Liquid-state structural asymmetry governs species-selective crystallization in multicomponent systems

Abstract

Multicomponent crystals are often assumed to form nearly random solid solutions when thermodynamically stable. However, crystal growth proceeds from structurally heterogeneous liquids, raising the possibility that the liquid state may influence which species are incorporated into the growing crystal. Here we demonstrate that liquid-state structural asymmetry can induce species-selective crystallization in multicomponent systems. Using molecular dynamics simulations of a multivalent rocksalt-type model (AgPbBiTe$_3$), we find that cations with higher valence readily form locally crystal-compatible coordination environments in the liquid and are efficiently incorporated into the growing lattice, whereas lower-valence cations exhibit more disordered liquid coordination and attach less efficiently at the crystal-liquid interface. This asymmetry leads to species-selective incorporation and slower crystal growth. Depth-resolved photoelectron spectroscopy measurements on AgPbBiTe$_3$ further reveal enhanced Ag concentration near grain-boundary and surface regions, consistent with the selective incorporation predicted by the simulations. These results demonstrate that structural compatibility between liquid-state structure and the target crystal motif governs selective incorporation during crystallization, providing a general kinetic mechanism by which compositional heterogeneity can emerge during growth of multicomponent crystals.

Figures (11)

• Figure 1: Schematic illustration of charge-selective crystallization. Higher-valence cations form locally rocksalt-compatible coordination with Te$^{2-}$ and attach efficiently to the growth front. In contrast, Ag$^+$ exhibits more disordered liquid coordination and is incorporated less efficiently. This liquid-state structural asymmetry leads to selective incorporation and compositional bias during crystal growth.
• Figure 2: Time evolution of the number of ions belonging to the largest crystalline cluster for AgPbBiTe$_3$ and the charge-unified ideal (CUI) system. Panels (a) and (b) show results for AgPbBiTe$_3$ using the SC and FCC criteria, respectively, while panels (c) and (d) show the corresponding results for CUI. AgPbBiTe$_3$ exhibits a markedly reduced incorporation of Ag$^+$, resulting in non-uniform crystallization, whereas CUI shows uniform incorporation across cation species. These differences demonstrate that the compositional inhomogeneity arises from charge diversity rather than ionic size.
• Figure 3: Color plot of (a) Ag$^{+}$ density and (b) Te$^{2-}$ density in the $xy$ plane at $z = 10$ and $t = 800$ (yellow: high density, blue: low density). The region enclosed by the red line corresponds to the high-density Te$^{2-}$ domain, identifying the crystalline region. Within this region the Ag$^{+}$ density is depleted, while enhanced Ag$^{+}$ density is observed near the surrounding growth front. (c) Correlation between $\rho_{Ag}$ and $\rho_{Te}$. Regions with $\rho_{Te} > 0.61$ correspond to crystalline order, where $\rho_{Ag}$ is reduced, consistent with the suppressed incorporation of Ag$^{+}$ ions in the crystal.
• Figure 4: Thermodynamic densification pathway during crystallization. Average local density of Te$^{2-}$ as a function of the crystallization progress ($N_{SC}/N_{SC}^{e}$, where $N_{SC}^{e}$ is the number of crystalline particles at the end of the simulation) for AgPbBiTe$_3$ and the CUI system. The nearly identical curves indicate that the thermodynamic pathway of densification is essentially unchanged between the two systems.
• Figure 5: (a) $\hat{W}_4$ histograms for each cation at $t$ = 200 in AgPbBiTe$_3$. In the multivalent system, the weaker Coulomb attraction of Ag$^+$ suppresses the formation of locally SC-like environments in the liquid, indicating that the structural asymmetry underlying charge-selective incorporation is already present before crystallization. The yellow region in the figure indicates the area classified as the SC-like structure. (b) Te-cation radial distribution functions at $t$ = 200 in AgPbBiTe$_3$. The broader and lower first peak for Ag$^+$ in AgPbBiTe$_3$ indicates larger and more widely distributed Ag-Te neighbor distances, consistent with the reduced local density. These liquid-state structural differences account for the inefficient incorporation of Ag$^+$ at the crystal-liquid interface.