Evaluation of morse parameters for metals

Pamuk, H. Önder; Halicioǧlu, T.

doi:10.1002/pssa.2210370242

Cited by 28 publications

(13 citation statements)

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“…We have compared this conjecture to the values of α found from experimental quantities for metals in [36,40,42,53,60]. We observe that the real ground-states of metals match with the expected ground-state given by our conjecture, according to the experimental values of α, only in few cases for both FCC and BCC structures.…”

Section: Introduction and Main Resultsmentioning

confidence: 66%

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Minimizing lattice structures for Morse potential energy in two and three dimensions

Bétermin

2019

Journal of Mathematical Physics

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We investigate the local and global optimality of the triangular, square, simple cubic, facecentred-cubic (FCC), body-centred-cubic (BCC) lattices and the hexagonal-close-packing (HCP) structure for a potential energy per point generated by a Morse potential with parameters (α, r 0 ). In dimension 2 and for α large enough, the optimality of the triangular lattice is shown at fixed densities belonging to an explicit interval, using a method based on lattice theta function properties. Furthermore, this energy per point is numerically studied among all twodimensional Bravais lattices with respect to their density. The behaviour of the minimizer, when the density varies, matches with the one that has been already observed for the Lennard-Jones potential, confirming a conjecture we have previously stated for differences of completely monotone functions. Furthermore, in dimension 3, the local minimality of the cubic, FCC and BCC lattices are checked, showing several interesting similarities with the Lennard-Jones potential case. We also show that the square, triangular, cubic, FCC and BCC lattices are the only Bravais lattices in dimensions 2 and 3 being critical points of a large class of lattice energies (including the one studied in this paper) in some open intervals of densities, as we observe for the Lennard-Jones and the Morse potential lattice energies. More surprisingly, in the Morse potential case, we numerically found a transition of the global minimizer from BCC, FCC to HCP, as α increases, that we partially and heuristically explain from the lattice theta functions properties. Thus, it allows us to state a conjecture about the global minimizer of the Morse lattice energy with respect to the value of α. Finally, we compare the values of α found experimentally for metals and rare-gas crystals with the expected lattice ground-state structure given by our numerical investigation/conjecture. Only in a few cases does the known ground-state crystal structure match the minimizer we find for the expected value of α. Our conclusion is that the pairwise interaction model with Morse potential and fixed α is not adapted to describe metals and rare-gas crystals if we want to take into consideration that the lattice structure we find in nature is the ground-state of the associated potential energy.

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Section: Introduction and Main Resultsmentioning

confidence: 66%

“…We now want to compare our Conjecture 1.8 with the values of α empirically obtained for metals in [36,40,42,53,60] and rare-gas crystals in [2,6,54,56]. In order to compare these values, we need a result we have already proved in [16,Thm 1.11] in the Lennard-Jones type potentials case.…”

Section: Comparison Of Our Conjecture With Some Experimental Values Omentioning

confidence: 95%

Minimizing lattice structures for Morse potential energy in two and three dimensions

Bétermin

2019

Journal of Mathematical Physics

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“…Both Ag and Pb surfaces have fcc structure. 6 The surface consists of three layers and the dimensions of each layer are 3.58ϫ 3.58 nm 2 ͑xy-plane͒ for Pb-surface and 3.50ϫ 3.50 nm 2 for Ag surface. Periodic boundary conditions were assigned along the x and y directions.…”

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confidence: 99%

“…Water was modeled as SPC/E model 3 and the interatomic interaction between solid atoms was modeled by using the Morse potential. 6 The Nosé-Hoover thermostat 7 was used to maintain the system tema͒ Author to whom correspondence should be addressed. perature at 300 K. The equation of motion was integrated by using the leapfrog algorithm with a time step of 2.0 fs.…”

