, Volume 15, Issue 2, pp 157–161 | Cite as

Electromechanical properties and defect chemistry of high-temperature piezoelectric materials

  • Michal Schulz
  • Jan Sauerwald
  • Denny Richter
  • Holger Fritze
Original Paper


Langasite and gallium phosphate are shown to exhibit piezoelectrically stimulated bulk acoustic waves up to at least 1,400 and 900 °C, respectively. Most critical issues are stoichiometry changes due to, e.g. low oxygen partial pressures, and high losses. Therefore, the paper discusses the atomistic transport and defect chemistry of those crystals and correlates them with the electromechanical properties. First, the defect chemistry of langasite is investigated. As long as the atmosphere is nearly hydrogen-free, the transport of charge carriers is governed by oxygen movement. A dominant role of hydrogen is observed in hydrogenous atmospheres. Based on the developed defect model, donors are expected to suppress the oxygen vacancy concentration and, thereby, the loss in langasite. The prediction is proven by niobium doping and found to be valid. A one-dimensional physical model of thickness shear mode resonators is summarized. The analysis of the resonance spectra showed that the loss of the resonators can be described satisfactorily by mechanical and electrical contributions expressed as effective viscosity and bulk conductivity, respectively. The mechanical loss in langasite is significantly impacted by the electrical conductivity due to the piezoelectric coupling. The effect of the piezoelectric coupling on the loss is negligible for gallium phosphate since it shows an extremely low electrical conductivity.


Langasite Gallium phosphate Piezoelectricity Gas sensors 


Piezoelectric materials play a very important role in the industry and home use. Applications include gas sensors for solid oxide fuel cells (SOFCs) and gas reformers, microbalances, temperature sensors, and actuators of any kind. However, commonly used materials like α-quartz (SiO2) and non-stoichiometric lithium niobate (LiNbO3) cannot be used at elevated temperatures. For example, the phase transition at 573 °C and the strong decreasing resonator quality factor (Q-factor) of quartz permits its use up to around 450 °C. The chemical instability of non-stoichiometric lithium niobate, i.e. its tendency to decomposite, limits its application temperatures to about 450 °C [1, 2].

Langasite (La3Ga5SiO14, LGS) and gallium orthophosphate (GaPO4) are promising materials for high-temperature piezoelectric applications [3, 4]. They exhibit bulk acoustic waves up to at least 1,400 and 900 °C [5], respectively. Understanding of the limiting factors of these materials like electric and ionic conductivity, viscosity, and defect chemistry permits better design of corresponding devices.

This paper focuses on the characterization and comparison of LGS and GaPO4 at elevated temperatures.


Nominally undoped as well as Sr- and Nb-doped LGS single crystals have been grown using the Czochralski method at the Institute for Crystal Growth, Berlin-Adlershof, Germany [6, 7]. GaPO4 single crystals have been purchased at Piezocryst GmbH, Graz, Austria. The growth process of GaPO4 is described, e.g., in [8].

Bulk acoustic wave (BAW) resonators have been prepared by cutting the crystals into about 270 μm-thick circular samples with a radius of 5 mm and subsequent deposition of a key-hole-shaped platinum electrodes. The surface of the samples is perpendicular to the Y-axis of the crystal structure. Such configuration leads to thickness shear mode vibrations, which are suited for gas sensing applications.

The conductivity data have been obtained by measurements of the electrical impedance of LGS and GaPO4 at low frequencies. The data have been acquired at frequencies ranging from 1 Hz to 1 MHz using a Solartron 1260 impedance analyzer. From the resulting semicircle, the bulk conductivities and dielectric coefficients of both materials have been calculated. In order to achieve a well-defined oxygen activity, all LGS samples have been pre-annealed in air at 1,050 °C for several hours.

In order to determine the electromechanical properties, the impedance spectra of LGS and GaPO4 resonators have been acquired in the vicinity of the resonance frequency using a HP E5100A network analyzer. The real and imaginary parts of the impedance have been fitted with the one-dimensional physical model of a vibrating body (see “One-dimensional physical model” section) in order to determine the electromechanical parameters. The bulk electrical conductivity and dielectric coefficient which are used in the physical model are taken from the low-frequency measurements described in the previous paragraph.

