Modeling elasticity in crystal growth.
By K. Elder, M. Katakowski, M. Haataja, Martin Grant. Physical Review Letters, 2001
773 citations recorded by the source corpus.
A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to time scales much larger than conventional atomic methods. The model is shown to be consistent with the predictions of Read and Shockley for grain boundary energy, and Matthews and Blakeslee for misfit dislocations in epitaxial growth.
Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/fd90c1ff7b2d1d65ef2a474f26b8699eb8827c8f
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Atomic and Molecular Physics, and Optics
In Materials Chemistry
Citations in the corpus
- Nanostructured surfaces: challenges and frontiers in nanotechnology (2004, positive): “During the growth of thin films, morphological instabilities may play an important role in the composition, structure and lateral ordering of the self-assembled nanostructures (Elder et al 2002, Gray et al 2002).”
- An introduction to phase-field modeling of microstructure evolution (2008, neutral): “Very recently a new continuum modeling approach, the phase-field crystal model, was introduced [200–202].”
- Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation (2009, methodology): “[3,4] solved the PFC equation using an explicit Euler scheme, where a high-order time step restriction ðs < Ch(6)Þ is required”
- The phase field technique for modeling multiphase materials (2008, background): “A systematic derivation of the sharp and thin interface limits of phase field models with general free energy functions was discussed by Elder et al [77].”
- The scalar auxiliary variable (SAV) approach for gradient flows (2018, background): “Gradient flows are frequently used in mathematical models for problems in many fields of science and engineering, particularly in materials science and fluid dynamics, see, for instance, [4, 1, 15, 6, 13, 2, 8, 25] and the references therein.”
- An unconditionally energy-stable method for the phase field crystal equation (2012, background): “Recently, a new theory has been put forward under the name of phase field crystal equation [17,18,42].”
- Grain boundary segregation engineering in metallic alloys: A pathway to the design of interfaces (2014, neutral): “While density functional theory is not an adequate method for such trend screens owing to the requirement of using periodic boundary conditions and small simulation cells, the phase field crystal model might be suited to systematically tackle such a task [132,133].”
- Tuned, driven, and active soft matter (2015, methodology): “sity eld. This model was successfully used to reproduce solidication and crystallization phenomena in conventional passive crystalline structures on particle-resolved length and diusive time scales [342, 343, 349, 473{476, 480{483]. The second prominent approach contained here stems from the macrosc”
- Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview (2012, methodology): “In the past decade, special attention has been paid to a similar model, whose mathematical formulation has been laid down decades earlier to address hydrodynamic instabilities [10] and to describe the transition to the antiferromagnetic state in liquid 3He or to a non-uniform state in cholesteric li”
- Classical dynamical density functional theory: from fundamentals to applications (2020, methodology): “[135] and later derived from DDFT by van Teeffelen et al.”