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Register a new userRole of the interplay between spinodal decomposition and crystal growth in the morphological evolution of crystalline bulk heterojunctions
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The stability of organic solar cells is strongly affected by the morphology of the photoactive layers, whose separated crystalline and/or amorphous phases are kinetically quenched far from their thermodynamic equilibrium during the production process. The evolution of these structures during the lifetime of the cell remains poorly understood. In this paper, a phase-field simulation framework is proposed, handling liquid-liquid demixing and polycrystalline growth at the same time in order to investigate the evolution of crystalline immiscible binary systems. We find that initially, the nuclei trigger the spinodal decomposition, while the growing crystals quench the phase coarsening in the amorphous mixture. Conversely, the separated liquid phases guide the crystal growth along the domains of high concentration. It is also demonstrated that with a higher crystallization rate, in the final morphology, single crystals are more structured and form percolating pathways for each material with smaller lateral dimensions.
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We present thermodynamic relationships between the free energy of the phase-field crystal (PFC) model and thermodynamic state variables for bulk phases under hydrostatic pressure. This relationship is derived based on the thermodynamic formalism for crystalline solids of Larche and Cahn [Larche and Cahn, Acta Metallurgica, Vol. 21, 1051 (1973)]. We apply the relationship to examine the thermodynamic processes associated with varying the input parameters of the PFC model: temperature, lattice spacing, and the average value of the PFC order parameter, $bar{n}$. The equilibrium conditions between bulk crystalline solid and liquid phases are imposed on the thermodynamic relationships for the PFC model to obtain a procedure for determining solid-liquid phase coexistence. The resulting procedure is found to be in agreement with the method commonly used in the PFC community, justifying the use of the common-tangent construction to determine solid-liquid phase coexistence in the PFC model. Finally, we apply the procedure to an eighth-order-fit (EOF) PFC model that has been parameterized to body-centered-cubic ($bcc$) Fe [Jaatinen et al., Physical Review E 80, 031602 (2009)] to demonstrate the procedure as well as to develop physical intuition about the PFC input parameters. We demonstrate that the EOF-PFC model parameterization does not predict stable $bcc$ structures with positive vacancy densities. This result suggests an alternative parameterization of the PFC model, which requires the primary peak position of the two-body direct correlation function to shift as a function of $bar{n}$.
Molecular dynamics simulations of the temperature dependent crystal growth rates of the salts, NaCl and ZnS, from their melts are reported, along with those of a number of pure metals. The growth rate of NaCl and the FCC-forming metals show little evidence of activated control, while that of ZnS and Fe, a BCC forming metal, exhibit activation barriers similar to those observed for diffusion in the melt. Unlike ZnS and Fe, the interfacial inherent structures of NaCl and Cu and Ag are found to be crystalline. We calculate the median displacement between the interfacial liquid and crystalline states and show that this distance is smaller than the cage length, demonstrating that crystal growth in the fast crystallizers can occur via local vibrations and so largely avoid the activated kinetics associated with the larger displacements associated with particle transport.
The atomic displacements associated with the freezing of metals and salts are calculated by treating crystal growth as an assignment problem through the use of an optimal transport algorithm. Converting these displacements into time scales based on the dynamics of the bulk liquid, we show that we can predict the activation energy for crystal growth rates, including activation energies significantly smaller than those for atomic diffusion in the liquid. The exception to this success, pure metals that freeze into face centred cubic crystals with little to no activation energy, are discussed. The atomic displacements generated by the assignment algorithm allows us to quantify the key roles of crystal structure and liquid caging length in determining the temperature dependence of crystal growth kinetics.
We consider the modification of the Cahn-Hilliard equation when a time delay process through a memory function is taken into account. We then study the process of spinodal decomposition in fast phase transitions associated with a conserved order parameter. The introduced memory effect plays an important role to obtain a finite group velocity. Then, we discuss the constraint for the parameters to satisfy causality. The memory effect is seen to affect the dynamics of phase transition at short times and has the effect of delaying, in a significant way, the process of rapid growth of the order parameter that follows a quench into the spinodal region.
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 times 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.
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