Electrical conductivity and defect chemistry

Electrical conductivity

The electrical conductivity of LGS and GaPO4 has been measured at temperatures ranging from 400 to 1,000 °C. As seen in Fig. 1, GaPO4 exhibits a conductivity which is lower by at least two orders of magnitude compared to that of LGS. Therefore, much lower electrical losses are expected in case of GaPO4-based resonators.
Fig. 1

Temperature dependence of the conductivities of LGS and GaPO4

The electrical conductivity of materials at elevated temperatures may be described using complex dielectric coefficients. In this approach, the imaginary part of the complex dielectric coefficient \(\underline{\varepsilon}\) is attributed to the electrical losses of a dielectric material and depends on the angular frequency ω and the bulk conductivity σ as follows [9]:
$$\label{complex_epsilon} \underline{\varepsilon} = \varepsilon -j\frac{\sigma}{\omega} $$
The dielectric coefficient in this form is used in the physical model.

Defect chemistry

A defect model for LGS has been developed by Seh et al. [10, 11, 12]. This model bases on the impedance data, concentration cell measurements and oxygen self-diffusion measured on nominally undoped and doped polycrystalline LGS. This model predicts the conductivity of LGS as a function of oxygen partial pressure, net dopand concentration [A]–[D], and temperature [12].

Acceptor-doped LGS exhibits a mixed ionic and electronic conductivity with a predominant role of ionic transport in the form of oxygen vacancy transport. Donor-doped LGS exhibits electronic conductivity in the entire experimental accessible oxygen partial pressure range (from 0.2 to 10 − 25 bar). The model predicts a perfectly compensated state of nominally undoped LGS, where the conductivity is minimized as visualized in Fig. 2. As shown in the next section, the increase of the electrical conductivity is correlated with the increase of loss in LGS.
Fig. 2

Prediction of the bulk conductivity of LGS at 1,000 °C and selected oxygen partial pressures as a function of net dopand level [12]

The existence of impurities and some amounts of unintended doping has to be taken into account. Therefore, the conductivity of as-grown nominally undoped LGS is higher than the value predicted by the model. In such case, the small amounts of doping may lead to decrease of the conductivity. In order to confirm it, the conductivity of Sr- and Nb-doped LGS has been measured. As seen in Figs. 3 and 4, the 0.5% doped LGS exhibits a significantly lower viscosity.
Fig. 3

The effective viscosity of the differently doped LGS at lower temperatures

Fig. 4

The inverse resonant quality factor of doped LGS at temperatures above 600 °C

Electrochemical properties

One-dimensional physical model

BAW resonators vibrating in the thickness shear mode may be approximated either using an Butterworth-van Dyke equivalent circuit or using a one-dimensional physical model. The first approach is suited to describe sensing properties of such resonators. In this paper, the second approach is used since it correlates the resonance behavior and the material properties directly. Since the majority of measurements are performed at elevated temperatures, the losses have to be taken into account. A detailed description of the model is given in [13]. The following paragraphs show the corresponding terms and equations required for the subsequent discussion, only. As already mentioned in the “Electrical conductivity” section, the electrical loss dielectric material is represented in the form of an imaginary part of the dielectric coefficient.

The mechanical losses may be attributed to the viscous behavior of a resonator. Here, similar to Eq. 1, the effective viscosity η is represented by the imaginary part of the complex stiffness coefficient \(\underline{c}_{66}\) as follows [9]:
$$ \underline{c}_{66} = c_{66} + j\omega\eta. $$
The real part of \(\underline{c}_{66}\) is the stiffness coefficient. Using the complex coefficients, the Newton’s equation of motion and the piezoelectric equations are solved resulting in a function which describes the complex impedance of a resonator dependent on frequency, electrical, and electromechanical parameters. This function is fitted to the impedance spectra measured in the vicinity of the resonance frequency. The material parameters to be determined (η, e, c 66) are the result of this fit procedure.
The shear modulus c 66 is extended by piezoelectric contributions [9]. The newly defined property is the piezoelectrically stiffed shear modulus. Expanding the property for its real and imaginary contributions results in [13]:
$$\label{eq:stiffness} \underline{c} = c_{66} + \frac{e^2}{\varepsilon + \sigma^2/\varepsilon\omega^2} + j\omega\left( \frac{\sigma}{1+\sigma^2/e^2\omega^2} + \eta \right) $$

It must be noted, that this shear modulus depends on the electrical conductivity and the resonance frequency of the sample. It means that the resonators with significantly higher resonance frequency yield a lower relative frequency shift of the signal as a function of the temperature-dependent electrical conductivity.


