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By Jerome J. English, Gordon W. Powell

An experimental investigation and mathematical analysis of the thermal-dilation behavior of the titanium alloy Ti-7Al-3Cb have shown that the linear dimensional changes associated with the polymorphic transformation need not be isotropic. The absolute magnitude of the linear dimensional change, which may be either positiue or negative, associated with the cr-p transformation is dependent upon the relutzve volumes of different orientations of the transformation product. It is hypothesized that the dilation irregulati-ties that have been observed during the polymorphic transformation of pure, coarse-grained titanium and other titanium-base alloys can be explained in the same manner. When titanium is heated above about 165O°F, the hcp a structure transforms to bcc 0. Thermal-dilatioh measurements have shown that the transformation is accompanied by a decrease in length of 0.16 pct.' Such dilation behavior would be expected because the volume of the hcp unit cell is about 0.3 to 0.4 pct greater than that of the bcc unit cell. A recent investigation2 of the thermal-dilation behavior of an experimental a-p* titanium alloy, Ti- 7A1-3Cb, containing 0.06 wt pct 0 showed that its dilation behavior during the polymorphic transformation differed substantially from that reported for unalloyed titanium. The first time the alloy was cycled through the transformation, the dilation curve closely duplicated that of unalloyed titanium. However, upon repeated cycling through the transformation temperature range, both the magnitude and the sign of the dimensional change associated with the transformation were observed to vary with each cycle. This investigation was undertaken to obtain additional data on the dimensional changes associated with the polymorphic transformation in the Ti-7A1-3Cb alloy and to determine the cause of the dimensional irregularities. After testing, the specimens were examined metallo-graphically. In addition, Laue back-reflection patterns were obtained from selected sections taken perpendicular to the specimen axes to determine the a orientations present in these sections. White radiation from a tungsten target and a 0.1-mm-diam collimator were used to produce the diffraction patterns. RESULTS Dilation Curves. Three types of thermal-dilation curves were obtained when the a-8 titanium alloy was heated and cooled through the transformation temperature range. These three types of curves are illustrated in Fig. 1. The type I curve represents what is considered normal behavior, because the dilation change is what would be expected on the basis of the volumes of the unit cells of a and p. The Type I1 curve is the inverse of Type I. Normal behavior is characterized by an expansion on cooling through the transformation, whereas a contraction takes place in the Type 11 curve. With Type ni behavior, no clearly distinguishable length change occurs during the transformation. No other anomalies that might be indicative of other phase transformations were observed in the dilation curves at lower temperatures. Apparently, the cooling rate was low enough for equilibrium to be reached during the 0 to a transformation. Table I lists the types of dilation curves observed during the polymorphic transformation as a function of the direction of measurement and cycle number. The A1 value was determined by extrapolating the low-temperature (a + 5 pct p) and high-temperature (100 pct p) segments of the dilation curves to a common temperature and measuring the difference in the or-dinates at that temperature, see Fig. 1. The transformation occurs over a temperature range in this alloy, so the magnitude of A1 is not an absolute value but depends on the choice of temperature. A mean temperature, T,, within the transformation temperature range was selected for the measurement. T, on cooling occurred about 100°C lower than T, on heating. The first time each of the three dilation specimens was heated to above the temperature, that is, Cycle 2, normal Type I behavior was observed. In Cycle 3, two deviations from normal behavior occurred. First, during cooling of the longitudinal specimen, a substantially larger expansion, +0.21 pct, was measured as 0 transformed to a compared with +0.03 pct in Cycle 2. Second, the thickness specimen was observed to undergo a contraction instead of the anticipated expansion on cooling. Continued cycling of the three specimens from room temperature to 2500°F produced additional changes in the dilation behavior. These changes did not seem to be related to the fabrication direction of the alloy because the values of a1 for the longitudinal, transverse, and thickness specimens varied unpredictably in magnitude and sign. Furthermore, both the longitudinal and transverse specimens showed all three types of dilation curves at least once during the six cycles that they received. Fig. 2 is a sketch of the transverse specimen after

