.png)
Classification of Materials
To put some order in the world we normally classify the items. In the world of piezo materials we have already seen two different kinds, the single crystals and the ceramics. Another classification would be man-made versus natural materials. However almost all piezo materials that are used technically are man-made. Only a few single crystals like Tourmaline are found in nature only .
The materials specialists use an overwhelming number of classifications criteria such as the fabrication method, the crystallographic aspects or chemical composition. For our purpose when we want to build a piezoelectric sensor a simple order of the sensitivity (for example the compression mode charge constant) makes most sense. Thereby we have to keep in mind that the piezoelectric constants for other modes like shear are mostly quite different.
Another practical aspect to use or choose a piezo material is the useful temperature range. We have seen that above the Curie-temperature the piezo effect is lost. In practice the maximal allowed operating temperature is even quite a bit below that.
Besides the Curie-temperature which is a real hard limit, there are other limiting temperature effects. One particular aspect is the internal electrical resistance of a piezo element which is strongly dependent on the temperature. We will see later that some important characteristics of a piezoelectric sensor are related to this resistance.
There are also materials even with a very high Curie-point which start to decompose at higher temperature. They might for example loose oxygen atoms at the surface and thereby loose the electric resistance.
Sensitivity vs. Maximum Operation Temperature
The picture shows a few piezo-materials with their sensitivity versus the maximum allowed operation temperature.
It shows the drastic decrease of basic sensitivity with increasing temperature capability of the material.
Lead Zirconate Titanate (PZT) is the most commonly used piezo ceramic with compression mode charge constants of a few hundred pC/N and reasonable operations temperatures.
PNM-PT is a group of recently developed single crystals with ultra high sensitivity. They show charge constants of 1000 to 2000 pC/N but with Curie-temperatures of 30 to 80°C.
The Bismuth Titanates (BT) are ceramics in the 500 to 600°C range with sensitivities of 10 to 20 pC/N
Finally there is a real high temperature group (all of them single crystals). Here we find Langatite and Langasite (LGT, LGS), Gallium Phosphate (GaPO), or the rare earth calcium oxoborates such as YCOB, with about 4 to 8 pC/N. This group includes also the natural crystal Tourmaline with 2 pC/N.
Internal Resistance
The internal resistance of a piezo element is the electrical resistance that we measure from one electrode to the other.
A piezo material is basically an insulator. That means the internal Resistance is extremely high. To measure it we need a so-called Teraohm-meter. This instrument indicates the resistance in decades like 10⁶, 10⁷, 10⁸, 10⁹ Ohms etc.
In order to get a proper electrical signal of an accelerometer the internal resistance must be as high as possible. That’s why it is an important characteristic of the material. At room temperature the internal resistance of a sound piezo element is normally in the order of 10¹² to 10¹⁴ Ohms.
If we look at the progression of the internal resistance versus temperature of a piezo material we find that the resistance decreases exponentially with increasing temperature. Depending on the material the resistance may decrease by one decade (ten times) up to more than two decades (one-hundred times) per 100°C of temperature increase.
This figure shows typical internal resistances vs temperature for common size piezo ring elements.
The internal resistance of a piezo element decreases with raising temperature about one decade per 100°C for a Tourmaline element and with more than two decades per 100°C for a PZT element.
Tourmaline
PZT
Before you contunue: ––
Did you know how to make piezo ceramics?
Surface versus Bulk Resistance
The “internal” resistance of a piezo element as for example of the disk we have seen before would be measured from one electrode to the other. In reality we have two electrical paths in parallel and both have their own resistance.
The first path is going through the material from one side to the other. This is the bulk resistance.
The second path is leading on the outer surface from one edge to the other. This is the surface resistance
Bulk resistance
The surface resistance depends besides the material on the physical size of the element, on the circumference of the two electrodes and the distance between them. However there are may other factors to consider like the surface roughness, surface pollution or the surrounding atmosphere, particularly the humidity.
When we carry out a physical test there is a third resistance to keep in mind. As we are measuring very high resistances we have also to consider the inherent insulation resistance of our measuring set-up. It is obvious that we cannot measure a higher value than this resistance which is in parallel with everything.
The higher the test voltage the more robust the measurement will be. This is the reason that for regular measurements of the insulation resistance 500 V are used. However for piezo elements it is not recommended to go over 100V DC because the electric field across the element might change the polarization. At elevated temperature 100 V could already be too much for certain materials.
Resistance and Resistivity
When choosing a piezo material to design an accelerometer we are interested in the bulk resistance of the material. It is the bulk resistance which will determine the internal resistance of the accelerometer, particularly at temperature.
In the material properties catalogues we find the resistivity ρ.
The resistance R we have to calculate considering the physical shape of the element:
R = ρ · t / A [R] = Ohm or Ω
The resistivity ρ is often given in Ohm·cm. In order to get the resistance R correctly it is easiest to transform first the dimensions of the element into cm.
As shown before the bulk resistance is following a certain exponentially decaying curve with increasing temperature.
It is easy to linearize this curve by introducing for the temperature axis a parameter τ
τ = 1/T(abs) · 1000 [τ] = 1/°K
T(abs) is the absolute scale temperature in degrees Kelvin.
If we plot the resistivity versus τ we get an almost perfectly linear distribution. This is true for practically all piezo materials.
Tourmaline
PZT
Surface resistance