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By K. P. Mukherjee, K. P. Gupta, J. Bandyopadhyaya

Even though a lot of work has been done in the past to establish phase equilibrium in the Cu-Si system a re cent investigation casts some doubt about the existence and crystal structure of some of the phases that form in the composition range of 15 to 25 at. pct Si in Cu. The present investigation was carried out using high temperature X-ray diffraction technique along with other standard techniques to study the phases in this composition range. The high temperature 6 phase appears to be tetragonal with parameters a,, = 8.815A, c, = 7.903A, and co/ao = 0.896. The reported bcc E phase exists at room temperature and at least up to 780°C and appears to undergo a transformation near 600°C. The phase appears to be cubic but not of the bcc type. The ? phase appears to undergo a transformation, as has been indicated by earlier investigators, and the low temperature form of .? phase is tetragonal with parameters a, = 7.267A, co = 7.8924, and co/ao = 1.086. THE Cu-Si binary system has been investigated by several investigators1" and several intermediate phases,?,e,?' at lower temperatures and ?,ß,0,e, and ? at higher temperatures, were observed between terminal solid solutions of copper and silicon. Even though the existence of the e phase and the transformation in the ? phase were reported in many early works, in a recent study of this system Nowotny and Bittner6 doubted the existence of the e phase and phase at 550°C. Among the high temperature phases, the 6 phase was reported to have a complex cubic structure with parameter a, = 8.805A.7 Nowotny and Bittner, however, suggested that the structure of the 6 phase might be of CsCl type. In order to check these contradictory reports the present study was taken up to investigate the Cu-Si binary system in the composition range of 17 to 25 at. pct Si. EXPERIMENTAL PROCEDURE Weighed amounts of copper (99.99 pct) and silicon (99.9 pct) were induction melted in recrystallized alumina crucibles under argon gas atmosphere. The alloys containing 17, 18, 20, 21, 21.2, 22, and 24 at. pct Si were annealed in evacuated and sealed quartz capsules at 700°C for 3 days and subsequently water quenched. Other than this annealing, the 21.2 at. pct Si and 24 at. pct Si alloys were annealed at 550°C for 10 days, the 17 at. pct Si alloy was annealed at 750°C for 3 days, and the 22 and 24 at. pct Si alloys were annealed at 780°C for 2 days. All annealing temperatures were controlled to within *l°C. Alloys after quenching were subjected to metallographic and X-ray diffraction investigation. A solution containing 5 g FeC13 + 10 cc HCl + 120 cc H2O diluted with six times its volume with water was used as etching reagent. A 114.6 mm diam Debye Scherrer camera was used for obtaining diffraction patterns. The 17, 21.2, and 24 at. pct Si alloys were subjected to high temperature diffractometry using a Tempress Research High temperature attachment and a GEXRD VI diffractometer. For the 6 phase (17 at. pct Si alloy) powder specimen from a 750°C annealed alloy was reheated to 750°C in the high temperature attachment for 1½ hr before taking a diffraction trace. A 550°C annealed and slowly cooled phase (24 at. pct Si) alloy was first reheated to 550°C. a diffraction trace was made after annealing it for 2 hr, and subsequently it was heated to 716OC and kept at this temperature for 2 hr before taking a diffraction trace. For the e phase (21.2 at. pct Si alloy) a 550°C annealed and slowly cooled specimen was heated first to 425°C and annealed at this temperature for 2 hr before taking a diffraction trace. Subsequently, the specimen temperature was raised to 495", 540°, 603", 635", 682", 720°, and 748°C and homogenized at each temperature for 1 hr before taking diffraction traces. The powder specimen temperature was controlled to within +2oC at each temperature and argon gas, purified by passing it at slow rate through a fused CaC12 column, hot (800°C) copper and titanium chips and finally through a P2O5 column, was used to prevent oxidation of the powder. For all X-ray work copper-radiations at 25 kv, 15 ma (for Debye Scherrer technique), and 40 kv, 20 ma (for diffractometer tech-nique) were used. RESULTS AND DISCUSSION At 700°C the alloys containing 17 to 21 at. pct Si showed two phases while the 21.2 at. pct Si alloy was found to be single phase. The X-ray diffraction patterns of the two-phase alloys were consistent with the phase (ßP-Mn type structure) and the phase (21.2 at. pct Si) patterns. The diffraction patterns of the 17 at. pct Si alloy quenched from 750" and 700°C were identical. According to the accepted Cu-Si phase dia-gram4,5,10 the 17 at. pct Si alloy at 750°C should be in the (k + 6) two-phase region and very close to the -phase boundary. The identical patterns possibly resulted from the decomposition of the 6 phase on

