Polarisation spontaneous

Another example of the coupling between microscopic and macroscopic properties is the flexo-electric effect in liquid crystals [33] which was first predicted theoretically by Meyer [34] and later observed in MBBA [35], Here orientational deformations of the director give rise to spontaneous polarisation. In nematic materials, the induced polarisation is given by... 

In the operation of ferroelectric liquid crystal devices, the applied electric field couples directly to the spontaneous polarisation Ps and response times depend on the magnitude E Ps. Depending on the electronic structure (magnitude and direction of the dipole moment as well as position and polarity of the chiral species) and ordering of the molecules P can vary over several orders of magnitude (3 to 1.2 x 10 ), giving response times in the range 1-100 ps. 

CB04. The spontaneous polarisation was measured by the pulse pyroelectric technique (Ps = 46 nC/cm ). The piezoelectric coefficient evaluated for CB04 was dsi = 1.6 pC/N. The estimation of the efficiency of the second harmonic generation for compound CB04 gives the value three times more than for quartz. 

Pyroelectric detectors depend on the use of a thin slice of ferroelectric material (deuter-ated triglycine sulphate (DTGS), Figure 3.14, is the standard example) - in which the molecules of the organic crystal are naturally aligned with a permanent electric dipole. The thin slab is cut and arranged such that the direction of spontaneous polarisation is normal to the large faces. Typically one surface of the crystal is blackened to enhance thermal absorption, and the entire assembly has very low thermal mass. 

The theoretical piezoelectric field in fully-strained GalnN layers grown on GaN with (0001) orientation was reported as shown in FIGURE 1 [5], This figure shows that large piezoelectric fields in the order of MV/cm can be induced. Based on the sign of piezoelectric constants, the expected direction of the piezoelectric field is <0001>. In this calculation the spontaneous polarisation could be neglected, because the measurable field depends only on the difference of the total polarisations across the... 

In Sect. 7.3, Eqs. (18) and (19) describe the Maxwell stress forces acting on a conductive tip when a combined d.c./a.c. voltage is applied. For the PFM set-up we have to complete the total interaction force by the additional effects of piezoelectricity, electrostriction and the spontaneous polarisation. Both electromechanical effects cause an electric field-induced thickness variation and modulate the tip position. The spontaneous polarisation causes surface charges and changes the Maxwell stress force. If the voltage U(t)=U[)c+UAc sin((Ot) is applied, the resulting total force Ftotai(z) consists of three components (see also Eq. 19) Fstatic, F(0 and F2m. Fstatic is the static cantilever deflection which is kept constant by the feedback loop. F2a contains additional information on electrostriction and Maxwell stress and will not be considered in detail here (for details see, e.g. [476]). The relevant component for PFM is F(0 [476, 477] ... 

In Eq. (20) the three terms are related to the Maxwell stress (first), piezoelectric effect (second) and electrostriction (third). In order to obtain information about ferroelectricity via piezoresponse measurements, we need a link between the spontaneous polarisation and the piezoelectric constant. According to Furukawa and Damjanovic, piezoelectricity in ferroelectrics can be explained as electrostriction biased by the spontaneous polarisation if their paraelectric phase is nonpolar and centrosymmetric [461, 495, 496]. Therefore the d33 constant depends on the spontaneous polarisation P5 ... 

When the electric field is higher than the coercitive field strength, the spontaneous polarisation is switched and the dipoles reorientate along the field lines. This process of domain switching for Eei=Ec can be described in three steps i) nucleation of an anti-parallel domain, ii) domain growth and iii) saturation of the polarisation [461, 462]. 

Spontaneous polarisation, that is polarisation in the absence of an electric field, has been calculated using both a Wannier function approach and a Berry s phase approach. Berry s phase involves an adiabatic change around a closed loop which results in a change of phase without change in energy. A recent paper by Ferretti et alP used the PAW method with ultrasoft pseudopotentials and Wannier functions to calculate the spontaneous polarisation of AIN in its wurtzite phase. 

