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1. Structural phase purification of bulk HfO ₂ :Y through pressure cycling

   https://doi.org/10.1073/pnas.2312571121  

   Musfeldt, J. L.; Singh, Sobhit; Fan, Shiyu; Gu, Yanhong; Xu, Xianghan; Cheong, S.-W.; Liu, Z.; Vanderbilt, David; Rabe, Karin M. (January 2024, Proceedings of the National Academy of Sciences)

   We combine synchrotron-based infrared absorption and Raman scattering spectroscopies with diamond anvil cell techniques and first-principles calculations to explore the properties of hafnia under compression. We find that pressure drives HfO ${}_2$:7%Y from the mixed monoclinic ( $P{2}_1/c$) $+$antipolar orthorhombic ( $\mathit{Pbca}$) phase to pure antipolar orthorhombic ( $\mathit{Pbca}$) phase at approximately 6.3 GPa. This transformation is irreversible, meaning that upon release, the material is kinetically trapped in the $\mathit{Pbca}$metastable state at 300 K. Compression also drives polar orthorhombic ( $Pca{2}_1$) hafnia into the tetragonal ( $P{4}_2/nmc$) phase, although the latter is not metastable upon release. These results are unified by an analysis of the energy landscape. The fact that pressure allows us to stabilize targeted metastable structures with less Y stabilizer is important to preserving the flat phonon band physics of pure HfO ${}_2$. 

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2. Stabilizing Ti ₃ C ₂ T _x MXene flakes in air by removing confined water

   https://doi.org/10.1073/pnas.2400084121  

   Fang, Hui; Thakur, Anupma; Zahmatkeshsaredorahi, Amirhossein; Fang, Zhenyao; Rad, Vahid; Shamsabadi, Ahmad A; Pereyra, Claudia; Soroush, Masoud; Rappe, Andrew M; Xu, Xiaoji G; et al (July 2024, Proceedings of the National Academy of Sciences)

   MXenes have demonstrated potential for various applications owing to their tunable surface chemistry and metallic conductivity. However, high temperatures can accelerate MXene film oxidation in air. Understanding the mechanisms of MXene oxidation at elevated temperatures, which is still limited, is critical in improving their thermal stability for high-temperature applications. Here, we demonstrate that Ti ${}_3$C ${}_2$T ${}_x$MXene monoflakes have exceptional thermal stability at temperatures up to 600 ${}^{°}$C in air, while multiflakes readily oxidize in air at 300 ${}^{°}$C. Density functional theory calculations indicate that confined water between Ti ${}_3$C ${}_2$T ${}_x$flakes has higher removal energy than surface water and can thus persist to higher temperatures, leading to oxidation. We demonstrate that the amount of confined water correlates with the degree of oxidation in stacked flakes. Confined water can be fully removed by vacuum annealing Ti ${}_3$C ${}_2$T ${}_x$films at 600 ${}^{°}$C, resulting in substantial stability improvement in multiflake films (can withstand 600 ${}^{°}$C in air). These findings provide fundamental insights into the kinetics of confined water and its role in Ti ${}_3$C ${}_2$T ${}_x$oxidation. This work enables the use of stable monoflake MXenes in high-temperature applications and provides guidelines for proper vacuum annealing of multiflake films to enhance their stability. 

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3. An optical atomic clock using $4D_J$ states of rubidium

   https://doi.org/10.1088/2058-9565/ad77ef  

   Duspayev, A.; Owens, C.; Dash, B.; Raithel, G. (September 2024, Quantum Science and Technology)

   Abstract We analyze an optical atomic clock using two-photon $5S_{1/2}\to 4D_J$transitions in rubidium. Four one- and two-color excitation schemes to probe the $4D_{3/2}$and $4D_{5/2}$fine-structure states are considered in detail. We compare key characteristics of Rb $4D_J$and $5D_{5/2}$two-photon clocks. The $4D_J$clock features a high signal-to-noise ratio due to two-photon decay at favorable wavelengths, low dc electric and magnetic susceptibilities, and minimal black-body shifts. Ac Stark shifts from the clock interrogation lasers are compensated by two-color Rabi-frequency matching. We identify a ‘magic’ wavelength near 1060 nm, which allows for in-trap, Doppler-free clock-transition interrogation with lattice-trapped cold atoms. From our analysis of clock statistics and systematics, we project a quantum-noise-limited relative clock stability at the ${10}^{-13}/\sqrt{\tau \left(s\right)}$-level, with integration timeτin seconds, and a relative accuracy of $\sim {10}^{-13}$. We describe a potential architecture for implementing the proposed clock using a single telecom clock laser at 1550 nm, which is conducive to optical communication and long-distance clock comparisons. Our work could be of interest in efforts to realize small and portable Rb clocks and in high-precision measurements of atomic properties of Rb $4D_J$-states. 

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4. Development of broad modulus profile upon polymer–polymer interface formation between immiscible glassy–rubbery domains

   https://doi.org/10.1073/pnas.2312533120  

   Gagnon, Yannic J; Burton, Justin C; Roth, Connie B (January 2024, Proceedings of the National Academy of Sciences)

   Interfaces of glassy materials such as thin films, blends, and composites create strong unidirectional gradients to the local heterogeneous dynamics that can be used to elucidate the length scales and mechanisms associated with the dynamic heterogeneity of glasses. We focus on bilayer films of two different polymers with very different glass transition temperatures ( $T_{\text{g}}$) where previous work has demonstrated a long-range (∼200 nm) profile in local $T_{\text{g}}\left(z\right)$is established between immiscible glassy and rubbery polymer domains when the polymer–polymer interface is formed to equilibrium. Here, we demonstrate that an equally long-ranged gradient in local modulus $\tilde{G}\left(z\right)$is established when the polymer–polymer interface ( $\approx$5 nm) is formed between domains of glassy polystyrene (PS) and rubbery poly(butadiene) (PB), consistent with previous reports of a broad $T_{\text{g}}\left(z\right)$profile in this system. A continuum physics model for the shear wave propagation caused by a quartz crystal microbalance across a PB/PS bilayer film is used to measure the viscoelastic properties of the bilayer during the evolution of the PB/PS interface showing the development of a broad gradient in local modulus $\tilde{G}\left(z\right)$spanning $\approx$180 nm between the glassy and rubbery domains of PS and PB. We suggest these broad profiles in $T_{\text{g}}\left(z\right)$and $\tilde{G}\left(z\right)$arise from a coupling of the spectrum of vibrational modes across the polymer–polymer interface as a result of acoustic impedance matching of sound waves with $\lambda \sim 5$nm during interface broadening that can then trigger density fluctuations in the neighboring domain. 

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5. Convolution identities for divisor sums and modular forms

   https://doi.org/10.1073/pnas.2322320121  

   Fedosova, Ksenia; Klinger-Logan, Kim; Radchenko, Danylo (October 2024, Proceedings of the National Academy of Sciences)

   Ribet, Kenneth (Ed.)

   We consider certain convolution sums that are the subject of a conjecture by Chester, Green, Pufu, Wang, and Wen in string theory. We prove a generalized form of their conjecture, explicitly evaluating absolutely convergent sums $\sum _{n_1\in \mathbb{Z}\setminus \{0,n\}}\phi (n_1,n-n_1){\sigma }_{2m_1}\left(n_1\right){\sigma }_{2m_2}(n-n_1),$ where $\phi (n_1,n_2)$is a Laurent polynomial with logarithms. Contrary to original expectations, such convolution sums, suitably extended to $n_1\in \{0,n\}$, do not vanish, but instead, they carry number theoretic meaning in the form of Fourier coefficients of holomorphic cusp forms. 

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