Jan 1, 1970

By R. G. Aspden

Crystals with an (001) [loo] initial orientation of an iron-base alloy containing 3 pct Si were cold rolled with and without the use of constraints. A major difference in the rolling and annealing textures was observed between crystals rolled with and without constraints. These data show that the contribution of constraints at grain boundaries in a poly crystalline sheet should be considered in applying textural data on single crystals to grains in an aggregate. SILICON-iron alloys with a cube texture have been recently developed and their magnetic characteristics reported.1-4 Of interest in the development of this texture were the textural changes of single crystals accompanying rolling and annealing and the influence of constraints at grain boundaries in an aggregate on the behavior of individual grains. The present study was primarily concerned with the effect of constraints during rolling on the textures of 3 pct Si-Fe crystals initially (001)[100]. Barrett and Levenson5 were among the first to observe an influence of constraints at grain boundaries on the textural changes of individual grains during deformation. They tested Taylor's6 theory of plastic deformation of face-centered-cubic metals in which deformation textures were predicted. About one-third of the grains in poly crystalline aluminum did not rotate as predicted. Grains of the same initial orientation were observed to rotate in different directions under the influence of applied stress and anisotropic flow of neighboring grains. Recently, the various inhomogeneities of flow of crystals in an aggregate have been studied7'8 and reviewed.9-11 Barrett and Levenson" rolled (001) [loo] iron single crystals inserted in close-fitting holes in copper to limit lateral flow and to simulate rolling of grains in an aggregate. Deformation bands were formed after a 90 pct reduction in thickness, and the cold-rolling texture contained two components described by rotating the (001)[100] about 35 deg in both directions around the normal of the rolling plane. No annealing textures were reported. Chen and Maddin13 rolled molybdenum single crystals initially (001) [loo]. The crystals were mounted between two hardened silicon-iron plates and 96 pct reduced in thickness by rolling at a low rate of reduction, about 0.0001 in. per pass. The deformation texture had the mean orientation of (001) [loo], and the azimuthal spread included orientations described by rotating (001) [loo] about 35 deg in both directions about the pole of the rolling plane. The presence of deformation bands were not reported by Chen and Maddin or detected in subsequent work of Ujiiye and Maddin.14 The ideal orientation of the annealing texture was (001) [loo]. Recently, Walter and Hibbard 15 reported on the textures of 3 pct Si-Fe alloy crystals initially near (001) [loo]. Each crystal was in an aggregate cut from a columnar ingot. After 66 pct reduction by rolling, the texture consisted of two symmetrical components which had the orientations described by rotating (001) [loo] about 30 deg in both directions about the pole of the rolling plane. Annealing texture was near (001) [loo]. In the above work, the textures of body-centered-cubic crystals were studied after rolling under the influence of constraints. The deformation textures varied from (001) [loo] to near the (001) [110] type and appeared sensitive to the manner in which the crystals were rolled. No textural data were available on the effect of rolling (001) [loo] crystals with and without constraints. The purpose of the present work was to evaluate the influence of constraints during rolling on the textures of 3 pct Si-Fe crystals initially (001) [loo]. Rolling and annealing textures were studied for a) crystals rolled with no constraints at different rates of reduction, and b) crystals rolled with constraints imposed by neighboring grains and by plates between which a crystal was "sandwiched". PROCEDURES AND EXPERIMENTAL TECHNIQUES Data are presented on four crystals which are representative of several crystals studied. The orientation of each crystal prior to rolling was (001) [loo] as determined by the Laue X-ray back-reflection method," i.e., each crystal had an (001) within 3 deg of the rolling plane and [100] within 3 deg of the rolling direction. These crystals were obtained from two iron-base alloys containing 3 pct Si by weight which were prepared by vacuum melting electrolytic iron and a commercial grade of silicon. Crystals 1, 2, and S-1 were cut from a large single crystal grown from the melt of one alloy by the Bridgman technique17 in an apparatus described by

Jan 1, 1960

By B. C. Allen

The interface energies of chronzium, molybdenunz. hugsten, and their solid-solution alloys Cv-35Re, MO-33Re, and UJ-25Re were studied at 0.6 to 1.0 of the absolllte liquidus ter)zpe,vature using fiz&apos;e )izethods. Liquid surface tension, yv , was deter mined clsing the pendant-drop and drop-weight methods. Results are, respectizlely, 1700, 2370, and 2480 +100 dynes per ct for the rhernium -containing alloys and essentially the same as tlwse reported for liquid chro)riln, trolybdenum, and tungsten. Average solid slrjace energy, rsv< xias ))zeasured using tlre fiber-extetlsion method. The ratio of ysS, the acerage high-angle grain-boundary energy, to ySV cclas jolnd fronz grain-bolzdary grooue angles fort)zed at the surface in an inert atrfizosphere. Absolllte iute?:face energies were deterawined using ?nultip/rase equilibria involzing suitable liquids of known surface tension (tin, silver). Interpretation of the experimented results in view of pvobable tenzperatzcre, orientation, and purity effects giz,e the follouling approximations in ergs per sq ctn: ysv (i2lo. Mo-33Re) - 2100, ySS (Mo, Mo-33Re) - 800, rr (defornzation twins in MO-33Re at 1200"C) - 800. ysV (Cr. Cr-35Re) - 2400. YSS (CY, Cr-35Re) - 1000. Probably Ylv- YSV- 2500 for tungsten and W-25Re, giving yss (It&apos;, W-25Re) - 900. The interface energies of solid and liqid ch?&apos;omiu?.z, nolybdenu?rr, and tungsten are not geatly aff&apos;ected by rhenium and therefore are not a ttlajor factor in the ductili zing rhenium effect in Croup VI-A metals. THE interface energies of the refractory Group VI-A metals, chromium, molybdenum, and tungsten, are not well-established. The objective of this investigation was to study the liquid surface tension, solid surface energy, and grain-boundary energy of these metals and compare them to those found for the bcc solid-solution alloys, Cr-35e,&apos; 0-33e,&apos; and -25e. Five techniques were used to measure interface energies in high-purity polycrystal rod, wire, and sheet at 0.6 to 1.0 of the absolute liquidus temperature. The alloys were chosen to see if there was any connection between interface-energy behavior and the ductilizing rhenium effecL4j5 EXPERIMENTAL WORK Materials. A description of the materials used is presented in Table I. Chromium rod was prepared by arc melting iodide process crystals supplied by Chromallo Cor., hot extruding, and warm swaging to 0.63-cm-diam rod.6 The sheet was prepared by rolling as-extruded rod to 95 pct reduction in area from a hydrogen furnace at 800" to 900°C and surface grinding off 0.02 cm from each face. Cr-35Re rod was prepared by arc melting sintered rhenium powder and iodide chromium crystals, warm rod rolling to 50 pct reduction in area in cans, and swaging to 60 pct reduction in area at 1100" to 1200°C. Some of the rod was warm-rolled to sheet and then surface-ground. Portions of swaged chromium and Cr-35Re were further reduced by swaging and drawing to 0.013-cm-diam wire by the General Electric Co. Mo-33Re and W-25Re rod, sheet, and wire were provided by Chase Brass and Copper Co. The molybdenum sheet consisted of two lots, both essentially the same except for the carbon content. Liquid Surface Tension. The liquid surface tension of Cr-35Re, Mo-33Re, and W-25Re was measured by a combination of pendant-drop and drop-weight methods using techniques already decribed." Following out-gassing, molten drops were formed on the ends of centerless-ground Mo-33Re and W-25Re rods by electron bombardment at 5 x 106 mm. Similar drops were formed on outgassed Cr-35Re rods by induction heating under 1 atm of 99.995 pct Ar. Solid Surface Energy. Solid surface energy was measured by conducting microcreep experiments on molybdenum, Mo-33Re, chromium, and Cr-35Re wires at 2350°, 2306, 1550°, and 180O°C, respectively. In preparation, gage marks -2.5 cm apart and -0.001 cm deep were circumferentially scribed on the wire with a razor blade. Weights of the wire material were then attached. Five to seven reasonably straight wires were hung in a container made out of the wire material. The free end was placed through a small hole in the removable top and secured by bending a small portion 90 deg. The containers not only tended to provide vapor-solid equilibrium for the wires but also protected them from gaseous impurities. They were nominally 2.5 cm in diam by 5 cm high and were made from extruded chromium rod, Cr-35Re arc casting, molybdenum bar stock, or welded Mo-33Re sheet. After deg re as ing, the assembly was outgassed at a relatively low temperature to 2 x 10"5 mm and then recrystallized 2 to 8 hr at the creep temperature in a rhenium-element resistance furnace. The static argon atmosphere was gettered by tantalum radiation shielding. Specimen temperature was measured optically to 25"C using calibration with known melting points and blackbody conditions. The wires generally developed a stable bamboo-type structure according to Fig, l(b), (c), and (d) and retained their gage marks [upper portion of Fig. l(d)]. One or two of the weights were clipped off to provide a low load for the creep anneal. To minimize the possibility of bending or breakage, the wires remained attached to the top of the annealing container which was held to keep the wires vertical. The distance between gage marks was

