• Journal for History of Mathematics
• /
• v.19 no.4
• /
• pp.97-106
• /
• 2006

The lattice originated from logic, not mathematics. Around 1880, Peirce thought that all the lattices were distributives, however $Schr{\"{o}}der$ corrected the error around 1890. In 1993, Birkhoff used the term lattice for the first time that had a different meaning from today's lattice. This paper introduces Peirce, and studies correlation among atomic lattices, atomistic lattices, J-lattices, strong lattices and distributive lattices.

• Journal of the Mineralogical Society of Korea
• /
• v.30 no.4
• /
• pp.161-172
• /
• 2017

Clay minerals play a major role in the geochemical cycles of metals in the Critical Zone, the Earth surface-layer ranging from the groundwater bottom to the tree tops. Atomistic scale research of the very fine particles can help understand the fundamental mechanisms of the important geochemical processes and possibly apply to development of hybrid nanomaterials. Molecular dynamics (MD) simulations can provide atomistic level insights into the crystal structures of clay minerals and the chemical reactivity. Classical MD simulations use a force field which is a parameter set of interatomic pair potentials. The ClayFF force field has been widely used in the MD simulations of dioctahedral clay minerals as the force field was developed mainly based on dioctahedral phyllosilicates. The ClayFF is often used also for trioctahedral mineral simulations, but disagreement exits in selection of the interatomic potential parameters, particularly for Mg atom-types of the octahedral sheet. In this study, MD simulations were performed for trioctahedral clay minerals such as brucite, lizardite, and talc, to test how the two different Mg atom types (i.e., 'mgo' or 'mgh') affect the simulation results. The structural parameters such as lattice parameters and interatomic distances were relatively insensitive to the choice of the parameter, but the vibrational power spectra of hydroxyls were more sensitive to the choice of the parameter particularly for lizardite.

• Korean Journal of Mineralogy and Petrology
• /
• v.33 no.3
• /
• pp.143-152
• /
• 2020

Birnessite is a layered manganese oxide mineral with ~7 Å of d-spacing. Because of its high cation exchange capacity, birnessite greatly impacts the chemical compositions of ground water and fluids in sediment pores. Understanding the cation exchange mechanisms requires atomistic investigations of the crystal structures and coordination environments of hydrated cations in the interlayer. In this study, we conducted classical molecular dynamics (MD) simulations, an atomistic simulation method of computational mineralogy, for triclinic Na-birnessite and K-birnessite whose chemical formula are from previous experiments. We report our MD simulation results of the crystal structures, coordination environments of Na⁺ and K⁺, and the polytypes of birnessite and compare them with available experimental results. The simulation results well reproduced experimental lattice parameters and provided atomic level information for the interlayer cation and water molecule sites that are difficult to distinguish in X-ray experiments. We also report that the polytype of the Mn octahedral sheets is identical between Na- and K-birnessite, but the cation positions differ from each other, demonstrating a correlation between the coordination environment of the interlayer cations and the crystal lattice parameters. This study shows that MD simulations are very promising in elucidating ion exchange reactions of birnessite.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.32 no.7
• /
• pp.60-68
• /
• 2004

High velocity impacts are accompanied with large deformations, which generate a large amount of heat due to plastic works, resulting in a significant temperature rise of the material. Because the elevated temperature affects the dynamic properties of materials, it is important to predict the temperature rise during high-stram-rate deformations. Both existing vacancies and excess vacancies are credited to the stored energy, yet it is difficult to distinguish one from another in contribution to the stored energy using macroscopic level materials models. In this study, an atomistic material model for fee materials such as copper is set up to calculate the stored energy using molecular dynamics (MD) simulations. It is concluded that excess vacancies play an important role for the stored energy during a high-strain-rate deformation.

• Journal of the Mineralogical Society of Korea
• /
• v.27 no.4
• /
• pp.271-281
• /
• 2014

The physicochemical properties of clay minerals have been investigated at the atomistic to nano scale. The microscopic studies are often challenging to perform by using experimental approaches alone. In particular, hydroxyl groups of octahedral sheets in 2:1 clay minerals have been hypothesized to impact the sorption process of metal cations; however, X-ray based techniques alone, a common tool for mineral structure examination, cannot properly test the hypothesis. The current study has examined whether computational mineralogy techniques can be applied to examine the hydroxyl structures of clay minerals. Based on quantum-mechanics and molecular-mechanics computational methods, geometry optimizations were carried out for representative dioctahedral and trioctahedral phyllosilicate minerals. Both methods well reproduced the experimental lattice parameters; however, for structural distortion occurring in the tetrahedral or octahedral sheets, molecular mechanics showed significant deviations from experimental data. The orientation angle of the hydroxyl with respect to (001) basal plane is determined by the balance of repulsion between the hydroxyl proton and Si cations of tetrahedral sites; the quantum-mechanics method predicted $25-26^{\circ}$ for the angle, whereas the angle predicted by the molecular-mechanics method was much higher by $10^{\circ}$ (i.e., $35^{\circ}$). These results demonstrate that computational mineralogy techniques are a reliable tool for clay mineral studies and can be used to further elucidate the roles of hydroxyls in metal sorption process.