ferry. River drainage area 16,000 sq. miles.DAM: Built in 1907; rebuilt of concrete in 1911. Maximum height 129.3 ft., length over all 720 ft.; elevation of crest 3621; elevation of bridge 3640; normal head 60'; normal tail water elevation 3568.5.SPILLWAY: Length over all 491 ft.; clear opening in 24 sections; 445' flashboards, 14 high to elevation 3635, which is 3.5' above Canyon Ferry normal tail . water elevation.PENSTOCKS: 5 of steel, 12 ft. diam., about 75 ft. long from canal to main turbines, and 3 40-inch diam. from canal to exciters.WHEELS: 5 main pairs, horizontal, center discharge, 48-inch bronze turbines, 225 rev., 4,000 h-p. at 60 ft. head, made by S. Morgan Smith Co., direct coupled to generators, and--3 single, horizontal, 25-inch units, direct coupled to exciters.GENERATORS: 5 W. E. & M. Co. water wheel type, revolving field, 2,800 k-w., 2,400 v., 225 r. p. m., 3 phase, 60 cycle alternators.OPERATION: The plant has a larger water storage than Canyon Ferry and can also use stored water from Canyon Ferry storage. Separate transmission lines 13 miles long connect to lines from Canyon Ferry to Butte, and the Plant operates in parallel with the Canyon Ferry plant."

Jan 1, 1913

By Charles Y. Clayton

A study of the literature shows that the greater part of research work on annealing of cold-worked iron has been for the purpose of studying the effect on grain-size and properties other than hardness. No reference has been found of experimental work of the same nature as that explained in this short paper. The material used throughout was Vismera iron, an iron containing 0.03 carbon and made several years ago by the Inland Steel Co. One-half inch stock was cut into cylinders % in. long. The cylinders were then compressed for 60 sec. in a Reihle testing machine under loads as indicated below: CoMPressiON, Average Length, Series Pounds Inches 1 10,000 0.693 2 15,000 .599 3 20,000 .501 4 25,000 .426 5 30,000 .378 6 35,000 .351 7 40,000 .311 Fig. 1 shows these cylinders after compression. Each series consisted of 17 specimens lettered 0, B, C, D, E, F, G, H, I, J, K, L, M, N, P, Q and R. One specimen of each series was reserved for study of the properties in the cold-worked condition. The other specimens were annealed in a Hump furnace for 1/2 hr. at the following temperatures: TEmpeRa- TempeRa- Letters tuRe,° C. LettERs tuRe °C. B............................... 250 J.............................. 650 C............................... 300 K............................. 700 D............................... 350 L.............................. 750 E............................... 400 M............................. 800 F................................ 450 N............................. 851 G............................... 500 0. . :........................... 900 H............................... 550 P.............................. 950 I................................ 600 Q............................. L000