Jan 1, 1967

By Y. A. Chang

Phase relationships in the system Cr-Si have been established based on the melting point, X-ray, metallo-graphic, and DTA studies. The three intermediate phases, Cr3Si, Cr5Si,, and CrSi,, melt congruently at 177V ± I@,Cr3Si, 1680"i 20°, and 1490" *20°C, respectively, while the fourth intermediate phase CrSi, melts peritectically at 1413" i 5°C to Cr5Si3 and a melt containing 51 at. pct Si. The temperatures and compositions of the four eutectic isotherms occurring in this system are given below: DTA and metallographic evidences indicate that Cr5Si, undergoes a phase transformation at 1505" i20°C. The high-temperature form of this phase could not be retained by the quenching techniques used in this study. TECHNOLOGICAL interest in the developing of composite systems, consisting of Sic on the one hand as a fiber-reinforced material and metallic substances such as chromium, nickel, or Cr-Ni alloys as a binding agent on the other hand, stimulated the present investigation of phase relationships in the binary system Cr-Si. Earlier works concerning this system have been evaluated and summarized by ansen and Anderko.&apos; Their phase diagram was based mainly on the works of Kieffer, Benesovsky, and schroth2 and Kurnakov.~ According to these authors, the three intermediate phases Cr3Si, CrSi, and CrSi, all melt congruently at approximately 1730°, 1600°, and 1550°C. However, they did not agree on the compositional stability of the fourth intermediate phase between Cr3Si and CrSi. Later Parthe, Nowotny, and schmid4 determined the structure of this phase to be tetragonal T-1 type using the single-crystal method, and concluded that this phase had a formula of Cr5Si3. Since the compilation of Hansen and Anderko,&apos; a new phase diagram for the system Cr-Si has been proposed by Elliott5 based on the works of Goldschmidt and rand,&apos; Guseva and ~vechkin,~ and Trusova, Kuzev, and Ormont8 and the earlier works quoted by Hansen and Anderko.&apos; According to this proposed phase diagram, all four intermediate phases have large ranges of homogeneity and all melt congruently. More recently, Svechnikov, Kocherzhinskii, and yupkog studied the system Cr-Si by the DTA-method. According to their findings, the three intermediate phases, Cr3Si, Cr5Si3, and CrSi,, melt congruently at 1700°, 1720°, and 1475"C, respectively, while the fourth intermediate phase, CrSi, melts peritectically at 1475°C to Cr5Si3 and a melt containing 50 at. pct Si. The temperatures and compositions of the four eutectic isotherms were found to be: In view of the discrepancies existing in the literature concerning the system Cr-Si, it was decided to rein-vestigate the phase relationships in this system. EXPERIMENTAL a) Starting Materials. Chromium disilicide and chromium or silicon powders were used in the present study to prepare the melting point and DTA samples. CrSi, was obtained by directly reacting cold-pressed elemental powders in an atmosphere of Hz at a temperature of about 1250°C. Chromium powder, purchased from Stark Chemical Co., had the following impurities in ppm: Fe, 200; Mg, 1000; and 0, 250; while silicon powder, purchased from the Welded Carbide Co., had the following impurities in ppm: Ca, 700; and Fe, 3500. b) Melting-Point Determination and Differential Thermal Analysis. Cylindrical melting-point samples of approximately 13 mm in diam and 30 mm in length with a rectangular groove in the center were prepared by hot-pressing of well-mixed powder mixtures in graphite dies. Before the melting-point determination, the hot-pressed samples were ground on a sand paper to remove any minute surface contamination of graphite. A small hole of 1 mm in diam, drilled on the center portion of the samples, served as a blackbody cavity for the temperature measurements. DTA samples approximately 13 mm in diam and 15 mm in length were prepared in a manner similar to the melting-point samples. Melting points were determined using the Pirani technique under a helium atmosphere of 40 psi. The design, performance, and operation of this apparatus have been described in detail by Rudy and ~ro~ulski.&apos;~ The temperature measurements were carried out with a calibrated disappearing-filament-type micro-pyrometer. The measured temperature was corrected for losses from the quartz window of the melting-point furnace and for deviations from blackbody conditions of the observation hole. The procedure for temperature correction has also been previously described." The DTA method of Heetderks, Rudy and Eckertl&apos; was also used to check any phase transformations of selected alloys in the system Cr-Si. It was not possible to make remated runs on the same sample once melt-

