Potential_Part_2

Potential_Part_2 - Fitting the parameters of the potential...

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University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei interstitials vacancies equilibrium Fitting the parameters of the potential to experimental data Thermal expansion Elastic and vibrational properties High pressure measurements
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University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei The term ~1/r ij 12 - the repulsion between atoms when they are brought close to each other. Its physical origin is related to the Pauli principle: when the electronic clouds surrounding the atoms starts to overlap, the energy of the system increases abruptly. The exponent 12 was chosen on a practical basis: Lennard-Jones potential is particularly easy to compute. In fact, on physical grounds an exponential behavior would be more appropriate. Exponential term for repulsion (Born-Mayer potential) is typically used in simulations where high-energy inter-atomic collisions are involved. The term ~1/r ij 6 , dominating at large distance, constitute the attractive part an describes the cohesion to the system. A 1/r 6 attraction describes van der Waals dispersion forces (dipole- dipole interactions due to fluctuating dipoles). These are rather weak interactions, which however are responsible for bonding in closed-shell systems, such as inert gases. Lennard – Jones potential (I) () σ σ ε = 6 ij 12 ij ij r r 4 r U Pauli repulsion Dipole-dipole attraction equilibrium
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University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei The potential provides a good description of van der Waals interaction in inert gases and
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Potential_Part_2 - Fitting the parameters of the potential...

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