Jan 1, 1926

By L. S. Birks

The bainite transformation in a 3.5 pct Ni-1.25 pct Cr steel was studied under various conditions of cooling and stress. Several characteristics may be specified: 1) transformation in the bainite region (925° to 575°F) is very little affected by the manner of cooling from the austenitizing temperature at 1600°F to 575°F)tothe upper limit of bainite transformation at 925°F; 2) starting time for the bainite transformation is the same order of magnitude for either isothermal transformation or continuous cooling, but the rate of transformation is somewhat greater for isothermal transformation; 3) tensile stress accelerates both isothermal and continuous cooling transformation, and 32,000 psi stress changes the form of the isothermal transformation diagram to correspond in appearance to the continuous cooling diagram; 4) transformation for nonlinear, continuous cooling may not be determined directly from the linear, continuous cooling transformation diagram, but may be predicted by assuming first that the fractional amount of austenite transformed in a given small temperature interval depends on the approximate linear cooling rate during that temperature interval and then by summing stepwise over the whole temperature range. IN a previous publication' an X-ray spectrometer was described with which the X-ray diffraction from a specimen could be observed continuously under controlled temperature and tensile stress. This instrument has now been applied to a study of the austenite-bainite transformation in a Ni-Cr steel for both isothermal and continuous cooling conditions, with and without stress. Certain characteristics of the transformation lead to a method of predicting the amount of transformation to be expected at a given temperature for any type of cooling curve. Material and Specimen Preparation The steel chosen for the investigation was a Ni-Cr steel having the composition in the following percentages: 0.30 C, 0.27 Mn, 0.019 P and S, 3.50 Ni, and 1.25 Cr. In order to fabricate specimens suitable for the X-ray spectrometer, a 1/4 in. plate was ground down to 0.060 in. and then cold rolled to about 0.035 in. Next it was heat treated by quenching in oil from 1650°F and tempering at 1200°F for 1 hr. Then it was etched in dilute nitric acid to reduce its thickness to 0.014 in. and cut into blanks in the shape of flat tensile specimens 3 1/4 Vi in. long, 7/16 in. wide, with a notch % in. long and 7/32 in. wide; see Fig. 1. X-Ray Technique Since the X-ray spectrometer has been described in detail elsewhere,' only a brief outline of the principles will be repeated here. A focusing, pow- der-diffraction arrangement' was used, as shown schematically in Fig. 1, and the specimen was mounted vertically in a vacuum furnace (not shown in the figure). The X-rays, moving in a horizontal plane, enter and leave the furnace through beryllium windows. As shown in the figure, X-rays diverging from the line source A are diffracted by the specimen B and converge at the detector slit C. The detector D and the slit C may be set at the proper angle in the horizontal plane to receive X-rays diffracted by either the face-centered phase (austenite) or the body-centered form (ferrite, bainite, martensite). The specimen is heated by electrical conduction between connectors E, and E,, and a Pt—Pt-10 pct Rh thermocouple spot-welded to the center of the notched region on the side away from the X-ray beam indicates the temperature continuously on a Brown recorder. Temperature control is exercised manually with a variable transformer on the input to E,-E,. Any desired time-temperature relationship is easily obtained by first drawing the desired curve on the temperature recorder chart and then adjusting the variable transformer during the run so that the thermocouple

Jan 1, 1957

By R. W. Diamond

THREE mills are now operated by the Consolidated Mining & Smelting Co. of Canada, Ltd:: (1) The Sullivan concentrator, Chapman, B. C. (near Kimberley, B. C.), (2) the St. Eugene concentrator, Moyie, B. C., and (3) the Tadanac (customs) concen-trator, Trail, B. C. Differential flotation is the only concentration method employed in all three plants. Tables are used for pilot work only. Flotation equip-ment and control are similar in the three mills, and the flow sheets at the St. Eugene and Tadanac mills, while much simpler, are modeled after that of the Sul-livan concentrator. Successful differential flotation of Sullivan ore com-menced in the spring of 1920, in the pilot concentrator at Trail. During 1920, 193,804 tons were treated by this process. This operation continued without interrup-tion and with steady growth. For the first 7 months of . 1923, which concluded the pilot plant operation, ap-proximately 1100 tons were treated daily. I believe the Sunnyside plant of the United States Smelting &. Refining Co. was the only successful and large scale operation practising differential flotation prior to 1920. in North America. The Sullivan ore, because of its high iron content, was quite a different problem from that at Sunnyside. The entire tonnage of Sullivan ore had to be separated into three sulfide concentrate products-lead concentrate, zinc concentrate and iron concentrate. The choice and arrangement of equipment, and the original flow sheet for the Sullivan concentrator were controlled by the results of the exhaustive pilot mill test. These covered a continuous period of 3 1/2 years and involved the treatment of 1,076,368 tons of Sullivan ore. Satisfactory recoveries are made from feed; 11.0 per cent lead and 7.5 per cent zinc in the form of lead concentrate containing 69 per cent lead, 4.5 per cent zinc, and zinc concentrate containing 3.0 per cent lead and 49 per cent zinc. (The pure zinc mineral in Sulli-van ore is marmatite, 'containing approximately 54.5 per cent zinc and 10 per cent iron. It is apparent, there-fore, that 49 percent concentrate is high grade for this particular ore.)

