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Nucleation and Post-Nucleation Growth in Diffusion-Controlled and Hydrodynamic Theory of Solidification. CRYSTALS 2021. [DOI: 10.3390/cryst11040437] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
Two-step nucleation and subsequent growth processes were investigated in the framework of the single mode phase-field crystal model combined with diffusive dynamics (corresponding to colloid suspensions) and hydrodynamical density relaxation (simple liquids). It is found that independently of dynamics, nucleation starts with the formation of solid precursor clusters that consist of domains with noncrystalline ordering (ringlike projections are seen from certain angles), and regions that have amorphous structure. Using the average bond order parameter q¯6, we distinguished amorphous, medium range crystallike order (MRCO), and crystalline local orders. We show that crystallization to the stable body-centered cubic phase is preceded by the formation of a mixture of amorphous and MRCO structures. We have determined the time dependence of the phase composition of the forming solid state. We also investigated the time/size dependence of the growth rate for solidification. The bond order analysis indicates similar structural transitions during solidification in the case of diffusive and hydrodynamic density relaxation.
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Lutsko JF. How crystals form: A theory of nucleation pathways. SCIENCE ADVANCES 2019; 5:eaav7399. [PMID: 30972366 PMCID: PMC6450691 DOI: 10.1126/sciadv.aav7399] [Citation(s) in RCA: 70] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2018] [Accepted: 02/12/2019] [Indexed: 05/09/2023]
Abstract
Recent advances in classical density functional theory are combined with stochastic process theory and rare event techniques to formulate a theoretical description of nucleation, including crystallization, that can predict nonclassical nucleation pathways based on no input other than the interaction potential of the particles making up the system. The theory is formulated directly in terms of the density field, thus forgoing the need to define collective variables. It is illustrated by application to diffusion-limited nucleation of macromolecules in solution for both liquid-liquid separation and crystallization. Both involve nonclassical pathways with crystallization, in particular, proceeding by a two-step mechanism consisting of the formation of a dense-solution droplet followed by ordering originating at the core of the droplet. Furthermore, during the ordering, the free-energy surface shows shallow minima associated with the freezing of liquid into solid shells, which may shed light on the widely observed metastability of nanoscale clusters.
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Affiliation(s)
- James F Lutsko
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Code Postal 231, Blvd. du Triomphe, 1050 Brussels, Belgium.
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Wang Z, Chern GW, Batista CD, Barros K. Gradient-based stochastic estimation of the density matrix. J Chem Phys 2018. [DOI: 10.1063/1.5017741] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Zhentao Wang
- Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996, USA
| | - Gia-Wei Chern
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
| | - Cristian D. Batista
- Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996, USA
- Quantum Condensed Matter Division and Shull-Wollan Center, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Kipton Barros
- Theoretical Division and CNLS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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Podmaniczky F, Tóth GI, Tegze G, Gránásy L. Hydrodynamic theory of freezing: Nucleation and polycrystalline growth. Phys Rev E 2017; 95:052801. [PMID: 28618608 DOI: 10.1103/physreve.95.052801] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2016] [Indexed: 05/12/2023]
Abstract
Structural aspects of crystal nucleation in undercooled liquids are explored using a nonlinear hydrodynamic theory of crystallization proposed recently [G. I. Tóth et al., J. Phys.: Condens. Matter 26, 055001 (2014)JCOMEL0953-898410.1088/0953-8984/26/5/055001], which is based on combining fluctuating hydrodynamics with the phase-field crystal theory. We show that in this hydrodynamic approach not only homogeneous and heterogeneous nucleation processes are accessible, but also growth front nucleation, which leads to the formation of new (differently oriented) grains at the solid-liquid front in highly undercooled systems. Formation of dislocations at the solid-liquid interface and interference of density waves ahead of the crystallization front are responsible for the appearance of the new orientations at the growth front that lead to spherulite-like nanostructures.
