Secondary pyroelectricity

The total pyroelectric response at constant stress, p , is the sum of the primary pyroelectic response, given by p, and the secondary pyroelectric response, which is the product of the direct piezoelectric stress coefficient gs, and the thermal expansion coefficients ... 

The only contribution to primary pyroelectricity is the change in dipole oscillations with temperature at fixed lattice constants (strain). The calculated values for the primary and secondary pyroelectric coefficients are plotted in Figure... 

Figure 11.2. Constant stress pyroelectric response as a function of temperature. Open squares, primary pyroelectricity open circles, secondary pyroelectricity filled diamonds, total (reprinted with permission from Carbeek and Rutledge. Copyright 1996, Elsevier Science Ltd).

The total pyroelectric response at constant pressure (or stress) is the sum of two contributions. Primary pyroelectricity, which is due to changes in the magnitude of the dipole oscillation with temperature, accounts for only about 9% of the total response of the crystal at 300 K. The remaining overwhelming contribution is due to secondary pyroelectricity—the coupling of the piezoelectric response and thermal expansion. 

Thermal expansion coefficients and the primary and secondary pyroelectric coefficients of animal bone. Nature 224, 798 (1969). 

The pyroelectric effect that is normally observed in a crystal is, in fact, composed of two separate effects called the primary (or true) pyroelectric effect and the secondary pyroelectric effect. If a crystal is fixed so that its size is constant as the temperature changes, the primary effect is measured. Normally, though, a crystal is unconstrained. An additional pyroelectric effect will now be measured, the secondary pyroelectric effect, caused by strains in the crystal produced by the thermal change. In general, the secondary effect is much greater than the primary effect, but both are utilised in devices. 

Note that besides the primary pyroeffect contribution, determined by polarization temperature variations, there can be the contributions from secondary and ternary pyroelectric effects. Latter effects are due to thermal expansion and inhomogeneous... 

The only contribution to primary pyroelectricity is the change in dipole oscillations with temperature at fixed lattice constants (strain). The calculated values for the primary and secondary pyroelectric coefficients are plotted in Figure 11.2 as a function of temperature. Primary pyroelectricity accounts for about 9% of the total response of the crystal at 300 K. The temperature dependence of secondary pyroelectricity is significant and determined by that of the thermal expansion coefficients. 

Table 48.3 shows primary and calculated secondary pyroelectric coefficients of PVF2 films, together with thermal expansion coefficients, and elastic stiffness coefficients, obtained by Kepler and Anderson [18]. The corresponding piezoelectric coefficients were earlier shown in Table 48.1. 

Primary as well as secondary pyroelectric effects are not allowed in polar-neutral crystals due to the symmetry. We can demonstrate this situation on secondary pyroelectric effects for a-quartz, where the thermal expansion as well as piezoelectric tensor is non-zero. Using the form of material tensors for thermal expansion and piezoelectricity for symmetry class 32 we can get... 

Since pyroelectric ceramics are also piezoelectric, a temperature change also induces a change in the polarization due to the secondary pyroelectric effect, which is described by the product of the thermal expansion strain times the piezoelectric coupling coefficient. While this secondary effect can be large in polymers due to their large thermal expansion coefficients, in ceramics, it is typically small compared with the (first-order) pyroelectric effect. 

Ye C, Tamagawa T, Polla DL (1991) Experimental studies on primary and secondary pyroelectric effects in Pb(Zr, Tij x,) , PbTiOj, and ZnO thin films. J Appl Phys 70(10) 5538-5543 Zampiceni E, Comini E, Faglia G, Sberveglieri G, Kaciulis S, Pandolfi L, Viticoli S (2003) Composition influence on the properties of sputtered Sn-W-0 films. Sens Actuators B 89 225-231 Zhang J-G, Benson DK, Tracy CE, Deb SK, Czanderna AW, Bechinger C (1996) Electrochromic mechanism in a-WO films. J Electrochem Soc 24 251-259... 

The sample preparation for a bulk pyroelectric measurement is very similar to what is required for a bulk piezoelectric measurement, namely a well-sintered ceramic disc that has been electrically poled. Determining the pyroelectric coefficient may be divided into two groups - the measurement of the pyroelectric current and the measurement of the charge. We will describe measurement techniques for both groups. In addition, the pyroelectric effect can be subdivided into primary and secondary effects. The primary effect is observed when the material is rigidly clamped under a constant strain to prevent any thermal expansion or contraction. Secondary effects occur when the material is permitted to deform, i.e. the material is under constant stress. Thermal expansion results in a strain that changes the spontaneous polarisation, attributable to the piezoelectric effect. Thus the secondary pyroelectric effect includes contributions caused by piezoelectricity. Exclusively measuring the pyroelectric coefficient under constant strain is experimentally very difficult. What is usually experimentally measured is the total pyroelectric effect exhibited by the material - the sum of the primary and secondary effects. 

Kepler and Anderson [8132] have conducted a aeries of experiments to determine the relative contribution of primary and secondary pyroelectricity in PVDF, and thus, to gain insight into the fundamental mechanisms invdved. The phnoekctric, Ibennal expansion. and elastk stifhess coeffidcnis of uniaxially and biaxiaUy oriented PVDF films... 

Nix et al. [84] have also conducted a aeries of experiments which show that not all the pyroelectric effect can be accounted for on the basis of secondary pyroelectricity. They measured the piezoelectric coefficients and calculated the secondary pyroelectric coefficient using Eq. (19). They found that secondary pyroelectricity could account frw only 10% to 60% of the total pyroelectric effect. The variations in the experimental results were attributed to variations in sample processing, and they concluded that the primary contribution varied from 90% to 40% depending on the method of sample preparatioo. 

In view of the pulse heating experimental results, Kepler and Anderson [82] suggested that a new effect, reversible i nges in crystallinity with temperature, could account for most, if not all, of the discrepancy between the measurements of secondary pyroelectricity and the total pyroelectric coefficient. 

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