Jan 8, 1927

By M. Hansen, C. C. Wang

THE 6 phase of the Cu-Sn system (Cu,Sn, = 32.53 pct Sn) was considered to be stable down to room temperature until Owen and Iball showed by X-ray analysis that it undergoes a eutectoid decomposition into the a and e phases at a temperature near 300°C. Their findings have been confirmed by other investigators,2-5 a11 of whom used X-ray diffraction studies of powdered specimens. The transformation temperature has been reported by various authors as lying between 300" and 380°C. To our knowledge, no microscopic evidence of the eutectoid reaction has been published, as yet. It was in connection with other work that longtime annealings at 300°C were conducted with alloys containing 22, 32.6, and 35 pct Sn (nominal compositions) prepared from electrolytic copper and electrolytic tin and cast in a small iron mold. The specimens were first annealed at 700°C for 5½ hr and quenched from 400 °C after cooling to, and annealing at, that temperature for 9½ hr. After this treatment the sample with 22 pct Sn was cold worked for 15 pct reduction in thickness; the 32.6 and 35 pct alloys were too brittle to be cold worked. The final anneal at 300°C was done in a sealed pyrex glass bulb for 63 days. Fig. 1 represents the microstructure of the annealed alloy with 22 pct Sn. It shows primary a solid-solution crystals in a matrix of the (a + 8)-eutectoid formed at 520 °C. The a crystals contain 8 inclusions which precipitated from a due to the decrease in the solubility of tin in copper with fall in temperature. The decomposition of the 8 phase into a (light) and E (dark) can clearly be seen in some areas of the (a + 8)-eutectoid matrix. However, the decomposition is far from being completed, even after the long-time anneal used. Figs. 2 and 3 depict the microstructures of the annealed 32.6 pct alloy, which was intended to consist entirely of 6 phase. Due to some loss in copper on melting, the composition is slightly higher in tin. Accordingly, the sample after quenching from 400 "C consisted of grains of the 8 phase with the e phase arranged along the grain boundaries and as a Wid-manstatten precipitate within the 6 grains. After an annealing time of 63 days, the eutectoid decomposition, 6 + a + e, is still in its early, initial state. The pearlitic type of eutectoid is nucleated at the c crystals, preferably those surrounding the grain boundaries of the 8 phase. The appearance of the (a + €)-eutectoid in the 35 pct Sn alloy was very similar to that shown in Figs. 2 and 3. Again, the eutectoid decomposition nucleated at the 6 phase and proceeded from there into the 8 areas. As is evident from Fig. 2, the rate of decomposition of the 6 phase at 300°C is extremely sluggish: In the representative area shown only about 5 pct of the 8 phase has undergone the eutectoid trans- formation after annealing for 63 days. On the other hand, Owen and Williams2 have reported that X-ray photographs of powdered samples with between 17.5 and 34 pct Sn did not show 8 lines after annealing for only five to seven days at 300°C. This is in accordance with the fact that the rate of reaction in powdered samples is higher than in massive specimens, as a result of the excess free energy of the powder (due to its greater surface area). The authors wish to express their thanks to C. A. Johnson for preparation of the micrographs.

Jan 1, 1952

By C. H. Hitchcock

Report C6 of the Second Geological Survey of Pennsylvania, by Charles E. Hall, describes the rocks of the Philadelphia belt, and sets forth conclusions widely different from those derived by others from the study of similar strata along the same stratigraphical line. Mr. Hall classifies these rocks into three groups: First, the Philadelphia schists and gneisses, well shown within the city limits and

Jan 1, 1884

By W. Buchanan, O. Johari

STEREOGRAPHIC projection has been one of the most useful aids in crystal-structure studies. With the increasing use of electron microscopy in metallurgy and other fields, stereographic projection is being used in many ways1 to interpret the results from electron diffraction patterns and transmission micrographs. For many of these applications, e.g., trace analysis, twinning, and so forth standard projections of various indices are required.

