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The Quartz Crystal Microbalance QCM is an higly-sensitive tool to weigh mass deposition in the micrometric range by measuring the frequency variation of a resonating quartz crystal.

Piezoelectric Effect

In 1890 Pierre and Jacques Curie brothers demonstrated the existence of the Piezoelectric Effect , which was initially theorized by the mineralogist René Just Hauy in 1817. The
 exploitation of the piezoelectric effect has led to a series of applications and tools of great interest for studying a wide range of physical, chemical and biological quantities.

Sauerbrey Equation

The Sauerbrey Equation is the primary tool in quartz crystal microbalance applications. It directly relates the changes in resonant frequency \Delta f to the mass \Delta m of a thin rigid film added to the quartz surface as:

\Delta f = -\frac{2f_0^2}{\sqrt{ \rho_Q \mu_Q } }\cdot \frac{\Delta m}{A} = -\frac{2f_0^2}{\rho_Q v_Q}\cdot \frac{\Delta m}{A}

where f_0 is the resonant frequency, A is the active electrode area, \rho_Q is the density, \mu_Q is the shear modulus and v_Q is the shear wave velocity of the quartz crystal [1].

QCM in liquid Kanazawa - Gordon Equation

Electro Mechanical Model and Small - Load Approximation

Index of Symbols

References

  1. Sauerbrey G., "Verwendung von Schwingquarzen zur Wägung dünner Schichten und zur Mikrowägung", Zeitschrift Für Physik, vol. 155, no. 2, pp. 206-222, 1959. DOI 110.1007/BF01337937

Additional Resources

  • openQCM the unique open source Quartz Crystal Microbalance