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Why are materials with specific characteristics more abundant than others? This is a fundamental question in materials science and one that is traditionally difficult to tackle, given the vastness of compositional and configurational space. We highlight here the anomalous abundance of inorganic compounds whose primitive unit cell contains a number of atoms that is a multiple of four. This occurrence-named here the rule of four -has to our knowledge not previously been reported or studied. Here, we first highlight the rule's existence, especially notable when restricting oneself to experimentally known compounds, and explore its possible relationship with established descriptors of crystal structures, from symmetries to energies. We then investigate this relative abundance by looking at structural descriptors, both of global (packing configurations) and local (the smooth overlap of atomic positions) nature. Contrary to intuition, the overabundance does not correlate with low-energy or high-symmetry structures; in fact, structures which obey the rule of four are characterized by low symmetries and loosely packed arrangements maximizing the free volume. We are able to correlate this abundance with local structural symmetries, and visualize the results using a hybrid supervised-unsupervised machine learning method., Competing Interests: Competing interestsThere are no competing interests to declare., (© The Author(s) 2024, corrected publication 2024.)

Layered Li-rich/Mn-rich NMC (LMR-NMC) is characterized by high initial specific capacities of more than 250 mA h g -1 , lower cost due to a lower Co content and higher thermal stability than LiCoO 2 . However, its commercialisation is currently still hampered by significant voltage fade, which is caused by irreversible transition metal ion migration to emptied Li positions via tetrahedral interstices upon electrochemical cycling. This structural change is strongly correlated with anionic redox chemistry of the oxygen sublattice and has a detrimental effect on electrochemical performance. In a fully charged state, up to 4.8 V vs. Li/Li + , Mn 4+ is prone to migrate to the Li layer. The replacement of Mn 4+ for an isovalent cation such as Sn 4+ which does not tend to adopt tetrahedral coordination and shows a higher metal-oxygen bond strength is considered to be a viable strategy to stabilize the layered structure upon extended electrochemical cycling, hereby decreasing voltage fade. The influence of Sn 4+ on the voltage fade in partially charged LMR-NMC is not yet reported in the literature, and therefore, we have investigated the structure and the corresponding electrochemical properties of LMR-NMC with different Sn concentrations. We determined the substitution limit of Sn 4+ in Li 1.2 Ni 0.13 Co 0.13 Mn 0.54-x Sn x O 2 by powder X-ray diffraction and transmission electron microscopy to be x≈ 0.045. The limited solubility of Sn is subsequently confirmed by density functional theory calculations. Voltage fade for x = 0 and x = 0.027 has been comparatively assessed within the 3.00 V-4.55 V (vs. Li/Li + ) potential window, from which it is concluded that replacing Mn 4+ by Sn 4+ cannot be considered as a viable strategy to inhibit voltage fade within this window, at least with the given restricted doping level.

Bi 2 Se 3 is a thermoelectric material and a topological insulator. It is slightly conducting in its bulk due to the presence of defects and by controlling the defects different physical properties can be fine tuned. However, studies of the defects in this material are often contradicting or inconclusive. Here, the defect structure of Bi 2 Se 3 is studied with a combination of techniques: high-resolution scanning transmission electron microscopy (HR-STEM), high-resolution energy-dispersive X-ray (HR-EDX) spectroscopy, precession electron diffraction tomography (PEDT), X-ray diffraction (XRD) and first-principles calculations using density functional theory (DFT). Based on these results, not only the observed defects are discussed, but also the discrepancies in results or possibilities across the techniques. STEM and EDX revealed interstitial defects with mainly Bi character in an octahedral coordination in the van der Waals gap, independent of the applied sample preparation method (focused ion beam milling or cryo-crushing). The inherent character of these defects is supported by their observation in the structure refinement of the EDT data. Moreover, the occupancy probability of the defects determined by EDT is inversely proportional to their corresponding DFT calculated formation energies. STEM also showed the migration of some atoms across and along the van der Waals gap. The kinetic barriers calculated using DFT suggest that some paths are possible at room temperature, while others are most probably beam induced.

