Surface Energy Relaxation Research Articles

Creation of quantum knots and links driven by minimal surfaces

Using an improved numerical code we investigate the creation and evolution of quantum knots and links as defects of the Gross–Pitaevskii equation. The particular constraints put on quantum hydrodynamics make this an ideal context for application of geometric and topological methods to investigate dynamical properties. Evolutionary processes are classified into three generic scenarios representing (i) direct topological cascade and collapse, (ii) structural and topological cycles, and (iii) inverse topological cascade of complex structures. Several examples and test cases are studied; the head-on collision of quantum vortex rings and the creation of a trefoil knot from initially unlinked, unknotted loops are realized for the first time. Each type of scenario is studied by carrying out a detailed evaluation of fundamental geometric and dynamical properties associated with evolution. Direct topological cascade that governs the decay of complex structures to small-scale vortex rings is identified by writhe measures, while picks of total curvature are found to provide a clear signature of reconnection events. We demonstrate that isophase minimal surfaces spanning knots and links have a privileged role in the decay process by detecting surface energy relaxation of complex structures. Minimal surfaces are shown to be critical markers for energy and prove to be appropriate detectors for the evolution of complex systems.

Calculation of the Surface Energy of Metals: Agreement of the Thermodynamic Vacancy Model with the First-Principles Theory

The thermodynamic vacancy model (TVM) of surface energy (SE) leads to the formula of the linear dependence of the minimum SE value of the low-index fcc (111) and bcc (110) faces on half of the vacancy formation energy or the 1/6 part of the cohesive energy of metals. Comparison of the numerical values of SE calculated by the TVM method with those calculated by the DFT method for the same faces shows negative deviations of the latter (from 2 to 17%). Using the values of these deviations, the surface energy relaxation of metals was calculated with a maximum value for Au and Pt and a minimum value for Ag and Pd.

Comparative Study on Surface Structure, Electronic Properties of Sulfide and Oxide Minerals: A First-Principles Perspective

First-principle calculations were used to investigate the surface structure and electronic properties of sulfide (pyrite, galena, and sphalerite) and oxide minerals (hematite, cerussite, and smithsonite). Surface relaxation and Femi energy, as well as projected DOS, are considered. Results show that the surface atoms of the sulfide minerals are more susceptible and more easily affected by the fracture bonds. The sulfide surfaces possess higher chemical potential than the corresponding oxide surfaces, and are more likely to be electron donors in reactions. The S 3p states are the mainly contributing states in the sulfide surface, while that in the oxide surface are O 2p states. The bonds of the sulfide surface have more covalent features and that of the oxide surface are ionic interactions. The O–M (M represents Fe, Pb or Zn) bonds are more stable, as the DOS of the oxide surfaces distribute in the lower energy range.

Structural, electronic properties and stability of AlCMn3 (1 1 1) surfaces by first-principles calculations

The directly cleaved AlMn3, terminations and constructed AlMn2, CMn terminations have been built for AlCMn3 (111) surface. The surface relaxation, cleavage and surface energies, surface grand potential along with the surface electronic structure have been calculated with the first-principles methods based on the density functional theory (DFT). Results of the relaxed structure for each termination show that the relaxation mainly occur on the uppermost two atomic layers, and larger rumpling locate at the first layer of the AlMn2 and CMn terminations. Analysis on of the surface energies and grand potential reveals that only the AlMn2 and C terminations can be formed and its stabilities depend on the range of the ΔμAl and ΔμMn. Furthermore, surface electronic calculations indicate that the AlMn bond is the largest bond population among the four terminations slabs and demonstrates that the outmost layer of AlCMn3 (111) surfaces have a preference of AlMn2 and C terminations.

Ab initio calculations of BaTiO3 (111) surfaces

The article presents the results of calculations of polar (111) surface relaxations and energetics using the ab initio code CRYSTAL and a hybrid description of exchange and correlation. Using a hybrid B3LYP approach, the surface relaxation has been calculated for the two possible Ti and BaO3 BaTiO3 (111) surface terminations. For both Ti- and BaO3-terminated BaTiO3 (111) surfaces, the upper layer atoms relax inward. The second layer atoms, with the sole exception of Ti-terminated BaTiO3 (111) surface Ba atom, relax outward. The calculated surface relaxation energy for Ti-terminated BaTiO3 (111) surface is more than two times larger than the surface relaxation energy for BaO3-terminated BaTiO3 (111) surface. The surface energy for Ti-terminated BaTiO3 (111) surface (7.28 eV/cell) is smaller, than the surface energy for BaO3-terminated (111) surface (8.40 eV/cell).

