The Normal Fluid Fraction in the Adsorbed Helium Film

The resonant frequency of a thickness-shear mode oscillating quartz crystal is lowered by virtue of the mass loading of any film laid down on its surfaces.1,2 For a uniformly deposited, thin solid film with thickness less than 1% or so of the crystal thickness this change Δf, is given by the formula $$ - \Delta f = 2(2{f^2}/c{\rho _q})\sigma $$ (1) Here σ represents that part of the mass per unit area which remains rigidly coupled to the substrate motion, f is the resonant frequency, c is the shear wave velocity in the crystal, and ρ q is the density of the quartz.