Research Article
The Melting Temperature of FCC Crystal Na Without the Criterion Lindemann's Melting Law
Nand Kishor*
,
Amar Kumar
Issue:
Volume 3, Issue 3, September 2026
Pages:
71-81
Received:
21 March 2026
Accepted:
9 April 2026
Published:
17 August 2026
Abstract: The Lindemann’s melting criterion, which posits that a crystal melts when the root-mean-square atomic displacement reaches a critical fraction of the interatomic distance, has been a cornerstone of simple melting theory for over a century. However, its phenomenological nature and system-dependent critical value limit its predictive power from first principles. This work presents a determination of the melting temperature (Tm) of face-centered cubic (FCC) crystalline sodium using molecular dynamics (MD) simulations, deliberately bypassing the Lindemann’s criterion. We employ a well-established embedded-atom method (EAM) potential to model interatomic interactions. The melting point is identified directly from the collapse of long-range order by monitoring the evolution of potential energy, radial distribution function, and mean-squared displacement (MSD) upon heating. Furthermore, we utilize the rigorous coexistence method (or "solid-liquid interface" method), where a direct two-phase simulation of solid FCC Na in contact with liquid Na is performed at various temperatures to pinpoint the true thermodynamic melting point as the state where the interface remains stationary. Our results for FCC Na, a model alkali metal, provide a benchmark melting temperature derived solely from direct observation of the solid-liquid phase transition. This approach not only offers a more fundamental determination of Tm but also allows for a critical assessment of the validity and limitations of the Lindemann’s rule when compared a posteriori with the computed atomic vibrational amplitudes at the predicted melting point.
Abstract: The Lindemann’s melting criterion, which posits that a crystal melts when the root-mean-square atomic displacement reaches a critical fraction of the interatomic distance, has been a cornerstone of simple melting theory for over a century. However, its phenomenological nature and system-dependent critical value limit its predictive power from first...
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Research Article
Study the Melting Curves of Metals to Very High Pressure and Temperature Can Be Predicted by the Theoretical Model in Lindemann’s Melting Law
Nand Kishor*,
Amar Kumar
Issue:
Volume 3, Issue 3, September 2026
Pages:
82-88
Received:
21 March 2026
Accepted:
9 April 2026
Published:
17 August 2026
Abstract: The study of melting curves of metals under very high pressures and temperatures is essential for understanding their thermodynamic and structural behavior in extreme conditions. In this research, a theoretical model has been developed to predict the pressure dependence of the melting temperature for selected metals based on the Lindemann’s melting law and its modifications. The model relates the melting temperature to vibrational properties of the lattice, atomic volume, and Grüneisen parameter, enabling estimation of melting points at pressures beyond experimental limits. The theoretical framework assumes that melting occurs when the amplitude of atomic vibrations reaches a critical fraction of the interatomic spacing, and this criterion is used to derive a quantitative relationship between pressure and melting temperature. The proposed model has been applied to various metals such as aluminum, copper, iron, and nickel to compute their melting curves up to several hundred gigapascals. The calculated results show a strong agreement with available experimental and simulation data, indicating that the model effectively captures the essential physics of the melting process. The study reveals that the melting temperature increases nonlinearly with pressure, primarily due to the compression of atomic volume and enhanced lattice stability at high pressures. Furthermore, the model provides valuable insights into the influence of atomic mass, bulk modulus, and an harmonic effects on the melting behavior of metals. Such theoretical predictions are particularly important for fields like materials science, geophysics, and planetary science, where direct experimental measurements at extreme conditions are challenging. Overall, the developed model offers a reliable and simplified approach to estimate melting curves, contributing to a deeper understanding of phase stability and thermodynamic properties of metals under extreme environments.
Abstract: The study of melting curves of metals under very high pressures and temperatures is essential for understanding their thermodynamic and structural behavior in extreme conditions. In this research, a theoretical model has been developed to predict the pressure dependence of the melting temperature for selected metals based on the Lindemann’s melting...
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Research Article
Microstructural Characterization of Lateritic Soil Stabilized with Nano-Silica and Plantain Peel Ash: SEM, EDX, and XRD Analysis
Ugbodaga Emesomiadeh Mercy,
Wasiu John,
Ibrahim Abdulrazaq Olayinka*
Issue:
Volume 3, Issue 3, September 2026
Pages:
89-103
Received:
21 April 2026
Accepted:
8 August 2026
Published:
2 September 2026
Abstract: Using scanning electron microscopy (SEM), energy dispersive X-ray spectroscopy (EDX), and X-ray diffraction (XRD), this study examines the microstructural changes of lateritic soil stabilized with plantain peel ash (PPA) and nano-silica (NS) from Ibienafe, South Ibie, Edo State, Nigeria. Sample 1 (2.5% PPA), Sample 2 (5.0% PPA), Sample 3 (2.5% NS), Sample 4 (5.0% PPA + 2.5% NS), and Sample 5 (5.0% NS) were the five dry weight soil mixes that were made. With extensive calcium silicate hydrate (C-SH) and calcium aluminate hydrate (C-A-H) gel formation, needle-like crystalline bridges, and few voids, Sample 4 showed the densest matrix, according to SEM analysis. This indicated strong pozzolanic bonding. EDX verified that Sample 4 had low carbon (3.70%) and high silica (15.45%) and alumina (16.46%), indicating optimal reactivity. Friedelite and DAP-O12 were detected by XRD in Sample 4, indicating advanced aluminosilicate bonding, whereas inert quartz and kaolinite were found in Samples 1 and 2, indicating limited pozzolanic activity. Although Sample 5 contained trace actinolite, indicating possible long-term durability concerns, Samples 3 and 5 showed cristobalite and alite, confirming silica-driven cementation. In Sample 4, the synergistic combination of 5.0% PPA and 2.5% NS produced the most robust microstructure and the highest California Bearing Ratio (48.55%), providing a sustainable and environmentally friendly method of lateritic soil stabilization for geotechnical applications. These results demonstrate how well agro-waste and nanomaterial blends can improve soil performance while supporting environmentally friendly building techniques.
Abstract: Using scanning electron microscopy (SEM), energy dispersive X-ray spectroscopy (EDX), and X-ray diffraction (XRD), this study examines the microstructural changes of lateritic soil stabilized with plantain peel ash (PPA) and nano-silica (NS) from Ibienafe, South Ibie, Edo State, Nigeria. Sample 1 (2.5% PPA), Sample 2 (5.0% PPA), Sample 3 (2.5% NS),...
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