Determining adsorbate diffusion coefficients on surfaces from helium-3 spin-echo measurements of atomistic dynamics

Surface diffusion is typically described using tracer diffusion coefficients <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>D</a:mi> <a:mi>s</a:mi> </a:msub> </a:math> , which provides a bridge between atomistic dynamics and macroscopic modeling. Here we introduce a new framework to convert helium-3 spin-echo (HeSE) coherent scattering information into tracer diffusion coefficients <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:msub> <b:mi>D</b:mi> <b:mi>s</b:mi> </b:msub> </b:math> , systematically distinguishing and treating three different diffusion regimes—Brownian, hopping, and correlated—within a single HeSE analysis framework. HeSE resolves adsorbate motion on both <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi>Å</c:mi> </c:math> length scales and picosecond timescales and yields highly accurate hopping rates and dephasing rates data across a broad range of systems, yet results are seldom reported directly as <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:msub> <d:mi>D</d:mi> <d:mi>s</d:mi> </d:msub> </d:math> because a standard conversion from the coherent intermediate scattering function has been lacking. By combining analytical models with molecular dynamics simulations where interadsorbate forces are explicitly included, we establish a unified workflow to extract <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:msub> <e:mi>D</e:mi> <e:mi>s</e:mi> </e:msub> </e:math> , and produce an initial benchmark library of HeSE-derived <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:msub> <f:mi>D</f:mi> <f:mi>s</f:mi> </f:msub> </f:math> for surface-diffusion studies, providing an experimentally derived tracer diffusion coefficients for a set of adsorbate-substrate systems.