Synthesis, Characterization, and Magnetic Properties of gamma-NaxCoO2 (0.70 < x <0.84)

Powder Na$_{x}$CoO$_{2}$ ($0.70\leq x\leq 0.84$) samples were synthesized and characterized carefully by X-ray diffraction analysis, inductive-coupled plasma atomic emission spectroscopy, and redox titration. It was proved that $\gamma$-Na$_{x}$CoO$_{2}$ is formed only in the narrow range of $0.70\leq x\leq 0.78$. Nevertheless, the magnetic properties depend strongly on $x$. We found, for the first time, two characteristic features in the magnetic susceptibility of Na$_{0.78}$CoO$_{2}$, a sharp peak at $T_{p}=16$ K and an anomaly at $T_{k}=9$ K, as well as the transition at $T_{c}=22$ K and the broad maximum at $T_{m}=50$ K which had already been reported. A type of weak ferromagnetic transition seems to occur at $T_{k}$. The transition at $T_{c}$, which is believed to be caused by spin density wave formation, was observed clearly for $x\geq 0.74$ with constant $T_{c}$ and $T_{p}$ independent of $x$. On the other hand, ferromagnetic moment varies systematically depending on $x$. These facts suggest the occurrence of a phase separation at the microscopic level, such as the separation into Na-rich and Na-poor domains due to the segregation of Na ions. The magnetic phase diagram and transition mechanism proposed previously should be reconsidered.Comment: 4 pages (2 figures included) and 2 extra figures (gif), to be published in J. Phys. Soc. Jpn. 73 (8) with possible minor revision

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

A common behavior of thermoelectric layered cobaltites: incommensurate spin density wave states in [Ca2_2Co4/3_{4/3}Cu2/3_{2/3}O4_4]0.62_{0.62}[CoO2_2] and [Ca2_2CoO3_3]0.62_{0.62}[CoO2_2]

Magnetism of a misfit layered cobaltite [Ca$_2$Co$_{4/3}$Cu$_{2/3}$O$_4$]$_x^{\rm RS}$[CoO$_2$] ($x \sim$ 0.62, RS denotes a rocksalt-type block) was investigated by a positive muon spin rotation and relaxation ($\mu^+$SR) experiment. A transition to an incommensurate ({\sf IC}) spin density wave ({\sf SDW}) state was found below 180 K (= $T_{\rm C}^{\rm on}$); and a clear oscillation due to a static internal magnetic field was observed below 140 K (= $T_{\rm C}$). Furthermore, an anisotropic behavior of the zero-field $\mu^+$SR experiment indicated that the {\sf IC-SDW} propagates in the $a$-$b$ plane, with oscillating moments directed along the c axis. These results were quite similar to those for the related compound [Ca$_2$CoO$_3$]$_{0.62}^{\rm RS}$[CoO$_2$], {\sl i.e.}, Ca$_3$Co$_4$O$_9$. Since the {\sf IC-SDW} field in [Ca$_2$Co$_{4/3}$Cu$_{2/3}$O$_4$]$_{0.62}^{\rm RS}$[CoO$_2$] was approximately same to those in pure and doped [Ca$_2$CoO$_3$]$_{0.62}^{\rm RS}$[CoO$_2$], it was concluded that the {\sf IC-SDW} exist in the [CoO$_2$] planes.Comment: 15 pages, 6 figures. accepted for publication in J. Phys.: Condens. Matte

Visualization and Quantification of Solute Diffusivity in Cracked Concrete by X-Ray CT

This paper explores the usage of microfocus X-ray computed tomography (CT) for visualization and quantification of diffusion phenomena in cracked concrete. Mortar specimens of varying shapes (prismatic and cylindrical), crack types (artificial and splitting tensile), and binder compositions (OPC and fly ash) were prepared. Cesium carbonate (Cs2CO3) was used as a tracer in the diffusion test because it has high X-ray absorption due to its high atomic number and thus contrasts with mortar and air voids in the CT images. Image processing and analysis was carried out to visualize and quantify the diffusion behavior in 3D space. In addition, the profile of the solute concentration in cracked mortar was determined based on the measured CT numbers. Fick’s second law could then be used to determine the diffusion coefficient of the solute. It was found that the diffusion coefficients along the crack were on the scale of 10-8 to 10-11 m2/s, which implies that the transport mechanism along the crack was not solely by diffusion but controlled by the degree of saturation as well as the crack opening width. Diffusivity in the uncracked matrix, however, was reduced to the scale of 10-12 m2/s. Fly ash mortar exhibited a lower diffusion coefficient in the uncracked matrix compared with the OPC mortar with an equivalent crack opening width

Lithium Diffusion & Magnetism in Battery Cathode Material LixNi1/3Co1/3Mn1/3O2

We have studied low-temperature magnetic properties as well as high-temperature lithium ion diffusion in the battery cathode materials LixNi1/3Co1/3Mn1/3O2 by the use of muon spin rotation/relaxation. Our data reveal that the samples enter into a 2D spin-glass state below TSG=12 K. We further show that lithium diffusion channels become active for T>Tdiff=125 K where the Li-ion hopping-rate [nu(T)] starts to increase exponentially. Further, nu(T) is found to fit very well to an Arrhenius type equation and the activation energy for the diffusion process is extracted as Ea=100 meV.Comment: Submitted to Journal of Physics: Conference Series (2014

Hidden magnetic transitions in thermoelectric layered cobaltite, [Ca2_2CoO3_3]0.62_{0.62}[CoO2_2]

A positive muon spin rotation and relaxation ($\mu^+$SR) experiment on [Ca$_2$CoO$_3$]$_{0.62}$[CoO$_2$], ({\sl i.e.}, Ca$_3$Co$_4$O$_9$, a layered thermoelectric cobaltite) indicates the existence of two magnetic transitions at $\sim$ 100 K and 400 - 600 K; the former is a transition from a paramagnetic state to an incommensurate ({\sf IC}) spin density wave ({\sf SDW}) state. The anisotropic behavior of zero-field $\mu^+$SR spectra at 5 K suggests that the {\sf IC-SDW} propagates in the $a$-$b$ plane, with oscillating moments directed along the c-axis; also the {\sf IC-SDW} is found to exist not in the [Ca$_2$CoO$_3$] subsystem but in the [CoO$_2$] subsystem. In addition, it is found that the long-range {\sf IC-SDW} order completes below $\sim$ 30 K, whereas the short-range order appears below 100 K. The latter transition is interpreted as a gradual change in the spin state of Co ions %% at temperatures above 400 K. These two magnetic transitions detected by $\mu^+$SR are found to correlate closely with the transport properties of [Ca$_2$CoO$_3$]$_{0.62}$[CoO$_2$].Comment: 7 pages, 8 figures. to be appeared in Phys. Rev.