Calamitic metallomesogens forming a chiral smectic C phase (SmC ) are ferroelectric materials. Due to the low symmetry of this phase when the helix is unwound (C2) the molecular dipoles are aUgned within the layers of the SmC phase, giving rise to ferroelectric order in the layers. Because the SmC phase has a helical structure, there is no net macroscopic dipole moment for the bulk phase. However, it is possible to unwind the helix by application of an external electric field or by surface anchoring in thin cells. Under such conditions, a well-aligned film of the ferroelectric liquid crystal can exhibit a net polarisation, called the spontaneous polarisation (Ps). Ferroelectric liquid crystals are of interest for display applications because the macroscopic polarisation can be switched very fast by an... 

Spontaneous polarisation can also be observed for chiral discotic metallomesogens forming columnar mesophases, when the chiral molecules are tilted with respect to the column axis. The tilt induces a dipole moment within the plane of the molecule. A net macroscopic polarisation can be obtained for rectangular columnar phases with Cz or P2i symmetry. Serrano and Sierra reported on ferroelectric switching in the columnar mesophase for chiral /3-diketonate complexes (Figure 2.52). ... 

Bowling [1988] describes van der Waals forces in the following way. At absolute zero temperature solids can exhibit local electric fields and above this temperature additional contributions come from the excitation of the atoms and molecules making up the solid material. Van der Waals forces include forces between molecules possessing dipoles and quadrapoles produced by the polarisation of the atoms and molecules in the material. These dipoles and quadrapoles may be present naturally or by induced polarity. Non-polar attractive forces may also be present. The non-polar van der Waals forces may also be referred to as London-van der Waals dispersion forces because London associated these forces with the cause of optical dispersion, i.e. spontaneous polarisation [Com 1966]. Such dispersion forces will make the major contribution to the intermolecular forces, except where the opportunity to polarise is small and the dipole moment is large. 

The interest in chiral dimers was stimulated to a large extent by the expectation that placing the chiral centre in the spacer, at least for even dimers, should increase its orientational order compared to that for a chiral centre located in a terminal chain and this in turn should result in an enhancement of the form chirality of the phase. This suggestion has still to be extensively investigated but the limited data available indicates that dimers having chiral spacers actually exhibit ferroelectric smectic C phases with low values of spontaneous polarisation [140]. 

Two series of polycatenar complexes containing the same metallic fragments were also reported [115]. As expected for polycatenar complexes, nematic (54 n=6, 10 and 11), Sc (54 n-lO and 11) and Colh (54 n=12-16) phases were obtained. Resolution of the pure enantiomers gave rise to the equivalent chiral phases for the same n (N and Sc ), and Colh phases (chiral ) for n> 12, with slight differences in the transition temperatures as compared to the racemic mixtures. Small spontaneous polarisations were measured. 

In Table 4 we report the structural parameters that define the equilibrium tetragonal structure for each Hamiltonian examined. In addition, we report the value of the spontaneous polarisation P calculated at both equilibrium and experimental structures of the two phases. Comparison with experiment [100, 102-104] enables us to identify the functional that best describes the fully distorted phase. As described in the previous sections, accurate results are achieved in the calculations only when the electronic, structural and dis-tortional properties of the material are reproduced simultaneously by the Hamiltonian under investigation. We have shown earher that each of these observables varies appreciably as a function of the mixing parameter in the hybrid F-BLYP series. The tetragonal phases of BaTiOs and KNbOs provide... 

In the case of a pyroelectric solid a change of temperature induces a polarisation change. The change in polarisation found on heating is reversed on cooling. Pyroelectric crystals are a subset of piezoelectrics. All pyroelectric crystals are piezoelectrics, but not all piezoelectrics demonstrate pyroelectricity. A material that is a pyroelectric is found to possess a spontaneous polarisation, Ps. This means that a pyroelectric crystal shows a permanent polarisation that is present both in the absence of an electric field and in the absence of mechanical stress. 

In some piezoelectrics, there is a spontaneous polarisation, Ps, when the applied electric field. 

Vaiies with crystal direction. Uj r and lower values are given when these differ substantially. Note 7c, Curie temperature P, spontaneous polarisation r, relative permittivity. 

In some pyroelectrics the spontaneous polarisation, Ps, is easily switched in an electric field, to give a ferroelectric. 

In the case of crystals showing spontaneous polarisation, the elementary dipoles are already... 

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