Ab initio calculations of the atomic and electronic structure of BaZrO3 (111) surfaces

The paper presents and discusses the results of calculations of surface relaxations and energetics for the polar (111) surface of BaZrO3 using a hybrid B3LYP description of exchange and correlation. On the (111) surface, both Zr- and BaO3-terminations were analyzed. For both Zr and BaO3-terminated BaZrO3 (111) surface upper layer atoms, with the sole exception of BaO3-terminated surface Ba atoms, relax inwards. The Zr-terminated BaZrO3 (111) surface second layer Ba atoms exhibit the strongest relaxation between all Zr and BaO3-terminated BaZrO3 (111) surface atoms. The calculated surface relaxation energy for Zr-terminated BaZrO3 (111) surface is almost fifteen times larger than the surface relaxation energy for BaO3-terminated BaZrO3 (111) surface. The surface energy for Zr-terminated BaZrO3 (111) surface (7.94eV/cell) is smaller, than the surface energy for BaO3-terminated (111) surface (9.33eV/cell). The calculated BaZrO3 optical bulk band gap, 4.79eV is in an excellent agreement with the experimental value, 5.00eV. The calculated optical band gap for the Zr- and BaO3-terminated BaZrO3 (111) surfaces becomes smaller with respect to the bulk optical band gap.

First-principles study on stability and electronic properties of W(001), W(110) and W(111) surfaces

Based on Density Functional Theory (DFT), using first-principles pseudopotential plane wave method, surface relaxation, surface energy and Density of states (DOS) of metal W on low index surfaces (001), (110) and (111) were calculated. The results showed that: the relaxation and surface energy were |Δ14(110)|<|Δ14(111)|<|Δ14(001)| and Esurf(110)<Esurf (111)<Esurf(001), respectively. The surface relaxation and surface energy of W(110) were both minimum, which proved that W(110) was the most stable surface. This result was in good agreement with experimental XRD pattern. According to Density of states, the essence of the distinct stability of W(001), W(110) and W(111) was discussed further.

Ab Initio Calculations of the Atomic and Electronic Structure of SrZrO3 (111) Surfaces

The paper presents and discusses the results of calculations of surface relaxations and energetics for the polar (111) surface of SrZrO3 using a hybrid B3LYP description of exchange and correlation. On the (111) surface, I consider both Zr- and SrO3-terminations. For both Zr and SrO3-terminated SrZrO3 (111) surfaces upper layer atoms relax inwards. The second layer atoms, with the sole exception of Zr-terminated SrZrO3 (111) surface Sr atom, relax outwards. The calculated surface relaxation energy for Zr-terminated SrZrO3 (111) surface is almost sixteen times larger, than the surface relaxation energy for SrO3-terminated SrZrO3 (111) surface. The surface energy for Zr-terminated SrZrO3 (111) surface (7.98 eV) is smaller, than the surface energy for SrO3-terminated SrZrO3 (111) surface (9.45 eV).

First-Principles Calculations of the Atomic and Electronic Structure of CaTiO3 (111) Surfaces

The results of calculations of CaTiO3 polar (111) surface relaxations, rumplings, energetics, optical band gaps, and charge distribution using the ab initio code CRYSTAL and a hybrid description of exchange and correlation are presented. Using a hybrid B3LYP approach, the surface relaxation for the two possible Ti and CaO3 CaTiO3 (111) surface terminations are calculated. For both Ti and CaO3-terminated CaTiO3 (111) surfaces upper layer atoms relax inwards, while the second layer atoms, with the sole exception of CaO3-terminated surface Ca atom, relax outwards. Calculated surface relaxation energy for Ti-terminated CaTiO3 (111) surface is more than five times larger than the surface relaxation energy for CaO3-terminated CaTiO3 (111) surface. The surface energy for Ti-terminated CaTiO3 (111) surface (4.18 eV/cell) is smaller, than the surface energy for CaO3-terminated CaTiO3 (111) surface (5.86 eV/ cell).

