VNA is best to get these values out from a pezieo thin films. Please contact Dr. Anne Bernassau on her email [email protected] who work in this area and may be able to help you to sort out your problem.
The Q value of acoustic thin films depends on combined elasticity, hardness (density of cohesion energy) film thickness and mass and lower plasticity. This will not only at least qualitatively predict the acoustic properties, but will help to select and optimize the film depositing process with which to improve these properties.
It is not so easy to give a value of Q for a film. I understand that you want to characterize the resonator you are making with a piezoelectric thin film. The Q of a FBAR strongly depend on haw it is made. The acoustic isolation is the main issue to consider. Is the device suspended? is it fabricated atop an acoustic reflector (Bragg mirror for instance)? The losses of acoustic energy are actually the main concern when Q is below 1000.
The intrinsic losses (viscoelastic) of the materials usually used in FBAR influence the Q in a second order, except if you use "soft" metals like Al, Cu or Au. As a general rule, as higher the acoustic velocity, the lower the losses are. To evaluate the properties of materials you must be able to fabricate very good performing resonators.