Jan 1, 1969

By M. C. Udy, F. W. Boulger

AN incomplete phase diagram for the U-Ti systern was determined earlier 1 and more recently, a tentative diagram was presented for the uranium-rich end of the system.&apos; In the present re-examination of the whole system of U-Ti alloys, high purity materials were used. Melting stock for the alloys was high purity uranium, containing about 0.09 pct C as the only appreciable impurity, and high purity iodide-process titanium purchased from New Jersey Zinc Co. Both metals were cold rolled to about 1/6 in. thickness, sheared to about I/&apos; in. squares, and cleaned by pickling. The alloys were arc melted under a helium atmosphere in a water-cooled copper crucible. A thoriated-tungsten electrode was used. The furnace chamber was evacuated, then flushed with helium, prior to each melting. It was finally filled with stagnant helium at one atmosphere pressure. Each alloy was remelted three times after the original melting, to insure homogeneity. The alloy button was turned bottom side up before each re-melting operation. Some 22 alloys were examined. Their compositions were spaced at appropriate intervals between 100 pct Ti and 100 pct U. Analyses were made on chips taken after fabrication. The major contaminant was carbon, which varied from 0.03 to 0.08 pct. It appeared in the microstructure as titanium carbide. Alloy compositions were calculated to a carbon-free basis for consideration on the diagram. Tungsten and copper, possible contaminants from the melting operation, were generally less than 100 parts per million each. Fabrication All alloys were forged and rolled to bars approximately V8 in. square. They were clad either in SAE 1020 steel or in a 5 pct Cr-3 pct Al-Ti-base alloy, depending on the fabrication temperature. A temperature of 1800°F (980°C) was used for alloys near the compound composition. This necessitated using the titanium-base alloy, since iron reacts with titanium at this temperature, producing a low melting alloy. Other alloys were fabricated at 1450°F (790°C), using steel jackets. No iron-titanium reaction occurred at this temperature. The jackets were welded in place in an argon atmosphere. Those alloys sheathed in steel were declad and then reclad between rolling and forging operations. On the other hand, those clad with the titanium alloy were cut to a roughly rectangular shape prior to clading and were then carried through both the forging and rolling operations without opening. Those alloys near the compound composition were found to be cracked when the clading was removed. The cracked materials had been plastically deformed, however, and at least some of the cracking had OCcurred during cooling. Heat Treatment The rolled bars, after being declad and shaped to remove surface contamination, were all given an homogenizing treatment of 160 hr at 2000°F. (Samples were taken for analysis following the declading and shaping operations.) All were heat treated at the same time in one furnace, but each was sealed in a purified argon atmosphere in an individual Vycor glass tube. Argon pressure was such that it was approximately atmospheric at temperature. One end of each tube contained titanium chips and this end was heated to 1200°F (650°C) for 10 min prior to the heat treatment. This purged the atmosphere of residual reactive gases. The balance of the tube was warmed during the purge to liberate adsorbed moisture and gases, which also reacted with the hot chips. The bars were furnace cooled from the homogenization treatment. Specimens of each alloy were water quenched after 2 hr heating at 1000°, 1200°, 1400°, 1600°, 1800°, and 2000°F (540°, 650°, 760°, 870°, 980°, and 1095°C). In addition, some were treated at intermediate temperatures of 1300°, 1500°, and 1700°F (705", 815", and 925°C) and at 2150°F (1175°C). Specimens, about &apos;/s in. cubes, were cut from the bars, sealed in individual Vycor tubes, and heat treated as described. All specimens heat treated at the same temperature were processed together. Samples were quenched by breaking the Vycor tube rapidly under water. Metallographic Examination Specimens were mounted in bakelite and ground wet on 180 grit paper held on a 1750 rpm disk. They were then ground wet by hand, using 240, 400, and 600 grit papers. The rough grinding was continued long enough to get well below the surface. Specimens were mounted separately because of the variation in the rate of etching between alloys. The specimens were polished with rouge on a 4 in., 1725 rpm wheel covered with Miracloth. Alloys on the titanium side of the compound composition were etched with a solution of 2 pct hydrofluoric acid in water saturated with oxalic acid. A few crystals of ferric nitrate were added as a bright -ener. Specimens were immersed 5 sec, polished to remove the etch, then re-etched. With the higher titanium alloys, it was often necessary to start the etch on the polishing wheel, because of the formation of a passive film. In some instances, a plain 2 pct hydrofluoric etch was satisfactory. For the alloys on the uranium side of the compound, a distinction between the compound and the uranium phase developed after standing a short time in air. This could be hastened by the application of heat, such as obtained by placing the specimen on a radiator. A deep etch was necessary to develop details in the uranium-rich phase, such as the Widmanstaetten pattern sometimes obtained by quenching y uranium. A 2 pct hydrofluoric acid solution was used for this deep etching.

