SITE- AND BOND-DIFFUSION ON REGULAR LATTICES

2009 ◽  
Vol 23 (24) ◽  
pp. 4943-4952
Author(s):  
LASKO BASNARKOV ◽  
VIKTOR URUMOV
Keyword(s):  
Transition Probability ◽  
Three Dimensional ◽  
Diffusion Constant ◽  
Single Step ◽  
Face Centered Cubic ◽  
Periodic Orbit Theory ◽  
Regular Lattices ◽  
Orbit Theory ◽  
Face Centered ◽  
Theoretical Results

We consider two types of motion, one with particle occupying only the sites on a given regular lattice and another when the bonds between neighboring lattice sites are displaced to the positions of the neighboring bonds. We refer to these models as site- and bond-diffusion. The latter is equivalent to site-diffusion on a lattice constructed from the middle points on each bond of the original lattice. The transition probability is assumed equal to all neighboring positions. The diffusion constant is obtained by periodic orbit theory for all Archimedean lattices, as well as some three-dimensional lattices (cubic, diamond, body centered cubic and face centered cubic lattice). Every single step of bond-motion is expressed through two site-motion steps. Analytic results for the diffusion constant for bond-diffusion for square, triangular and Kagomé lattice are also obtained. Kurtosis is calculated for site-diffusion on square and (4, 82)-lattice, to estimate the deviation of the distribution of displacements from the Gaussian. All theoretical results are verified with numerical simulation.

Epitaxial Ni nanoparticles on CaF2(001), (110) and (111) surfaces studied by three-dimensional RHEED, GIXD and GISAXS reciprocal-space mapping techniques

2017 ◽  
Vol 50 (3) ◽  
pp. 830-839 ◽  
Author(s):  
S. M. Suturin ◽  
V. V. Fedorov ◽  
A. M. Korovin ◽  
N. S. Sokolov ◽  
A. V. Nashchekin ◽  
...  
Keyword(s):  
Lattice Structure ◽  
Three Dimensional ◽  
Grazing Incidence ◽  
High Energy ◽  
Reciprocal Space ◽  
Mapping Technique ◽  
Face Centered Cubic ◽  
X Ray ◽  
Cubic Lattice ◽  
Face Centered

The development of growth techniques aimed at the fabrication of nanoscale heterostructures with layers of ferroic 3dmetals on semiconductor substrates is very important for their potential usage in magnetic media recording applications. A structural study is presented of single-crystal nickel island ensembles grown epitaxially on top of CaF2/Si insulator-on-semiconductor heteroepitaxial substrates with (111), (110) and (001) fluorite surface orientations. The CaF2buffer layer in the studied multilayer system prevents the formation of nickel silicide, guides the nucleation of nickel islands and serves as an insulating layer in a potential tunneling spin injection device. The present study, employing both direct-space and reciprocal-space techniques, is a continuation of earlier research on ferromagnetic 3dtransition metals grown epitaxially on non-magnetic and magnetically ordered fluorides. It is demonstrated that arrays of stand-alone faceted nickel islands with a face-centered cubic lattice can be grown controllably on CaF2surfaces of (111), (110) and (001) orientations. The proposed two-stage nickel growth technique employs deposition of a thin seeding layer at low temperature followed by formation of the islands at high temperature. The application of an advanced three-dimensional mapping technique exploiting reflection high-energy electron diffraction (RHEED) has proved that the nickel islands tend to inherit the lattice orientation of the underlying fluorite layer, though they exhibit a certain amount of {111} twinning. As shown by scanning electron microscopy, grazing-incidence X-ray diffraction (GIXD) and grazing-incidence small-angle X-ray scattering (GISAXS), the islands are of similar shape, being faceted with {111} and {100} planes. The results obtained are compared with those from earlier studies of Co/CaF2epitaxial nanoparticles, with special attention paid to the peculiarities related to the differences in lattice structure of the deposited metals: the dual-phase hexagonal close-packed/face-centered cubic lattice structure of cobalt as opposed to the single-phase face-centered cubic lattice structure of nickel.

scholarly journals Generalization of the Unified Analytic Melt-Shear Model to Multi-Phase Materials: Molybdenum as an Example

