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By John Griffen

THEORY HYDRAULIC classification as explained by Rittinger and others was largely restricted to conditions wherein the free-falling velocities of the particles were conceived as governing the separations effected (see chapter 9). The laws governing classification under free-falling conditions have been summarized by Chapman and Mott as follows: 1 Nomenclature r represents, in a particle of irregular shape, the round-hole screen through which the particle would pass, or some other linear dimen¬sion of the particle equivalent to d, the diameter of a sphere. s, the specific gravity of the particle. 1, the specific gravity of the water used as a medium. K, a constant. W, the velocity of the water. In an Upward Current of Water 1. A particle will move upward if [W > KVr(s-1)] and, by suitably regulating the speed of the water current, the larger and heavier particles may be made to fall downward against the current, leaving the smaller, lighter particles in suspension in the current. 2. Particles such that [T1= s2-1] cannot be separated in an upward-current classifier with any one velocity of current. Coal particles having a specific gravity of 1.35 cannot be separated from refuse particles of 2.5 sp. gr. Unless 2.5-1 the ratio of diameters is less than [1.35-1 or 4.3 to 1,] and the raw coal must be screened to size limits within this ratio if they are to be separated. Cone¬-shaped vessels or vessels of other shapes that allow the use of&apos; different velocities of current at different points in the flow are used to modify this limitation. 3. During the initial stages of motion, coal particles ascend more rapidly than refuse particles of the same size. 4. A particle will ultimately fall if [W < KVr(s-1).] If particles of

Jan 1, 1950

Receipts, Jan. 1, 1914, to Dec. 31, 1914 Cash on hand, Jan, 1 1914 General Funds $1,843.54 Special Funds 1,039.00 $2,882.54 Initiation Fees $8,500.00 Annual Dues 44,060.84 Life Memberships 1,950.00 54,510.84 Sale of Transactions 4,798.87 Sale of Binding 10,029.06 Sale of Bulletins and Pamphlets 2,508.25 Sale of Special Editions 1,290.74 Sale of Advertising 8,783.29 Sale of Library Books 54.97 Sale of Pins and Fobs 347.65 Miscellaneous Sales 21.66 Space Released 5,943.00 Interest on Investments and Bank Deposits 230.15 34,016.64

Jan 1, 1917

LIST OF THE MEETINGS OF THE INSTITUTE AND THEIR LOCALITIES FROM ITS ORGANIZATION Transactions Number Place Date Vol Page 1 Wilkes-Barre, Pa May, 1871 1 3 2 Bethlehem, Pa August, 1871 1 10 3 Troy, N Y November, 1871 1 13 4 Philadelphia, Pa February, 1872 1 17 5 New York, N Y May, 1872 1 20 6 Pittsburg, Pa October, 1872 1 25 7 Boston, Mass February, 1873 1 28 8 Philadelphia, Pa May, 1873 2 3 9 Easton, Pa October, 1873 2 7 10 New York, N Y February, 1874 211 11 St Louis, Mo May, 1874 3 3 12 Hazleton, Pa October, 1874 3 8 13 New Haven, Conn February, 1875 3 15 14 Dover, N J May, 1875 4 3 15 Cleveland, 0 October, 1875 4 9 16 Washington, D C February, 1876 4 18 17 Philadelphia, Pat June, 1876, 5 3 18 Philadelphia, Pa October, 1876 5 9 19 New York, N Y February, 1877 5 27 20 Wilkes-Barre, Pa May, 1877 6 3 21 Amenia, N Y October, 1877 6 10