Jan 1, 1955

By Leonard R. Weisberg

HE procedure of directional freezing by the Bridgman technique1 is frequently used in crystal preparation. On those occasions where the crystal is regrown, it can be advantageous to Crop part of the ingot before regrowth to achieve purification. This note describes some simple, yet interesting, observations concerning the effects of cropping an ingot between successive freezes. First, it is not effective to Crop the front end of an ingot, whether or not the distribution coefficient, k , of the impurities is greater or less than unity. This can be shown as follows. The concentration C, of an impurity in a directionally frozen ingot of length d with a uniform cross section is given by where x is the distance along the ingot, and C0 is the initial concentration per unit length. It is assumed in deriving this equation that diffusion is negligible in the solid, is complete in the melt, and that k is constant. Consider that a section of the ingot Ad is removed from the front end. Then the average impurity concentration in the remaining (d- Ad) section of the ingot can be shown by integration to be given by When the ingot is remelted and refrozen, the new impurity distribution is given by where xl is the distance along the refrozen ingot. Substituting the value of c into Eq. [3], one finds This is identical to Eq. [11 when x = (x, Ad), which represents the original impurity distribution in the (d - Ad) section of the ingot after the first directional freeze. Therefore, the cropping and re-freezing accomplished nothing. This can also be seen physically by realizing that the average impurity content in the melt after the first Ad section is frozen, is identical to that after the resulting ingot has been cropped and remelted. Hence, it is assumed in the following sections that only the tail end of the ingot is cropped. However, it must be realized that for impurities with k greater than one, the pieces cropped from the tail end are purer, and are therefore saved. After cropping an amount Ad from the tail end of an ingot, the average impurity concentration of impurities in the remaining portion of the ingot is given by wheref= d/d. For the case of k < 1, the purification is defined as c,/c. It is obvious from Eq. [5] that the purification increases asf increases, but the increase in purification is not large. For example, iff is doubled from 0.1 to 0.2, the purification increases by only 10 pct for k = 0.5, by only 24 pct for k = 0.1, and by 32 pct for k =0.01. Much smaller values off than 0.1 are not desirable since insufficient purification is achieved. These figures indicate that much larger values off do not lead to substantial improvement, especially considering that much of the original ingot is lost. Therefore, it is generally useful to Crop about 1/10 of the ingot to achieve purification. As compared to doubling the value off, it is much more helpful to remelt, refreeze, and crop the ingot twice. Using Eq. [51 reiteratively, and assuming f= 0.1, it is found that the purification after this process is found to be increased over the purification after a single freeze and cropping by 33 pct for k= 0.5, 450 pct for k = 0.1, and 4100 pct for k = 0.01. This indicates that considerable purification can be obtained by this procedure. However, if purification is the main goal, one should resort to zone refining,3

Jan 1, 1962

By H. H. Pentz

This paper gives the derivation of a practical formula for the calculation of slopes in seismic reflection prospecting. The derived formula is an approximation and can be used where the slope of the reflecting horizon is less than 250 ft. per 1000 and the depth to the reflecting horizon is greater than 2500 ft. The slope of sediments in oil regions is generally considerably less than 250 ft. per 1000. This is particularly true of the Gulf Coast, with the exception of the salt domes, which usually have the sediments at a greater slope than 260 ft. per 1000. Derivation In Fig. 1, o represents the image of the shot point a. Then the length of the path acb is equal to ob and ae&apos;d is equal to od. In the triangle aob, p is equal to ob, x is equal to , and c is equal to ao. The angle u is the apparent dip of the reflecting horizon. Angle oab is equal to (90" - u). The quantity m is the slope of a line tangent to the curve, defined by equation 1, at the point (p, x). The quantity m&apos; is the slope of the line tangent to the curve at the point (p&apos;, 2&apos;).

Jan 1, 1940

By H. H. Pentz

This paper gives the derivation of a practical formula for the calculation of slopes in seismic reflection prospecting. The derived formula is an approximation and can be used where the slope of the reflecting horizon is less than 250 ft. per 1000 and the depth to the reflecting horizon is greater than 2500 ft. The slope of sediments in oil regions is generally considerably less than 250 ft. per 1000. This is particularly true of the Gulf Coast, with the exception of the salt domes, which usually have the sediments at a greater slope than 260 ft. per 1000. Derivation In Fig. 1, o represents the image of the shot point a. Then the length of the path acb is equal to ob and ae&apos;d is equal to od. In the triangle aob, p is equal to ob, x is equal to , and c is equal to ao. The angle u is the apparent dip of the reflecting horizon. Angle oab is equal to (90" - u). The quantity m is the slope of a line tangent to the curve, defined by equation 1, at the point (p, x). The quantity m&apos; is the slope of the line tangent to the curve at the point (p&apos;, 2&apos;).

Jan 1, 1940

By W. N. Logan

WHAT is mineral wool? This question is frequently asked by those unacquainted with its manufacture. The word "mineral" suggests that it is of mineral origin; the word "wool" suggests that it is of animal origin; but the only similarities it has to wool are its fibrous character and its white fleecyness. Mineral wool is a fiber produced by melting rock to a glasslike condition and blowing the glass into fine white, wool-like threads. A -number of the products fabricated from-mineral wool are used for some form of insulation, but mineral wool is adaptable to many other uses. It is used in the manufacture-of pipe covering designed to with; stand the high temperatures produced in steam pipes. In a similar form of insulation it is used to cover boilers and furnaces. It is used in ,the fabrication of upholstery tow for sofas and car seats: In acoustics it has many uses, such as acoustifibroblock, which is used in floors to destroy sound and vibration, and acoustic mat, which is used under carpets to destroy sound. In the insulation of houses, loose wool and granulated wool are used beneath attic floors and between the studding in frame buildings to prevent the escape of heat in winter and the entrance of heat in summer. Mineral wool is used also in fabrication of linofelt, which is a quilted form of insulation; in fibrofelt, which is an insulating board; in the fabrication of lith, which is an insulating block; in anti-fibroblock ,which is used in insulation and refrigeration; in flexfelt; in loose wool; in pressed block; in heavy oiled wool; in dark oiled block; and for many other purposes. The materials used in the manufacture of mineral wool are of two kinds. The first is a rock which contains silt, clay and silica, with smaller amounts of lime and magnesia. The second is a more highly calcareous rock which may carry a small amount of magnesia. The latter is used as flux to assist in the melting of the former. The relative proportion of the alumina-iron-silica content to the lime-magnesia content is normally as fifty to fifty but a considerable range is possible.

