Phase transitions in self-dual generalizations of the Baxter-Wu model

We study two types of generalized Baxter-Wu models, by means of transfer-matrix and Monte Carlo techniques. The first generalization allows for different couplings in the up- and down triangles, and the second generalization is to a $q$-state spin model with three-spin interactions. Both generalizations lead to self-dual models, so that the probable locations of the phase transitions follow. Our numerical analysis confirms that phase transitions occur at the self-dual points. For both generalizations of the Baxter-Wu model, the phase transitions appear to be discontinuous.Comment: 29 pages, 13 figure

Understanding the Electrochemical Formation and Decomposition of Li₂O₂ and LiOH with <i>Operando</i> X‑ray Diffraction

The lithium air, or Li–O₂, battery system is a promising electrochemical energy storage system because of its very high theoretical specific energy, as required by automotive applications. Fundamental research has resulted in much progress in mitigating detrimental (electro)­chemical processes; however, the detailed structural evolution of the crystalline Li₂O₂ and LiOH discharge products, held at least partially responsible for the limited reversibility and poor rate performance, is hard to measure <i>operando</i> under realistic electrochemical conditions. This study uses Rietveld refinement of <i>operando</i> X-ray diffraction data during a complete discharge–charge cycle to reveal the detailed structural evolution of Li₂O₂ and LiOH crystallites in 1,2-dimethoxyethane (DME) and DME/LiI electrolytes, respectively. The anisotropic broadened reflections confirm and quantify the platelet crystallite shape of Li₂O₂ and LiOH and show how the average crystallite shape evolves during discharge and charge. Li₂O₂ is shown to form via a nucleation and growth mechanism, whereas the decomposition appears to start at the smallest Li₂O₂ crystallite sizes because of their larger exposed surface. In the presence of LiI, platelet LiOH crystallites are formed by a particle-by-particle nucleation and growth process, and at the end of discharge, H₂O depletion is suggested to result in substoichiometric Li­(OH)_1–<i>x</i>, which appears to be preferentially decomposed during charging. <i>Operando</i> X-ray diffraction proves the cyclic formation and decomposition of the LiOH crystallites in the presence of LiI over multiple cycles, and the structural evolution provides key information for understanding and improving these highly relevant electrochemical systems

Impact of Nanostructuring on the Phase Behavior of Insertion Materials: The Hydrogenation Kinetics of a Magnesium Thin Film

Nanostructuring is widely applied in both battery and hydrogen materials to improve the performance of these materials as energy carriers. Nanostructuring changes the diffusion length as well as the thermodynamics of materials. We studied the impact of nanostructuring on the hydrogenation in a model system consisting of a thin film of magnesium sandwiched between two titanium layers and capped with palladium. While we verified optically the coexistence of the metallic α-MgD_<i>x</i> and the insulating β-MgD_2–<i>y</i> phase, neutron reflectometry shows significant deviations from the thermodynamic solubility limits in bulk magnesium during the phase transformation. This suggests that the kinetics of the phase transformation in nanostructured battery and hydrogen storage systems is enhanced not only as a result of the reduced length scale but also due to the increased solubility in the parent phases

<i>Operando</i> Nanobeam Diffraction to Follow the Decomposition of Individual Li₂O₂ Grains in a Nonaqueous Li–O₂ Battery

Intense interest in the Li–O₂ battery system over the past 5 years has led to a much better understanding of the various chemical processes involved in the functioning of this battery system. However, detailed decomposition of the nanostructured Li₂O₂ product, held at least partially responsible for the limited reversibility and poor rate performance, is hard to measure <i>operando</i> under realistic electrochemical conditions. Here, we report <i>operando</i> nanobeam X-ray diffraction experiments that enable monitoring of the decomposition of individual Li₂O₂ grains in a working Li–O₂ battery. Platelet-shaped crystallites with aspect ratios between 2.2 and 5.5 decompose preferentially via the more reactive (001) facets. The slow and concurrent decomposition of individual Li₂O₂ crystallites indicates that the Li₂O₂ decomposition rate limits the charge time of these Li–O₂ batteries, highlighting the importance of using redox mediators in solution to charge Li–O₂ batteries