Lithium’s Work Function Alters with Isotope and Temperature

Scientists have long sought to understand the subtle interplay between electronic and ionic degrees of freedom in simple metals, and new research focusing on lithium provides compelling evidence of this complexity. Atef A. Sheekhoon, Abdelrahman O. Haridy, and Vitaly V. Kresin, all from the Department of Physics and Astronomy at the University of Southern California, report measurements of the work functions of lithium-6 and lithium-7 isotopes as a function of temperature, revealing a significant isotope effect. Their findings, obtained through photoionization of isolated metal nanoparticles, demonstrate that the temperature variation of the work function exhibits a curvature exceeding expectations based solely on electron gas density changes. This work enhances the characterisation of lithium as a material where electronic and ionic contributions are nontrivial and necessitates more sophisticated theoretical models to fully explain its behaviour, while also confirming predictions based on the Third Law of thermodynamics regarding work function behaviour at low temperatures.

New measurements reveal a surprising link between an atom’s mass and how easily it releases electrons. This subtle effect could refine materials design and improve performance in next-generation devices. Scientists found the curvature of this temperature variation to be significantly larger than may be ascribed purely to a change in the electron gas density.

These findings enhance the characterisation of lithium as a quantum material in which the interplay between electronic and ionic degrees of freedom is nontrivial, and call for a microscopic understanding beyond simple models. Interestingly, the presence of vibrational excitations can also affect equilibrium properties of electron spectra. Specifically, this work probes the influence of thermal vibrations on the electronic work function. While the temperature dependence of the work function is not as steep as that of transport coefficients, an accurate measurement of this effect elucidates a distinctive connection between electronic and vibrational degrees of freedom.

To spotlight the role of the latter, we focus on the isotope effect by comparing the temperature variations of the work functions of Li and Li. In addition to having two abundant stable isotopes with sufficiently separated masses, lithium metal possesses other features that make it an interesting subject. The low atomic mass, substantial zero-point motion, and high Debye temperature (320, 440 K) result in a significant enhancement of quantum effects in its lattice structure and dynamics, giving rise to a range of unusual structural and phase transitions and even superconductivity with an anomalous isotope effect.

Alongside the low mass, lithium is distinguished by the relatively weak shielding of the atomic nucleus by the 1s core electrons, exposing its conduction electrons to a hard and nonlocal pseudopotential. As a result, for example, their optical and thermal effective masses are much more enhanced relative to the free-electron value than in the other alkali metals.

The work function can be expressed as follows: W = − − where e is the magnitude of the electron charge, is the electron chemical potential inside the metal referred to the electrostatic potential in the interior, and φ is the difference between the latter and the electrostatic potential in the vacuum outside the metal. This implies that for lithium, quantum effects will influence the dependence of W on the temperature and on the isotopic mass. As the material warms up and undergoes thermal expansion, not only does the electron gas density change but so do the band structure, the electron-vibrational coupling strength, the effective mass, the behaviour of the surface dipole layer, etc.

Simple electrostatic models that can reproduce W(T) for other metals aren’t as successful for Li, which underscores the need for a more quantitative theory. While lithium is a very interesting material to study, many of its physical and chemical properties can be impacted by contamination. Despite sometimes being characterised as “the least reactive” of the alkali group, it is the only alkali metal that significantly reacts with nitrogen, and in the molten state vigorously attacks glass, ceramics, copper, and graphite.

Contaminants significantly influence spectroscopic and structural measurements and can strongly distort work function values even in minute presence on the sample surface. Since dW/dT ~ 10-4 eV/K, precise and contamination-free measurements are necessary to trace out the W(T) curve and resolve the isotopic variations. We accomplish this by determining the work functions via photoionization of free isolated nanoparticles.

Their short flight time within the nanocluster beam apparatus and small surface area ensure the absence of contamination; then a careful measurement of their near-threshold photoionization provides the requisite fraction-of-a-percent precision in assigning the ionization energy over a wide temperature range. The apparatus uses a beam of metal nanoparticles, with standard errors of approximately 0.3% derived from multiple measurements at each temperature.

The plot shows two options: thermal effective mass m 2.2m and band effective mass m* 1.3m. Neither one can reproduce the curvature of the experimental plot (using the free electron mass m would increase the discrepancy even more), not the magnitude of the isotope splitting. This attests to the fact that the effect of lattice vibrations on the electronic work function extends beyond only an electron gas density change. A model endeavoring to approximate this effect by replacing the ionic pseudopotential radius by a thermally dilated value did predict a steeper W(T) dependence for Li, indicating that the ionic potential correction is indeed relevant.

Isotope-dependent work function variations and thermal expansion in lithium nanoparticles

Measurements of the work functions for both 7Li and 6Li reveal a distinct isotope effect in their temperature variation. Specifically, the experimental data demonstrate that the work functions differ as a function of temperature, a phenomenon not previously observed to this extent in alkali metals. Initial analysis of the temperature dependence of the work function showed a curvature substantially exceeding that attributable solely to changes in electron gas density.

Beyond observing the isotope effect, the research quantified the volume thermal expansion coefficients for each lithium isotope; 7Li exhibited a greater thermal expansion coefficient than 6Li, aligning with its steeper temperature-dependent work function. However, a direct comparison with an electron gas-based image charge model, successful for sodium and potassium, revealed a significant discrepancy.

The experimental W(T) curves were demonstrably steeper than predicted by the electron gas model, even when accounting for exchange and correlation effects. These findings suggest that the interplay between electronic and ionic degrees of freedom in lithium is more complex than previously understood, necessitating a more sophisticated theoretical framework.

Isotopic variations in lithium nanoparticles redefine understanding of metallic bonding

Scientists have long understood that lithium presents peculiar behaviour, yet recent measurements of its work function in isolated nanoparticles reveal subtle but significant differences between its isotopes. These findings aren’t merely a technical refinement of existing data; they point towards a deeper complexity in how lithium’s electrons and atomic nuclei interact.

For decades, modelling metallic behaviour relied on treating electrons as a largely independent gas, with atomic vibrations considered a secondary effect. However, this work demonstrates that, in lithium at least, those vibrations, and the isotope mass influencing them, play a more substantial role than previously appreciated. Establishing this isotope effect required painstaking precision, measuring the work function of nanoparticles demands isolating single atoms, a feat of experimental control that eliminates confounding factors present in bulk materials.

Now, with these refined measurements, the field can move beyond simplified models and begin to explore the interplay between electronic and ionic motion within lithium. This is not simply academic; lithium’s role in battery technology means even small improvements in understanding its fundamental properties could translate into more efficient energy storage.

Still, questions remain. The observed variations, while measurable, are small, and disentangling them from other potential influences, such as nanoparticle size or surface contamination, is an ongoing challenge. Further research should focus on extending these measurements to other alkali metals, testing whether this enhanced sensitivity to nuclear mass is a characteristic of the group.

Beyond that, theoretical work is needed to develop models that accurately capture these subtle effects, potentially incorporating quantum mechanical treatments of both electrons and atomic nuclei. Ultimately, this work serves as a reminder that even well-studied materials can still hold surprises, and that a deeper understanding of fundamental physics is often the key to technological advancement.