Jan 1, 1917

By Willard R. Jillson

Within the last ten years Kentucky has become celebrated for its low-sulfur bituminous coals. Prior to this time, many investigators had discnvered the abundance of this coal but the fact was unknown to the general public until the last extension of Kentucky&apos;s mountain railroads&apos; was completed. The coals of. Kentucky are, broadly, separated into two geographic units—the eastern and the western coal fields. On a basis of their sulfur content these coal fields fall into three units, which are indicated on the accompanying map, by numbers, 1, 2, and 3. The area marked 1, the very southeastern part of the state, shows the lowest sulfur, all coals being averaged. In this field the maximum is 1.04 per cent. and the minimum as low as 0.68 per cent.—both averages and not individual analyses, which would of course show much greater variation. Included in this group are the following counties: Lawrence, 0.87 per cent.; Martin, 0.75 per cent.; Johnson, 0.73 per cent.; Magoffin, 0.87 per cent.; Floyd, 0.88 per cent.; Pike, 0.68 per cent.; Knott, 1.04 per cent.; Perry, 0.77 per cent.; Letcher, 0.80 per cent.; Leslie, 0.70 per cent.; Harlan, 0.79 per cent.; Knox, 0.86 per cent.; and Bell, 0.92 per cent. The total average sulfur content for these thirteen counties is 0.82 per cent. Bordering the restricted low-sulfur field of eastern Kentucky is the No. 2 belt (slightly darker), &apos;which is commonly known as the western border of the eastern coal field. Here the maximum sulfur is 2.91 per cent. and the minimum 1.05 per cent. Again these are averages and not individual analyses. The counties in this group are: Greenup, 2.60 per • cent.; Boyd, 1.67 per cent.; Carter, 1.07 per cent.; Morgan, 1.40 per cent.; Wolfe, 1.83 per cent.; Lee, 2.93 per cent.; Breathitt, 1.85 per cent.; Owsley, 1.09 per cent.; Jackson, 1.06 per cent.; Rockcastle, 2.30 per cent.; Clay, 1.09 per cent.; Laurel, 1.08 per cent.; Pulaski, 2.24 per cent.; Whitley, 1.05 per cent.; McCreary, 1.50 per cent.; and Wayne. The sulfur percentage average for this area including fifteen important counties is 1.65 per cent. In the western Kentucky field, the great increase in the percentage of sulfur is at once apparent. Ohio County with 3.78 per cent. is the highest and Hancock with 2.87 per cent. is the lowest. The percentages by counties is as follows: Hancock, 2.87 per cent.; Henderson, 3.22 per cent.; McLean, 3.27 per cent.; Muhlenberg, 3.31 per cent.; Hopkins,

Jan 1, 1920

By W. Kauenhowen

The production of petroleum in Germany during 1932 totaled about 1,608,558 bbl., a slight increase over the 1, 602,517 bbl. produced in 1931. A decline, as shown in Table 1, occurred chiefly in the Volkenroda (Thuringia) field. The total production of the other fields (salt domes), however. reached a new record, about 21 per cent above 1931. Table 1.—Oil Production of Germany by Fields and Oil Provinces, 1928-1932 (Barrels of 42 Gallons)" Salt Dome Province __________________________________________________|_________________________________________________________________________________________________________________________ 1928 274,323 322,742 679 46,319 644,021 644,315 1929 310,891 337,582 10,535 67,578 719,901 720,069 1930 586,404 427,539 100,716 72,485 1,186,969 29,806 1,220,296 1931 506,548 403,634 213,549 116,088 1,242,598 360,885 1,602,517 1932 769,405 366,982 230 979 130,711 1,498,077 110,481 1,608,558 " Official figures published in Germany are given in metric tons. For the above conversion into barrels a factor of 1 metric ton equaling 7 barrels has been used. Includes a very small production from Hcide, Holstein. c Includes a very small production from Tegernsee, Bavaria, and Bruchsal, Baden. Nienhagen-Hanigsen Field In 1932 the Nienhagen-Hanigsen yielded about 51 per cent of the production from the four German salt dome fields. During 1932 the productive area was again extended, chiefly towards the northwest in the so-called north district, to which the present drilling activity is confined almost entirely. Since the discovery of the north district in 1928, about 45 wells have been drilled in it, of which only two were

Jan 1, 1933

[Trans. No. Place Date Vol. Page 1. Wilkes-Barre, Pa.* May, &apos;71.. 1 3 2. Bethlehem. Pa Aug., &apos;71.. 1 10 8. Troy, N. Y Nov., &apos;71.. 1 1S 4. Philadelphia, PaFeb., &apos;72.. 117 5. New York, N. Y.*May: &apos;78.. 120 5. Pittsburgh, PaOct., &apos;72.. 125 7. Boston, MassFeb., &apos;78.. 128 8. Philadelphia, Pa.* May, &apos;78.. 2 3 9. Easton, POct., &apos;78.. 27 10. New York. N. YFeb.. &apos;74.. 2 11]

