Nucleation and phase selection in undercooled Fe-Cr-Ni melts: Part I. Theoretical analysis of nucleation behavior
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I.
INTRODUCTION
IT is well established that metastable phases can be produced upon supercooling of melts.[1] In order to determine the phase crystallizing from a melt of prescribed composition, the effect of liquid supercooling on the nucleation probability of solid phases with different structure and composition must be considered. A first description of nucleation processes originates from the fundamental work of Volmer and Weber[2] and Becker and Do¨ring.[3] It was applied to the solidification of metallic systems by Turnbull and Fisher.[4] According to this theory, density fluctuations within the melt lead to the spontaneous formation of clusters of a solid phase lowering the Gibbs free energy. The gain of Gibbs free energy is opposed by a positive energy contribution through the formation of the melt-crystal interface. Accordingly, the Gibbs free energy during the growth of a cluster first increases until a maximum DG*(r*) is reached at the critical radius r*. In this way, the crystallization is retarded by the interface formation energy, thereby enabling considerable amounts of melt supercooling.[1] The Fe-Cr-Ni alloy system, which represents the basis for the technically important stainless steels, seems to be very convenient for investigations of competitive crystallization phenomena of alternative phases. The primary solidification phase for near-equilibrium crystallization conditions depends on the chemical constitution. It changes from the ferritic (bcc) to the austenitic (fcc) solidification mode if the Ni/Cr atomic fraction ratio exceeds ;0.5. By contrast, phase selection under rapid solidification conditions does not solely depend on the alloy composition. Process conditions, such as cooling rate or melt undercooling prior to solidification, are equally important factors. Accordingly, alternative phase formation phenomena in rapT. VOLKMANN, Scientific Collaborator, and D.M. HERLACH, Leader of the Metalphysics Group, are with the Institute for Space Simulation, German Aerospace Research Establishment (DLR), D-51170 Ko¨ln, ¨ SER, Senior Scientist, is with the Institute for Solid State Germany. W. LO and Materials Research (IFW) Institute for Metallic Materials, D-01171 Dresden, Germany. Manuscript submitted December 23, 1994. METALLURGICAL AND MATERIALS TRANSACTIONS A
idly solidified samples of selected stainless steel alloys have been reported by several authors.[5-13] There is a remarkable difference in alternative phase formation tendencies for different solidification techniques. In droplet processing techniques the metastable d-ferrite phase seems to be promoted,[5,6,7] whereas, in rapid solidification processes on cooling substrates, the metastable g-austenite phase formation is preferred.[8-13] In a pioneering work of Kelly et al., the alternative metastable bcc phase formation in a droplet-processed type 303 stainless steel was analyzed in terms of the classical nucleation theory.[5] Competitive dendrite growth of the bcc and fcc phases was calculated by several authors[11-15] and compared wit
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