Point Contacts
The equations concerning viscoelastic properties assume planar layer systems. A frequency shift is also induced when the crystal makes contact with discrete objects across small, load-bearing asperities. Such contacts are often encountered with rough surfaces. It is assumed that the stress–speed ratio may be replaced by an average stress–speed ratio, where the average stress just is the lateral force divided by the active area of the crystal.
Often, the external object is so heavy that it does not take part in the MHz oscillation of the crystal due to inertia. It then rests in place in the laboratory frame. When the crystal surface is laterally displaced, the contact exerts a restoring force upon the crystal surface. The stress is proportional to the number density of the contacts, NS, and their average spring constant, κS. The spring constant may be complex (κS* = κS’ + iκS’’), where the imaginary part quantifies a withdrawal of energy from the crystal oscillation (for instance due to viscoelastic effects). For such a situation, the small-load approximation predicts
The QCM allows for non-destructive testing of the shear stiffness of multi-asperity contacts.
Read more about this topic: Quartz Crystal Microbalance
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