Jan 1, 1967

The Committee on Nominations begs to submit the following names as its nominees for the respective offices indicated: For President, SIDNEY J. JENNINGS, New York. For Vice-Presidents, WALTER H. ALDRIDGE, New York; MARK L. REQUA, San Francisco. For Directors, J. E. JOHNSON, JR., New York; ALLEN H. ROGERS, Boston; HOWARD N. EAVENSON, West Virginia; ROBERT M. RAYMOND New York; WILLET G. MILLER, Canada.

Jan 12, 1916

[MINING AND EXPLORATION DIVISION Established as Mining, Geology and Geophysics Division, Sept. 27, 1949 Name changed February 19, 1958. Lyman H. Hart, Chairman Robert J. Lacy, Assistant Chairman Vice Chairmen: John C. Wangaard, Membership J. M. Ehrhorn, Program John G. Hall, Publications C. E. Nelson, Secretary American, Smelting and Refining Co. 120 Broadway New York 5, New York Editor, Rock-in-the-Box: J. W. Chandler.]

Jan 1, 1961

By A. E. Powers, J. F. Libsch

THE simultaneous influence of time and temperature upon the tempering process in steel is well known. Hollomon and Jaffe¹ have expressed the effect of time and temperature upon the progress of tempering by a single parameter, T (c + log t); where T is the absolute temperature; t, the tempering time; and c, a constant characteristic of the steel and treatment. It was found that when hardness data for plain carbon and low alloy steels were plotted vs. this parameter, a master tempering curve was obtained which satisfied all the data for a given steel and a given hardening treatment. Roberts, Grobe, and Moersch² successfully applied the tempering parameter to various tool steels, including high speed steel for tempering times ranging from 6 min to 100 hr. The influence of tempering time and temperature upon the physical properties of high speed steel has also been extensively investigated.'" Recently, the use of induction heating for very rapid tempering treatments has received attention. The authors% have shown that tempering treatments of only a few seconds duration may be successfully applied to plain carbon and low alloy steel. However, the influence of such short tempering treatments in high speed steel has not been explored. Since high speed steel is a highly alloyed steel exhibiting physical reactions during tempering that are often relatively slow and large in magnitude, it is an interesting steel for the study of tempering reactions. It was the purpose of the present investigation, therefore, to study the early progress of reactions leading to secondary hardness in high speed steel, type 6-5-4-2, and to determine if induction-tempering treatments of a few seconds duration are able to produce results equal to those of more conventional long-time tempering cycles. Experimental Details The chemical compositions for two different heats of W-Mo high speed steel used in this study are given in Table I. Table II summarizes the heat treatment given various groups of specimens cut 21/2 in. long and centerless ground to ¼ in. diam. Hardening treatments consisted of preheating to 1600°F (870°C) for V2 hr and then oil quenching from 2250°F (1230°C). Heat I was subjected to the high temperature in a salt bath for 3 min, while specimens of heat II were austenitized in a carbon-block muffle furnace for 10 min. Specimens of series E were immediately refrigerated to — 318°F (— 195°C) in liquid nitrogen following the hardening treatment to transform the major portion of the retained aus-tenite. Specimens of series F and G were subzero cooled to — 100°F (-75°C) in a dry ice-alcohol mixture. Induction tempering was performed with a Lepel high frequency converter operating at a frequency of approximately 300,000 cycles per sec. Heating cycles were controlled and recorded for each specimen using a chromel-alumel thermocouple, percussion welded to the surface of the specimen, and a modified high speed instrument with a timer previously used and described.' Temperature oscillation of the specimens, while being held at the tempering temperature, was ± 15°F (8°C). Tempering Treatments: After hardening, specimens were tempered between 900" and 1500°F (480" and 815°C) to study the progress of retained austenite decomposition and secondary hardening. The specimens tempered in salt for 1 hr (series C, G, and I) were considered to represent conventional treatment and are used for comparison with rapid tempering treatments. Several induction-tempering cycles were employed: 1—flash tempering, i.e., induction heating to the tempering temperature and immediately cooling (series A, E, and F); 2—induction heating for 60 sec at temperature (series B); and 3—double-induction tempering by two successive heating and cooling cycles (series D). All specimens tempered by induction were heated at an initial rate of 450°F (250°C) per sec except those of series E, which were heated at an initial rate of 1300 °F