Jan 1, 1932

By R. M. Asimow

Both smith1 and wells2 have shown that the dif-fusivity of carbon in austenite increases rapidly with increasing carbon concentration. Smith has shown, in addition, that part but not all of this increase can be attributed to the concentration dependence of the activity coefficient of carbon in austenite. From the work of Eshelby&apos;, it is known that, because of the image displacements, there is a uniform dilatation of the material in a body containing random centers of dilatation. It is thus tempting to explain the enhanced diffusivity as resulting from this apparent negative pressure caused by the interstitial carbon atoms.* That is, the activation free energy for diffusion is not directly a function of concentration if we consider that the alloy is subjected to a concentration-dependent pressure. To proceed with a quantitative solution, it is necessary to determine the activation volume AV for the diffusion process. An exact calculation of AV is quite a difficult problem and does not appear to have been solved as yet. A simpler procedure is to use the semiempirical, macroscopic theory of seyes&apos; which relates the activation free energy AG to AV. Keyes has shown that for many types of diffusion processes the following relationship is valid Where p is the Gruneisen constant and x the compressibility. This relationship is based on the assumption that AG can be identified with strain-energy terms. In general there will also be contributions to AG due to a change in the energy of the valence electrons of the metal; thus the relation must be considered largely empirical. Surprisingly, for self-diffusion where it is well-known that the electronic contribution is quite important,&apos; the Keyes relation works quite well for many systems. For interstitial diffusion where it might be expected that the relationship is on a firmer theoretical basis, the limited experimental data available is not in particularly good agreement as can be seen from Table I. However, it must be remembered that besides the uncertain basis of the Keyes formula there is considerable uncertainty in some of the experimental values of AV. The only real justification for using the Keyes formula in the present analysis is that it gives a result which satisfactorily solves the problem at hand and, further, there are no more reliable procedures for calculating AV available. The coefficient 3 in Eq. [I] is determined such that the room-temperature value for x is to be used. The activation entropy AS is estimated as 8.95 x 10"3 kcal per OK mole using the values in Table I1 and the Zener" relation AS = PAHIT, where p is a dimensionless thermal coefficient of Young&apos;s modulus which is to be evaluated at low values of T/T,, aH is the activation enthalpy, and T, is the melting temperature of the alloy. The resulting value of AG at 1000°C is 25.6 kcal per mole. The Gruneisen constant (p = 3cup/XC,), where p is the density, is evaluated from the room-temperature data in Table I1 after calculating C, from the relation. A value of p = 8.32 g per cu cm based on the value of a. in Table I is used. The result is C, = 5.0 x lo6 erg per g, H = 2.32, and AV = 3.41 cu cm per mole at 1000°C and infinite carbon dilution. It is assumed that the activation volume is not a function of carbon concentration. The theory could be refined to consider AV a function of concentration, but due to the uncertainties in the parameters there seems little justification for this. Carbon dissolved in austenite forms a nonideal solid solution, so that in writing an equation for. the diffusivity of carbon it is necessary to take into account the change in activity coefficient with concentration. The resulting equation is16

Jan 1, 1964

By John F. Elliott, David L. Schroeder

SURFACE depletion can be a significant source of error in the use of the effusion method for determining the thermodynamic properties of alloys, particularly in the case of solid alloys.&apos; However, as yet this problem has not been treated quantitatively by experimentalists in the field.1-3 The method necessitates diffusive transport of material out of the source alloy to obtain a relevant measurement. The general character of the system is shown in Fig. 1. The diffusive flux (nD) at the alloy surface is equal to the effusive flux (nE): where D is the diffusion coefficient of the diffusing substance, C is its concentration, X is the distance from the surface into the source alloy, p is the density of the alloy, and AS is the actual available surface of the alloy. The concentration of the diffusing substance at the surface is CS, and Here fE is the Clausing factor, AE is the area (sq cm) of the orifice, y is the activity coefficient of the substance in the alloy, PO is the vapor pressure (Torr) of the pure substance, M is the molecular weight of the effusing species, and T is the absolute temperature. The differential equation for diffusive transport in the source alloy is Fick&apos;s second law. Its solution is dependent on the geometry of the source alloy. Two boundary conditions must be established to obtain the proper solution, the first being Eq. [1], or its equivalent. The solutions for several important forms of the source alloy are considered below.

Jan 1, 1967

By Charles W. DeWitt

The ore treated at the reduction plant (called Yangdei) of the Chiksan Mining Co., Korea, is brought from four of the company mines, and from the small tribute mines. The largest shipments come from Sajunkohl mine, situated about a mile and a half from the mill (Fig. 1). The ore is quartz of medium hardness. The average assay value in gold is $6.95 per ton. At the mine the ore is put into bins, and is then trammed over an 8 per cent, grade to the tipple bins above the mill, where the ore is drawn through the mill holes as desired. The capacity of the tipple bins is about 3,500 tons. Ore from Moonsukohl, Chung Tarrie, Yang Chun, and the tribute mines is brought in by bulls and bull wagons. The bulls carry from 350 to 800 lb.; the average wagon load is about 1,200 1b. (Fig. 2). One shovelful of ore out of every ten is taken as a sample. Considerable ore is brought in from the outside mines, and this method of sampling is

