Lanthanide-based heteroepitaxial core-shell nanostructures: compressive versus tensile strain asymmetry

Heteroepitaxial core-shell nanostructures have been proven advantageous in a wide variety of applications, ranging from luminescence enhancement, band gap engineering, multimodal theranostics, to catalysis. However, precisely tailoring the epitaxial growth is challenging, and a general understanding of the parameters that impact epitaxial growth remains unclear. Here we demonstrate the critical role of the sign of the lattice mismatch of the shell relative to the core (compressed/tensile) in generating lanthanide-based core-shell structures, a parameter conventionally not considered in heteroepitaxial design. We took advantage of the very gradual contraction of lanthanide ions along the series to control precisely both the magnitude and the sign of lattice mismatch and investigated multiple sodium lanthanide fluoride (NaLnF4) core-shell heterostructures of variable composition and size. We discovered that the tensile strained shells adapt to the core crystallite shape (i.e., conformal) and lattice structure (i.e., coherent), while under identical magnitude of mismatch, the compressively strained shells are neither conformal nor coherent to the core. This striking asymmetry between the tensile and compressively strained epitaxial growth arises from the fundamental anharmonicity of the interatomic interactions between the attractive and repulsive pairs. From a broader perspective, our findings redefine the a priori design consideration and provide a fundamental insight on the necessity to include the sign of lattice mismatch and not just its magnitude in designing heteroepitaxial core-shell nanostructures.