Variational theory of crystal growth and its application for analysis of forming processes for metastable phases in overcooled metallic melts with eutectic composition

Abstract

Forming of metastable phases in strongly overcooled eutectic systems of multi-component metallic melts arises increased interest in connection with development and putting into practice the commercial production of amorphous and nano-crystal metals, i. e. at Ashinsky metallurgical plant, the largest Russian producer of such metals [1–3]. These metals are characterized by the unique mechanical and physical properties, first of all — magnetic properties. Conventional theoretical models uses assumption about local equilibrium near the growing crystal surface in description of crystallization processes in such systems [4]. However, this assumption is valid only in the case when crystal growth is limited by diffusion transfer of the components from initial melt. In this case phase equilibrium diagrams characterizing the examined macro-system are used for determination of regularities of micro-processes passing on the boundary “melt – crystal”. Growth of the new phase during crystallization of strongly overcooled multi-component metallic melts occurs in any cases with such high speed that crystallization front catches the atoms of melt components [3]. Thereby speeds of diffusion flows in this case don’t determine regularities of a phase boundary transition. The arising effects don’t correspond to the usual understanding of crystals growth regularities. In particular, deviation from the local equilibrium conditions on the boundary “melt – crystal” is observed [2, 4–7]. At the same time, these deviations have non-linear feature, and the methods of linear non-equilibrium thermodynamics become not valid for description of this system. In this connection, the new methods for description of such systems were developed last time [2]. The phase field theory [2, 8–12] can be noted as one of directions for such investigations. This theory describes a transition layer near growing nucleus via variational methods and allows to take into account non-linear effects connected with impurity trapping. Calculation allows predicting crystal growth regularities as well as determining the form of growing crystal dynamically. The authors previously developed the new variational approach for description of crystal growth [13, 14]. The advantages of this approach conclude in complex description of mutually connected thermal and diffusion processes in the system “growing crystal – melt”, taking into account the influence of non-linear effects on the phase boundary. The developed theory is used in this work for analysis of crystallization of dual-component eutectic melt in the conditions of deep overcooling. The developed mathematical model was applied for examination of Fe-B eutectic alloy having serious importance for many industries. The process of mutual influence of growth of crystals nuclei for several phases (i. e. metastable phases) is analyzed. The metastable analogue of Variational theory of crystal growth and its application for analysis of forming processes for metastable phases in overcooled metallic melts with eutectic composition