Jan 1, 1952

By R. A. Deju, R. B. Bhappu

The basic structural unit of all silicate minerals is a tetrahedron with a silicon atom at the center and four oxygen atoms at the corners. The oxygen-silicon distance is about 1.6 & and the oxygen-oxygen distance about 2.6 &. The different types of oxygen-silicon frameworks in the various silicates are based entirely on the combinations of the tetra-hedral oxygen-silicon groups through sharing of oxygen atoms. In recent years, infrared spectroscopy has permitted estimation of the ratio of the ionic character of the oxygen-silicon bond to be a few times that of the oxygen-carbon bond and the ratio of electro-negativity of the two bonds has also substantiated this finding. On this basis, it is generally accepted that the oxygen-silicon bond is the strongest one occurring in silicate minerals. As the oxygen-silicon ratio increases from quartz to the olivines, a greater percentage of the oxygen bonding power is available for bonding to cations other than silicon. Hence, with an increasing oxygen-silicon ratio, there is increasing oxygen-to-metal bonding. Upon the fracturing of a silicate mineral crystal, the oxygen-metal bond, which is almost entirely ionic in character, should break more easily than the stronger oxygen-silicon bond, resulting in a greater number of unsatisfied negative forces on the surface. If, then the mineral is immersed in a liquid containing hydrogen ions, these negative forces should tend to be neutralized by hydrogen ions from solution, resulting in a change of the pH of the solution. An increase in the degree of adsorption of hydrogen ions is to be expected as the oxygen-silicon ratio in the crystal structure increases. This study attempted to correlate the oxygen-silicon ratio for various representative silicate minerals to the adsorption of hydrogen ions. Experiments to determine the effect of surface area on this adsorption and to investigate the effect of surface iron were also conducted. It is believed that such studies of the surface properties of silicate minerals will supply pertinent information about their behavior in froth flotation systems. EXPERIMENTAL PROCEDURE Ion Exchange: Carefully selected, hand-picked samples of the minerals investigated were dry-crushed in a ceramic ball mill and sieved to obtain a minus 100 plus 200-mesh sample. The sized samples were then run through the electro-magnetic separator to remove any iron-bearing particles. A 10-g sample of each mineral was placed in 100 ml of freshly deionized water previously adjusted to a pH of 3.50 with HCl. The beaker containing the sample and the water was placed under a bell jar from which the air was displaced at once by nitrogen gas from a tank. All experiments were carried out in a nitrogen atmosphere. The sample and solution were stirred gently but continuously during the entire experiment, the stirring speed being kept about the same for all runs. Changes in pH were followed with a Beckman Zeromatic pH meter and recorded on a

Jan 1, 1967

At a large meeting of the members of the American Fund for French Wounded it which Mr. Franklin D. Roosevelt presided and at which Mrs. B. Girault Lathrop, President of the Paris Administration A. F.F. W., gave a most interesting address, special rows of seats were reserved for the members of the W. A. A. I. M. E. Those who were unable to be present will be glad to hear that Mrs. Lathrop complimented our organization on having supplied the largest dispensary operated by the A. F. F. W. and the Red Cross in northern France. The A. F. F. W. is going to erect an American Memorial Hospital at Rheims and it is hoped that the one hundred beds in the hospital will be endowed in memory of the men who gave their lives for the liberty of the world. It will be possible not only to endow beds, for which sums of $6000 each are needed, but also to give, as. memorials, sun- parlors at a cost of $10,000 each, two roof gardens at $5000 each, a laundry at $10,000 and a garage at $10,000. The New York Section has undertaken to endow a heel in memory of members of the A. I. M. E. who gave their lives in the Great War. Perhaps other Sections or groups of Sections may wish to do the same thing, or if no other Section cares to assume so much responsibility possibly individuals may like to join the fund already growing in New York, in which case they should send their contributions to Mrs. W. Y. Westervelt, 1 Lexington Ave., New York, N. Y.