Solar-energy plays an important role in solving serious environmental problems and meeting high-energy demand. However, the lack of suitable materials hinders further progress of this technology. Here, we present the largest inorganic solar-cell material search to date using density functional theory (DFT) and machine-learning approaches. We calculated the spectroscopic limited maximum efficiency (SLME) using Tran-Blaha modified Becke-Johnson potential for 5097 non-metallic materials and identified 1997 candidates with an SLME higher than 10%, including 934 candidates with suitable convex-hull stability and effective carrier mass. Screening for 2D-layered cases, we found 58 potential materials and performed G 0 W 0 calculations on a subset to estimate the prediction-uncertainty. As the above DFT methods are still computationally expensive, we developed a high accuracy machine learning model to pre-screen efficient materials and applied it to over a million materials. Our results provide a general framework and universal strategy for the design of high-efficiency solar cell materials. The data and tools are publicly distributed at: https://www.ctcms.nist.gov/~knc6/JVASP.html, https://www.ctcms.nist.gov/jarvisml/, https://jarvis.nist.gov/ and https://github.com/usnistgov/jarvis.

Copper chalcogenides find applications in different domains including photonics, photothermal therapy and photovoltaics. CuTe nanocrystals have been proposed as an alternative to noble metal particles for plasmonics. Although it is known that deviations from stoichiometry are a prerequisite for plasmonic activity in the near-infrared, an accurate description of the material and its (optical) properties is hindered by an insufficient understanding of the atomic structure and the influence of defects, especially for materials in their nanocrystalline form. We demonstrate that the structure of Cu 1.5±x Te nanocrystals can be determined using electron diffraction tomography. Real-space high-resolution electron tomography directly reveals the three-dimensional distribution of vacancies in the structure. Through first-principles density functional theory, we furthermore demonstrate that the influence of these vacancies on the optical properties of the nanocrystals is determined. Since our methodology is applicable to a variety of crystalline nanostructured materials, it is expected to provide unique insights concerning structure-property correlations.

Correction for 'First-principles analysis of the spectroscopic limited maximum efficiency of photovoltaic absorber layers for CuAu-like chalcogenides and silicon' by Marnik Bercx et al., Phys. Chem. Chem. Phys., 2016, 18, 20542-20549.

Chalcopyrite semiconductors are of considerable interest for application as absorber layers in thin-film photovoltaic cells. When growing films of these compounds, however, they are often found to contain CuAu-like domains, a metastable phase of chalcopyrite. It has been reported that for CuInS2, the presence of the CuAu-like phase improves the short circuit current of the chalcopyrite-based photovoltaic cell. We investigate the thermodynamic stability of both phases for a selected list of I-III-VI2 materials using a first-principles density functional theory approach. For the CuIn-VI2 compounds, the difference in formation energy between the chalcopyrite and CuAu-like phase is found to be close to 2 meV per atom, indicating a high likelihood of the presence of CuAu-like domains. Next, we calculate the spectroscopic limited maximum efficiency (SLME) of the CuAu-like phase and compare the results with those of the corresponding chalcopyrite phase. We identify several candidates with a high efficiency, such as CuAu-like CuInS2, for which we obtain an SLME of 29% at a thickness of 500 nm. We observe that the SLME can have values above the Shockley-Queisser (SQ) limit, and show that this can occur because the SQ limit assumes the absorptivity to be a step function, thus overestimating the radiative recombination in the detailed balance approach. This means that it is possible to find higher theoretical efficiencies within this framework simply by calculating the J-V characteristic with an absorption spectrum. Finally, we expand our SLME analysis to indirect band gap absorbers by studying silicon, and find that the SLME quickly overestimates the reverse saturation current of indirect band gap materials, drastically lowering their calculated efficiency.