Jan 1, 1916

LEAD and tin mixed together make an alloy through an attachment of natural affinity which they have with each other, so that when they are mixed it is difficult to recognize by the sight which one it is, if the essences of their qualities are not surpassed by more than half. If, indeed, one can be recognized, it is the tin which gives off a certain sharp odor to the sense of smell, besides having a greater hardness and whiteness. The best of these is the one that is the purest in its kind. In the alloy of tin it is the one that is the whitest and hardest, or, when it is bent or some thin end of it is held tightly by the teeth, is heard to crackle as frozen water does. Because this happens more with this than with other metals, I do not wish now to inquire into it. It is enough that it be a sign for recognizing when tin is pure or mixed. Pewterers say that it should be joined in alloy with lead and that it is better for working when it contains four or six pounds to the hundred because it makes it softer to the hammer and more fluid in casting. But I do not like to hear this, even if all they say is true, for I see that the tin that comes from England, when worked as well as in cakes that show it to be pure, is much more beautiful and better in all works than is that made in Venice. And I believe that it is not better for any work when mixed than when pure, except for the advantage of the master who, if he does nothing else, sells lead that is worth little for tin that is worth much. I find that when mixed it serves in only two things. One is when it is wished to make a solder for copper, for use when it is not worth while to solder the bottoms and large pieces of vessels with low-grade silver as should be done. The other is when master potters calcine it in order to make glazes and to apply white to their vases. I consider lead to be useless in all other works of any kind of metal, since it unites with none of the other metals of good company except tin.

Jan 1, 1942

By F. R. Ingalsbe

THE proposed revision of the mining law as set forth in the Arentz Bill, now before Congress, is centered about the pretty commonly acknowledged f act that the present law is outlawed both by the large mining companies and the United States Land Office. By common agreement, the law of the apex is non-opera¬tive as between adjacent properties in many instances, and this practice is becoming more common. - If this is a fact, there is no escape from the conclusion that the law is antiquated and should be revised to meet modern conditions more equitable. The thing to be considered seriously is in what direction and to what extent the laws should be changed. Before deciding this, it is logical to inquire in what particulars the present law is troublesome or useless. This was all threshed out by the committee of the Bureau of Mines that worked out the proposed bill, but their testimony was not placed before the public, so far as 1 am aware. Most mine managers and engineers connected with producing properties are a unit in agreeing that the law as applied to the underground extension of orebodies, that is, the "law of the apex," as it is called, is the source of more litigation and expense than any other phase of the law, or perhaps than all other phases combined. This being true, it seems that this part of the law should be changed. Another phase which is troublesome and will continue to be so long as there is unpatented mineral land on the Public Domain, is the discovery requirement. The present law requires that a dis¬covery be made before a claim is staked and the courts certainly agree that such must be the case before patent issues.

Jan 7, 1922

By K. S. Milliken

NORMAN W. Lord&apos; has shown that the resultant impurity distribution after n zone passes is given by in the ingot section OSa<N—n, where a is the displacement in zone lengths, N is the ingot length in zone lengths, C,, is the initial uniform impurity concentration, k is the segregation constant = Ceoll C,,,,,,,, at equilibrium, and The foregoing expression is formidable in respect to computational labor. However, the triple sum can be reduced as follows is better if computing for only a single value of n. For k<l, it can be shown that this last equation is equivalent to The infinite series is useful only when k is small enough to force rapid convergence. In such cases, the absence of subtraction from unity has the definite advantage of preserving accuracy. Acknowledgments It is a pleasure to acknowledge stimulating correspondence with Dr. Howard Reiss of Bell Telephone Laboratories Inc. This note is published by permis-sion of the Deputy Minister, Dept. of Mines and Technical Surveys, Ottawa, Ont., Canada.

Jan 1, 1956

By Joseph E. Pogue

Price is a complicated concept, for price is both a cause and an effect. This reciprocal aspect is commonly overlooked and the oversight is the source of many economic maladjustments. Price is the resultant of the ratio between supply and demand, but it differs from a mathematical concept of a proportion, by itself constituting an economic force which continuously alters the elements that determine the relationship. Price, therefore, is not merely the outcome of other forces but is in its own right one of the most powerful of economic agents. Price accordingly does not play a passive role; nor can it be sterilized or rendered inactive. In consequence, price cannot be fixed or at least kept fixed, except by the elimination of all freedom of choice on the part of producers and consumers. A primary objective of all economic activity is equilibrium. The same is true of a unit of economic activity, the single industry. The plane upon which equilibrium centers may shift in the course of time, but equilibrium itself is the point of departure and the point of return. If an industry is in equilibrium, that industry is operating effectively. The motivating forces of an industry—profits or the common good—are not to be confused with the prerequisite of equilibrium, but this mistake is often made. The producer is dominated by the profit motive; the consumer, or his collective representative, by the general welfare motive. No one is the advocate for equilibrium; that status is supposed to be arrived at automatically. If the forces of competition are perfectly free, such is the tendency. Equilibrium For the purposes of this analysis, equilibrium needs to be broadly defined and is conceived to involve: (1) balance between supply and demand; (2) internal equipoise amongst the elements within an industry; and (3) symmetry in respect to the whole economy. This definition implies flexibility and case of adjustment; a ready accommodation to change. Equilibrium does not postulate profits or nonprofits, social objectives or the lack of them. A decadent industry may be in equilib-

