| Summary: | 博士 === 國立清華大學 === 動力機械工程學系 === 95 === This dissertation uses atomistic-continuum mechanics (ACM) based on the finite element method (FEM) to investigate the elastic properties of the nanoscale single crystal group IV in different crystallography planes of (100), (110), and (111) under uniaxial tensile loading and modal analysis. The measured elastic modulus of SCS is in reasonable agreement with the results reported in the literature based on macro and micro scale experiments. The effect of strain through the variation of prescribed displacement on the measured mechanical properties was also investigated. It could be observed that the elastic modulus was nearly constant and relatively insensitive to the strain (0.1%~1%). Meanwhile, different interatomic potential functions were adopted to simulate and compare the mechanical properties, including the Stillinger-Weber and Tersoff potential. The ACM simulation results for both Stillinger-Weber and Tersoff potentials show a similar trend in the estimation of mechanical properties. The discrepancy of the elastic modulus between the Stillinger-Weber and Tersoff potential function on the (110) crystal plane were within 5%.
Furthermore, an analytic solution of single crystal silicon of diamond and diamond-like structure was derived to estimate the elastic (linear) behaviors of single lattice silicon based on the truss analysis of static mechanics. Through this analytical solution could reduce the complexity of the real bulk silicon an agreement on trends between the predicted elastic modulus and the corresponding bulk value is achieved. In addition, this analytic solution could apply to the other diamond and diamond-like structure, includes carbon, germanium and gallium arsenide. Moreover, the larger deformation was also considered to investigate the mechanical properties of the single crystal silicon.
In addition to the tensile test method, the modal analysis is also employed to estimate the elastic modulus of materials at nanoscale range. From simulation results showed that the natural frequency and mode shape are agree with the analytic solution base on the Euler-Bernoulli beam theory.
The size dependence of elastic properties of SCS at nanoscale was studied using ACM with Stillinger-Weber potential function. It was found that the mechanical properties are highly size dependent at nanoscale. Furthermore, fracture behavior of SCS at the nanoscale was also simulated using ACM. The simulation results reveal that the fracture phenomena prediction was accurate and appropriate using atomistic-continuum mechanics.
Finally, the defected model was constructed to investigate the elastic modulus of single crystal silicon under different crystalline plane using atomistic-continuum mechanics. The ACM simulation result reveals that the elastic modulus monotonously decreases with the concentration of vacancies defect increasing. This dissertation also investigates the size dependence elastic modulus with defect formation.
According to abovementioned simulation results, the use of an atomistic-continuum mechanics and analysis solution in the investigation of nanoscale materials was not limited to single crystal silicon, but it can also be applied to other nano-structured materials once the interatomic potential and the atomic structure of the material are always known. Therefore, atomic model is constructed using atomistic-continuum mechanics not only to apply in axis tensile loading test but also in the modal analysis. And the estimated of material properties under tensile loading and modal analysis was agreed with the bulk value of experiments in the literatures
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