Though extensively studied, hardness, defined as the resistance of a material to deformation, still remains a challenging issue for a formal theoretical description due to its inherent mechanical complexity. The widely applied Teter's empirical correlation between hardness and shear modulus has been considered to be not always valid for a large variety of materials. Here, inspired by the classical work on Pugh's modulus ratio, we develop a theoretical model which establishes a robust correlation between hardness and elasticity for a wide class of materials, including bulk metallic glasses, with results in very good agreement with experiment. The simplified form of our model also provides an unambiguous theoretical evidence for Teter's empirical correlation.

Previous research has demonstrated that AtPHR1 plays a central role in phosphate (Pi)-starvation signaling in Arabidopsis thaliana. In this work, two OsPHR genes from rice (Oryza sativa) were isolated and designated as OsPHR1 and OsPHR2 based on amino acid sequence homology to AtPHR1. Their functions in Pi signaling in rice were investigated using transgenic plants. Our results showed that both OsPHR1 and OsPHR2 are involved in Pi-starvation signaling pathway by regulation of the expression of Pi-starvation-induced genes, whereas only OsPHR2 overexpression results in the excessive accumulation of Pi in shoots under Pi-sufficient conditions. Under Pi-sufficient conditions, overexpression of OsPHR2 mimics Pi-starvation stress in rice with enhanced root elongation and proliferated root hair growth, suggesting the involvement of OsPHR2 in Pi-dependent root architecture alteration by both systematic and local pathways. In OsPHR2-overexpression plants, some Pi transporters were upregulated under Pi-sufficient conditions, which correlates with the strongly increased content of Pi. The mechanism behind the OsPHR2 regulated Pi accumulation will provide useful approaches to develop smart plants with high Pi efficiency.

The search for new two-dimensional monolayers with diverse electronic properties has attracted growing interest in recent years. Here, we present an approach to construct MA2Z4 monolayers with a septuple-atomic-layer structure, that is, intercalating a MoS2-type monolayer MZ2 into an InSe-type monolayer A2Z2. We illustrate this unique strategy by means of first-principles calculations, which not only reproduce the structures of MoSi2N4 and MnBi2Te4 that were already experimentally synthesized, but also predict 72 compounds that are thermodynamically and dynamically stable. Such an intercalated architecture significantly reconstructs the band structures of the constituents MZ2 and A2Z2, leading to diverse electronic properties for MA2Z4, which can be classified according to the total number of valence electrons. The systems with 32 and 34 valence electrons are mostly semiconductors. Whereas, those with 33 valence electrons can be nonmagnetic metals or ferromagnetic semiconductors. In particular, we find that, among the predicted compounds, (Ca,Sr)Ga2Te4 are topologically nontrivial by both the standard density functional theory and hybrid functional calculations. While VSi2P4 is a ferromagnetic semiconductor and TaSi2N4 is a type-I Ising superconductor. Moreover, WSi2P4 is a direct gap semiconductor with peculiar spin-valley properties, which are robust against interlayer interactions. Our study thus provides an effective way of designing septuple-atomic-layer MA2Z4 with unusual electronic properties to draw immediate experimental interest.

Are social media posts with pictures more popular than those without? Why do pictures with certain characteristics induce higher engagement than some other pictures? Using data sets of social media posts about major airlines and sport utility vehicle brands collected from Twitter and Instagram, the authors empirically examine the influence of image content on social media engagement. After accounting for selection bias on the inclusion of image content, the authors find a significant and robust positive mere presence effect of image content on user engagement in both product categories on Twitter. They also find that high-quality and professionally shot pictures consistently lead to higher engagement on both platforms for both product categories. However, the effect of colorfulness varies by product category, while the presence of human face and image–text fit can induce higher user engagement on Twitter but not on Instagram. These findings shed light on how to improve social media engagement using image content.