Jan 1, 1937

By C. D. Demond

IN reverberatory smelting, fuel is the chief item of expense, as it commonly is in processes using large percentages of it. Hence the most suitable supply is eagerly sought; that is, the supply which, in the end, yields the greatest net profit. The better grades are not infrequently bought, even at an advanced price, because they are apt to be decidedly more economical. High price, of itself, however, is no merit, for freight is generally the largest part of the cost of fuel, and the nearby supply may yield as high efficiency as that from a greater distance. If a poorer grade is reasonably good, and if its cost is low enough to more than offset the decreased technical efficiency, it is of course the more suitable. Any smelting, operation depends for both efficiency and economy on raising the furnace atmosphere considerably above the "critical" temperature; that is, above the temperature at which smelting is completed. If this temperature is not exceeded, smelting stops, no matter how much coal is burned; and the real value of a fuel depends on the number of degrees that the temperature is continuously kept above this point. For example, if one fuel maintains 2,500° F. and another only 2,100° F., while the "critical" temperature is 2,000° F., the first is worth at least five times as much as the second, although the increase above atmospheric temperature is only one-fifth more in one case than in the other. This "margin of temperature" above the smelting point is much more significant than the total number of heat units developed from the fuel. The case is parallel to that of water flowing from a pipe. The reservoir may contain a billion gallons of water; but, even though the fluid has come to the nozzle, not a drop will run out, where it can be of practical use, unless the level in the reservoir is higher than the nozzle; and the speed and volume of flow depend on how much higher the level is in the reservoir than at this point. If the temperature inn a furnace is not above the critical level there will be no slag to flow over the skimming plate, even though there are enough heat units to bring an unlimited quantity of charge up to the point of slag formation; and just as the value of a water supply for the purpose of putting out a fire depends largely on the effective head, so the difficulties of furnace management

Jan 8, 1914

By Arthur F. Taggart

PROGRESS in a technical art is of several kinds. It springs .from many diverse sources. It comprises invention, mechanical improvement, operating advance, analytical study, education. Invention is, by definition, a relatively great, essentially individual step, taken quickly. Operating advance is the slow, cumulated march of practice; in contrast, it moves at the pace of the tortoise, but over, the years its effects rival and, in some cases, surpass those of invention. Mechanical improvement- is a usual concomitant of the reduction of invention. to operating practice; thereafter it is a primary tool of operating advance. Analytical study is the process of mental digestion of the fruits of invention and practice. Its purpose is to render these into a form assimilable by the art as a whole, and by the perennial crop of would be practitioners. Education, disseminating the results of such study, consolidates and maintains the positions gained. Thus, slowly at first, but continuously accelerating, the tide of progress grows- to flood. Such growth, in mathematical parlance, is expressible in the general form y = mxn, where x is time, n is some positive number greater than one, m is another positive number, and y is the state of the action at instant x. When n is 2, the readers will recognize the graph of the equation as one branch of the familiar square parabola, whose property it is to become parallel to the y-axis; i.e., to move at an infinite rate, in that never-never

Jan 1, 1947

By Benjamin Gildersleeve

Uniquely colored, thin-bedded quartzite is quarried between Crossville and Crab Orchard in Cumberland County, Tenn. It is produced in all sizes up to the limits of transportation from beds usually ranging in thickness from less than Vi in. to 6 in. The stone is very resistant to wear and weathering and is marketed throughout the country for many different purposes in exterior and interior construction. The annual production exceeds 36,000 tons, valued at nearly $1,000,000. THE building stone of the Crab Orchard District is a fine-grained, thin-bedded sandstone which is so strongly cemented by silica that it may be classed as quartzite. As used in this paper the term building stone includes dimension stone, rubble, ashlar, flagstone, and rough broken stone. The Crab Orchard District is in the central portion of Cumberland County, Tenn. It is named from the town of Crab Orchard near which the stone was quarried first for industrial use. The heart of the district is an area of some 1200 acres from 1 to 3 miles east of Crossville which is 70 miles west of . Knoxville and 125 miles east of Nashville (fig. 1). At the present time, there are about 15 quarries worked by companies and individuals. Geology: The Crab Orchard District is on the Cumberland Plateau, or Cumberland Mountain as it is called frequently. Most of the area is characterized by a comparatively even surface from 1800 to 2000 ft in elevation and is drained by streams flowing into the Tennessee River. Included in the district are two quarries located 7 miles west of Cross-ville and this area is drained by tributaries of the Cumberland River. Most of the quarries are located near the 1800-ft contour which is just below the general upland surface. The surface rock over most of the district is the Rockcastle sandstone which has a thickness of about 260 ft.1 It is the topmost of the six formations of

Jan 1, 1951

By Benjamin Gildersleeve

Uniquely colored, thin-bedded quartzite is quarried between Crossville and Crab Orchard in Cumberland County, Tenn. It is produced in all sizes up to the limits of transportation from beds usually ranging in thickness from less than Vi in. to 6 in. The stone is very resistant to wear and weathering and is marketed throughout the country for many different purposes in exterior and interior construction. The annual production exceeds 36,000 tons, valued at nearly $1,000,000. THE building stone of the Crab Orchard District is a fine-grained, thin-bedded sandstone which is so strongly cemented by silica that it may be classed as quartzite. As used in this paper the term building stone includes dimension stone, rubble, ashlar, flagstone, and rough broken stone. The Crab Orchard District is in the central portion of Cumberland County, Tenn. It is named from the town of Crab Orchard near which the stone was quarried first for industrial use. The heart of the district is an area of some 1200 acres from 1 to 3 miles east of Crossville which is 70 miles west of . Knoxville and 125 miles east of Nashville (fig. 1). At the present time, there are about 15 quarries worked by companies and individuals. Geology: The Crab Orchard District is on the Cumberland Plateau, or Cumberland Mountain as it is called frequently. Most of the area is characterized by a comparatively even surface from 1800 to 2000 ft in elevation and is drained by streams flowing into the Tennessee River. Included in the district are two quarries located 7 miles west of Cross-ville and this area is drained by tributaries of the Cumberland River. Most of the quarries are located near the 1800-ft contour which is just below the general upland surface. The surface rock over most of the district is the Rockcastle sandstone which has a thickness of about 260 ft.1 It is the topmost of the six formations of

Jan 1, 1951