Model for Interpreting Surface Crystallization Using Quartz Crystal Microbalance: Theory and Experiments

Surface crystallization of calcium sulfate was investigated using a dissipation crystal quartz microbalance (QCM-D) together with microscopy to understand the mechanical property changes occurring during the growth process. The use of optical microscopy and SEM revealed that needle-shaped crystals grow as clusters on the QCM sensor’s surface, not in uniform layers. As crystallization growth progressed, QCM-D revealed inversions between negative and positive frequency shifts. This behavior, a function of the growth of crystals in clusters, is not adequately predicted by existing models. As such, a new mass-to-frequency conversion model is proposed herein to explain the observed frequency inversions. This model is derived from a lumped element approach with point-contact loading and Mason equivalent circuit theory. Critically, the physical phenomena occurring form the basis of the model, particularly addressing the three sources of impedance. When a crystal nucleates and grows, its inertial impedance is considered along with a Kelvin–Voigt link with a hydration layer. A comparison between the proposed model and experimental data, of both frequency and dissipation data for the first four harmonics, shows good agreement for the supersaturations (S = C/C*) of S = 3.75, S = 3.48, and S = 3.22. Additionally, significant improvements over existing models for the case of surface crystallization are observed. The proposed model was therefore able to explain that frequency inversions are caused by a shift from inertia-dominated to elastic-dominated impedance, occurring as a result of crystal growth. Using the nucleation induction time and nucleation rates, determined with imaging, an additional understanding of the crystals’ mechanical properties (stiffness and dampening) was obtained.