# Temperature compensation for measured frequency and dissipation values

Hello,

I am using the openQCM Q-1 to measure particle adsorption from liquid media. I have been performing the experiments in an air-conditioned lab, where temperature is usually controlled within 1.5 degree celsius.

While taking measurements, I have noticed that the readings follows the trend of the temperature measurements, whereby when temperature decreases, frequency decreases while dissipation increases. The temperature fluctuations are not large, typically within 1 degree celsius throughout the experiment, but sudden fluctuations (e.g. due to surrounding movement or air condition cycles) affects the frequency and dissipation values measured.

I have previously worked with the QCM200 system from Stanford Research Systems, and they had provided temperature coefficients of 8Hz/°C and 4Ω/°C for frequency and resistance, respectively (values are for AT-cut, 5MHz crystals in water under static conditions). May I know if there is a similar method that I can use to perform temperature compensation on the measured frequency and dissipation values using the openQCM Q-1 device?

I would greatly appreciate your advice regarding this matter to ensure the validity of my data. Thank you in advance for your time and assistance.

## Comments

• Hi huijeanlim,
regarding your question, each quartz has a T-freq dependance. This is due to the variation of the wave propagation along with the quartz thickness. Anyway, it is important to underline that every single quartz has a different T behavior with respect to another one because of its intrinsic physical difference. (see the below image)

So to give only one T coefficient can be certainly useful but in my opinion not sufficient.
Regarding the T-freq relation, QCM sensors have a dependence well described by a 6th-degree polynomial.
You can easily take account of this effect by experimentally build a T-freq curve with a clean sensor in your experimental environment (eg.: air, vacuum pr liquid medium).

Once retrieved this curve (that can differ from sensor to sensor) you can subtract this effect from your experimental data.

Below you can observe an example of T vs freq curve (red are experimental data and blue are fitted data)

I hope this will help you.
• Hi Raffaele,

Thanks for your reply, I will give it a try.
• You are welcome and thank you too!
• Hi, we have kind of a very similar problem. We are trying to generate a similar characterization curve as the one Raffaele showed in his previous post. We are using the openQCM Q-1- shield. We were wondering how you performed that experiment because we see in our data a time lag between the temperature measured (the temperature sensor is placed on the shield?) and the frequency reading.

Thanks for the help
• Hi Vince90, I do not if huijeanlim will answer and how he performed the calibration. Anyway, a temporal lag can be due to the distance from the QCM sensor from the T sensor. As matter of fact each system has its proper thermal inertia. I can only say you that in a complete Q-1 device the T sensor is just 1-2 mm below the QCM sensor.
• Hi @Vince90, I've noticed a time lag of 100s between the temperature and frequency readings in my experiments, which was consistent across many runs/different crystals. So I've simply removed this time lag by shifting the T measurements 100s forward. From there, the T-freq curves have a good R2 value of >0.99 for both the 6th degree polynomial and a linear function. In my case, I've just used the linear function to perform T compensation on my frequency data since I'm dealing with very small T fluctuations, and I am able to get R2>0.99 for the linear function. Hope this helps.
• Great @huijeanlim ... your approach is absolutely correct!
• Hi @raffaele.battaglia , could you kindly provide the reference for the T-freq relation of QCM sensors - particularly on the 6th degree polynomial fit mentioned in your comment above. Thanks a lot for your help!
• Hi @huijeanlim, did you intend the "zero" point Temperature?
• Hi @raffaele.battaglia , was referring to this statement:

"Regarding the T-freq relation, QCM sensors have a dependence well described by a 6th-degree polynomial."

was hoping you could provide the reference for this as I would like to have a look at it too!
• Hi @huijeanlim.... first sorry for my reply delay.

The discussion is more complex than it seems. So, it is better to describe how the temperature affects the frequency baseline behavior.
So, in order to exploit the piezoelectric properties of quartz, especially as a resonant element, a "mother" crystal must be cut to obtain elements suitable for a wide range of applications.
The cutting procedures, therefore, follow specific rules that determine the size and orientation of the element with respect to the crystallographic reference system (Figure 1).

Fig.1: Representation of some of the main quartz cuts (Bradshaw, 2000).

In fact, by means of suitable cuts, piezoelectric elements are manufactured to obtain performances that are aimed at the final uses of the product.

A crystal X, for example, is generally used at resonance frequencies below 1.0 MHz. This cut allows the generation of relatively high voltages
Specifically, this cut allows generating relatively high voltages when, due to the direct piezoelectric effect, the element is subject to compression. By exploiting, instead, the inverse piezoelectric effect, the vibration mode induced on the X-shear elements occurs by bending, twisting, and/or sliding (Figure 2).

Fig. 2: Vibration modes of quartz resonant elements.

The resonant frequency shows for these cuts a characteristic quadratic trend with the temperature.
A voltage with a similar magnitude can also be generated by one shear deformation acting on a Y-type crystal. When stressed, the resonant element Y generally vibrates with frequencies greater than 1.0 MHz and the frequency-temperature trend can be represented with a third-degree polynomial.
Among the cuts schematized in Figure 1, the AT-cut (to which we will refer from now on) has become the most classic in the production of quartz for oscillators. The choice of the AT elements for the production of oscillators is dictated above all by the high stability of frequency that these present with respect to the temperature variation (Figure 3).

Fig. 3: Frequency dependences on temperature for different quartz cuts.

The AT-cut is carried out with an angle θ (Figure 4) with respect to the crystal axis z typically centered around 35° 20’ but may vary depending on the applications for which is used.

Fig. 4: Representation of an AT-cut angle

The choice of AT elements for the production of oscillators is mainly due to their high-frequency stability with respect to temperature variations (Figure 3). The
AT cutting is carried out at an angle θ (Figure 4) with respect to the crystallographic axis z typically centered around 35°20’. but can vary according to the applications for which it is used.
The plate is generally a disc, whose thickness determines the oscillation frequency and the mechanical deformation.
When a potential difference is applied between the two faces of the piezoelectric element, a stationary wave travels through the thickness of the crystal, inducing a "displacement" of the layers of the crystal along with the thickness (Fig. 5).

Fig. 5: An AT-cut quartz element, to which a sinusoidal voltage is applied, vibrates by "sliding" along with the thickness.

The greatest displacement will occur precisely on the surfaces of the crystal in the direction normal to the wave propagation. At resonance, an odd number of half-waves are encompassed along with the thickness of the crystal. Figure 6 shows the frequency-temperature curves for an AT element. In an AT-cut, the temperature behavior curve varies according to a third-degree (better 6th degree) polynomial with an inflection point between +25 ◦C and +35 ◦C.
The slope of the curve around the inflection point depends on the cut angle of the piezoelectric element. For this reason, the thickness is the first factor that determines the resonance frequency of a vibrating AT crystal in TSM mode AT crystals are generally produced to operate in frequency ranges between ∼ 1 MHz to ∼ 30 MHz (fundamental frequency) and from ∼ 30 MHz to ∼ 250 MHz (eg.: overtones: 3° , 5° , 7° and 9°).

Fig.6: Frequency-Temperature dependence curves for different AT-cuts angles θ

• Hi @raffaele.battaglia , thank you very much for the explanation on the temperature dependence of the QCM crystals!
• You are welcome and thank you too!
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