Jan 1, 1946

PRESIDENT. CHARLES F. RAND,1 NEW YORK, N. Y. PAST PRESIDENTS. CHARLES KIRCHHOFF,1 NEW YORK, N. Y. JAMES F. KEMP,2 NEW YORK, N. Y. FIRST VICE-PRESIDENT. BENJAMIN B. THAY ER,1 NEW YORK, N. Y. TREASURER. GEORGE C. STONE,1 NEW YORK, N. Y.

Jan 4, 1913

By Fred P. Dewey

IN preparing material for the exhibit of the National Museum at the New Orleans Exposition in 1881, it was decided to attempt to photograph the interior of a coal-mine, in order to get a strictly truthful representation of a thick coal-seam, and to show incidentally the methods of mining. While we have many drawings, both mechanical and artistic, illustrating the subject, they are not satisfactory for these purposes, simply because they are drawings. Aside from this, much interest attaches to pictures of inaccessible places, and the enlarged copies (30 inches by 40 inches) of the photographs we succeeded in obtaining, have attracted a large amount of attention from the visitors to the Museum. The Kohinoor colliery, Shenandoah City, Pa., was selected as most suitable for the attempt, principally on account of the fine exposure of the Mammoth bed, and the comparatively level character of the workings, in that colliery. This is one of the many anthracite-mines of the Philadelphia and Reading Coal and Iron Company. A detailed section of the fiftyfoot or Mammoth bed in this colliery is as follows: Feet. Inches. 1 0 Clod. 1 7 0 Coal. 1 0 Slate. Top Split. 8 0 Coal. 1 6 Slate divider.* 6 0 Coal. 1 0 6 Slate. 2 6 Coal. 0 5 Slate. 1 8 Coal. 1 2 Charcoal. 5 0 coal. 1 0 Bone and Coal. „ „ Coal. [ Bottom Split. 0 6 Bone and Slate. 3 0 Coal. 0 10 Bone and coal. 1 2 Coal. 0 2 Bone. 4 4 Coal. 0 1 Bone. 0 8 Coal.

Jan 1, 1888

By D. R. de Fontaine

By computing the values of the resolved shear stress for a great many orientations of the tensile axis on all 12 (111) <110> slip systems, Taylor and Elam&apos; were able to map out a stereogram of slip systems, given here, Fig. 1, in Diehl&apos;s notation (see, for example Hauser and Jackson&apos;). The purpose of the present note is to derive such a stereogram by mathematical reasoning and to give a simple method of defining the system with highest resolved shear stress for any direction of the tensile axis, thereby eliminating tedious computation of the Schmid factor. Let the tensile axis, of direction cosines [xyz], make the angles 0 and relative to the slip plane normal [HKL] and the slip direction [hkl] respectively. Fig. 2 shows a simple cubic cell whose edges define a Cartesian coordinate system. Let A be a unit vector of origin 0 supported by the tensile axis. Its end point [xyz] then lies on a sphere of unit radius, on the positive hemisphere of which the planes z = 0, x = y, y = z limit the so called primitive triangle of a standard [loo] stereographic projection. For any point of this triangle, the following hold: 0«2 «y *sx « 1 [l] Now, for given [xpz], the most highly stressed system will be the one for which the following expression of the Schmid factor has the largest possible value: (HKL) belonging to the form (111) and [hkl] to the form <110>, the denominator on the right hand side of Eq. [2] is equal to 1.fi.a. The unknowns H, ... h, . . . can now be determined by correctly distributing +1 and -1 to H, K, L, and +1, -1,O to h,k, 1 giving the numerator of Eq. [2] its greatest positive value (the angles 0 and cpare chosen acute) subject to the condition: Hh+Kk+Ll = 0 [3] since the slip direction must lie in the slip plane. Condition [3] can be satisfied only by having one of its terms vanish and the other two equal to +1 and -1. Taking the case of the tensile axis lying in the primitive triangle, x2y, z and therefore Hh will be chosen equal to +1 with H = h = +1 in order to retain a maximum of + signs. There remain two alternatives: either 1 = 0 or k = 0. 1) take 2 = 0 Then Kk = -1 and the numerator of [2] becomes: Retaining a maximum of + signs gives L = k = +1 and becomes: 2) take k = 0 Then L1 = -1and, likewise, the numerator of [2] becomes: xz - z2 + xy + yz [5] But the difference [5] - [4] can be written: (y - z)(x+y +z) [6] positive or zero by virtue of [I]. If [6] is positive (y > z), then the largest possible value for the numerator of [2] for any xyz inside the primitive triangle is given by [5], i.e., for: That is to say, the active slip system corresponding to an orientat:~on of the tensile axis inside the primitive triangle is:

Jan 1, 1962

LIST OF THE MEETINGS OF THE INSTITUTE AND THEIR LOCALITIES FROM ITS ORGANIZATION Transactions Number Place Date Vol Page 1 Wilkes-Barre, Pa May, ?71 1 3 2 Bethlehem, Pa August, ?71 1 10 3 Troy, N Y November, ?71 1 13 4 Philadelphia, Pa February, ?72 1 17 5 New York, N Y May, ?72 1 20 6 Pittsburg, Pa October, ?72 1 25 7 Boston, Mass February, ?73 1 28 8 Philadelphia, Pa May, ?73 2 3 9 Easton, Pa October, ?73 2 7 10 New York, N Y February, ?74 211 11 St Louis, Mo May, ?74 3 3 12 Hazleton, Pa October, ?74 3 8 13 New Haven, Conn February, ?75 3 15 14 Dover, N J May, ?75 4 3 15 Cleveland, 0 October, ?75 4 9 16 Washington, D C February, ?76 4 18 17 Philadelphia, Pat June, ?76, 5 3 18 Philadelphia, Pa October, ?76 5 9 19 New York, N Y February, ?77 5 27 20 Wilkes-Barre, Pa May, ?77 6 3 21 Amenia, N Y October, ?77 6 10 22 Philadelphia, Pa. May, ?78 6 18 23 Chattanooga, Tenn May ?78 7 3

Jan 1, 1923

By G. P. Tiwari

Recrystallization and grain growth in thoria dispersed nickel and nichrome were recently studied by Webster as a function of temperature and deformation. The unexpected part of these results was that specimens which had received heavier deformation developed greater resistance to recrystallization. Retardation of recrystallization was accompanied by the formation of voids around thoria dispersion. To explain these results, Webster suggested that the formation of void around the particles increased the effective size of thoria particles. This resulted in greater impediment to the grain-boundary migration and as a consequence the recrystallization of the matrix is retarded. In the present note an alternative and more probable explanation for the effect of voids on recrystallization is presented. The exact mechanism of void formation in thoria dispersed nickel or nichrome is not known. However, it is reasonably certain that it must be preceded by the stress concentration in the matrix around thoria dispersion during the deformation.&apos;&apos; The resulting stress concentration must be sufficient enough to supply the surface energy for the new surfaces created. Further, the decrease in the strain energy of the matrix surrounding the potential void nucleus must be larger than the surface energy of the newly created surface. The release of strain energy due to formation of crack results in a strain free cylinder of the material around the voids.13 If the void formation is not localized, at few points only (as is the case here), this process may lead to considerable amount of release of strain energy of the matrix. The pattern of recrystallization behavior of single phase homogeneous matrix as well as the matrix having a second phase dispersion is same except for the fact recovery and recrystallization are more clearly delineated.14 In general, the recrystallization temperature is lowered (i.e., recrystallization is easier) with increase in the amount of cold work. This is due to the increase in stored energy in the matrix with increasing amount of deformation. If somehow there is a relaxation of strain energy in the matrix, the recrystallization should become difficult because of the decrease in the amount of stored energy available for recrystallization. Since the formation of voids leads to a decrease in the strain energy of matrix, the recrystallization of the matrix would be inhibited due to the formation of voids during deformation prior to recrystallization. It has been observed by earlier workers15&apos;16 that the presence of preexisting voids in a matrix retards the recrystallization. The essential issue here is how do the voids act to produce this effect. If the voids influence recrystallization only by blocking the grain boundary migration, then the effect should be maximum when they are present almost exclusively along grain boundary. These conditions are obtained during high temperature deformation. However, the voids produced due to creep along grain boundary are not able to prevent recrystallization17 suggesting that they are not effective in blocking grain boundary movement. Recently it was shown by Davies and Williams that the voids can act as sinks for vacancies." As a result the processes dependent on vacancy diffusion like recovery, recrystallization, dislocation climb, and so forth, will be hindered. This fact may be responsible for inhibition of recrystallization during subsequent deformation and annealing cycles. It is to be noted here that there is a large difference between the density of voids in creep experiments and the other experiments where retarding effect of voids on recrystallization is seen. The voids in former may number up to l04 to l05 per sq cm whereas in latter cases the voids density is typically around 1010 to 1013 per sq cm. It appears that the decrease in supply of vacancies in creep is insufficient to adversely affect the recrystallization due to low void population. The author is grateful to P. Das Gupta and S. P. Ray for helpful discussions. Author&apos;s Reply D. Webster Tiwari appears to have misunderstood the nature of grain boundary-particle interactions. Tiwari (quoting Cahn) states that second phase particles become more effective as they become smaller, therefore as the voids in TDNiC make the thoria particles effectively bigger their ability to resist grain boundary movement is impaired. This particle size argument was originally proposed in the form of an equation by Zener 20 years agol9 and is not necessarily valid as is discussed below. However, assuming it is valid, it predicts a greater boundary restraining effect by smaller particles simply because their combined cross sectional area is greater at a constant volume. If the number of particles remains the same and their effective size increases, as in the present case, Zener&apos;s equation predicts a greatly reduced grain size. This is because the effect