Crystals ◽  
2019 ◽  
Vol 9 (2) ◽  
pp. 86 ◽  
Author(s):  
Leonid Burakovsky ◽  
Darby Luscher ◽  
Dean Preston ◽  
Sky Sjue ◽  
Diane Vaughan
Keyword(s):  
Shear Modulus ◽  
Solid Phase ◽  
Model Parameters ◽  
Quantum Molecular Dynamics ◽  
Face Centered Cubic ◽  
Shear Model ◽  
Bcc Structure ◽  
Face Centered ◽  
Multi Phase ◽  
Theoretical Results

The unified analytic melt-shear model that we introduced a decade ago is generalized to multi-phase materials. A new scheme for calculating the values of the model parameters for both the cold ( T = 0 ) shear modulus ( G ) and the melting temperature at all densities ( ρ ) is developed. The generalized melt-shear model is applied to molybdenum, a multi-phase material with a body-centered cubic (bcc) structure at low ρ which loses its dynamical stability with increasing pressure (P) and is therefore replaced by another (dynamically stable) solid structure at high ρ . One of the candidates for the high- ρ structure of Mo is face-centered cubic (fcc). The model is compared to (i) our ab initio results on the cold shear modulus of both bcc-Mo and fcc-Mo as a function of ρ , and (ii) the available theoretical results on the melting of bcc-Mo and our own quantum molecular dynamics (QMD) simulations of one melting point of fcc-Mo. Our generalized model of G ( ρ , T ) is used to calculate the shear modulus of bcc-Mo along its principal Hugoniot. It predicts that G of bcc-Mo increases with P up to ∼240 GPa and then decreases at higher P. This behavior is intrinsic to bcc-Mo and does not require the introduction of another solid phase such as Phase II suggested by Errandonea et al. Generalized melt-shear models for Ta and W also predict an increase in G followed by a decrease along the principal Hugoniot, hence this behavior may be typical for transition metals with ambient bcc structure that dynamically destabilize at high P. Thus, we concur with the conclusion reached in several recent papers (Nguyen et al., Zhang et al., Wang et al.) that no solid-solid phase transition can be definitively inferred on the basis of sound velocity data from shock experiments on Mo. Finally, our QMD simulations support the validity of the phase diagram of Mo suggested by Zeng et al.

scholarly journals Interactions between dislocations and three-dimensional annealing twins in face centered cubic metals

2019 ◽  
Vol 161 ◽  
pp. 371-378 ◽  
Author(s):  
Yanxiang Liang ◽  
Xiaofang Yang ◽  
Mingyu Gong ◽  
Guisen Liu ◽  
Qing Liu ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Face Centered Cubic ◽  
Cubic Metals ◽  
Annealing Twins ◽  
Face Centered

Electromagnetic Thermal Energy Transfer in Nanoparticle Assemblies Below Diffraction Limit

2020 ◽  
Vol 13 (2) ◽  
Author(s):  
Anil Yuksel ◽  
Edward T. Yu ◽  
Michael Cullinan ◽  
Jayathi Murthy
Keyword(s):  
Three Dimensional ◽  
Close Packing ◽  
Face Centered Cubic ◽  
Copper Nanoparticle ◽  
Colloidal Solutions ◽  
Plasmonic Coupling ◽  
Nanoparticle Assemblies ◽  
Enhanced Absorption ◽  
Face Centered ◽  
Insight Into

Abstract Fabrication of micro- and nanoscale electronic components has become increasingly demanding due to device and interconnect scaling combined with advanced packaging and assembly for electronic, aerospace, and medical applications. Recent advances in additive manufacturing have made it possible to fabricate microscale, 3D interconnect structures but heat transfer during the fabrication process is one of the most important phenomena influencing the reliable manufacturing of these interconnect structures. In this study, optical absorption and scattering by three-dimensional (3D) nanoparticle packings are investigated to gain insight into micro/nano heat transport within the nanoparticles. Because drying of colloidal solutions creates different configurations of nanoparticles, the plasmonic coupling in three different copper nanoparticle packing configurations was investigated: simple cubic (SC), face-centered cubic (FCC), and hexagonal close packing (HCP). Single-scatter albedo (ω) was analyzed as a function of nanoparticle size, packing density, and configuration to assess effect for thermo-optical properties and plasmonic coupling of the Cu nanoparticles within the nanoparticle packings. This analysis provides insight into plasmonically enhanced absorption in copper nanoparticle particles and its consequences for laser heating of nanoparticle assemblies.

