Extrinsic contribution

The total polarization of dielectric material results from all the contributions discussed above. The contributions from the lattice are called intrinsic contributions, in contrast to extrinsic contributions. 

Figure 2.1 Schematic illustrations of intrinsic and extrinsic contributions to the piezoelectric constant of perovskite ferroelectrics. (a) and (b) correspond to the intrinsic unit cell shape (a) without and (b) with applied electric field, (c) and (d) correspond to the extrinsic response associated with the change in position of a non-180° domain wall (shown as a black line) (c) before and (d) after an electric field is applied. Note that both intrinsic and extrinsic responses lead to a change in shape of the material due to application of an electric field (and hence to a piezoelectric response). In both cases, the actual distortions are significantly exaggerated to make visualization easier.

It is also important to realize that piezoelectricity implies a linear coupling between dielectric displacement and strain, for example. However, in many ferroelectric materials, this response is linear only over a relatively limited field range (See for example, Figure 2.2). Non-linearity is especially important in ferroelectric materials which show a strong extrinsic contribution to the piezoelectric response [5], In addition, it is quite common for the response to be hysteretic. The amount of hysteresis that is observed depends strongly on the measurement conditions. Larger amplitude excitations often result in larger extrinsic contributions to the coefficients, and more non-linearity and hysteresis in the response. 

Piezoelectric coefficients are also temperature dependent quantities. This is true for both the intrinsic and the extrinsic contributions. Typically, the piezoelectric response of a ferroelectric material increases as the transition temperature is approached from below (See Figure 2.3) [3], Where appropriate thermodynamic data are available, the increase in intrinsic dijk coefficients can be calculated on the basis of phenomenology, and reflects the higher polarizability of the lattice near the transition temperature. The extrinsic contributions are also temperature dependent because domain wall motion is a thermally activated process. Thus, extrinsic contributions are lost as the temperature approaches OK [4], As a note, while the temperature dependence of the intrinsic piezoelectric response can be calculated on the basis of phenomenology, there is currently no complete model describing the temperature dependence of the extrinsic contribution to the piezoelectric coefficients. 

Two types of contributions to dielectric and piezoelectric properties of ferroelectric ceramics are usually distinguished [6], [9-12], One type is called an intrinsic contribution, and it is due to the distortion of the crystal lattice under an applied electric field or a mechanical stress. The second type is called an extrinsic contribution, and it results from the motion of domain walls or domain switching [8], To provide an understanding of material properties of pzt, several methods to separate the intrinsic and extrinsic contributions were proposed. These methods are indirect, and are based on measurements of the dielectric and piezoelectric properties of ferroelectric ceramics [8], [10-12], In the experiments reported in this paper a different approach is adopted, which is based on measurements of high-resolution synchrotron X-ray powder diffraction. The shift in the positions of the diffraction peaks under applied electric field gives the intrinsic lattice deformation, whereas the domain switching can be calculated from the change in peak intensities [13,14],... 

Analysis of intrinsic and extrinsic contributions to the macroscopic strain... 

It is well known that nanocrystals with free surfaces have considerable lattice contraction induced by the large surface/volume ratio. The lattice contraction increases as the size of the nanocrystals decreases. In this contribution, we have considered the size-dependence of the Curie temperature of PZT induced by lattice contraction when the particles size goes into nanometer range. Useful results have been obtained. However, we have neglected the extrinsic contributions on properties, which are caused by domain wall, defect motion, and/or surface charge, etc. The extrinsic properties are more or less affected by the materials processing technology and discussion of them is out of the scope of the present study. 

A similar approach was used to discriminate between intrinsic noise, stochastic fluctuations that arise from fluctuations of the molecules directly involved in gene expression, and extrinsic contributions that arise form fluctuations in other molecules that regulate or otherwise contribute to the process [22]. The latter are uniform within a cell but vary from cell to cell while the former produce fluctuations over time within an individual cell. The two forms of noise were distinguished by determining the extent of correlation between the expression of cyan and yellow fluorescent proteins under the control of identical promoters in the same cell. The intrinsic noise was measured as the difference in fluorescence intensity of the YFP and CFP. The extrinsic noise was determined by using the fact that the square of the total noise equals the sum of the squares of the intrinsic and extrinsic noises. The results show that both types of noise contribute significantly. 

When QDs are embedded into a matrix or assembled onto substrates as an optical system for chemical vapor sensing, complexities may appear as a result of the interaction of the composite material with the light source. This hght-matter interaction will result in a combination of photophysical and photochemical effects with both intrinsic and extrinsic contributions. Therefore, a study of the QD/matrix sensing mechanism as a whole is important to advance the research and development of QD-based materials for sensing applications. 

The first section details the purely intrinsic response of ferroelectrics and discusses their anisotropic properties, the useful application of which can be controlled by the correct orientation of a sin e crystal or by texturing a polycrystalline material. Attention is then focused on one of the most significant extrinsic contributions to the polarization response of ferroelectrics, namely the motion of domain walls. The effect of the domain wall contribution can be controlled by the hardening-softening of... 

In the continuum models of Brazovskii and Kirova [35] and Fesser et al. [36] (the FBC model), the preferred sense of bond alternation is introduced through an extrinsic contribution to the gap parameter A. sls A = zlo + Je. where Aq is the contribution to the gap due to the Peierls mechanism and Je is the extrinsic contribution. It is useful to define a confinement parameter y, as y = AJ2 A, where A is the effective electron-phonon coupling constant such that A = exp[y]. 

In general, grain size is reduced with the decrease of thickness in polycrystalline thin films [61]. The effect of the decrease of grain size in films on the electrical properties is proved here for PbTi03 ferroelectric thin films. Below a certain film thickness, grain size is reduced to such a value that 90° ferroelectric domains disappear (Figure 27.21a-c). This reduces extrinsic contributions to... 

Apart from these conceptual problems one has to consider that in a photoconduction experiment there is always an extrinsic contribution to photogeneration such as sensitization due to inadvertent impurities and exciton dissociation at an electrode. The former usually dominates at low to moderate electric fields. It originates from charge transfer from bulk excitons towards mostly acceptor-type of impurities such as oxidation products and can be rationalized in terms of Arkhipov et al. s theory [58]. It is worth mentioning, though, that at high electric fields, photogeneration is, in fact, intrinsic as evidenced by the concomitant decrease of fluorescence [26]. 

Swain, P.S., Elowitz, M.B., Siggia, E.D. Intrinsic and extrinsic contributions to stochasticity in gene expression. PNAS 99, 12795-12800 (2002)... 

The pre-factor / is an adjustable parameter, which should cover both intrinsic and extrinsic contributions. The Ad K) is the contraction of the mean bond length, and Ac K,m) the perturbation to the mean cohesive energy of a nanograin. 

The T-BOLS predictions match reasonably well to aU measurements. The perfect match of the IHPR for NiP alloy and Ti02 compound may adequately evidence that the current T-BOLS and LBA approaches are close to the true situations of IHPR involving both intrinsic and extrinsic contributions. As can be seen from Table 28.1, changing the/values from 0.5 to 0.668 has no effect on the critical size for materials with TmCO) > 1,000 K, or TITJiQ)) < 1/3, and therefore, for the examined samples, using / = 0.5 or 0.663 makes no difference. The small /values for TiO2(0.01) and Si(0.1) may be dominated by the bond nature alteration that lowers the T x, m) insignificantly. 

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