Structural properties and diffusion processes of the Cu 3Au (0 0 1) surface

The surface relaxation and surface energy of both the mixed AuCu and pure Cu terminated Cu 3Au (0 0 1) surfaces are simulated and calculated by using the modified analytical embedded-atom method. We find that the mixed AuCu termination is energetically preferred over the pure Cu termination thereby the mono-vacancy diffusion is also investigated in the topmost few layers of the mixed AuCu terminated Cu 3Au (0 0 1) surface. In the mixed AuCu terminated surface the relaxed Au atoms are raised above Cu atoms for 0.13 Å in the topmost layer. All the surface atoms displace outwards, this effect occurs in the first three layers and changes the first two inter-layer spacing. For mono-vacancy migration in the first layer, the migration energies of Au and Cu mono-vacancy via two-type in-plane displace: the nearest neighbor jump (NNJ) and the second nearest neighbor jump (2NNJ), are calculated and the results show that the NNJ requires a much lower energy than 2NNJ. For the evolution of the energy requirements for successive nearest neighbor jumps (SNNJ) along three different paths: circularity, zigzag and beeline, we find that the circularity path is preferred over the other two paths due to its minimum energy barriers and final energies. In the second layer, the NN jumps in intra- and inter-layer of the Cu mono-vacancy are investigated. The calculated energy barriers and final energies show that the vacancy prefer jump up to a proximate Cu site. This replacement between the Cu vacancy in the second layer and Cu atom in the first layer is remunerative for the Au atoms enrichment in the topmost layer.

Surface relaxation and tilting in SrHfO 3 orthorhombic perovskite: Hybrid HF-DFT LCAO calculations

HF-DFT LCAO hybrid simulations on (0 0 1) and (1 1 0) surfaces of orthorhombic and (0 0 1) surface of cubic SrHfO 3 perovskite are performed using a single slab model framework. PBE0 exchange-correlation functional is used for this study. The energy and crystal structure of bulk cubic and orthorhombic phases are calculated and compared. It is found that orthorhombic modification is more stable than cubic one by 24 kJ mol –1 per formula unit. Calculated average surface energies and relaxation energies proved to be similar for all orthorhombic surfaces. Atomic displacements along the direction normal to the surface are primarily determined by the type of termination and weakly depend on the surface indices. Without symmetry constraining, cubic surfaces are unstable with respect to reconstruction to corresponding orthorhombic surfaces at T = 0 K. While the upright displacements of the topmost atoms are mainly due to additional distortions of the surface octahedra, the lateral atomic displacements are closely related to changing in surface group tilting. The approach for the analysis of surface octahedron tilting is proposed and applied to the relaxed orthorhombic surfaces of SrHfO 3 perovskites. It is shown that the HfO 5 group on the HfO 2-termianted surfaces undergoes a considerable turn upon relaxation, resulting in alignment of Hf–O–Hf bonds to corresponding pseudo-cubic directions.

SIZE-DEPENDENT ELASTIC MODULUS AND FRACTURE TOUGHNESS OF THE NANOFILM WITH SURFACE EFFECTS

The effective elastic modulus and fracture toughness of the nanofilm were derived with the surface relaxation and the surface energy taken into consideration by means of the interatomic potential of an ideal crystal. The size effects of the effective elastic modulus and fracture toughness were discussed when the thickness of the nanofilm was reduced. And the dependence of the size effects on the surface relaxation and surface energy was also analyzed.

Density Functional Study of the Effects of Strains on the Adsorption of Methoxide and its Decomposed Intermediates on Cu(100) Surface

Periodic density functional slab models were used to investigate adsorption of methoxide and its decomposed intermediates on optimized and strained (−5% to +5%) Cu(100) surfaces. Surface relaxation energies and adsorption energies of methoxide and its decomposed intermediates were systematically studied and quantified. Reaction energetics of methoxide C–H and C–O bond breaking were quantified on the strained Cu(100) surfaces.