scholarly journals Structure and stacking order in crystals of asymmetric dumbbell-like colloids

2015 ◽  
Vol 48 (1) ◽  
pp. 238-243 ◽  
Author(s):  
Antara Pal ◽  
Janne-Mieke Meijer ◽  
Joost R. Wolters ◽  
Willem K. Kegel ◽  
Andrei V. Petukhov
Keyword(s):  
Crystalline Structure ◽  
Diffuse Scattering ◽  
Colloidal Particles ◽  
Three Dimensional ◽  
Stacking Faults ◽  
Face Centered Cubic ◽  
Hexagonal Close Packed ◽  
Stacking Order ◽  
X Ray Scattering ◽  
Face Centered

The crystalline structure assembled out of charge-stabilized asymmetric dumbbell-like colloidal particles in ethyl alcohol by sedimentation has been probed using small-angle X-ray scattering with microradian resolution. The existence of plastic face-centered cubic crystals was inferred from the observed Bragg peaks. The presence of stacking faults and the mosaic structure of the sample lead to the appearance of diffuse scattering, forming Bragg scattering cylinders in the three-dimensional reciprocal space. The quality of the crystalline structure, as ascertained from a detailed analysis of the diffuse scattering intensity distribution, indicates the presence of only 1.5% of stacking faults between the hexagonal close-packed layers.

A three-dimensional photonic crystal model: Hollow-spherical non-closed-packed face-centered cubic structure

2006 ◽  
Vol 381 (1-2) ◽  
pp. 289-293 ◽  
Author(s):  
Hong-Bo Chen ◽  
Yan-Ling Cao ◽  
Yong-Zheng Zhu ◽  
Yan-Ping Wang ◽  
Yuan-Bin Chi
Keyword(s):  
Photonic Crystal ◽  
Three Dimensional ◽  
Face Centered Cubic ◽  
Dimensional Photonic Crystal ◽  
Crystal Model ◽  
Cubic Structure ◽  
Face Centered

scholarly journals A Micromechanical Model of Additively Manufactured Aluminum Alloys

2019 ◽  
Vol 221 ◽  
pp. 01016
Author(s):  
Evgeniya Emelianova ◽  
Varvara Romanova ◽  
Olga Zinovieva ◽  
Ruslan Balokhonov ◽  
Aleksandr Zinoviev ◽  
...  
Keyword(s):  
Aluminum Alloys ◽  
Plastic Anisotropy ◽  
Micromechanical Model ◽  
Three Dimensional ◽  
Face Centered Cubic ◽  
Melt Pool ◽  
Grain Structures ◽  
Face Centered ◽  
Three Dimensional Models ◽  
Packing Method

A micromechanical model is developed to predict the deformation behavior of additively manufactured aluminum alloys. Three-dimensional models of grain structures typical for different microregions of the melt pool are generated by the step-by-step packing method. A crystal plasticity-based constitutive model accounting for the elastic-plastic anisotropy of face-centered cubic crystals is employed to simulate the microscale deformation in an additively manufactured aluminum alloy under loading. The grain shape and texture effects on the plastic strain localization patterns are analyzed.

A Numerical Study on the Large Compressive Deformations of Closed-Celled Rubber Foams

2013 ◽  
Vol 444-445 ◽  
pp. 23-26
Author(s):  
Zhi Geng Fan
Keyword(s):  
Strain Energy ◽  
Potential Model ◽  
Numerical Study ◽  
Three Dimensional ◽  
Face Centered Cubic ◽  
Energy Potential ◽  
Compressive Stresses ◽  
Order Of Magnitude ◽  
Face Centered ◽  
In Cells

Three dimensional (3D) cubic models with spherical pores ranged as Face-Centered Cubic (FCC) lattices are constructed to simulate the microstructures of rubber foams with various relative densities. The Mooney-Rivlin strain energy potential model is adopted to characterize the hyperelasticity of the constituent solid from which the foams are made. Large compressive deformations of closed-celled rubber foams are calculated by the iterative algorithm. Numerical results show that with the decreasing of foam relative densities, the effects of air pressures in cells on foam compressive stresses increase. When the ratio of initial Yangs modulus of cell material to the initial air pressure in cells reaches 2 order of magnitude, the influence of air pressures in cells can neglect.

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