Jan 1, 1970

By F. R. Jones

AT Tahawus, N. Y., National Lead Co. operates the MacIntyre development. Here the world&apos;s largest titanium mine produces 5200 long tons of ore per day and pours 8000 long tons of waste rock over its dumps. Concentrated ilmenite is sent by rail to National Lead Co. pigment plants, and a second product, magnetite, is sold to steel producers in raw form or is agglomerated and shipped as sinter. Several earlier attempts had been made to produce iron from the deposits, which have been known since 1826. These attempts failed, chiefly because of titanium impurity. In 1941 the present owners reestablished the operation for production of war-scarce ilmenite, and the impurity became the main product. The Ore: The MacIntyre ore zone is about 2400 ft long and 800 ft wide in horizontal measurements. Ore outcrops were found on the northwest side of Sanford Hill, 450 ft above Sanford Lake and 2500 ft southeast. The zone dips at about 45" toward the lake and plunges to the southwest. The ore minerals, ilmenite and magnetite, are unevenly distributed in bands roughly parallel to the long axis of the ore zone and are interspersed with bands and horses of waste. Hanging wall ores are fine grained and grade from rich ore to waste rock or gabbro. Footwall ores are coarse grained and are almost entirely ilmenite and magnetite. The foot-wall waste rock, anorthosite, is the common country rock. Several faults cut the ore zone. These faults have no great displacement but do contribute to the great physical variations in ore rock and surrounding waste. The Mine: The MacIntyre mine is an open pit operation, with benches at 35-ft intervals. The lowest bench is now 54 ft below lake level. Loading equipment consists of three electric-powered shovels (a P & H model 1400 with 4-yd dipper and two Bucyrus-Erie models 85-B with 2%-yd dippers) and one diesel-powered shovel (a Northwest model 80D with 2%-yd dipper). Ore and waste are transported to a 48x60-in. jaw crusher in ten 22-ton Euclid trucks with 300-hp diesel engines. Ordinarily the two Bucyrus-Erie 2 % -yd shovels load ore into a fleet of three or four trucks. This combination works two 8-hr shifts per day, moving 5200 long tons of ore to the crusher and removing a small portion of the waste rock. The P & H model 1400 shovel, with a fleet of four trucks, loads waste on three shifts per day. The mine operates on a 5-day week, with a small maintenance crew working Saturday. Oversize rock is broken by a dropball handled by an Osgood model 825 rubber-mounted crane.&apos; Ore and waste are broken by drilling and blasting 9-in. diam vertical holes behind the benches. Bucyrus-Erie 42-T churn drills are used to drill the holes, which are extended 4 ft below the bench level on which the broken rock will fall. Drilling and Blasting History: In its early years the mine was equipped with Bucyrus-Erie 29-T churn drills, which drilled 6-in. holes. To keep up with production requirements the hole diameter was soon increased to 9 in., and by 1950 the three 42-T drills now in use had been acquired. Early blasting experiments with different kinds and grades of explosive led to adoption of 90 pct straight gelatin dynamite as standard. It was recognized that this explosive was expensive, and from the start of operations until 1950 extensive experiments were made using blasting agents of the ammonium nitrate family. Results were recorded as uniformly poor, with great build-up of oversize rock. The expense of these experiments, and the discouraging results, caused the abandonment of any expectation of breaking MacIntyre rock with anything but 90 pct straight gelatin dynamite. Further standardization led to 9-in. well drillhole spacings set at 16 ft in ore and 18 ft in waste, exceptions being permitted only for unusual conditions. The hole burdens were theoretically about 22 ft. Due to the extreme back-slope of bench faces, caused by blasting with heavy charges of dynamite, actual burdens were commonly well over 30 ft. Lack of precise control resulted in many holes having a burden as light as 15 ft. General practice was to stem 6 or 7 ft of hole with magnetite concentrate, the amount of stemming being left to the discretion of the pit foreman. Usually all holes in a row were fired instantaneously with Primacord detonating fuse. Millisecond delays were