First-principles calculations of atomic and electronic structure ofSrTiO3(001) and (011) surfaces

We present and discuss the results of the calculations of surface relaxation and rumpling on ${\text{SrTiO}}_{3}$ (001) and (011) surfaces. We consider both SrO and ${\text{TiO}}_{2}$ terminations of the (001) surface, and three terminations (Sr, TiO, and O) of the polar (011) surface. The calculations are based on hybrid Hartree--Fock and density-functional theory exchange functionals by using Becke's three-parameter method combined with the nonlocal correlation functionals of Perdew and Wang. We find that all top-layer atoms for ${\text{TiO}}_{2}$ and SrO-terminated ${\text{SrTiO}}_{3}$ (001) surfaces relax inward, with the exception of SrO-terminated surface O atoms, whereas all second-layer atoms relax outward. The surface rumpling for the TiO-terminated ${\text{SrTiO}}_{3}$ (011) surface, which is 11.28% of the bulk lattice constant, is considerably larger than the relevant surface rumplings for SrO and ${\text{TiO}}_{2}$-terminated (001) surfaces. The surface rumplings for the SrO and ${\text{TiO}}_{2}$-terminated (001) surfaces are in excellent agreement with relevant low-energy electron diffraction and reflection high-energy electron diffraction experimental data, and the surface relaxation energies on both surfaces are similar. In contrast, the different terminations of the (011) surface lead to large differences in relaxation energies. The O-terminated (011) surface has the lowest surface relaxation energy $(\ensuremath{-}1.32\text{ }\text{eV})$. The TiO-terminated (011) surface has a much higher surface relaxation energy of $\ensuremath{-}1.55\text{ }\text{eV}$, while the Sr-terminated (011) surface has the highest surface relaxation energy $(\ensuremath{-}1.95\text{ }\text{eV})$. Our calculations indicate a considerable increase in the Ti-O bond covalency $(0.130e)$ near the TiO-terminated (011) surface relative to the bulk $(0.088e)$, which is much larger than that for the (001) surface $(0.118e)$. The Ti-O bond populations are considerably larger in the direction perpendicular to the TiO-terminated (011) surface $(0.188e)$ than in the plane $(0.130e)$.

Harmonic behavior of silicon nanowire by molecular dynamics

Silicon nanowires (SiNW) have attracted increasing interests as potential core parts for nanoscale devices due to their distinguished mechanical and electrical properties. Using molecular dynamics (MD) method, we investigated the vibration behaviors of SiNW on the atomic scale, including the fundamental mode frequency and quality factor. The quality factor as low as 120 is attributed to the energy loss process coming from atomic friction and nonlinearity. We also found that the energy of lattice vibration (phonon energy) is much larger than the macroscale beam vibration energy. And both the energies are less than the surface relaxation energy of the beam. The comparison between MD and FEM has been made to discuss the validity of continuum approximation for the study of SiNW.

Surface relaxation and surface energy of face–centered cubic metals

Surface relaxation and surface energy are calculated for Rh, Ir, Pb, Ca, Sr, and Th, for three low-index surfaces, using the equivalent crystal theory (ECT) method. The surfaces are the (100), (110) and (111) faces. In this study, we only considered perpendicular relaxation where the relaxation was determined by the minimization of the total energy. The results obtained are analyzed with good agreement to experiment and first – principles calculations where available. Journal of Applied Sciences and Environmental Management Vol. 10(1) 2006: 37-42

Surface charge relaxation and the pearling instability of charged surfactant tubes

The pearling instability of bilayer surfactant tubes was recently observed during the collapse of fluid monolayers of binary mixtures of Dimyristoylphosphocholine (DMPC): Palmitoyloleoylphosphoglycerol (POPG) and Dipalmitoylphosphocholine (DPPC):POPG surfactants. It can be explained by a Rayleigh-like instability under the action of the bilayer surface tension. The magnitude of surface tension is dictated by the electrostatic interaction between charged surfactants. Relaxation of charged molecules is proposed here as an additional mechanism driving the instability. We find the functional dependence of the electrostatic surface tension and relaxation energies on the screening length kappa(-1) explicitly. Relaxation lowers the cost of bending a tube into pearls making the cylindrical tube even more unstable. It is known that for the weak screening case in which the tube radius is smaller than the screening length of the solution, this effect is important. However, for the case of strong screening it is negligible. For the experiments mentioned, the situation is marginal. In this case, we show that the effect of relaxation remains small. It contributes about 20% to the total electrostatic energy.

