Solids, Volume 6, Issue 4 (December 2025) – 8 articles

Most machine learning algorithms operate on vectorized data with Euclidean structures because of the significant mathematical advantages offered by Hilbert space, but improved representational efficiency may offset more involved learning on non-Euclidean structures. Recently, a method that integrates the marginalized graph kernel into the Gaussian process regression framework was used to learn directly on molecular graphs. Here, we describe an implementation of this method for crystalline materials based on effective crystal graph representations: the molecular graphs of 128-atom supercells of body-centered cubic (BCC) iron with periodic boundary conditions. Regressors trained on hundreds of time steps of a density functional theory molecular dynamics (DFT-MD) simulation achieved root mean square errors of less than 5 meV/atom. The mechanical stability of BCC iron was investigated at high pressure and elevated temperature using regressors trained on short DFT-MD runs, including at conditions found in the inner core of the earth. Phonon dispersions obtained from the short runs show that BCC iron is mechanically stable at 360 GPa when the temperature is above 2500 K. Atoms in the super cell were displaced in the direction of the first, second, and third nearest-neighbors from selected configurations that included thermal atomic displacements, and forces exerted on the displaced atoms were computed by numerical differentiation of the regressors. Full article

Phonons, the quantized lattice vibrations, are fundamental for a wide range of phenomena in condensed matter systems. In particular, low-frequency phonons significantly influence electrical conductivity, thermal transport, and the optical properties of solid-state materials. Although there is considerable literature on cadmium sulfide (CdS) phonons—studied, for example, using resonance Raman spectroscopy—up-to-date information on the low-frequency phonons of this important semiconductor is still lacking. In this study, Raman spectroscopy under off- and near-resonance conditions is employed to investigate the low-frequency phonon in wurtzite CdS single crystals. Under off-resonance conditions, the spectrum exhibits multiple low-intensity peaks, which were analyzed through curve fitting. In contrast, the near-resonance spectrum shows an intense, broad band that was deconvoluted into its constituent components, including an antiresonance feature that was mathematically modeled for the first time in CdS. The results demonstrate that Raman scattering intensity in both regimes provides valuable insights into the low-frequency phonon modes of CdS. These findings enhance our understanding of the material’s vibrational properties and may facilitate the development of more efficient CdS-based optoelectronic devices. Full article

Composites in which finely dispersed particles of the metallic phase are uniformly distributed over the surface of expanded graphite can be used as magnetic sorbents for crude oil and petroleum products, as well as a basis for creating screens that protect against electromagnetic radiation. The literature describes various approaches to obtaining such materials, but from a technological point of view, the most promising is the method in which the formation of a metal-containing phase on the surface of expanded graphite is directly combined with its expansion. For this purpose, graphite intercalation compounds with chlorides of metals of the iron triad (GIC-MCl_x) were obtained: GIC-FeCl₃ of I-VII stages, GIC-CoCl₂ of I/II stage and GIC-NiCl₂ of II/III stage, which were treated with liquid NH₃ or CH₃NH₂ in order to obtain an occlusive complex, which, due to the presence of a large amount of bound RNH₂, would be capable of effective thermal expansion during heating in an inert atmosphere with the formation of low-density expanded graphite, and the presence of reducing properties in ammonia and methylamine would lead to the reduction of the metal from chloride. The structure of GIC-MCl_x and GIC-MCl_x treated by NH₃ and CH₃NH₂ was investigated by XRD analysis and Mossbauer spectroscopy. The composition of the metal-containing phase in expanded graphite/metal composite was determined by XRD analysis and its quantity by the gravimetric method. The distribution of metals particles is investigated by SEM, TEM and EDX methods. Expanded graphite/metal composites are characterized by the high saturation magnetization (up to ≈ 50 emu/g) at a bulk density of 4–6 g/L. Full article

This study presents a green and sustainable approach for synthesizing zinc oxide nanoparticles (ZnO-NPs) using Melia azedarach leaf extract as a reducing and stabilizing agent, with zinc acetate as the precursor. The synthesized nanoparticles were thoroughly characterized to assess their structural, morphological, and physicochemical properties, revealing nanoscale dimensions, enhanced crystallinity, and improved stability compared to commercial ZnO. Controlled release experiments under plant-relevant pH conditions demonstrated a gradual and sustained release of Zn²⁺ ions, accompanied by buffering effects and re-precipitation of Zn(OH)₂, highlighting their potential for long-term nutrient availability in soil systems. Unlike conventional studies that focus mainly on synthesis or characterization, this work emphasizes the functional performance of ZnO-NPs as nanofertilizers, combining eco-friendly production with practical agricultural applications. The plant-mediated synthesis yielded nanoparticles with uniform size distribution, enhanced dispersion, and stability, which are critical for efficient nutrient delivery and persistence in soil. Overall, this study provides a cost-effective, scalable, and environmentally benign strategy for producing ZnO nanoparticles and offers valuable insights into the development of sustainable nanofertilizers aimed at improving crop nutrition, soil fertility, and agricultural productivity. Full article