Jan 1, 1957

By W. N. Tanner

THE wire-rope hoisting conditions at the mines of the Anaconda Copper Mining Co. in Butte, Mont., are very severe because of the conditions under which it is necessary to operate. A study was made, in the fall of 1919, for the purpose of changing these conditions in order to obtain longer rope and sheave life. There are at present in Butte, hoisting engines equipped with wire rope as follows: 9 main hoists using flat ropes. 7 main hoists using 1 ½ in. rope. 5 main hoists using 1 ¼ in. rope. 6 shafts using 1 1/8 in. rope. 2 chippy hoists using 1 ¼ in. rope. 9 chippy hoists using 1 1/8 in. rope. 15 shafts using 1 in. rope. 7 shafts using 7/8 in. rope. 1 shaft using ¾ in. rope. In addition, there are a number of sinking engines using 5/8 in., ¾ in., 7/8 in., and 1 in. (15.9, 19, 22, and 25 mm. rope.) The flat ropes run from ½ by 7 ½ in. (12.7 by 190.5 mm.) to ½ by 4 ½ in. (9.5 by 114 mm.) and are used on the older hoisting-engines, which are set comparatively close to the shaft. Because of swelling and moving ground at some of the shafts, these ropes present certain difficulties in operation that are more pronounced than with round ropes; they are, therefore, being superseded by round ropes as newer engines are being installed. They are, however, much more easily inspected and repaired than round ropes.

Jan 2, 1922

LIST OF THE MEETINGS OF THE INSTITUTE AND THEIR LOCALITIES FROM ITS ORGANIZATION Transactions Number Place Date Vol Page 1 Wilkes-Barre, Pa May, ?71 1 3 2 Bethlehem, Pa August, ?71 1 10 3 Troy, N Y November, ?71 1 13 4 Philadelphia, Pa February, ?72 1 17 5 New York, N Y May, ?72 1 20 6 Pittsburg, Pa October, ?72 1 25 7 Boston, Mass February, ?73 1 28 8 Philadelphia, Pa May, ?73 2 3 9 Easton, Pa October, ?73 2 7 10 New York, N Y February, ?74 211 11 St Louis, Mo May, ?74 3 3 12 Hazleton, Pa October, ?74 3 8 13 New Haven, Conn February, ?75 3 15 14 Dover, N J May, ?75 4 3 15 Cleveland, 0 October, ?75 4 9 16 Washington, D C February, ?76 4 18 17 Philadelphia, Pat June, ?76, 5 3 18 Philadelphia, Pa October, ?76 5 9 19 New York, N Y February, ?77 5 27 20 Wilkes-Barre, Pa May, ?77 6 3 21 Amenia, N Y October, ?77 6 10 22 Philadelphia, Pa. May, ?78 6 18