Mass Transport Driven by Atomic Relocations Under High Flux Ion Irradiation at Elevated Temperatures

Experiments with a nitrogen torch at atmospheric pressure have been performed in order to identify the role of surface processes in the mechanism of nitrogen transport during nitriding of stainless steel AISI 304. The unusually thick (~175 μm) layers of supersaturated nitrogen solid solution fcc phase were obtained after treatment for 10 min at 450°C. A radically different structure occurs in specimens treated at 550°C. Scanning electron microscopy (SEM) surface and cross-sectional micrographs reveal that the surface topography indicates the degree of modification occurring in the nitrided layer. Surface vacancies generated by surface instabilities move deeply into the bulk at elevated temperatures and form a highly defected layer with pores and microcracks. The transport of nitrogen in austenitic stainless steel is driven by the flux es of matrix atoms directed to stabilise surface instabilities. Nitrogen depth profiles simulated on the basis of the model with the surface atom relocation process and an activation energy of 1·1-1·5 eV, and including balanced flux es of atoms in the bulk for relax ation of surface energy are in quantitative agreement with ex perimental results.

Nitriding of an austenitic stainless steel in plasma torch at atmospheric pressure

Experiments with a nitrogen torch at atmospheric pressure have been performed in order to identify the role of surface processes in the mechanism of nitrogen transport during nitriding of stainless steel AISI 304. Unusually thick (∼175 μm) layers of supersaturated N solid-solution f.c.c. phase have been obtained for 10 min at 450 °C. Samples treated at 550 °C have a radically different structure. The scanning electron microscopy (SEM) surface and cross-sectional micrographs reveal that surface topography is an indicator of the degree of modification occurring in the nitrided layer. Surface vacancies generated by surface instabilities move deeply into the bulk at elevated temperatures and form a highly defective layer with pores and microcracks. The transport of nitrogen in austenitic stainless steel is driven by the fluxes of matrix atoms directed to stabilize surface instabilities. Nitrogen depth profiles simulated on the basis of a model with a surface-atom relocation process and activation energy of 1.15 eV, and including balanced fluxes of atoms in the bulk for relaxation of surface energy, are in qualitative agreement with experimental results.

Type I FA (Rb +, Cs +) and II FA (Li +, Na +) tunable laser activities and donor-acceptor properties of O and O − at KCl (001) surface: first principle calculations

Type I F A (Rb +, Cs +) and II F A (Li +, Na +) tunable laser activities, adsorptivity and donor-acceptor properties of O and O − adsorbates at the flat surface of KCl crystal were investigated using an embedded cluster model and ab initio methods of molecular electronic structure calculations. Ion clusters were embedded in a simulated Coulomb field that closely approximates the Madelung field of the host surface, and the nearest neighbor ions to the defect site were allowed to relax to equilibrium. Based on the calculated Stokes shifted optical transition bands, F A tunable laser activities were found to be inversely proportional to the size of the dopant cation (Li +, Na +, Rb +, Cs +) relative to the host cation (K +). This relation was explained in terms of the axial perturbation of the impurity cation. The probability of orientational bleaching attributed to the RES saddle point ion configuration along the 〈110〉 axis was found to be inversely proportional to the size of the dopant cation, with activation energy barriers of ca. 0.44–3.34 eV. Surface relaxation energies of type II F A centers were more important than those of type I F A centers. In terms of defect formation energies, the products of type II F A center imperfection were more stable than those of type I F A. The difference between F or F A band energies and exciton bands depended almost exclusively on the size of the positive ion species. As far as the adsorptivity of O and O − is concerned, the results confirm that surface imperfection enhances the adsorption energies by ca. 4.38–16.37 eV. O and O − penetrate through the defect-containing surface. The energy gap between the adsorbate and the defect containing surface and the donor-acceptor property of adsorbate play the dominant role in the course of adsorbate substrate interactions and the results were explained in terms of electrostatic potential curves and Mulliken population analysis.