Kinetic transition in the order–disorder transformation at a solid/liquid interface

Phase-field analysis for the kinetic transition in an ordered crystal structure growing from an undercooled liquid is carried out. The results are interpreted on the basis of analytical and numerical solutions of equations describing the dynamics of the phase field, the long-range order parameter as well as the atomic diffusion within the crystal/liquid interface and in the bulk crystal. As an example, the growth of a binary A50B50 crystal is described, and critical undercoolings at characteristic changes of growth velocity and the long-range order parameter are defined. For rapidly growing crystals, analogies and qualitative differences are found in comparison with known non-equilibrium effects, particularly solute trapping and disorder trapping. The results and model predictions are compared qualitatively with results of the theory of kinetic phase transitions (Chernov 1968 Sov. Phys. JETP 26, 1182–1190) and with experimental data obtained for rapid dendritic solidification of congruently melting alloy with order–disorder transition (Hartmann et al. 2009 Europhys. Lett. 87, 40007 (doi:10.1209/0295-5075/87/40007)). This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’. © 2018 The Author(s) Published by the Royal Society. All rights reserved.Russian Science Foundation, RSF: 16-11-1009550WM1541Deutsche Forschungsgemeinschaft, DFGData accessibility. This article has no additional data. Authors’ contributions. All the authors contributed equally to the present research paper. Competing interests. The authors declare that they have no competing interests. Funding. This work was supported by the Russian Science Foundation (grant no. 16-11-10095), the German Space Center Space Management (under contract number 50WM1541) and the Deutsche Forschungsgemeinschaft (DFG) (under grant no. Re1261/8-2)

Effects of Local Nonequilibrium in Rapid Eutectic Solidification—Part 2: Analysis of Effects and Comparison to Experiment

The developed model of diffusion-limited and diffusionless solidification of a eutectic alloy describes the relation “undercooling (ΔT)-velocity (V)-interlamellar spacing (λ)” for two cases. Namely, when the solidification front velocity V is smaller than the solute diffusion speed in bulk liquid VD, V < VD, the model predicts a regime of eutectic solidification similarly to known classical models. If the solidification front velocity V is higher than the diffusion speed, V > VD, the solidification is mainly controlled by kinetic and thermal undercoolings. New expressions for the solute distribution coefficient and slope of the liquidus lines are supplied. The influence of the model parameters on the growth kinetics during eutectic solidification is discussed. Model predictions are compared with experimental data for the solidification of an Fe–B alloy with eutectic composition. Computational results show that the model agrees well with experimental data especially for low and high undercoolings, extending the undercooling range that can be covered by sharp interface modeling. © 2021 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons Ltd.This work was also financially supported by the German Science Foundation (DFG) GA1142/11-1, the Science and Technology Program of Shaanxi Province (No. 2016KJXX-87), and the Foundation of Shaanxi Provincial Department of Education (No. 18JS050). Open access funding enabled and organized by Projekt DEAL

A classical description of subnanometer resolution by atomic features in metallic structures

Recent experiments have evidenced sub-nanometer resolution in plasmonic-enhanced probe spectroscopy. Such a high resolution cannot be simply explained using the commonly considered radii of metallic nanoparticles on plasmonic probes. In this contribution the effects of defects as small as a single atom found on spherical plasmonic particles acting as probing tips are investigated in connection with the spatial resolution provided. The presence of abundant edge and corner sites with atomic scale dimensions in crystalline metallic nanoparticles is evident from transmission electron microscopy (TEM) images. Electrodynamic calculations based on the Finite Element Method (FEM) are implemented to reveal the impact of the presence of such atomic features in probing tips on the lateral spatial resolution and field localization. Our analysis is developed for three different configurations, and under resonant and non-resonant illumination conditions, respectively. Based on this analysis, the limits of field enhancement, lateral resolution and field confinement in plasmon-enhanced spectroscopy and microscopy are inferred, reaching values below 1 nanometer for reasonable atomic sizes