Jan 6, 1919

By R. Lagneborg

WhEN mechanical twins initiate cracking it has been proposed1 that the friction stress for dislocation motion, in the Cottrell criterion for brittle fracture2 should be replaced by the stress required to propagate a twin, ttp. TF is the fracture stress, d the grain diameter, ß a geometric constant, u shear modulus, and y the effective surface energy. Since TTp is likely to vary with grain size, it cannot be substituted by a constant in Eq. [I]. If an expression for the energy change caused by a twin in a stressed material could be obtained, it is in principle possible to compute the critical size of the twin, i.e., the size at which the system can decrease its energy spontaneously, as a function of applied stress, thus giving the stress required to just barely propagate the twin, i.e., TTP. Consider a circular twin disc with a radius r and having a lenticular cross section, Fig. 1. Twin dislocations3 of strength b exist in the twin boundary parallel to the twin plane, one loop on each atomic plane. Assume that the total numbers of loops, n, can be replaced by one circular loop of a multiple dislocation, nb with a radius r. The energy change of the system, AW, due to such a twin in an applied stress field can then be calculated: The first term is the total twin surface energy, the second the elastic energy due to the twin dislocations, and the third the energy released by the twin in the applied stress field. yt is the twin boundary energy, r, the radius of the dislocation core, and T the applied

