Random internal electric fields

In electrically neutral semiconductor samples, random internal electric fields can be present at low temperature because of the compensation and/or of the simultaneous presence of the electrically-charged deep centres. The following estimation of the effect of random internal electric fields on shallow impurity levels is taken from [123] who used it for a qualitative explanation of the broadening of some donor lines in NTD silicon [67], and from [64], who presented it in a more general form. 

When investigating the polar structure by photo-induced light scattering we assume that the largest contribution to the initial optical noise is due to diffraction of the pump beam on optical inhomogeneities located at boundaries of ferroelectric domains [9], Figure 9.12 illustrates this concept schematically. Internal electric fields Ei (random fields) yield local perturbations 5n of the index of refraction via the linear electro-optic effect 5n = - n rssEi. 

Normally, the dipoles are randomly oriented in the material, and the resulting internal electric field is zero. In the presence of an external applied electric field, the dipoles become oriented as shown in Figure 4.13. 

We have recently shown that the presence of phase-separated structures in polymer-blend microparticles can be indicated qualitatively by a distortion in the two-dimensional diffraction pattern. The origin of fringe distortion from a multi-phase composite particle can be understood as a result of refraction at the boundary between domains of different polymers, which typically exhibit large differences in refractive index. Thus, the presence of separate sub-domains introduces optical phase shifts and refraction resulting in a randomization (distortion) in the internal electric field intensity distribution that is manifested as a distortion in the far-field diffraction pattern. 

Polar molecules display the property that they can be oriented along an electric field dipolar polarization phenomenon). In the absence of this phenomenon, dipoles are orientated at random and molecules submitted to Brownian movement only. In the presence of a continuous electric current, aU the dipoles are lined up together in the same direction. If submitted to an alternating current, the electric field is inversed at each alternance with a subsequent tendancy for dipoles to move together to follow the field. Such a characteristic induces stirring and friction of molecules which dissipates as internal homogeneous heating (Scheme 21). 

In the event that the Mdssbauer absorber is unsplit or is a random polycrystal, the observed spectrum shows no new features. However, if both source and absorber are directionally polarised by a magnetic field which can be internal in origin or by an electric field such as is associated with the electric field gradient tensor in a single-crystal absorber the polarisation of each emission line becomes important. 

A nanochannel is a conduit between two reservoirs of fluid with a characteristic internal diameter of roughly one to several tens of nanometers. A nanometer is a billionth of a meter (10 m). The fluid is assumed to be an electrolyte, that is, water with some dissolved salts that dissociate into positive and negative ions. Electrokinetic flow refers to fluid flow generated in such a chaimel when an externally applied electric field is the primary motive force. Ion transport refers to the average drift of the ions along the channel due to the electric field superimposed on the random molecular motion and collisions with the surrounding water molecules and channel walls. 

The proposed theory allows explaining the peculiarities of almost all properties of relaxor ferroelectrics including nonlinear (on external electric field E) effects, see [38] and references therein. Since the internal random fields are large enough in relaxor ferroelectrics, the nonlinear contributions of these fields can essentially influence their physical properties. Let us demonstrate this. 

Manifestations of the gradient-flux law are not due to a random process but due the equilibrium between external force and internal friction. The positive sign results from the special sign convention used for electric currents and fields. 

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