The losses in resonators may be described using the resonant quality factor Q, which follows from the bandwidth Δf at half maximum of the admittance peak and the resonance frequency f as follows [14]:
$$ Q = \frac{f}{\Delta f}. $$

In the discussed piezoelectric materials, two main contributors of losses are distinguished. The mechanical loss attributed to the effective viscosity dominates at lower temperatures, where the conductivity of material is negligible. As soon as the temperature exceeds 650 °C approximately, the conductivity and the piezoelectric coupling have to be taken into account. The contribution of electrical conductivity to the total loss becomes dominant.

The imaginary part of the shear module \(\underline{c}\) which is shown in Eq. 3 is attributed to the losses in piezoelectric material. It is clearly visible that the total effective loss depends on both the viscosity and the conductivity of the sample as follows
$$ Im(\underline{c}) = \omega\eta + \frac{\omega\sigma}{1 + \sigma^2/e^2\omega^2}. $$
The conductivity related term reaches its maximum at the dielectric relaxation frequency, that is ω = σ/ε and its contribution to the total loss decreases with increasing frequency. The dependence of the electrical and mechanical contributions to the total loss is summarized in Fig. 5.
Fig. 5

Calculated loss in LGS. R M , R η and R σ are related to the total loss, the viscosity, and the electrical loss, respectively

Application limits

Operation in nominally hydrogen-free atmospheres

According to the defect model mentioned in the “Defect chemistry” section, the formation of oxygen vacancies \(\mathrm{V}_\mathrm{O}^{\bullet\bullet}\) at low oxygen partial pressures has to be expected. With decreasing oxygen partial pressure, the reduction reaction \(\mathrm{O}_\mathrm{O} \leftrightarrow \mathrm{V}_\mathrm{O}^{\bullet\bullet} + 1/2 \mathrm{O}_2 + 2e^{−}\) controls the concentration of electrons and oxygen vacancies.

In an acceptor-doped material, the negative charge contribution of the dopands is compensated by the oxygen vacancies formed in the crystal lattice. Under such condition, the electrical conductivity of LGS at higher oxygen partial pressures is kept constant. When the oxygen partial pressure decreases, the reaction of reduction starts to control the total conductivity. There, the conductivity depends on the oxygen partial pressure as follows
$$ \sigma_{el} \propto p_\mathrm{O_2} ^ {-1/4}. $$
Further decrease of oxygen partial pressure will result in the generation of additional free electrons and oxygen vacancies because of the reduction process. The amount of the oxygen vacancies obtained through the reaction of reduction will be much higher than the one of vacancies introduced for charge compensation. The oxygen partial pressure dependence will obey the following equation
$$ \sigma_{\text{el}} \propto p_\mathrm{O_2} ^ {-1/6}. $$

The donator-doped samples exhibit a predominant electronic conductivity. In such cases, the charge introduced to the crystal lattice by doping is compensated by the electrons. At higher oxygen partial pressures, the conductivity is constant.

At very low oxygen partial pressures, the concentration of oxygen vacancies and electrons obtained from the reaction of reduction exceeds the amount of electrons used for charge compensation. Under such conditions, the electrical conductivity depends on the oxygen partial pressure as follows:
$$ \sigma_{\text{el}} \propto p_\mathrm{O_2} ^ {-1/6}. $$

The formation of oxygen vacancies is calculated to result in frequency shifts lower than ±4 Hz at 800 °C for oxygen partial pressures above 10 − 24 bar.

Operation in water containing atmospheres

LGS belongs to the same class of crystals as quartz, and therefore, similar conductivity mechanisms driven by protonic transport have to be expected. Especially, the transport of protons along the Z-axis of the crystals should be much faster than any other type of diffusion. The proton-related conductivity has been described in detail by Schulz et al. [15, 16]. It should be noted, that this transport phenomenon is anisotropic. The proton transport along the X- and Y-axes incorporates the oxygen vacancies. The transport along the Z-axis is much faster and does not require defective oxygen vacancies.

In atmospheres containing hydrogen and water, there is a dynamical equilibrium between oxygen, water, and hydrogen partial pressures. For example, at 800 °C the partial pressure of water is constant at oxygen partial pressures above 10 − 18 bar. Below, there is a linear dependence between water vapor and oxygen partial pressure. Since the concentration of water vapor at higher oxygen partial pressures is constant, its impact on the performance of resonators is negligible. However, under highly aggressive conditions, the protonic conductivity impacts the overall performance of LGS.


