Assumptions of the Standard Model

A standard model has emerged for the calculation of the resonance frequencies of quartz crystal resonators coated with planar layers [37,42-45]. We first 

The resonator and all cover layers are laterally homogeneous and laterally infinite. 

The distortion of the crystal is given by a transverse plane wave with the k vector perpendicular to the surface normal (thickness-shear mode). There are neither compressional waves [24] nor flexural contributions to the displacement pattern [46]. There are no nodal fines in the plane of the resonator. The standard model ignores anharmonic side bands (spurious modes) [23]. 

All stresses are proportional to strain. linear viscoelasticity holds [47]. 

The voltage across the crystal is a boundary condition controlled by the experimentalist. The current through the electrodes is the primary parameter of the measurement. 

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In Section III, we discussed the implications of the assumptions of the standard model for the validity of the usual Kramers-type slow variable... 

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