A finite temperature continuum theory based on interatomic potential in crystalline solids

2008 ◽  
Vol 42 (4) ◽  
pp. 531-541 ◽  
Author(s):  
Albert C. To ◽  
Wing Kam Liu ◽  
Adrian Kopacz
Keyword(s):  
Finite Temperature ◽  
Interatomic Potential ◽  
Continuum Theory ◽  
Crystalline Solids

A Finite-Temperature Continuum Theory Based on Interatomic Potentials

2005 ◽  
Vol 127 (4) ◽  
pp. 408-416 ◽  
Author(s):  
H. Jiang ◽  
Y. Huang ◽  
K. C. Hwang
Keyword(s):  
Temperature Dependence ◽  
Finite Temperature ◽  
Interatomic Potential ◽  
Coefficient Of Thermal Expansion ◽  
Harmonic Approximation ◽  
Continuum Theory ◽  
Single Wall Carbon Nanotubes ◽  
Interatomic Potentials ◽  
Atomistic Models ◽  
Continuum Theories

There are significant efforts to develop continuum theories based on atomistic models. These atomistic-based continuum theories are limited to zero temperature (T=0K). We have developed a finite-temperature continuum theory based on interatomic potentials. The effect of finite temperature is accounted for via the local harmonic approximation, which relates the entropy to the vibration frequencies of the system, and the latter are determined from the interatomic potential. The focus of this theory is to establish the continuum constitutive model in terms of the interatomic potential and temperature. We have studied the temperature dependence of specific heat and coefficient of thermal expansion of graphene and diamond, and have found good agreements with the experimental data without any parameter fitting. We have also studied the temperature dependence of Young’s modulus and bifurcation strain of single-wall carbon nanotubes.

Cauchy–Born rule and stability of crystalline solids at finite temperature

2021 ◽  
Vol 19 (6) ◽  
pp. 1461-1490
Author(s):  
Tao Luo ◽  
Yang Xiang ◽  
Jerry Zhijian Yang ◽  
Cheng Yuan
Keyword(s):  
Finite Temperature ◽  
Crystalline Solids ◽  
Born Rule

Mechanics of Carbon Nanotubes: A Continuum Theory Based on Interatomic Potentials

2007 ◽  
Vol 340-341 ◽  
pp. 11-20 ◽  
Author(s):  
Han Qing Jiang ◽  
Keh Chih Hwang ◽  
Young Huang
Keyword(s):  
Carbon Nanotubes ◽  
Interatomic Potential ◽  
Coefficient Of Thermal Expansion ◽  
Constitutive Models ◽  
Continuum Theory ◽  
Mechanical Deformation ◽  
Deformation Energy ◽  
Interatomic Potentials ◽  
Linear Elastic ◽  
Defect Nucleation

It is commonly believed that continuum mechanics theories may not be applied at the nanoscale due to the discrete nature of atoms. We developed a nanoscale continuum theory based on interatomic potentials for nanostructured materials. The interatomic potential is directly incorporated into the continuum theory through the constitutive models. The nanoscale continuum theory is then applied to study the mechanical deformation and thermal properties of carbon nanotubes, including (1) pre-deformation energy; (2) linear elastic modulus; (3) fracture nucleation; (4) defect nucleation; (5) electrical property change due to mechanical deformation; (6) specific heat; and (7) coefficient of thermal expansion. The nanoscale continuum theory agrees very well with the experiments and atomistic simulations without any parameter fitting, and therefore has the potential to be utilized to complex nanoscale material systems (e.g., nanocomposites) and devices (e.g., nanoelectronics).

Freeze fracture imaging and computer simulation of liposome structure: Membrane geometry and defects

1983 ◽  
Vol 41 ◽  
pp. 646-647
Author(s):  
Joseph A. Zasadzinski
Keyword(s):  
Liquid Crystalline ◽  
Freeze Fracture ◽  
Continuum Theory ◽  
Closed Surfaces ◽  
Straight Line ◽  
Low Weight ◽  
Concentric Spheres ◽  
Membrane Geometry ◽  
Dupin Cyclides ◽  
Limiting Case

At low weight fractions, many surfactant and biological amphiphiles form dispersions of lamellar liquid crystalline liposomes in water. Amphiphile molecules tend to align themselves in parallel bilayers which are free to bend. Bilayers must form closed surfaces to separate hydrophobic and hydrophilic domains completely. Continuum theory of liquid crystals requires that the constant spacing of bilayer surfaces be maintained except at singularities of no more than line extent. Maxwell demonstrated that only two types of closed surfaces can satisfy this constraint: concentric spheres and Dupin cyclides. Dupin cyclides (Figure 1) are parallel closed surfaces which have a conjugate ellipse (r1) and hyperbola (r2) as singularities in the bilayer spacing. Any straight line drawn from a point on the ellipse to a point on the hyperbola is normal to every surface it intersects (broken lines in Figure 1). A simple example, and limiting case, is a family of concentric tori (Figure 1b).To distinguish between the allowable arrangements, freeze fracture TEM micrographs of representative biological (L-α phosphotidylcholine: L-α PC) and surfactant (sodium heptylnonyl benzenesulfonate: SHBS)liposomes are compared to mathematically derived sections of Dupin cyclides and concentric spheres.

The need of electron microscopy in the study of domains and domain walls in ferroelectrics

1994 ◽  
Vol 52 ◽  
pp. 550-551
Author(s):  
Wenwu Cao
Keyword(s):  
Domain Wall ◽  
Domain Walls ◽  
High Mobility ◽  
Continuum Theory ◽  
Polarization Vector ◽  
Ferroelectric Materials ◽  
Dielectric Constants ◽  
Nonlocal Coupling ◽  
Cubic Symmetry ◽  
Gradient Energy

Domain structures play a key role in determining the physical properties of ferroelectric materials. The formation of these ferroelectric domains and domain walls are determined by the intrinsic nonlinearity and the nonlocal coupling of the polarization. Analogous to soliton excitations, domain walls can have high mobility when the domain wall energy is high. The domain wall can be describes by a continuum theory owning to the long range nature of the dipole-dipole interactions in ferroelectrics. The simplest form for the Landau energy is the so called ϕ model which can be used to describe a second order phase transition from a cubic prototype,where Pi (i =1, 2, 3) are the components of polarization vector, α's are the linear and nonlinear dielectric constants. In order to take into account the nonlocal coupling, a gradient energy should be included, for cubic symmetry the gradient energy is given by,

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