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Calculation of Elastic Bond Constants in Atomistic Strain Analysis.

Chen H, Wang J, Ashalley E, Li H, Niu X - Nanoscale Res Lett (2015)

Bottom Line: At the atomistic level, this approach is within the framework of linear elastic theory and encompasses the neighbor interactions when an atom is introduced to stress.Departing from the force equilibrium equations, the relationships between ν, K, and spring constants are successfully established.Both the two-dimensional (2D) square lattice and common three-dimensional (3D) structures are taken into account in the procedure for facilitating, bridging the gap between structural complexity and numerical experiments.

View Article: PubMed Central - PubMed

Affiliation: State Key Laboratory of Electronic Thin Film and Integrated Devices, University of Electronic Science and Technology of China, Chengdu, 610054, China.

ABSTRACT
Strain analysis has significance both for tailoring material properties and designing nanoscale devices. In particular, strain plays a vital role in engineering the growth thermodynamics and kinetics and is applicable for designing optoelectronic devices. In this paper, we present a methodology for establishing the relationship between elastic bond constants and measurable parameters, i.e., Poisson's ratio ν and systematic elastic constant K. At the atomistic level, this approach is within the framework of linear elastic theory and encompasses the neighbor interactions when an atom is introduced to stress. Departing from the force equilibrium equations, the relationships between ν, K, and spring constants are successfully established. Both the two-dimensional (2D) square lattice and common three-dimensional (3D) structures are taken into account in the procedure for facilitating, bridging the gap between structural complexity and numerical experiments. A new direction for understanding the physical phenomena in strain engineering is established.

No MeSH data available.


Related in: MedlinePlus

a A schematic illustration of 2D square system and b the selected atom (upper left in a) responded to forces
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Fig1: a A schematic illustration of 2D square system and b the selected atom (upper left in a) responded to forces

Mentions: Assuming that the displacements of atoms, thus the infinitesimal changes of bond lengths, are along the axial direction, Poisson’s ratio ν is often expressed as ν = − dεtrans/dεaxial, where εtrans and εaxial represent the transverse and axial strains, respectively. The unit cell of a 2D square system demonstrated in Fig. 1a is composed of four atoms and has two types of spring bonds along the side and diagonal directions, respectively, with constants K1 and K2. By the Poisson’s ratio definition, when a stretching force F is exerted along the y direction, the resulted two length variations along x and y directions are expressed as δ1 and δ2, respectively, in which a represents the lattice constant and δ1,2 ≪ a. The change in diagonal length can be easily obtained by the simple trigonometric function. The total diagonal bond length is . Owing to the minuscule length variations, it can be approximately expressed as by ignoring the small second-order terms. Thus, the bond length change in the diagonal direction is described as .Fig. 1


Calculation of Elastic Bond Constants in Atomistic Strain Analysis.

Chen H, Wang J, Ashalley E, Li H, Niu X - Nanoscale Res Lett (2015)

a A schematic illustration of 2D square system and b the selected atom (upper left in a) responded to forces
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4608958&req=5

Fig1: a A schematic illustration of 2D square system and b the selected atom (upper left in a) responded to forces
Mentions: Assuming that the displacements of atoms, thus the infinitesimal changes of bond lengths, are along the axial direction, Poisson’s ratio ν is often expressed as ν = − dεtrans/dεaxial, where εtrans and εaxial represent the transverse and axial strains, respectively. The unit cell of a 2D square system demonstrated in Fig. 1a is composed of four atoms and has two types of spring bonds along the side and diagonal directions, respectively, with constants K1 and K2. By the Poisson’s ratio definition, when a stretching force F is exerted along the y direction, the resulted two length variations along x and y directions are expressed as δ1 and δ2, respectively, in which a represents the lattice constant and δ1,2 ≪ a. The change in diagonal length can be easily obtained by the simple trigonometric function. The total diagonal bond length is . Owing to the minuscule length variations, it can be approximately expressed as by ignoring the small second-order terms. Thus, the bond length change in the diagonal direction is described as .Fig. 1

Bottom Line: At the atomistic level, this approach is within the framework of linear elastic theory and encompasses the neighbor interactions when an atom is introduced to stress.Departing from the force equilibrium equations, the relationships between ν, K, and spring constants are successfully established.Both the two-dimensional (2D) square lattice and common three-dimensional (3D) structures are taken into account in the procedure for facilitating, bridging the gap between structural complexity and numerical experiments.

View Article: PubMed Central - PubMed

Affiliation: State Key Laboratory of Electronic Thin Film and Integrated Devices, University of Electronic Science and Technology of China, Chengdu, 610054, China.

ABSTRACT
Strain analysis has significance both for tailoring material properties and designing nanoscale devices. In particular, strain plays a vital role in engineering the growth thermodynamics and kinetics and is applicable for designing optoelectronic devices. In this paper, we present a methodology for establishing the relationship between elastic bond constants and measurable parameters, i.e., Poisson's ratio ν and systematic elastic constant K. At the atomistic level, this approach is within the framework of linear elastic theory and encompasses the neighbor interactions when an atom is introduced to stress. Departing from the force equilibrium equations, the relationships between ν, K, and spring constants are successfully established. Both the two-dimensional (2D) square lattice and common three-dimensional (3D) structures are taken into account in the procedure for facilitating, bridging the gap between structural complexity and numerical experiments. A new direction for understanding the physical phenomena in strain engineering is established.

No MeSH data available.


Related in: MedlinePlus