This study investigates CaCu_3−xSr_xTi₄O₁₂ (CCSTO) systems synthesized using the solid-state method, with x compositions of 0.00, 0.15, and 3.00. The samples were modified using 6 wt% graphene oxide (GO) and reduced GO (rGO) prepared via Hummer’s method to evaluate their performance as electrodes in supercapacitors. The results indicate that the addition of 6wt% rGO to CCTO (CCTO-6rGO) led to an improvement in specific capacitance, reaching 237.76 mF·g⁻¹ at a scan rate of 10 mV/s, compared to 29.86 mF·g⁻¹ for pure CCTO and only 7.83 mF·g⁻¹ for CCTO-6GO, suggesting that rGO enhances charge storage. For the CCTO15Sr samples, CCTO15Sr-6rGO exhibited the highest specific capacitance, with 321.63 mF·g⁻¹ at 10 mV/s, surpassing both pure CCTO15Sr (80.19 mF·g⁻¹) and CCTO15Sr-6GO (25.73 mF·g⁻¹). These results stem from oxygen and metal vacancies, which aid charge accumulation and ion diffusion. In contrast, adding GO generally reduced specific capacitance in all samples. The findings highlight CCSTO’s potential—especially with rGO modification—as a supercapacitor electrode while also indicating areas for further optimization. Full article

This study investigates the microstructure and mechanical properties of copper (Cu) and graphene/Cu (Gr/Cu) composites produced via high-pressure torsion (HPT) under 5 GPa at room temperature. Microstructural analysis revealed significant grain refinement, with average grain sizes of 0.39 μm for pure Cu and 0.35 μm for Gr/Cu composite. The Gr/Cu composite exhibited slightly higher microstrains and effective stacking fault energy (SFE). Tensile tests showed ultimate tensile strengths of 689 MPa (pure Cu) and 674 MPa (Gr/Cu), with the latter demonstrating improved ductility (~10% elongation). Ab initio calculations confirmed a 27% increase in SFE for Gr/Cu, aligning with experimental results. These findings highlight the potential of Gr/Cu composites for applications requiring high strength and efficient heat dissipation. Full article

Nuclear fuel cladding serves as the primary barrier to the release of radioactive fission products and is subjected to high-temperature and high-pressure environments during both normal reactor operation and accident scenarios such as loss of coolant accidents (LOCAs). Predicting the burst behavior of cladding is essential for ensuring structural integrity, especially under varying heating rates—an aspect inadequately addressed in existing empirical models. In this study, a finite element-based damage model is developed to simulate the ballooning and burst behavior of Zircaloy-4 cladding. The model incorporates creep deformation, stress triaxiality, and time-dependent damage accumulation. Material behavior is characterized using experimentally determined creep constants and the model is calibrated against burst test data from the literature. A new heating-rate-dependent burst correlation is proposed based on model outputs. The results indicate that increasing the heating rate raises the burst temperature due to reduced exposure time in the temperature regime where creep damage accumulates significantly. The model accurately reproduces burst behavior across a wide range of internal pressures (1–10 MPa) and heating rates (5–100 °C/s). The newly developed correlation improves predictive capability in accident analysis tools and can be directly implemented into safety analysis codes for Indian pressurized heavy water reactors (PHWRs), contributing to enhanced reactor safety evaluations. Full article

This work presents a theoretical investigation of ionic conductivity in cubic zirconia (c-ZrO₂) doped with magnesium, using density functional theory (DFT) with the hybrid B3LYP functional as implemented in the CRYSTAL23 software package. It was found that the spatial arrangement of magnesium atoms and oxygen vacancies significantly affects the energy barriers for oxygen ion migration. Configurations with magnesium located along and outside the migration path were analyzed. The results show that when Mg²⁺ is positioned along the migration trajectory and near an oxygen vacancy, stable defect complexes are formed with minimal migration barriers ranging from 0.96 to 1.32 eV. An increased number of Mg atoms can lead to a further reduction in the barrier, although in certain configurations the barriers increase up to 3.0–4.6 eV. When doping occurs outside the migration path, the energy profile remains symmetric and moderate (0.9–1.1 eV), indicating only a weak background influence. These findings highlight the critical role of coordinated distribution of Mg atoms and oxygen vacancies along the migration pathway in forming efficient ion-conducting channels. This insight offers potential for designing high-performance zirconia-based electrolytes for solid oxide fuel cells and sensor applications. Full article