Thermal properties interatomic potentials

Molecular dynamics simulations entail integrating Newton s second law of motion for an ensemble of atoms in order to derive the thermodynamic and transport properties of the ensemble. The two most common approaches to predict thermal conductivities by means of molecular dynamics include the direct and the Green-Kubo methods. The direct method is a non-equilibrium molecular dynamics approach that simulates the experimental setup by imposing a temperature gradient across the simulation cell. The Green-Kubo method is an equilibrium molecular dynamics approach, in which the thermal conductivity is obtained from the heat current fluctuations by means of the fluctuation-dissipation theorem. Comparisons of both methods show that results obtained by either method are consistent with each other [55]. Studies have shown that molecular dynamics can predict the thermal conductivity of crystalline materials [24, 55-60], superlattices [10-12], silicon nanowires [7] and amorphous materials [61, 62]. Recently, non-equilibrium molecular dynamics was used to study the thermal conductivity of argon thin films, using a pair-wise Lennard-Jones interatomic potential [56]. 

A molecular dynamics calculation was performed for thorium mononitride ThN(cr) in the temperature range from 300 to 2800 K to evaluate the thermophysical properties, viz. the lattice parameter, linear thermal expansion coefficient, compressibility, heat capacity (C° ), and thermal conductivity. A Morse-type function added to the Busing-Ida type potential was employed as the potential function for interatomic interactions. The interatomic potential parameters were semi-empirically determined by fitting to the experimental variation of the lattice parameter with temperature. 

To obtain an accurate estimate of thermodynamic properties for crystalline silica polymorphs, one needs an accurate description of the phonon density of states. Given the complexity of the problem, this is tractable only with several assumptions. For example, it is often assumed that the calculated phonon spectra are not strongly dependent on temperature. Certainly this will be a satisfactory assumption in the absence of any thermal expansion, and any changes in the interatomic potentials as a function of temperature. In this case, the force constants, and consequently the dynamical properties like phonon frequencies and density of states, will be independent of temperature. 

However, the drawback of ab initio calculations is that they usually refer to the athermal limit (T = 0 K), so that pressure but not temperature effects are included in the simulation. Although in principle the ab initio molecular dynamics approach[13] is able to overcome this limitation, at the present state of the art no temperature-dependent quantum-meehanieal simulations are feasible yet for mineral systems. Thus thermal properties have to be dealt with by methods based on empirical interatomic potential functions, containing parameters to be fitted to experimental quan-tities[14,15, 16]. The computational scheme applied here to carbonates is that based on the quasi-harmonic approximation for representing the atomic motion[17]. 

The shapes of the interatomic potential curves are approximations chosen for mathematical convenience. Such potential functions are generally used in discussions on a variety of properties of molecules and lattices optical absorption and luminescence, laser action, infrared spectroscopy, melting, thermal expansion coefficients, surface chemistry, shock wave processes, compressibility, hardness, physisorption and chemisorption rates, electrostriction, and piezoelectricity. The lattice energies and the vibration frequencies of ionic solids are well accounted for by such potentials. On heating, the atoms acquire a higher vibrational energy and an increasing vibrational amplitude until their amplitude is 10-15% of the interatomic distance, at which point the solid melts. 

I tested the GAP models on a range of simple materials, based on data obtained from Density Functional Theory. I built interatomic potentials for the diamond lattices of the group IV semiconductors and I performed rigorous tests to evaluate the accuracy of the potential energy surface. These tests showed that the GAP models reproduce the quantum mechanical results in the harmonic regime, i.e. phonon spectra, elastic properties very well. In the case of diamond, I calculated properties which are determined by the anharmonic nature of the PES, such as the temperature dependence of the optical phonon frequency at the F point and the temperature dependence of the thermal expansion coefficient. Our GAP potential reproduced the values given by Density Functional Theory and experiments. 

The advent of computational simulation techniques as an accepted component of material development is one of the most important advances in material research. Molecular Dynamics (MD) is nowadays well established as a powerful tool to provide an atomic scale picture of the structure and insight into the behavior of complex glasses in different environments and under different conditions. Recent advances in the construction of interatomic potential allow the correct quantitative evaluation of the numerical values of stractural, mechanical, thermal, electrical and transport properties for simple glasses [9-15]. However, accurate and reliable evaluation of the same properties for multicomponent glasses has proved far more difficult. 

The correlation earlier developed by Hanley (1974) for the dilute-gas thermal conductivity was calculated for the 11-6-8 interatomic potential with parameters a and /k from fitting both transport and equilibrium properties. The correlation of Kestin et al. (1984) is a universal correlation based on the extended principle of corresponding states (see Chapter 11) for transport and equilibrium properties. The correlation of... 

Use the interatomic bonding potentials for a qualitative discussion of properties such as thermal expansion coefficients, compressibility, optical behavior, and chemisorption rate. 

Metropolis Monte Carlo (MC) simulations (Allen and Tildesley 1987 Frenkel and Smit 2002) have been used to predict the structural and thermodynamic properties of mixtures of elemental semiconductors as also compound semiconductors. MC simulations have been conducted using both the VFF and Tersoff potential models to describe the interatomic interactions. The structural properties determined include lattice constants, thermal expansion coefQdents and bond lengths. The temperature versus composition miscibility diagram of ternary alloys at a given pressure, and the miscibility envelope for quaternary alloys at given temperature and pressure conditions have been determined using the transition matrix Monte C arlo (TMMC) method. 

The optical phonon spectrum is one of the most fundamental characteristics of the crystals. It reflects the specific features of the interatomic interactions and gives very comprehensive and detailed information about the thermal and optical properties involving the efficiency of the optoelectronic devices. The vibrational properties in all the nitride systems have heen investigated in detail over the years by Raman scattering (RS) spectroscopy. Recent studies of nonpolar a-plane GaN by RS confirmed the finding in the c-plane GaN [107, 108]. However, in some cases there is a lack of agreement between the values of some phonon deformation potentials and strain-free phonon-mode positions in GaN and AlN, as determined theoretically and by employing RS spectroscopy. The nonpolar materials allow an access to the complete set of phonons by infrared spectroscopic ellipsometry (IRSE). This provides an alternative tool to study the vihrational properties and to establish very important and useful fundamental parameters of the nitrides. 

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