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Configuration of the three KSiNW samples in present work. (a) The equilibrium position of a spring connected to a point mass. The right end is stretched by an external force (with fixing left end). This mass spring oscillator starts to oscillate after is removed. (b)–(d) The three studied KSiNW samples S1, S2, and S3. Left end is fixed. Tips on the right ends are in blue online. Cartesian coordinate system: x is along axial direction from left to right, and z is the viewing direction of structures shown here.
Energy oscillation due to the mechanical oscillation in KSiNW S1. Energies are with reference to the value just before the actuation of the mechanical oscillation (i.e., t = 0). The curve above (bellow) zero is the kinetic (potential) energy. The energy oscillates between kinetic and potential energy at frequency f = 31.26 GHz, corresponding to the mechanical oscillation. The total energy is the horizontal line at zero, demonstrating a good energy conservation in the NVE ensemble. Two cosine functions (red online) are used as guides to the eye. We note that the energy oscillation frequency is double of the mechanical oscillation frequency.
Vibrational displacements of the tip at the right end in KSiNWs. Top to bottom: results for S1, S2, and S3. ux , uy , and uz are the vibration in three Cartesian directions.
The energy spectrum, i.e., the Fourier transform of the kinetic energy time history. The first several low-frequency oscillation modes are denoted for all of the three studied samples. With decreasing aspect ratio from S1, S2 to S3, the second transverse mode in y (TA y 2) undergoes a transition from one-dimensional nanowire behavior into three-dimensional bulk behavior. Inset: Fourier transform of ux , uy , and uz for S3.
Frequency (GHz) of the spring-like mechanical oscillation in three samples actuated with two different actuation strains and 0.02.
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