Jan 1, 1968

By H. I. Aaronson, H. A. Domian, G. M. Pound

The thernodyna,nics of I the Proeutectoid ferrite re-action ha1.e been investigated on the bases of three diifevent descviptions of the statistical thernzodynamics of interstitzal solid solutions. Especially at low ternperatures, substantial dijeretzces are found in the valltes of the extrapolated y/y + a and cr/a + y equilibriurn curls, and in the To- co7nposilion metastable eqliilibriunz curl-es thus co,npited. Although neither actiztity nor phase-diagram date are able to distingrish udeqiutely among the various descviptions, the statustics of Lacher, Fouller, and Guggenheinz provide the ?nost conplete epresentation az3ailable of the single carbon-ctrbon interaction energy (w) nzodel of an intevstitiril solid solution, and the relationships deduced frojrl then2 are accordingly pre.ferred. The findings tlzut w in austenite 'aries significu?ztly uith tenpevntrue and that phase-diagawr data arc not accurately con?palible usith eqcrctions deduced on the basis of actility infoation indicate, hou'e13er, that a wzore cornplex nlodel of the uustenite , und pvobably of the .feyrite, solirl solutions will have to forn the basis of f4tuve statistical t1.eat1nents. Some suggestions for such a ruodel arc advanced. Althoug11 w represents a vepltlsio energy in austozite, it was found to corvcsporzd in ferrite to a binding energy, in qualitatit.e accord zc,itlz the internal-friclion results of Keefer and wert. ThE transformation of austenite to proeutectoid fer-rite is becoming recognized as an exceptionally useful vehicle for quantitative studies of the kinetics of phase transformations.'" Reasons for this popularity include well-characterized microstructures which develop on a convenient scale with acceptable kinetics within a considerable temperature-composition region, the absence of great sensitivity to common impurities, and, especially. the availability of a unique wealth of the ancillary information indispensable for the quantitative interpretation of kinetic measurements, including phase diagram,3 crystallographies diffusivity,5 inter-facial energy,=17 elastiit," specific vlume, ''' and ativity'-' data. Development of considerable amounts of additional thermodynamic information from activity data is of particular importance with respect to kinetic studies, since much of this information is needed in temperature-composition regions not directly accessible to presently available techniques for the measurement of equilibrium properties. A generally useful approach to the thermodynamics of solid solutions, which is of especial value in this situation, is based upon the formulation of the free energy of such solutions as a function of temperature and composition. The free energy of solid solutions has been resolved into many components. Particularly in the case of interstitial solutions, with which we shall be concerned in the present study, however, only the positional entropy component has been intensively studied. The other components are conventionally taken into account by fitting equations for the activity of the interstitial species or the temperature-composition path of phase boundaries, derived principally from positional entropy considerations, to experimental information on these quantities through adjustment of one or more constants in the equations. A number of studies of the thermodynamics of interstitial solid solutions have been made primarily on this basis,'"25 but only Kaufman, Radcliffe, and cohenZ2 (hereafter KRC) and ener''% ave applied the results of such studies to develop relationships for the thermodynamic quantities of interest in the austenite —- proeutectoid ferrite transformation. KRC made use of a model developed by cheil'' (on the basis of a previous study by ohansson'), and subsequently rede-rived correctly by Speiser and retnak,' in which a carbon atom is considered to inhibit occupancy of a certain number of its nearest-neighboring interstitial sites. schei120 determined the number of sites in austenite thus excluded by matching calculated and experimentally measured curves for the variation of carbon activity with the mole fraction of carbon. zener17 used a different approach. He assumed that the positional entropy of carbon is ideal both in austenite and in ferrite (i.e., no excluded interstitial sites), and included all other contributions of carbon in a temperature-independent "free-energy change" accompanying the transfer of 1 mole of carbon between the two phases. This quantity was determined by "pinning" an equation derived for the boundaries of the a + y region to experimental data on the compositions of these boundaries at a single temperature. In the present investigation, three different approaches to the thermodynamics of the proeutectoid ferrite reaction are examined comparatively: I) the method of Zener; 2) the model employed by KRC and predecessors; and 3) the more detailed statistical thermodynamic treatment of the same model developed by acher and Fowler and uenheim, ' in which the problem of overlapping regions of influence of individual interstitial atoms is resolved. In order to make these comparisons, it is necessary to undertake an extension of one aspect of Zener's method; since the Lacher- Fowler -Guggenheim (LFG) treatment has not been previously used in the present context, the necessary thermodynamic "superstructure" for this treatment will be developed in parallel

Jan 1, 1967

NEW YORK SECTION J. E. Johnson, Jr., Chairman Edgar Rickard, Vice Chairman. D. M. Liddell, Secretary, 7 Wall St., New York, N.Y. C. A. Bohn, Treasurer John V. N. Dorr Lewis W. Francis. The annual meeting of the New York Section was held on Wednesday, June 6, with about 40 members in attendance. The treasurer re a brief summary of-the financial statement for the year, and the secretary's report was read. These reports were ordered placed on file together with the report of the auditors for the two previous years.

Jan 8, 1917

EXECUTIVE COMMITTEES OF LOCAL SECTIONS New York LOUIS D. HUNTOON, Chairman. ARTHUR S. DWIGHT, Vice-Chairman. THOMAS T. READ, Secretary, Woolworth Bldg., New York, N. Y. E. MALTBY SHIPP. Treasurer. GEORGE F. KUNZ, W. De L. BENEDICT. Boston ROBERT H. RICHARDS, Chairman. ALBERT SAUVEUR, Vice-Chairman. AUGUSTUS H. EUSTIS, Secretary-Treasurer, 131 State St., Boston, Mass. TIMOTHY W. SPRAGUE. HENRY A. WENTWORTH. Columbia F. A. THOMSON, Chairman. GEORGE W. RODDEWIG, Vice-Chairman. LYNDON K. ARMSTRONG, Secretary-Treasurer. P. O. Drawer 2154, Spokane, Wash. R. S. McCAFFERY. S. H. RICHARDSON.

Jan 5, 1914