2 Atomic Force Acoustic Microscopy

Abbreviations a 1 , a 2 , a 3 , a 4 and A 1 , A 2 , A 3 , A 4 Constants in the shape function y(x) a C Contact radius α Wave number of the flexural waves A Cross-section area of the cantilever b Thickness of the cantilever c P Ratio φ Lat /φ d Y 0 , d X0 Normalized amplitude of the sensor tip in y-and x-direction, respectively δ n , δ L Normal, lateral contact deflection (in the coordinate system of the sample surface) E Young's modulus of the cantilever E * Reduced Young's modulus of the contact ε Displacement of the additional mass m L from the center of the beam E T , E S Young's modulus of the tip, the surface G * Reduced shear modulus of the contact G T , G S Shear modulus of the tip, the surface F n , F L Normal, lateral forces (in the coordinate system of the sample surface) f Frequency ϕ Tilt angle of the cantilever φ, φ Lat Dimensionless normal, lateral contact function Φ Phase γ , γ Lat Normal, lateral contact damping h Height of the sensor tip η Air Damping constant describing losses by air I Area moment of inertia L Length of the cantilever L 1 Distance from the fixed end of the cantilever to the position of the tip L 2 Distance from the free end of the beam to the tip k * , k * Lat Normal, lateral contact stiffness k C Static spring constant of the cantilever