Snowflake growth provides a fascinating example of spontaneous pattern formation in nature. Attempts to understand this phenomenon have led to important insights in non-equilibrium dynamics observed in various active scientific fields, ranging from pattern formation in physical and chemical systems, to self-assembly problems in biology. Yet, very few models currently succeed in reproducing the diversity of snowflake forms in three dimensions, and the link between model parameters and thermodynamic quantities is not established. Here, we report a modified phase field model that describes the subtlety of the ice vapour phase transition, through anisotropic water molecules attachment and condensation, surface diffusion, and strong anisotropic surface tension, that guarantee the anisotropy, faceting and dendritic growth of snowflakes. We demonstrate that this model reproduces the growth dynamics of the most challenging morphologies of snowflakes from the Nakaya diagram. We find that the growth dynamics of snow crystals matches the selection theory, consistently with previous experimental observations. npj Computational Materials (2017) 3:15 ;
Simulating ice crystal growth is a major issue for meteorology and aircraft safety. Yet, very few models currently succeed in reproducing correctly the diversity of snow crystal forms, and link the model parameters to thermodynamic quantities. Here, we demonstrate that the new three-dimensional phase-field model developed in Demange et al. [npj Comput. Mater. 3, 1 (2017)2057-396010.1038/s41524-017-0015-1] is capable of reproducing properly the morphology and growth kinetics of snowflakes in supersaturated atmosphere. Aside from that, we show that the growth dynamics of snow crystals satisfies the selection theory, consistently with previous experimental observations. Finally, we link the parameters of the phase-field model to atmospheric parameters.
Motivated by the discovery of multiferroicity in the geometrically frustrated triangular antiferromagnet CuCrO2 below its Néel temperature TN , we investigate its magnetic and ferroelectric properties using ab initio calculations and Monte Carlo simulations. Exchange interactions up to the third nearest neighbors in the ab plane, inter-layer interaction and single ion anisotropy constants in CuCrO2 are estimated by series of density functional theory calculations. In particular, our results evidence a hard axis along the [110] direction due to the lattice distortion that takes place along this direction below TN . Our Monte Carlo simulations indicate that the system possesses a Néel temperature TN ≈ 27 K very close to the ones reported experimentally (TN = 24 − 26 K). Also we show that the ground state is a proper-screw magnetic configuration with an incommensurate propagation vector pointing along the [110] direction. Moreover, our work reports the emergence of spin helicity below TN which leads to ferroelectricity in the extended inverse Dzyaloshinskii-Moriya model. We confirm the electric control of spin helicity by simulating P -E hysteresis loops at various temperatures.
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