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A new electromechanical coupling model was built to quantitatively analyze the tuning fork probes, especially the complex ones. A special feature of a novel, soft tuning fork probe, that the second eigenfrequency of the probe was insensitive to the effective force gradient, was found and used in a homemade bimodal atomic force microscopy to measure power dissipation quantitatively. By transforming the mechanical parameters to the electrical parameters, a monotonous and concise method without using phase to calculate the power dissipation was proposed

The Model Analysis of a Complex Tuning Fork Probe and Its Application in Bimodal Atomic Force Microscopy