where 𝑝 q is the density of quartz, 𝐺 q is the shear modulus of quartz, 𝑓 0 is the resonance frequency of the crystal, ∆𝑓 is the frequency shift (in Hz), 𝑛 is the n th overtone order (odd number integer), ∆𝑚 is the change in mass and 𝐴 is the surface area of the quartz crystal. Here we refer to the ∆𝑚/𝐴 term as "mass evolution" in arbitrary units due to the uncertainty in the quartz crystal surface area.