# Main Page

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.

## Contents

## 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 to the mass of a thin rigid film added to the quartz surface as:

where is the resonant frequency, is the active electrode area, is the density, is the shear modulus and 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

- ↑ 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