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Pivotal influence of ligand field stabilization energy on the extraction order of divalent metal ions by acidic extractants.

React Chem Eng
Raiguel S, Binnemans K.
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Phase field crystal modeling of grain boundaries

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Displacive phase-field crystal model

Physical Review Materials, 2020
A phase-field crystal model that spontaneously undergoes displacive phase transitions is introduced by explicitly studying a two-component two-dimensional square crystal reminiscent of a perovskite. When the intercomponent free energy is a simple polynomial, the crystal undergoes displacive transitions in the $\ensuremath{\langle}10\ensuremath{\rangle}$
Eli Alster, Peter Voorhees, K R Elder
exaly   +2 more sources

The Kirkendall effect in the phase field crystal model

Philosophical Magazine, 2011
The Kirkendall effect stems from unequal mobilities of atomic species, which give rise to a net flux of vacancies during interdiffusion in substitutional alloys. In this work, we study a simple binary phase field crystal model to include unequal atomic mobilities and demonstrate that the model captures many phenomena associated with the Kirkendall ...
Thornton K, J J Hoyt
exaly   +2 more sources

Reductive renormalization of the phase-field crystal equation

Physical Review E, 2012
It has been known for some time that singular perturbation and reductive perturbation can be unified from the renormalization-group theoretical point of view: Reductive extraction of space-time global behavior is the essence of singular perturbation methods.
Y, Oono, Y, Shiwa
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Efficient numerical algorithms for the phase field crystal equation

International Journal of Modeling, Simulation, and Scientific Computing, 2021
In this paper, based on the Lagrange Multiplier approach in time and the Fourier-spectral scheme for space, we propose efficient numerical algorithms to solve the phase field crystal equation. The numerical schemes are unconditionally energy stable based on the original energy and do not need the lower bound hypothesis of the nonlinear free energy ...
Qingqu Zhuang, Shuying Zhai, Zhifeng Weng   +2 more
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