High-temperature heterogeneous equilibria in the unit activity approximation: I. alumina-carbon-chlorine system
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to the interparticle distance and to the distribution of the particles. To elucidate the slip distribution in the small ~ p a r ticles after deformation of the a-/~ alloys, X - r a y rock-. ing curve studies of the ~ particles and/3 matrix are being currently c a r r i e d out employing X - r a y diffraction methods previously developed in this laboratory. 2's The rocking curve analysis combined with X - r a y topography c o r r o b o r a t e the electron microscope results shown in Fig. 5(c) of this paper, namely that strain hardening of the-small ~ particles (size ~0.4 ~t) is accompanied by homogeneous slip inside the particles. The results will be published v e r y shortly. 1. T. Hamajima,G. l.s and S. Weissmann:Met. Trans., 1972,vol.3, pp. 2805-10. 2. S. Weissmann:./. Appl. Phys., 1956,vo|.27, p. 389. 3. S. Weissmann:Trans.ASM, 1960,vol.52, p. 599.
Authors' Reply T. HAMAJIMA, G. LUTJERING, AND S. WEISSMANN I T seems to us that in principle there exists no e s s e n tial contradiction between our results and those obtained by Margolin e t a l . regarding the ductility of the a - ~ alloys. In both studies It was found that the a p a r ticles deformed plastically prior to the ~ matrix. The brittleness of the alloys discussed in our paper r e f e r s to alloys with v e r y small ~ particles ranging from 0.4 to 1.0 ~, and the decline in ductility shown in Figs. 2 and 3 was closely associated with the decrease in interparticle distance. The essential point stated in our paper was that for alloys of such small a particle size the system behaves like a dispersion-hardening s y s tem, with ~ particles dispersed in the ~ matrix. It was shown, however, that when the particle size increased, beyond a critical small particle size, viz., ~1 ~t, the ductility increased rapidly (Table I), attaining large values Independent of tnterparticle distance and volume fraction. This behavior is characteristic of ~-/~ alloys, and is in agreement with the observations made by Margolin et a l . The morphology of the small a particles associated with the brittleness of the a - ~ alloys r e f e r r e d to equiaxed particles such as those shown in Fig. 4(a). As described in a previous publication,* which elucidated the phase relations of the Ti-Mo-A1 system, this m o r phology is obtained by direct aging into the two-phase region. It did not contain particles of Widmanst~ltten structure. As shown in Fig. 2 of Ref. 1, such structure was obtained by annealing after quenching from the phase, and since such alloys were extremely brittle we have excluded them f r o m our investigations of m e chanical properties. In our study a concentrated effort was made to determine for a given volume fraction not only the a v e r age size of a particles but also the important p a r a m eter of interparticle distance (Table I). This p a r a m eter, besides providing information about the distribution of the ct particles In the B matrix, has also significant implication regarding the particle-dislocation interaction. It should be noted that Margolin e t a l . on
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