Jan 1, 1923

PRESIDENT. CHARLES F. RAND,1 NEW YORK, N. Y. PAST PRESIDENTS. CHARLES KIRCHHOFF,1 NEW YORK, N. Y. JAMES F. KEMP,2 NEW YORK, N. Y. FIRST VICE-PRESIDENT. BENJAMIN B. THAYER,1 NEW YORK, N. Y. TREASURER. GEORGE C. STONE,1 NEW YORK, N. Y. SECRETARY EMERITUS. ROSSITER W. RAYMOND NEW YORK, N. Y.

Jan 5, 1913

PRESIDENT WILLIAM L. SAUNDERS,1 NEW YORK, N. Y. PAST PRESIDENTS CHARLES F. RAND,1 NEW York , N. Y. BENJAMIN B. THAYER,2 . NEW YORK, N. Y. FIRST VICE-PRESIDENT PHILIP N. MOORE,1 ST. Louis, Mo. TREASURER GEORGE C. STONE,1 NEW YORK, N.Y. SECRETARY EMERITUS ROSSITER W. RAYMOND, NEW York, N. Y.

Jan 4, 1915

PRESIDENT BENJAMIN B. THAYER,1 NEW YORK, N. Y. PAST PRESIDENTS JAMES F. KEMP,1 NEW YORK, N. Y. CHARLES F. RAND,2 NEW YORK, N. Y. FIRST VICE-PRESIDENT SIDNEY J. JENNINGS,1 NEW YORK, N. Y. TREASURER GEORGE C. STONE,1 NEW YORK, N. Y. SECRETARY EMERITUS ROSSITER W. RAYMOND, NEW YORK, N. Y.

Jan 4, 1914

By F. A. Crossley

The key to disagreements between Blackburn&apos;s findings and mine is the word equilibrium". My work attempted to define the equilibrium diagram of the titanium-rich end of the Ti-A1 system. It can readily be shown that Blackburn&apos;s conclusions are based primarily on the examination of structures substantially removed from equilibrium. The diagram presented in Fig. 16 is properly labeled a "phase diagram". However, it appears that Blackburn either does not understand or does not accept the difference between "phase diagram" and "equilibrium diagram" as defined in the Metals Handbook.17 The conflict lies not in Blackburn&apos;s data but in his interpretation of it, and his use of "transformation", "phase diagram", and "equilibrium diagram" as synonymous terms. I share his view that the light microscope is much inferior to the transmission electron microscope for the study of transformations; but this fact does not render the light microscope useless or untrustworthy. The difficulties experienced with the Ti-A1 system have not been due to the limitations of the light microscope, but rather to the extreme sluggishness in achieving equilibrium at temperatures below 1000° C. Were it not for the light microscope employed with polarized light, the twin phase syndrome&apos; might still be unrecognized and, as a consequence, still adding to the confusion of Ti-A1 investigations. (Ref. 1 should read ... Contract No. N161-25952 ... vol. 236.) Other, more sophisticated techniques, including electron transmission, simply confirm the erroneous tentative conclusions drawn from observations of structures due to the twin-phase syndrome. By the standards of most of the investigations of the Ti-A1 systems, seven of the fifteen compositions investigated by Blackburn were seriously contaminated with oxygen. The writer has found that 0.1 wt pct 0 shifts the a + Ti3A1 boundary to 1 at. pct lower A1 content at 700°C. At constant aluminum content, this corresponds to a temperature shift of the boundary of +25°c.18 Blackburn advises that the first group of alloys contained 0.1 to 0.15 wt pct 0, bur he does say whether the analyses were performed on as-received material or on specimens in their final state of heat treatment. This is especially important considering the 20-mil-thick starting materials. If specimens had been annealed in the two-phase a + 6 region it would have provided an indication of the final degree of oxygen contamination since up to about 12 at. pct A1 the boundaries of this region are well-defined for low-oxygen alloys. Blackburn questions the capability of light microscopy in determining phase boundaries in the Ti-A1 system. I submit that the a/a + Ti3A1 boundary in Fig. 1 of Ref. 1 over the composition range from 10 to 18 at. pct A1 was determined by dilatometry and supported by electron diffraction. Specimens of alloys containing 8, 10, 12, and 14 at. pct A1 were aged at 550°C for 1000 hr (under stress of 5000 psi to accelerate the tendency to equilibrium) and then fractured in tension at room temperature. Collodion was applied to the as-fractured (unetched) surface and, when stripped, carried away particles identified by electron diffraction as Ti3A1. Perhaps Blackburn will explain why these electron diffraction data were ignored. At this time, a technique for revealing or indicating