Jan 1, 1967

By Jei Y. Choi, Paul G. Shewmon

The surface self-diffusion coefficient of copper (D,) has been measured between 847° and 1069 "C for six different orientations. These were the(111), (110, (100, and three higher index surfaces. The activation energy for Ds (designated Q s) was found to be about 49 kcal per mol for all six surfaces, and Do about 2 x 104 sq cm per sec. At any temperature Ds varied by no more than a factor of three over these orientations. It is shown that, if the free energy of a surface atom is uniquely determined by its number of nearest neighbors, it follows from the Principle of microscopic reversibility that Qs should have the same value for all surface orientations, and Ds should vary little with orientation. This model also suggests that for clean fee metals Qs ~ 2/3 AH, (heat of vaporization). This is true for copper. ALTHOUGH it has been appreciated for several decades that atoms can diffuse more rapidly on a surface than through the bulk of a crystal, it has only been in the last few years that reliable values of the surface self-diffusion coefficient (Ds) have become available. Tracer studies of Ds had been attempted prior to this period, but when a tracer is placed on a surface, an ever increasing fraction of it is drained off into the lattice. The correction for this loss involves a very difficult, and as yet unperformed calculation. Those who have worked with tracers have not corrected for this loss.1, 2 Thus their results indicate that Ds is greater than the self-diffusion coefficient in the lattice (Dl), but it has not been established that they give quantitative data on Ds. A procedure which avoids the problem of tracer loss is to study the rate of mass-transfer under the effect of surface tension. If the surface asperity being studied is very small, the mass transfer occurs entirely by surface diffusion. The kinetics at which a grain boundary groove forms on an initially plane surface is a well-studied case of this type. The smoothing of a slight scratch in an otherwise flat surface is another procedure that has been studied. If these grooves are up to 20 to 30 µ in width, the dominant mechanism for mass transfer is surface diffusion (at least in the case of metals with low vapor pressures), and the widths can easily be measured with an interference microscope. Of these two, mass-transfer techniques only in the case of grain boundary grooving has a rigorous mathematical treatment been given. This was done by Mullins.3,4 His analysis predicted that in the case of copper in an atmosphere of an inert gas, surface diffusion should be the dominant transport mechanism. This analysis gave an equation for the groove profile and predicted that the width of the groove would increase as (time)1/4. Mullins and Shewmon showed that both of these predictions agreed with experiments.5 Thus the validity of the values of Ds given by this procedure seems to be well established. Gjostein has used copper bicrystals and the grain boundary grooving technique to determine Ds and the activation energy for surface selfdiffusion (9,) in the [001] direction on surfaces ranging between the (100) and (110) planes.= He reported that Qs = 41 kcal per mole and Do = 6.5 x 102 sq cm per sec for all orientations studied. Since the results did not change with the dew-point of the dry hydrogen atmosphere or the type of refractory tube used, he concluded that the surfaces were clean, or at least that the results were not influenced by any impurities chemisorbed from the atmosphere. The work reported here reproduces and extends Gjostein's study in that D s and Q s were determined for copper over a wider range of orientations. To study the effects of impurities, two purities of copper were used as well as cathodic etching to remove any possible electropolishing film. Gjostein postulated that the diffusing atoms on a surface near a low index plane are the few atoms which are adsorbed on the smooth region between ledges or steps in the surface. A more rigorous derivation of the equation relating Ds to the concentration and jump frequency of these adsorbed atoms is given here. Using this treatment, our empirical observation that Q s and D s are essentially the same for all surface orientations can be shown to follow from the assumption that the free energy of a surface atom is uniquely determined by its number of nearest neighbors. The studies of D s using the scratch technique have been carried out by Blakely and Mukura on nickel,' and by Geguzin and Oveharenko on copper. The latter study using copper gives values of D s roughly

Jan 1, 1962

(Under this heading will he published notes sent to the Secretary of the Institute by members or other persons introduced by members.) Member, mining engineer, technical education with 9 years' varied experience as superintendent and operating engineer, desires position with mining or manufacturing company requiring the services

Jan 3, 1918

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Jan 1, 1936

By William P. Blake

The late Dr. Ebenezer Emmons of Albany, one of the geologists of the Survey of New York and the author of The Taconic System, brought to notice as early as 1838" a peculiar concretionary and lamellar form of phosphate of lime, to which he gave the name Eupyrchroite, from the Greek words for fire and color, with the pefix

Jan 1, 1893

Jan 1, 1931

Jan 1, 1889

By E. J. Schmitz

This trip, beginning at Springfield, August 12, 1897, and ending at the same place fourteen days later, extended south and southeast through Christian, Ozark and Taney counties,

Jan 1, 1899

By T. F. Witherbee

The following calculation of heat requirement covers the working of the furnace from January 25th to February 14th, inclusive. A short time previous to the first date the furnace had been working rather badly, so that 300 lbs. of ore and 500 lbs. of limestone were taken off. Within the time mentioned the quality of the iron passed

Jan 1, 1910

By H. T. Mulryan

For the producer of industrial rocks and minerals, marketing is often the only means of survival. His material must be sold. There is little of the impersonal force of the market regulating supply and demand. No commodity exchanges facilitate his efforts to dispose of the material he produces, and the success or failure of his business depends primarily on prompt and correct response to market needs and requirements. This response is particularly vital where materials of low unit value must be shipped to distant consumers owing to a relative rarity of suitable deposits. The advantage of positive response to change can best be illustrated by hypothetical cases showing how problems can be turned into opportunity through marketing ingenuity. Three such cases dealing with materials of unit values in the range of $5 to $100 per ton are outlined below.

Jan 7, 1969

By L. G. Schulz

THE possibility of using reflected X-rays to produce images of crystals was explored by Barrettl who developed simple experimental procedures for X-ray microscopy and who showed by numerous examples the great range of information that could be made available. In his method characteris radiation is used to produce an image of a limited area of the sample on fine-grained film, this image subsequently being enlarged approximately X100. A somewhat different method will be described here;' white radiation from a fine-focus X-ray tube-"' is used to produce an image of a relatively large area of a single-crystal surface. part of the sample; therefore, white radiation is needed. The resolution in the image formed on the photographic film will depend on the size of the focal spot of the X-ray tube. If the sample is made

Jan 1, 1955

By W. F. Burns

(Butte Meeting, August, 1913.) ATTEMPTS were made in 1908, at the Great Falls Works, to produce ingots direct from the Butte precipitate by smelting- the material in a reverberatory refining furnace. The ingots produced in this manner averaged 99.4 per cent. of copper and 0.40 per cent. of arsenic and antimony. The copper content being considered too low, it was decided to cast the copper into anodes and to treat the anodes in the electrolytic plant. No.1 Furnace, in which the precipitate was treated, was a regular cathode refining furnace previously employed in making wire bar, cake, and ingot from electrolytic cathodes. The hearth of the furnace was 24 by 12 ft., having a capacity of 100,000 lb. of cathodes. The furnace was coal fired, and the copper was dipped by means of trolley ladles.

Jan 7, 1913