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confidence: 99%

Diffusion of water submonolayers on hydrophilic surfaces

Park

Aluru

2008

Applied Physics Letters

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In this letter, we investigate using molecular dynamics simulations the diffusion of water submonolayers on hydrophilic surfaces. In contrast to a strong hydrophilic Ag surface, on a weak hydrophilic Pb surface, the diffusion coefficient is remarkably enhanced at a critical surface coverage and a ⌳-shape anomaly with surface coverage is observed, i.e., the diffusion coefficient increases with the increase in surface coverage until a critical surface coverage, beyond which the diffusion coefficient decreases. We explain the anomalous diffusion of water on hydrophilic surfaces by a detailed understanding of molecular cavities and monolayer tail contributing to three-dimensional hydrogen bonding. © 2008 American Institute of Physics. ͓DOI: 10.1063/1.3054640͔ Transport of liquid submonolayers on solid substrates has gained significant attention recently because of applications in nanolithography, nanoprinting, wetting/dewetting of nanopatterned surfaces, etc.1 Diffusion of submonolayer liquids can be markedly different from diffusion of bulk liquids or diffusion of thick ͑thicknesses of the order of several nanometers͒ liquid films on surfaces. For example, diffusion of n-alkane and long polyethylene glycol submonolayers exhibits nonmonotonic dependence on the surface coverage, i.e., the surface diffusion increases with increasing surface concentration and then decreases abruptly.2 Even though water is considered to be the most fundamental and basic working fluid, diffusion of water submonolayers on solid substrates has not been investigated so far.In this letter, we use molecular dynamics simulations to investigate diffusion of water on hydrophilic surfaces when the surface coverage is less than a monolayer-also referred to as incomplete coverage. Two typical hydrophilic surfaces-namely, a Ag surface and a Pb surface-were considered. The Ag surface is considered as a strong hydrophilic surface with ͑6-12͒ Lennard-Jones parameters of Ag = 0.2544 nm and ⑀ Ag = 33.2664 kJ/ mol ͓⑀ Ag-OW = 4.6508 kJ/ mol, where OW is the oxygen atom inextended simple point charge ͑SPC/E͒water 3 ͔ while the Pb surface is considered as a weak hydrophilic surface with Pb = 0.3197 nm and ⑀ Pb = 22.8067 kJ/ mol. 4 For each surface, various surface coverages ͑denoted by ⌫͒ ranging from ⌫ = 0.201 mg/ m 2 to ⌫ = ⌫ full = 0.376 g / m 2 for Pb surface and ⌫ = 0.201 mg/ m 2 to ⌫ = ⌫ full = 0.393 g / m 2 for Ag surface were considered. The surface coverage is measured as the ratio of the total mass of the water molecules to the surface area. Figure 1 summarizes the various cases considered for Pb surface. For Pb surface, when the surface coverage is smaller than ⌫ = 0.201 mg/ m 2 , the water layer is separated completely into two parts while for the Ag surface when ⌫ Ͻ 0.322 mg/ m 2 , we hardly see the transport of molecules. From the view point of density, the surface is considered to be fully covered for ⌫ full = 0.376 mg/ m 2 for Pb surface and ⌫ full = 0.393 mg/ m 2 for Ag surface. Beyond this coverage, a second layer starts to form ͑see the de...

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“…The relaxation, on the other hand, greatly reduced the peak heightsof YDF, in particular for the first peak. We have mentioned amorphous iron [11] amorphous iron [25] F~,,P,, before that the two subpeaks around r = 1.67 and 2.0 (T are related to the existence of tetrahedral units in the assemblies and to three-membered collineation; respectively. I n the relaxed structures, the numbers of such correlations betweeen atoms are reduced.…”

Section: Pair Distribution Functionmentioning

confidence: 99%

Structural relaxation of the dense random packing model for amorphous iron

Yamamoto

Matsuoka

Doyama

1978

Phys. Stat. Sol. (a)

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Using Johnson's potential of α‐iron, three dense random packing (DRP) assemblies constructed by Ichikawa's method for k = 1.05, 1.2, and 1.4, are relaxed under a free boundary condition. The assembly with k = 1.2 is relaxed also by the potential obtained by Pak and Doyama and the long range oscillatory potential of liquid iron. The pair distribution function (PDF) of the relaxed model with k = 1.2 using Johnson's potential is in excellent agreement with the experimental PDF of the amorphous iron. On the other hand, the greatest packing fraction, η = 0.59, is achieved using the potential by Pak and Doyama. It is shown that the relaxation procedure using an appropriate potential is the indispensable process to construct realistic models of glassy metals.

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Evaluation of morse parameters for metals

Cited by 28 publications

References 8 publications

Minimizing lattice structures for Morse potential energy in two and three dimensions

Minimizing lattice structures for Morse potential energy in two and three dimensions

Diffusion of water submonolayers on hydrophilic surfaces

Structural relaxation of the dense random packing model for amorphous iron

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