Jan 1, 1969

By C. G. Dunn, F. W. Daniels, M. J. Bolton

IN recent papers on interface energies in metals¹,² the concept of an equilibrium of forces has been used in the measurement of interfacial tensions. Mathematically the equilibrium of three forces is given by the relations: where the 2&apos;s are the interfacial tensions (interface energies per unit area of interface) of three phases or grains meeting at angles 21 22 and 23 (212 relates to the 1-2 boundary formed by grains 1 and 2;223 to the 2-3 boundary, etc.). If these relationships are valid, one can calculate relative values of the interface energies from measured boundary angles on specimens which have been brought to equilibrium. Since Eq 1 may be derived through a mathematical process of minimizing the grain boundary energy under the restriction that the ?&apos;s be independent of boundary orientation: the concepts of surface tensions and equilibrium of forces are not particularly essential. To deal with the general case involving dependence of boundary energy on boundary orientation, it becomes desirable to drop certain concepts formerly held (namely that energy per unit area is identical with force per unit length or surface tension) and to use the energy concept alone. It is appropriate, therefore, to use E in place of ? in deriving and using the more general equations that express the anisotropic nature of the grain boundary energy. Herring3# &apos; recently has derived the required general equations using the principle of minimization of energy. Specifying the boundary orientations in terms of angles (4) measured with reference to crystal axes within the grains, Herring&apos;s equations take the form E23 + E21 cos?8 + E12 cos?2 — sin ?12 + sin?2-?E12/?12 =O [2] where the partial derivatives are measured in the direction of counterclockwise rotation of the boundaries. Eq 2 implies that an infinitesimal displacement of the triple point along the 2-3 boundary produces no change in the boundary energy. Similar equations apply for infinitesimal displacements along each of the other two boundaries. From such equations Herring obtains the following general relationship (1 + E1 E2) sin?8 + (E2 — E1) cos?3 ________ E38______________ = (1+ E2 E8) sin ?1+ (E3— E2) cos ?1 __________^5____________[3] (1 + E sin ?2, + (E1 — E8,) COS ?2 1 E28 where E1 = 1/E23- E25 and PC and c8 have similar expressions. It is apparent that Eq 3 reduces to Eq 1 when the c&apos;s vanish. Eq 3 also reduces to Eq 1 when the E&apos;S are all equal. Shockley and Read&apos; have pointed out one limitation to these equations. When E plotted versus 4 appears as an energy cusp, as their theory requires, for example, for the energy near a twin boundary position, then Eq 3 (and therefore Eq 1 also) no longer applies if one boundary is in the minimum energy position. One of the equations of form Eq 2, however, applies if the infinitesimal displacement is along the boundary associated with the energy cusp. From the foregoing treatment it will be apparent that equilibrium angles alone are not sufficient in general for calculating relative interface energies.

Jan 1, 1951

By CHARLES F. RAND

PRESIDENT CHARLES F. RAND,1 NEW YORK, N. Y. PAST PRESIDENTS CHARLES KIRCHHOFF,1 NEW YORK, N. Y. JAMES F. KEMP,2 NEW YORK, N.. Y. FIRST VICE-PRESIDENT BENJAMIN B. THAYER,1 NEW YORK, N. Y. TREASURER GEORGE C. STONE,1 NEW YORK, N. Y. SECRETARY EMERITUS ROSSITER. W. RAYMOND, NEW. YORK; N. Y. SECRETARY BRADLEY- STOUGHTON NEW YORK, N. Y.

Jan 2, 1914