Mathematical modeling of dendrite growth in an Al–Ge alloy with convective flow

A theory of stable dendrite growth in an undercooled binary melt is developed for the case of intense convection. Conductive heat and mass transfer boundary conditions are replaced by convective conditions, where the flux of heat (or solute) is proportional to the temperature or concentration difference between the surface of the dendrite and far from it. The marginal mode of perturbation wavelengths is calculated using the linear morphological stability analysis. Combining this analysis with the solvability theory, we have derived a selection criterion that represents the first condition to define a combination of dendrite tip velocity and tip diameter. The second condition—the undercooling balance—is derived for intense convection. The theory under consideration determines the dendrite tip velocity and tip diameter for low undercooling. This convective theory is combined with the classical theory of dendritic growth (conductive boundary conditions), which is valid for moderate and high undercooling. Thus, the entire range of melt undercooling is covered. Our results are in good agreement with experiments on Al–Ge crystallization. © 2021 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons Ltd.Ministry of Education and Science of the Russian Federation, Minobrnauka: 075-02-2021-1387; Russian Science Foundation, RSF: 21-19-00279; Foundation for the Advancement of Theoretical Physics and Mathematics: 21-1-3-11-1L.V.T. acknowledges financial support from the Ministry of Science and Higher Education of the Russian Federation (project 075-02-2021-1387 for the development of the regional scientific and educational mathematical center “Ural Mathematical Center”) for the linear stability analysis. Moreover, she is grateful to the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS” (project No. 21-1-3-11-1) for the development of solvability theory. P.K.G. and D.V.A. acknowledge the Russian Science Foundation (Project No. 21-19-00279) for the stitching of selection criteria, computer simulations, and comparison with experimental data. Open Access funding enabled and organized by Projekt DEAL

Thermodynamics of rapid solidification and crystal growth kinetics in glass-forming alloys

Thermodynamic driving forces and growth rates in rapid solidification are analysed. Taking into account the relaxation time of the solute diffusion flux in the model equations, the present theory uses, in a first case, the deviation from local chemical equilibrium, and ergodicity breaking. The second case of ergodicity breaking may exist in crystal growth kinetics of rapidly solidifying glass-forming metals and alloys. In this case, a theoretical analysis of dendritic solidification is given for congruently melting alloys in which chemical segregation does not occur. Within this theory, a deviation from thermodynamic equilibrium is introduced for high undercoolings via gradient flow relaxation of the phase field. A comparison of the present derivations with previously verified theoretical predictions and experimental data is given. This article is part of the theme issue 'Heterogeneous materials: Metastable and nonergodic internal structures'. ©2019 The Author(s) Published by the Royal Society

Diffusionless (chemically partitionless) crystallization and subsequent decomposition of supersaturated solid solutions in Sn-Bi eutectic alloy

Results of a study on microstructural evolution of eutectic Sn-57wt.% Bi processed with cooling rates of 10-2, 1Ks-1 and approximately 105 Ks-1 are presented. In order to distinguish different mechanisms of microstructure formation, a comparison with microstructures of different hypoeutectic alloys with compositions down to below the maximum solubility of Bi in Sn-Bi is undertaken. It is found that at the cooling rates of 10-2 and 1Ks-1, coupled eutectic growth occurs, leading to lamellar structures with different length scales. At the rapid quenching rates of approximately 105 Ks-1, structure formation in the eutectic alloy is qualitatively different. Partitionless solidification resulting in a supersaturated solid solution with the initial composition is observed in both eutectic and hypoeutectic alloys. It is shown that the observed microstructure of the rapidly solidified alloys forms by the decomposition of the supersaturated solid solution. This article is part of the theme issue 'Heterogeneous materials: Metastable and non-ergodic internal structures'. ©2019 The Author(s) Published by the Royal Society

Dendrite growth in undercooled Al-rich Al-Ni melts measured on Earth and in Space

The dendrite growth velocity in Al₇₅Ni₂₅ melts has been measured in a containerless procedure as a function of undercooling using an electromagnetic levitation technique both in the Earth laboratory and in Space on board the International Space Station. The growth shows an anomalous behavior inasmuch as the growth velocity decreases with increasing undercooling, confirming previous experiments on Earth. Within the scatter of experimental data, results obtained on Earth and in Space do not show significant differences. Thus, convection effects as the origin of the anomalous growth characteristics can be excluded. However, high-speed video recording exhibits multiple nucleation events in front of the growing solid-liquid interface. This effect is identified as the origin of the anomalous dendrite growth characteristics in undercooled melts of Al-rich Al-Ni melts