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Gravitational lensing has developed into a tool of observational astronomy. It is used to detect the presence and distribution of dark matter, provide a "natural telescope" for observing distant galaxies, and to obtain an independent estimate of the Hubble constant. Statistical evaluations of lensing data provide valuable insight into the structural evolution of galaxies.[115]
Whenever the ratio of an object's mass to its radius becomes sufficiently large, general relativity predicts the formation of a black hole, a region of space from which nothing, not even light, can escape. In the currently accepted models of stellar evolution, neutron stars of around 1.4 solar masses, and stellar black holes with a few to a few dozen solar masses, are thought to be the final state for the evolution of massive stars.[123] Usually a galaxy has one supermassive black hole with a few million to a few billion solar masses in its center,[124] and its presence is thought to have played an important role in the formation of the galaxy and larger cosmic structures.[125]
Astronomical observations of the cosmological expansion rate allow the total amount of matter in the universe to be estimated, although the nature of that matter remains mysterious in part. About 90% of all matter appears to be dark matter, which has mass (or, equivalently, gravitational influence), but does not interact electromagnetically and, hence, cannot be observed directly.[141] There is no generally accepted description of this new kind of matter, within the framework of known particle physics[142] or otherwise.[143] Observational evidence from redshift surveys of distant supernovae and measurements of the cosmic background radiation also show that the evolution of our universe is significantly influenced by a cosmological constant resulting in an acceleration of cosmic expansion or, equivalently, by a form of energy with an unusual equation of state, known as dark energy, the nature of which remains unclear.[144]
To understand Einstein's equations as partial differential equations, it is helpful to formulate them in a way that describes the evolution of the universe over time. This is done in "3+1" formulations, where spacetime is split into three space dimensions and one time dimension. The best-known example is the ADM formalism.[175] These decompositions show that the spacetime evolution equations of general relativity are well-behaved: solutions always exist, and are uniquely defined, once suitable initial conditions have been specified.[176] Such formulations of Einstein's field equations are the basis of numerical relativity.[177]
One attempt to overcome these limitations is string theory, a quantum theory not of point particles, but of minute one-dimensional extended objects.[197] The theory promises to be a unified description of all particles and interactions, including gravity;[198] the price to pay is unusual features such as six extra dimensions of space in addition to the usual three.[199] In what is called the second superstring revolution, it was conjectured that both string theory and a unification of general relativity and supersymmetry known as supergravity[200] form part of a hypothesized eleven-dimensional model known as M-theory, which would constitute a uniquely defined and consistent theory of quantum gravity.[201]
In general, poor thermal stability and cycle performance of nickel-rich layered oxide mainly stem from chemical reactions between delithiated cathodes and nonaqueous electrolytes at elevated temperature, which cause decomposition of cathode material and oxidation of electrolytes. The overdelithiated cathode would release oxygen from its lattice due to its high oxidability. Further, the electrolyte could react with oxygen to generate heat. If the heat generation and accumulation are more than its dissipation, a catastrophic failure of the cell will happen [81]. For the sake of designing safe cathode materials with high capacity, mechanisms of structure evolution, thermal stability and oxygen release in cathode materials during cycling should be thoroughly demonstrated. For example, some researchers investigated the structure evolution mechanism of NCM111 during cycling by in situ high-resolution synchrotron radiation diffraction and neutron powder diffraction. As shown in Fig. 3a and b, when the charge voltage is below 4.2 V, NCM111 maintains layered hexagonal phase H1 structure with slightly increased c and decreased a lattice parameters. When the voltage region is from 4.2 to 4.4 V, a new hexagonal phase H2 is detected and gradually intensified. When it is charged to a high voltage above 4.6 V, irreversible structure change appears from the original layered structure phase to a layered hexagonal phase H3 and a cubic spinel phase. After full lithiation, lattice parameters do not go back to its original ones, indicative of an irreversible structure evolution after charging to high voltage [82].
In the microlevel, Ni-rich cathode materials consist of some secondary micrometer particles, which is aggregated by primary micrometer particles. The microstructural evolution of the single Li(Ni0.8Co0.15Al0.05)O2 particle during electrochemical cycling was further demonstrated by using in situ electron microscopy (Fig. 3f, g). Compared with the as-prepared particles, the particles after three cycles showed obvious cracks, which allow penetration of electrolytes between primary particles. The above result suggests that loss of grain-to-grain connectivity between particles would result in capacity fading and performance degradation [84]. Furthermore, more exposed cathode surface during cycling will intensify reactions between cathodes and electrolytes, which would aggravate capacity fade.
Above all, with the aid of advanced characterization techniques, the reasons, for structure evolution as well as side reaction between the electrolytes and the primary particles of cathode materials, have been deeply understood in the microlevel, which would guide us to design safe cathodes.
Design better particles The layered oxide materials are commonly prepared by the co-precipitation method with round-shape primary particles randomly aggregating into large secondary particles. Anisotropic lattice volume expansion or contraction between the primary particles during cycling will result in microcracks, and electrolytes will penetrate into microcracks, causing severe side reaction.
Another way to eliminate cracks in the secondary particles is directly using single-crystal cathodes. Dahn et al. compared single-crystal and polycrystalline NCM523-positive electrode materials for high-voltage LIBs. The results show that single-crystal materials yield to longer lifetime for LIBs at both 40 and 55 C when tested at an upper cutoff potential of 4.4 V. The reasons for superior performance of the single-crystal-based cells were explored by using thermogravimetric analysis/mass spectrometry experiments on the charged electrode materials, showing that single-crystal materials are extremely resistant to oxygen loss below 100 C compared with the polycrystalline materials [108].
A sequence of four optical micrographs showing the time evolution of color in the electrode: a-I the fresh electrode, a-II charge for 6 h, a-III charge for 9 h and a-IV charge for 13 h. Reproduced with permission from Ref. [226]. Copyright 2010, Elsevier. SEM images of the bulk LiCoO2 electrode synthesis by magnetic templating b the top view and c the side view. Reproduced with permission from Ref. [227]. Copyright 2016, Nature Publishing Group. d Schematic diagram of the working mechanism of the carbon framework-based LFP Li-ion battery. SEM images of the carbon framework-based LFP electrode: e the top view, f the side view and g the enlarged view of the side of the electrode. 2ff7e9595c
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