[Paper Review] Positronium in MOFs: the Atom out of the box

P. Crivelli, D. Cooke+7 more|arXiv (Cornell University)|Sep 25, 2013

Radiation Detection and Scintillator Technologies22 citations

TL;DR

This study provides definitive experimental evidence that positronium (Ps) forms long-lived, delocalized Bloch states in metal–organic frameworks (MOFs), confirmed by measuring Ps emission energy into vacuum. Using time-of-flight spectroscopy and Kronig–Penney potential modeling, the authors demonstrate that Ps energy levels scale with MOF lattice size, validating Ps delocalization and enabling control of Ps state populations via positron implantation energy.

ABSTRACT

Recently, evidence for positronium (Ps) in a Bloch state in self-assembled metal--organic frameworks (MOFs) has been reported [Dutta et al., Phys. Rev. Lett. 110, 197403 (2013)]. In this paper, we study Ps emission into vacuum from four different MOFs crystals: MOF-5, IRMOF-8, FMA and IRMOF-20. Our measurements of Ps yield and emission energy into vacuum provide definitive evidence of Ps delocalization. We determine with a different technique Ps diffusion lengths in agreement with the recently published results. Furthermore, we measure that a fraction of the Ps is emitted into vacuum with a distinctly smaller energy than what one would expect for Ps localized in the MOFs' cells. We show that a calculation assuming Ps delocalized in a Kronig--Penney potential reproduces the measured Ps emission energy.

Motivation & Objective

• To provide direct experimental evidence of positronium (Ps) delocalization in metal–organic frameworks (MOFs) through measurement of Ps emission energy into vacuum.
• To confirm the long diffusion lengths of Ps in MOFs reported in prior work using an independent experimental technique.
• To investigate the energy spectrum of Ps emitted from MOFs with varying lattice parameters to probe the quantum mechanical nature of Ps states.
• To determine whether Ps exists in a Bloch state or is localized within MOF pores by comparing measured emission energies with theoretical predictions.
• To explore the potential of Ps Bloch states as a probe for pore connectivity and structural inhomogeneities in microporous materials.

Proposed method

• Employed a slow positron beam (1–20 keV) with time-tagged implantation to study Ps formation and emission in MOF crystals.
• Used microchannel plate (MCP) detection of secondary electrons to tag positron implantation time (t₀) for time-of-flight (TOF) measurements.
• Measured Ps emission energy into vacuum using a time-of-flight (TOF) spectrometer with a BGO crystal and lead collimator.
• Applied a three-spectrometer setup: BaF₂ for Ps lifetime and fraction in the target, BGO array for vacuum Ps yield and lifetime, and TOF for emission energy.
• Modeled Ps energy levels using the Kronig–Penney potential with lattice parameters derived from literature for each MOF (IRMOF-20, IRMOF-8, MOF-5, FMA).
• Fitted time-of-flight spectra to extract energy components and track time evolution of Ps state populations (delocalized, localized, continuum).

Experimental results

Research questions

• RQ1 Does positronium (Ps) in MOFs exist in a delocalized Bloch state, as evidenced by its emission energy into vacuum?
• RQ2 Can the measured Ps emission energy be explained by a quantum mechanical model of Ps in a periodic potential, such as the Kronig–Penney model?
• RQ3 How do the energy levels of emitted Ps correlate with the lattice parameters of different MOFs in the isoreticular series?
• RQ4 Can Ps diffusion length and state population be controlled by tuning the positron implantation energy?
• RQ5 To what extent can Ps Bloch states serve as a probe for pore connectivity and structural inhomogeneities in microporous frameworks?

Key findings

• The lowest-energy component of Ps emission into vacuum (120–162 meV) is significantly lower than expected for Ps localized in MOF cells, indicating delocalization.
• The measured emission energy for each MOF (e.g., 125 ± 5 meV for MOF-5, 162 ± 5 meV for FMA) matches theoretical predictions from the Kronig–Penney model with lattice size a derived from literature.
• Ps diffusion lengths in MOFs, inferred from emission yield and time-of-flight data, are consistent with the long diffusion lengths reported in Dutta et al. (2013), confirming delocalization.
• The population of the delocalized Bloch state in MOFs increases with higher positron implantation energy, demonstrating tunable control over Ps state occupation.
• The time evolution of Ps state populations shows that the delocalized state dominates at longer times, with lifetimes exceeding 100 ns, supporting long-lived Bloch wave behavior.
• The observed energy components (e.g., 120–162 meV, 300–400 meV, up to 2400 meV) are well-reproduced by the Kronig–Penney model, validating the quantum mechanical description of Ps in periodic MOF lattices.