The electrical conductivity of LGS is relatively low and may be decreased by means of donator doping, whereas the conductivity of GaPO4 is extraordinary low. It is at least two orders of magnitude lower than that of LGS. Both materials exhibit very good Q-factors at elevated temperatures. It has been found that small donator doping suppresses the electrical conductivity and the losses in LGS in the entire temperature range of measurement.

The phase transformation of GaPO4 limits its operation to temperatures below 970 °C, whereas LGS has been shown to exhibit the bulk acoustic wave vibrations up to at least 1,400 °C. Although the electrical losses in LGS are larger compared to GaPO4, the poor availability of GaPO4 single crystals and an expensive, time-intensive growth process limit its large-scale applications.

Resonators based on LGS have been already integrated in many applications. For example, a high-temperature sensor system has been built by Richter et al. [17]. It consists of CeO2-coated LGS resonators, a small-size custom-built network analyzer, and software. The system exhibits sensitivity to CO and H2 gases commonly found in SOFCs and gas reformers and allows one to distinguish both gases.



The financial support of the German Science Foundation (Deutsche Forschungsgemeinschaft) made this work possible. The authors thank Prof. H. L. Tuller and Dr. H. Seh from the Massachusetts Institute of Technology for a very fruitful collaboration. In addition, the authors thank Mr. E. Ebeling for mechanical machining and preparation of the samples.


  1. 1.
    Fachberger R, Bruckner G, Knoll G, Hauser R, Biniasch J, Reindl L (2004) IEEE Trans Ultrason Ferroelectr Freq Control 51:1427CrossRefGoogle Scholar
  2. 2.
    Bruckner G, Hauser R, Stelzer A, Maurer L, Reindl L, Teichmann R, Biniasch J (2003) In: IEEE int. freq. contr. symp. p 942Google Scholar
  3. 3.
    Smythe R, Helmbold RC, Hague GE, Snow KA (2000) IEEE Trans Ultrason Ferroelectr Freq Control 47:355CrossRefGoogle Scholar
  4. 4.
    Fritze H, Tuller HL (2001) J Appl Phys Lett 78:976CrossRefGoogle Scholar
  5. 5.
    Sauerwald J, Fritze H, Ansorge E, Schimpf S, Hirsch S, Schmidt B (2005) In: International workshop on integrated electroceramic functional structures. Berchtesgaden, GermanyGoogle Scholar
  6. 6.
    Jacobs K, Hofmann P, Klimm D, Reichow J, Schneider M (2000) J Solid State Chem 149:180CrossRefGoogle Scholar
  7. 7.
    Ganschow S, Cavalloni C, Reiche P, Uecker R (1995) Proc SPIE 55:2373Google Scholar
  8. 8.
    Reiter C, Krempl PW, Thanner H, Wallnöfer W, Worsch PM (2001) Ann Chim Sci Mat 26:91CrossRefGoogle Scholar
  9. 9.
    Ikeda T (1990) Fundamentals of piezoelectricity. Oxford University Press, OxfordGoogle Scholar
  10. 10.
    Seh H, Tuller H, Fritze H (2004) J Eur Ceram Soc 24:1425CrossRefGoogle Scholar
  11. 11.
    Seh H (2004) Langasite bulk acoustic wave resonant sensor for high temperature applications. Ph.D. Thesis, MITGoogle Scholar
  12. 12.
    Seh H, Fritze H, Tuller HL (2007) J Electroceram 18:139CrossRefGoogle Scholar
  13. 13.
    Fritze H (2007) Electromechanical properties and defect chemistry of high-temperature piezoelectric materials. Habilitation thesis, Clausthal University of TechnologyGoogle Scholar
  14. 14.
    Göpel W, Hesse J, Zehmel J (1994) Sensors: a comprehensive survey, vol. 7. VCH WeinheimGoogle Scholar
  15. 15.
    Schulz M (2007) Untersuchung der eigenschaften von langasit für hochtemperaturanwendungen. Ph.D. thesis, Clausthal University of TechnologyGoogle Scholar
  16. 16.
    Schulz M, Fritze H (2008) Renew Energy 33:336CrossRefGoogle Scholar
  17. 17.
    Richter D, Fritze H, Schneider T, Hauptmann P, Bauersfeld N, Kramer KD, Wiesner K, Fleischer M, Karle G, Schubert A (2006) Sens Actuators B 118:466CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Michal Schulz
    • 1
  • Jan Sauerwald
    • 1
  • Denny Richter
    • 1
  • Holger Fritze
    • 1
  1. 1.LaserApplicationCentreClausthal University of TechnologyClausthal-ZellerfeldGermany

Personalised recommendations