The rate of nucleation of crystals determines the stability of either undercooled melts or glassy phases. In some cases, this rate can be very high so that a nanocrystalline material is produced by crystallization of a metallic glass. The driving force for nucleation of ultrafine crystals can be adequately understood with a detailed description of the thermodynamics of the undercooled liquid and of the amorphous phase.In the present paper the thermodynamics of primary crystal nucleation from liquid and amorphous alloys is investigated. The driving force for nucleation in primary transformation is related to the difference in the chemical potential of a pure component between the liquid (amorphous) and solid phases. The maximum driving force determines the composition of the nucleus, which can be found with the parallel tangents construction. Examples based on simple thermodynamic models are reported and the effect of different parameters is briefly discussed. In the case of the ideal solution model, the driving force for nucleation and the composition of the nucleus can be calculated by simple formulae In the case of the regular solution model, the solution of the equations can be only obtained numerically.A thermodynamic analysis of metallic glass-forming systems is reported by means of a CALPHAD assessment, in which account is taken of the short range order in the undercooled liquid through the existence of an excess specific heat. Al-Nd and Fe-B systems have been investigated for Al-rich and Fe-rich compositions, respectively. Experimental data available in the literature for equilibrium and metastable phases have been also collected. For Al-Nd, a reliable description of the metastable phase diagrams can be achieved only by considering thermodynamic data of the amorphous phase. The results demonstrate a stabilization of the liquid phase on undercooling up to the glass transition temperature, where a significant heat capacity difference between liquid and solid phases has been estimated. The thermodynamic properties of intermetallic compounds are also reassessed. For the Fe-B system, different behaviours for the specific heat of liquid iron have been considered. In the case of the SGTE approach, where the heat capacity of undercooled liquid gradually reaches that of the solid phases, the experimental data cannot be well reproduced. On the contrary, considering a C_p liq = cost for pure iron in the temperature range between the melting and the isoentropic temperatures, a better agreement is reached.From the calculated free energies, the driving force for nucleation of a primary phase has been computed as a function of temperature and composition. The crystal nucleation of either a solid solution (fccAl or bccFe) or an intermetallic compound has been considered.Due to the stabilization of the liquid phase at high under-cooling, the two crystalline phase show comparable driving forces for the nucleation from the amorphous phase. In conclusion, the nucleation of primary crystalline phases during the crystallization of a metallic glass can be significantly different from what is suggested by the equilibrium phase diagram.
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