Diffusion constants are typically considered to be independent of particle size with the benefit of nanosizing materials arising solely from shortened transport paths. We show that for materials with one-dimensional atomic migration channels, the diffusion constant depends on particle size with diffusion in bulk being much slower than in nanoparticles. This model accounts for conflicting data on LiFePO4, an important material for rechargeable lithium batteries, specifically explaining why it functions exclusively on the nanoscale.

/pdf/particle-size-dependence-of-the-ionic-diffusivity-5asmvzaiwq.pdf

Particle size dependence of the ionic diffusivity.

Resonant (elastic) soft x-ray scattering (RSXS) offers a unique element, site and valence specific probe to study spatial modulations of charge, spin and orbital degrees of freedom in solids on the nanoscopic length scale. It is not only used to investigate single-crystalline materials. This method also enables one to examine electronic ordering phenomena in thin films and to zoom into electronic properties emerging at buried interfaces in artificial heterostructures. During the last 20 years, this technique, which combines x-ray scattering with x-ray absorption spectroscopy, has developed into a powerful probe to study electronic ordering phenomena in complex materials and furthermore delivers important information on the electronic structure of condensed matter. This review provides an introduction to the technique, covers the progress in experimental equipment, and gives a survey on recent RSXS studies of ordering in correlated electron systems and at interfaces.

https://iopscience.iop.org/article/10.1088/0034-4885/76/5/056502/pdf

Resonant elastic soft x-ray scattering

Resonant (elastic) soft x-ray scattering (RSXS) offers a unique element, site, and valence specific probe to study spatial modulations of charge, spin, and orbital degrees of freedom in solids on the nanoscopic length scale It cannot only be used to investigate single crystalline materials This method also enables to examine electronic ordering phenomena in thin films and to zoom into electronic properties emerging at buried interfaces in artificial heterostructures During the last 20 years, this technique, which combines x-ray scattering with x-ray absorption spectroscopy, has developed into a powerful probe to study electronic ordering phenomena in complex materials and furthermore delivers important information on the electronic structure of condensed matter This review provides an introduction to the technique, covers the progress in experimental equipment, and gives a survey on recent RSXS studies of ordering in correlated electron systems and at interfaces

Resonant Elastic Soft X-Ray Scattering

Measurements of polarized neutron scattering were performed on a S=1/2 chain multiferroic LiCu2O2. In the ferroelectric ground state with the spontaneous polarization along the c axis, the existence of transverse spiral spin component in the bc plane was confirmed. When the direction of electric polarization is reversed, the vector spin chirality as defined by C_(ij)=S_(i)xS_(j) (i and j being the neighboring spin sites) is observed to be reversed, indicating that the spin-current model or the inverse Dzyaloshinskii-Moriya mechanism is applicable even to this e_(g)-electron quantum-spin system. Differential scattering intensity of polarized neutrons shows a large discrepancy from that expected for the classical-spin bc-cycloidal structure, implying the effect of large quantum fluctuation.

Correlation between spin helicity and an electric polarization vector in quantum-spin chain magnet LiCu2O2.

Single crystals of iron(IV) rich oxides $\mathrm{Sr}\mathrm{Fe}{\mathrm{O}}_{3\ensuremath{-}\ensuremath{\delta}}$ with controlled oxygen content $(0\ensuremath{\leqslant}\ensuremath{\delta}\ensuremath{\leqslant}0.31)$ have been studied by M\"ossbauer spectroscopy, magnetometry, magnetotransport measurements, Raman spectroscopy, and infrared ellipsometry in order to relate the large magnetoresistance (MR) effects in this system to phase composition and magnetic and charge order. It is shown that three different types of MR effects occur. In cubic $\mathrm{Sr}\mathrm{Fe}{\mathrm{O}}_{3}$ $(\ensuremath{\delta}=0)$ a large negative MR of 25% at $9\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ is associated with a hitherto unknown $60\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ magnetic transition and a subsequent drop in resistivity. The $60\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ transition appears in addition to the onset of helical ordering at $\ensuremath{\sim}130\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. In crystals with vacancy-ordered tetragonal $\mathrm{Sr}\mathrm{Fe}{\mathrm{O}}_{3\ensuremath{-}\ensuremath{\delta}}$ as the majority phase $(\ensuremath{\delta}\ensuremath{\sim}0.15)$ a coincident charge-antiferromagnetic ordering transition near $70\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ is considered as the origin of a negative giant MR effect of 90% at $9\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. A positive MR effect is observed in tetragonal and orthorhombic materials with increased oxygen deficiency $(\ensuremath{\delta}=0.19,0.23)$ which are insulating at low temperatures. Phase mixtures can result in a complex superposition of these different MR phenomena. The MR effects in $\mathrm{Sr}\mathrm{Fe}{\mathrm{O}}_{3\ensuremath{-}\ensuremath{\delta}}$ differ from those in manganites as no ferromagnetic states are involved.

Magnetoresistance effects in Sr Fe O 3 − δ : Dependence on phase composition and relation to magnetic and charge order

Growth and characterization of high-quality SrFeOx single crystals

Growth of Sr3Fe2O7−x single crystals by the floating zone method

Floating zone growth of lithium iron (II) phosphate single crystals

We report susceptibility, specific heat, and neutron diffraction measurements on ${\mathrm{NaCu}}_{2}{\mathrm{O}}_{2}$, a spin-$1∕2$ chain compound isostructural to ${\mathrm{LiCu}}_{2}{\mathrm{O}}_{2}$, which has been extensively investigated. Below 12 K, we find a long-range ordered, incommensurate magnetic helix state with a propagation vector similar to that of ${\mathrm{LiCu}}_{2}{\mathrm{O}}_{2}$. In contrast to the Li analog, substitutional disorder is negligible in ${\mathrm{NaCu}}_{2}{\mathrm{O}}_{2}$. We can thus rule out that the helix is significantly influenced by impurities. A spin Hamiltonian with frustrated longer-range exchange interactions provides a good description of both the ordered state and the paramagnetic susceptibility.

https://arxiv.org/pdf/cond-mat/0411753.pdf

Helicoidal magnetic order in the spin-chain compound NaCu 2 O 2

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Growth and characterization of high-quality SrFeOx single crystals

Growth of Sr3Fe2O7−x single crystals by the floating zone method

Floating zone growth of lithium iron (II) phosphate single crystals

Helicoidal magnetic order in the spin-chain compound NaCu 2 O 2