• Journal for History of Mathematics
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• v.19 no.4
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• pp.97-106
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• 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 Chungcheong Mathematical Society
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• v.20 no.3
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• pp.211-221
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• 2007

In this paper, we define ${\bigwedge}$-structure, ${\bigvee}$-structure to generalize some lattices, and study the conditions that a lattice which has ${\bigwedge}$-structure or ${\bigvee}$-structure to be continuous or algebraic.

• Proceedings of the Korean Vacuum Society Conference
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• 2014.02a
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• pp.425.1-425.1
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• 2014

Thermal transport in nanomaterials is not only scientifically interesting but also technological important for various future electronic, bio, and energy device applications. Among the various computation approaches to investigate lattice thermal transport phenomena in nanoscale, the atomistic nonequilibrium Green's function approach based on first-principles density functional theory calculations appeared as a promising method given the continued miniaturization of devices and the difficulty of developing classical force constants for novel nanoscale interfaces. Among the nanometerials, carbon atomic chains, namely the cumulene (all-doulble bonds, ${\cdots}C=C=C=C{\cdots}$) and polyyne (alternation of single and triple bonds, ${\cdots}C{\equiv}C-C{\equiv}C{\cdots}$) can be considered as the extream cases of interconnction materials for nanodevices. After the discovery and realization of carbon atomic chains, their electronic transport properties have been widely studied. For the thermal transport properties, however, there have been few literatures for this simple linear chain system. In this work, we first report on the development of a non-equilibrium Green's function theory-based computational tool for atomistic thermal transport calculations of nanojunctions. Using the developed tool, we investigated phonon dispersion and transmission properties of polyethylene (${\cdots}CH2-CH2-CH2-CH2{\cdots}$) and polyene (${\cdots}CH-CH-CH-CH{\cdots}$) structures as well as the cumulene and polyyne. The resulting phonon dispersion from polyethylene and polyene showed agreement with previous results. Compared to the cumulene, the gap was found near the ${\Gamma}$ point of the phonon dispersion of polyyne as the prediction of Peierls distortion, and this feature was reflected in the phonon transmission of polyyne. We also investigated the range of interatomic force interactions with increase in the size of the simulation system to check the convergence criteria. Compared to polyethylene and polyene, polyyne and cumulene showed spatially long-ranged force interactions. This is reflected on the differences in phonon transport caused by the delicate differences in electronic structure.

• Journal of the Korean Ceramic Society
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• v.44 no.8
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• pp.412-418
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• 2007

The atomic scale details of the melting of solid argon were monitored with the aid of molecular dynamics simulations. The potential energy distribution is substantially disturbed by an increase in the interatomic distance and the random of set distance from the lattice points, with increasing temperature. The potential energy barriers between the lattice points decrease in magnitude with the temperature. Eventually, at the melting point, these barriers can be overcome by atoms that are excited with the entropy gain acquired when the atoms obtain rotational freedom in their atomic motion, and the rotational freedom leads to the collapse of the crystal structure. Furthermore, it was found that the surface of crystals plays an important role in the melting process: the surface eliminates the barrier for the nucleation of the liquid phase and facilitates the melting process. Moreover, the atomic structure of the surface varies with increasing temperature, first via surface roughening and then, before the bulk melts, via surface melting.

• Proceedings of the Polymer Society of Korea Conference
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• 2006.10a
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• pp.11-12
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• 2006

Incorporation of chromophores into multi-chromophore-containing dendrimers is shown to lead to a significant enhancement in electro-optic activity. These results are reasonably well simulated by pseudo-atomistic Monte Carlo calculations that permit dendrimers to interpenetrate (entangle). Calculations also lead to the correct prediction of material densities. An even greater enhancement in electro-optic activity is observed when such dendrimer materials are doped with a second chromophore. This latter effect may reflect an Ising-lattice-type phenomenon where one chromophore impacts the ordering of the other and vice versa.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.1083-1088
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• 2003

Molecular dynamics simulations on the deformation behavior of single-walled carbon nanotube are performed. Formation energies of CNT's by interatomic potentials are computed and compared with ab initio results. Bending and axial compression are applied under lattice statics and NVT ensemble conditions. Specifically, we focus on the mechanism of kink formation in bending. The simulation results are comprehensively explained in the framework of atomistic energetics. The effects of temperature and chirality on the deformation of carbon nanotube are also studied.

• Korean Journal of Mineralogy and Petrology
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• v.33 no.3
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• pp.143-152
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• 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 Mineralogical Society of Korea
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• v.30 no.4
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• pp.161-172
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• 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.

• Tribology and Lubricants
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• v.23 no.1
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• pp.9-13
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• 2007

Despite numerous researches on atomic-scale friction have been carried out for understanding the origin of friction, lots of questions about sliding friction still remain. It is known that friction at atomic-scale always shows unique phenomena called 'stick-slips' which reflect atomic lattice of a scanned surface. In this work, experimental study on the effects of system stiffnesses and load on the atomic-scale stick-slip friction of graphite was performed by using an Atomic Force Microscope and various cantilevers/tips. The objective of this research is to figure out the dependency of atomic-scale friction on the nanomechanical properties in sliding contact such as load, stiffness and contact materials systematically. From this work, the experimental observation of transitions in atomic-scale friction from smooth sliding to multiple stick-slips in air was first made, according to the lateral cantilever stiffness and applied normal load. The superlubricity of graphite could be verified from friction vs. load experiments. Based on the results, the relationship between the stickslip behaviors and contact stiffness was carefully discussed in this work. The results or this work indicate that the atomic-scale stick-slip behaviors can be controlled by adjusting the system stiffnesses and contact materials.

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