• A mechanical vibration propagates along the surface.
• The amplitude decays exponentially in the material.
• The penetration depth reduces with increasing frequency.
• Measurable wave parameter - phase velocity:

for homogeneous, isotropic material:
E = Young’s modulus,
nju = Poisson’s ratio,
rho = density,

low frequency deep penetration substrate determines the wave velocity

high frequency low penetration film determines the wave velocity

• It follows: In coated materials, the surface wave velocity depends on frequency, termed dispersion.

frequency => 0: Phase velocity -> velocity of the substrate
frequency => infinitely: Phase velocity -> velocity of the film,

Phase velocity depending on frequency:

• The velocity depends on frequency. The curve may ascend or descend, depending on the ratio of Young’s modulus to density is higher for the film or for the substrate.

 

Pure substrate:

The phase velocity is constant, e.g. it does not depend on frequency.

• film modulus - the slope,
• substrate modulus - velocity at zero frequency,

1. Measuring the dispersion curve.
2. Fitting a theory to the measured curve to calculate the material parameters.