Nucleation kinetics of the liquid-liquid phase separation under extreme external conditions
Final Report Abstract
Within this project, the nucleation kinetics of first order phase transformations (according to the classification by Ehrenfest) that start from a homogeneous liquid state have been investigated. For this reason, a statistical approach has been utilized that had originally been developed for cancer research. Particular attention was paid in this project on the transformations occurring in alloy systems that present a miscibility gap in the stable or undercooled liquid state. Both, liquid-to-crystal and liquid-liquid phase transformations have been investigated. The most important results obtained in this work are summarized below. • The quantitative analysis of nucleation rates has revealed that transitions of the nucleation mechanism are prone to occur at high undercooling levels (and within complex constitutional phase diagrams), causing maxima of the nucleation rates and discontinuous jumps of the undercooling level and the nucleation rates. Such nucleation transitions, although not often observed, should be generally considered when either deep undercooling or fast cooling conditions occur, i.e. when the phase formation proceeds under conditions far from equilibrium, in order to be able to describe the solidification of highly undercooled melts. Such conditions are likely to be experienced also in applications in our daily life, e.g. during soldering. • In the current work, the calculation of the thermodynamic “driving force” for crystal nucleation in a monotectic system within the composition range of the miscibility gap has been corrected. The current analysis indicates that the presence of a liquid-liquid miscibility gap enhances the activation barrier for homogeneous nucleation and reduces the probability for the occurrence of heterogeneous nucleation. In systems with a metastable miscibility gap, transitions of the dominant nucleation mechanism can be expected to occur, depending on the proximity of the system to the metastable binodal. • With the application of fast scanning chip calorimetry and careful selection of a model alloy, the kinetic transition between homogeneous – and heterogeneous nucleation have been experimentally mapped. The quantitative analyses of the kinetic pre-factor Γ and the activation energy ΔG* obtained from nucleation rate measurements and by applying classical nucleation theory indicate a continuous kinetic transition from heterogeneous to homogeneous nucleation for cooling rates around 1000−2000 K/s. Such a continuous transition that can be described as a cooling rate-dependent selection of the nucleation mechanism was experimentally observed. It is important to note that this cooling rate regime is also accessible in real-world processing, e.g., during added manufacturing and 3D printing, and thus presents a usable “tuning fork” for heterogeneous nucleant selection/deselection and the corresponding microstructure formation, even in industrial processing environments. • Measurements on the early stages of a liquid-liquid phase separation transformation have shown that a distinct transition exists between a spinodal – and a nucleation regime, depending on the proximity to the critical consolute point. The activation barrier for the nucleation of liquid-liquid phase separation is rather low and amounts to about 8 kBT for Cu-Co alloys with off-critical composition. • High precision nucleation rate measurements, especially when conducted such that a large rate range is covered in calorimetric experiments can be used to quantitatively determine the solid-liquid interface excess free energy density.
Publications
- Effect of undercooling on particle size distribution in phase separated Cu75Co25-xMx (M = Ni, Fe) alloys with low M content. Journal of Alloys and Compounds, 596 (2014) 55-57
Zhang, Y., Wu, Z.K., Wang, M.M., Yang, C., Wilde, G.
(See online at https://doi.org/10.1016/j.jallcom.2014.01.182) - Morphology and aspect ratio of bismuth nanoparticles embedded in a zinc matrix. Applied Physics Letters, 105 (2014) 241902
Song, T.-E., Wilde, G., Peterlechner, M.
(See online at https://doi.org/10.1063/1.4904462) - Nucleation transitions in an undercooled Cu70Co30 immiscible alloy. Applied Physics Letter, 105 (2014) 041908
Zhang, Y., Simon, C.,Volkmann, T., Kolbe, M., Herlach, D., Wilde, G.
(See online at https://doi.org/10.1063/1.4892070) - Particle size distribution and composition in phase-separated Cu75Co25 alloys under various magnetic fields. Scripta Materialia, 82 (2014) 5-8
Zhang, Y., Gao, J., Yasuda, H., Kolbe, M., Wilde, G.
(See online at https://doi.org/10.1016/j.scriptamat.2014.03.003) - Experimental determination of the nucleation rates of undercooled micron-sized liquid droplets based on fast chip calorimetry. Thermochimica Acta, 603 (2015) 39-45
Simon, C., Peterlechner, M., Wilde, G.
(See online at https://doi.org/10.1016/j.tca.2014.10.027) - Nucleation Kinetics Analyses of Deeply Undercooled Metallic Liquids by Fast Scanning Calorimetry. Book Chapter in “Fast Scanning Calorimetry”, ed. By C. Schick and V. Mathot, Springer (2016), ISBN 978-3-319- 31327-6, pp. 661-691
Simon, C., Zhang, Y., Wilde, G.
(See online at https://doi.org/10.1007/978-3-319-31329-0_20) - Continuous Transformations of the Nucleation Mechanism in the Undercooled State. Crystal Growth and Design, 18 (2017) 2905-2911
Zhang Y., Simon C., Volkmann T., Kolbe M., Lei Y., Li L., Wilde G.
(See online at https://doi.org/10.1021/acs.cgd.7b01759) - Fast scanning calorimetric study of nucleation rates and nucleation transitions of Au-Sn alloys. Scripta Materialia 139 (2017) 13-16
Simon, C., Gao, J., Mao, Y., Wilde, G
(See online at https://doi.org/10.1016/j.scriptamat.2017.06.004) - Determining solid/liquid interfacial energies in Al-Cu by curvature controlled melting point depression. Acta Materialia, 147 (2018) 113-121
Lippmann S., Simon C., Zechel S., Seyring M., Schubert U., Wilde G., Rettenmayr M.
(See online at https://doi.org/10.1016/j.actamat.2018.01.012)
