Signal Conditioning

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Conversion factor from thickness to mass per area


I am using a quartz crystal monitor to measure mass changes on the quartz crystal during deposition. The sensor gives the mass changes in terms of the thickness of the material deposited. That is a problem because that means that I have to input the density values of the materials I deposit. I would like to make the sensor give out the mass changes in terms of ng/cm^2. I have to use the so called Sauerbrey equation to do that.The sensor also gives out frequency values of the quartz crystal during a deposition.


Here is the equation:

\Delta f = { -2\Delta m f_0^2 \over A \sqrt{ \rho_q \mu_q } }  = -\frac{2f_0^2}{A \sqrt{ \rho_q \mu_q } }\Delta m.

Equation 1 – Sauerbrey’s equation

f0Resonant frequency (Hz)
Δf – Frequency change (Hz)
Δm – Mass change (g)
A – Piezoelectrically active crystal area (Area between electrodes, cm2)
ρqDensity of quartz (ρq = 2.648 g/cm3)
μqShear modulus of quartz for AT-cut crystal (μq = 2.947x1011 g/cm.s2)


How do I go about converting from frequency to mass? I know I can use the formula but what do I put for measured change in frequeny? The instrument will measure the frequency when i deposit but the formula needs a frequency change.





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sounds like a homework problem, but:

use a little bit of algebra and solve for deltaM.  

if the frequency is at one value before deposition of material, and depositing materials changes said frequency value, that would be your deltaF.

does that help?


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Message 2 of 3

Hi Sicelo,


Are you curious if there is a LabVIEW function that performs this task?  This is most likely a function that you will have to program into LabVIEW by either a Function Node or by using the LabVIEW enviroment to complete. 




Kyle S

Applications Engineer
National Instruments
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