Kinetics of the Topochemical Transformation of (PbSe)_m(TiSe₂)_n(SnSe₂)_m(TiSe₂)_n to (Pb_0.5Sn_0.5Se)_m(TiSe₂)_n

Abstract

Solid-state reaction kinetics on atomic length scales have not been heavily investigated due to the long times, high reaction temperatures, and small reaction volumes at interfaces in solid-state reactions. All of these conditions present significant analytical challenges in following reaction pathways. Herein we use in situ and ex situ X-ray diffraction, in situ X-ray reflectivity, high-angle annular dark field scanning transmission electron microscopy, and energy-dispersive X-ray spectroscopy to investigate the mechanistic pathways for the formation of a layered (Pb_0.5Sn_0.5Se)_1+δ(TiSe₂) _m heterostructure, where m is the varying number of TiSe₂ layers in the repeating structure. Thin film precursors were vapor deposited as elemental-modulated layers into an artificial superlattice with Pb and Sn in independent layers, creating a repeating unit with twice the size of the final structure. At low temperatures, the precursor undergoes only a crystallization event to form an intermediate (SnSe₂)_1+γ(TiSe₂) _m(PbSe)_1+δ(TiSe₂) _m superstructure. At higher temperatures, this superstructure transforms into a (Pb_0.5Sn_0.5Se)_1+δ(TiSe₂) _m alloyed structure. The rate of decay of superlattice reflections of the (SnSe₂)_1+γ(TiSe₂) _m(PbSe)_1+δ(TiSe₂) _m superstructure was used as the indicator of the progress of the reaction. We show that increasing the number of TiSe₂ layers does not decrease the rate at which the SnSe₂ and PbSe layers alloy, suggesting that at these temperatures it is reduction of the SnSe₂ to SnSe and Se that is rate limiting in the formation of the alloy and not the associated diffusion of Sn and Pb through the TiSe₂ layers.