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Affiliation(s)
- Frigyes Podmaniczky
- Research Institute for Solid State Physics and Optics, P.O. Box 49, H-1525 Budapest, Hungary
| | - Gyula I Tóth
- Research Institute for Solid State Physics and Optics, P.O. Box 49, H-1525 Budapest, Hungary
- Department of Physics, University of Bergen, Allégaten 55, 7005 Bergen, Norway
| | - György Tegze
- Research Institute for Solid State Physics and Optics, P.O. Box 49, H-1525 Budapest, Hungary
| | - László Gránásy
- Research Institute for Solid State Physics and Optics, P.O. Box 49, H-1525 Budapest, Hungary
- BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, United Kingdom
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Berryman JT, Anwar M, Dorosz S, Schilling T. The early crystal nucleation process in hard spheres shows synchronised ordering and densification. J Chem Phys 2016; 145:211901. [DOI: 10.1063/1.4953550] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Affiliation(s)
- Joshua T. Berryman
- Theory of Soft Condensed Matter, Université du Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Muhammad Anwar
- Theory of Soft Condensed Matter, Université du Luxembourg, L-1511 Luxembourg, Luxembourg
- Department of Mechanical Engineering, Institute of Space Technology, Islamabad, Pakistan
| | - Sven Dorosz
- Theory of Soft Condensed Matter, Université du Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Tanja Schilling
- Theory of Soft Condensed Matter, Université du Luxembourg, L-1511 Luxembourg, Luxembourg
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Archer AJ, Walters MC, Thiele U, Knobloch E. Solidification in soft-core fluids: Disordered solids from fast solidification fronts. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:042404. [PMID: 25375507 DOI: 10.1103/physreve.90.042404] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2014] [Indexed: 06/04/2023]
Abstract
Using dynamical density functional theory we calculate the speed of solidification fronts advancing into a quenched two-dimensional model fluid of soft-core particles. We find that solidification fronts can advance via two different mechanisms, depending on the depth of the quench. For shallow quenches, the front propagation is via a nonlinear mechanism. For deep quenches, front propagation is governed by a linear mechanism and in this regime we are able to determine the front speed via a marginal stability analysis. We find that the density modulations generated behind the advancing front have a characteristic scale that differs from the wavelength of the density modulation in thermodynamic equilibrium, i.e., the spacing between the crystal planes in an equilibrium crystal. This leads to the subsequent development of disorder in the solids that are formed. In a one-component fluid, the particles are able to rearrange to form a well-ordered crystal, with few defects. However, solidification fronts in a binary mixture exhibiting crystalline phases with square and hexagonal ordering generate solids that are unable to rearrange after the passage of the solidification front and a significant amount of disorder remains in the system.
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Affiliation(s)
- A J Archer
- Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom
| | - M C Walters
- Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom
| | - U Thiele
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm Klemm Str. 9, D-48149 Münster, Germany and Center of Nonlinear Science (CeNoS), Westfälische Wilhelms Universität Münster, Corrensstr. 2, 48149 Münster, Germany
| | - E Knobloch
- Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
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Palberg T. Crystallization kinetics of colloidal model suspensions: recent achievements and new perspectives. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:333101. [PMID: 25035303 DOI: 10.1088/0953-8984/26/33/333101] [Citation(s) in RCA: 51] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Colloidal model systems allow studying crystallization kinetics under fairly ideal conditions, with rather well-characterized pair interactions and minimized external influences. In complementary approaches experiment, analytic theory and simulation have been employed to study colloidal solidification in great detail. These studies were based on advanced optical methods, careful system characterization and sophisticated numerical methods. Over the last decade, both the effects of the type, strength and range of the pair-interaction between the colloidal particles and those of the colloid-specific polydispersity have been addressed in a quantitative way. Key parameters of crystallization have been derived and compared to those of metal systems. These systematic investigations significantly contributed to an enhanced understanding of the crystallization processes in general. Further, new fundamental questions have arisen and (partially) been solved over the last decade: including, for example, a two-step nucleation mechanism in homogeneous nucleation, choice of the crystallization pathway, or the subtle interplay of boundary conditions in heterogeneous nucleation. On the other hand, via the application of both gradients and external fields the competition between different nucleation and growth modes can be controlled and the resulting microstructure be influenced. The present review attempts to cover the interesting developments that have occurred since the turn of the millennium and to identify important novel trends, with particular focus on experimental aspects.
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Affiliation(s)
- Thomas Palberg
- Institut für Physik, Johannes Gutenberg Universität Mainz, 55099 Mainz, Germany
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