Li-ion batteries gradually lose their capacity with time and use; therefore, ageing forecasts are key to designs of battery powered systems. So far, cell-type-specific studies without standardised testing practices have lead to a variety of ageing mo
dels in which generality, simplicity, and accuracy seem exclusive. Previous studies hint to an interplay of multiple mechanisms leading to capacity loss, which depend on cell chemistry and are affected by temperature, state of charge, and cycling rate. Here we show that, despite this complexity, the time dependence of the actual capacity follows a unique master curve, for several cell types aged under various different conditions. We discuss the statistical origin of this common behaviour, and the testing practice required for the characterisation of a model. The master curve is a stretched exponential that describes many other phenomena in nature and is theoretically justified within a diffusion-to-traps depletion model. These findings provide a simple and broadly applicable framework for accurate life-time predictions.
The compound EuCo{2-y}As2 with the tetragonal ThCr2Si2 structure is known to contain Eu{+2} ions with spin S = 7/2 that order below a temperature TN = 47 K into an antiferromagnetic (AFM) proper helical structure with the ordered moments aligned in t
he tetragonal ab plane, perpendicular to the helix axis along the c axis, with no contribution from the Co atoms. Here we carry out a detailed investigation of the properties of single crystals. Enhanced ordered and effective moments of the Eu spins are found in most of our crystals. Electronic structure calculations indicate that the enhanced moments arise from polarization of the d bands, as occurs in ferromagnetic Gd metal. Electrical resistivity measurements indicate metallic behavior. The low-field in-plane magnetic susceptibilities chi{ab}(T < TN) for several crystals are reported that are fitted well by unified molecular field theory (MFT), and the Eu-Eu exchange interactions Jij are extracted from the fits. High-field magnetization M data for magnetic fields H||ab reveal what appears to be a first-order spin-flop transition followed at higher field by a second-order metamagnetic transition of unknown origin, and then by another second-order transition to the paramagnetic (PM) state. For H||c, the magnetization shows only a second-order transition from the canted AFM to the PM state, as expected. The critical fields for the AFM to PM transition are in approximate agreement with the predictions of MFT. Heat capacity Cp measurements in zero and high H are reported. Phase diagrams for H||c and H||ab versus T are constructed from the high-field M(H,T) and Cp(H,T) measurements. The magnetic part Cmag(T, H = 0) of Cp(T, H = 0) is extracted and is fitted rather well below TN by MFT, although dynamic short-range AFM order is apparent in Cmag(T) up to about 70 K, where the molar entropy attains its high-T limit of R ln8.
The metallic compound EuCo2P2 with the body-centered tetragonal ThCr2Si2 structure containing Eu spins 7/2 was previously shown from single-crystal neutron diffraction measurements to exhibit a helical antiferromagnetic (AFM) structure below TN = 66.
5 K with the helix axis along the c axis and with the ordered moments aligned within the ab-plane. Here we report crystallography, electrical resistivity, heat capacity, magnetization and magnetic susceptibility measurements on single crystals of this compound. We demonstrate that EuCo2P2 is a model molecular-field helical Heisenberg antiferromagnet from comparisons of the anisotropic magnetic susceptibility chi, high-field magnetization and magnetic heat capacity of EuCo2P2 single crystals at temperature T < TN with the predictions of our recent formulation of molecular field theory. Values of the Heisenberg exchange interactions between the Eu spins are derived from the data. The low-T magnetic heat capacity ~ T^3 arising from spin-wave excitations with no anisotropy gap is calculated and found to be comparable to the lattice heat capacity. The density of states at the Fermi energy of EuCo2P2 and the related compound BaCo2P2 are found from the heat capacity data to be large, 10 and 16 states/eV per formula unit for EuCo2P2 and BaCo2P2, respectively. These values are enhanced by a factor of ~2.5 above those found from DFT electronic structure calculations for the two compounds. The calculations also find ferromagnetic Eu-Eu exchange interactions within the ab-plane and AFM interactions between nearest- and next-nearest planes, in agreement with the MFT analysis of chi{ab}(T < TN).
Geometrization of dynamics consists of representing trajectories by geodesics on a configuration space with a suitably defined metric. Previously, efforts were made to show that the analysis of dynamical stability can also be carried out within geome
trical frameworks, by measuring the broadening rate of a bundle of geodesics. Two known formalisms are via Jacobi and Eisenhart metrics. We find that this geometrical analysis measures the actual stability when the length of any geodesic is proportional to the corresponding time interval. We prove that the Jacobi metric is not always an appropriate parametrization by showing that it predicts chaotic behavior for a system of harmonic oscillators. Furthermore, we show, by explicit calculation, that the correspondence between dynamical- and geometrical-spread is ill-defined for the Jacobi metric. We find that the Eisenhart dynamics corresponds to the actual tangent dynamics and is therefore an appropriate geometrization scheme.
A relation between the freezing temperature ($T^{}_{rm g}$) and the exchange couplings ($J^{}_{ij}$) in metallic spin-glasses is derived, taking the spin-correlations ($G^{}_{ij}$) into account. This approach does not involve a disorder-average. The
expansion of the correlations to first order in $J^{}_{ij}/T^{}_{rm g}$ leads to the molecular-field result from Thouless-Anderson-Palmer. Employing the current theory of the spin-interaction in disordered metals, an equation for $T^{}_{rm g}$ as a function of the concentration of impurities is obtained, which reproduces the available data from {sl Au}Fe, {sl Ag}Mn, and {sl Cu}Mn alloys well.
Alkaline earth mono-silicides ({AE}Si, {AE} $=$ Ca, Sr, Ba) are poor metals and their transport properties are not solely determined by the Zintl anion, in contrast to their Zintl-type composition. Their conducting network is formed by the depopulate
d ${}^{1}_{infty}$[Si$^{2-}$] $pi$-system and {AE}-$d$ states. This justifies the special local coordination of the metal atoms and the planarity of the silicon chains. The low density of carriers seems to be a playground for magnetic instabilities and the triangular prismatic arrangement of {AE} atoms responsible for the observed weak glassy behavior.
In this paper, the general disagreement of the geometrical lyapunov exponent with lyapunov exponent from tangent dynamics is addressed. It is shown in a quite general way that the vector field of geodesic spread $xi^k_G$ is not equivalent to the tang
ent dynamics vector $xi^k_T$ if the parameterization is not affine and that results regarding dynamical stability obtained in the geometrical framework can differ qualitatively from those in the tangent dynamics. It is also proved in a general way that in the case of Jacobi metric -frequently used non affine parameterization-, $xi^k_G$ satisfies differential equations which differ from the equations of the tangent dynamics in terms that produce parametric resonance, therefore, positive exponents for systems in stable regimes.
