Polarization saturation

Above the solution treatment temperature (ca 1250°C), the alloy is single phase with a bcc crystal stmcture. During cooling to ca 750—850°C, the sohd solution decomposes spinodally into two other bcc phases a and lattice parameter composition. The matrix a-phase is rich in Ni and Al and weakly magnetic as compared with which is rich in Fe and Co. The a -phase tends to be rod-like in the (100) dkection and ca 10 nm in diameter and ca 100 nm long. As the temperature is decreased, segregation of the elements becomes mote pronounced and the difference between the saturation polarizations of the two phases increases. 

It generally is accepted that the mechanism of coercivity in the Alnicos is incoherent rotation of single-domain particles of the a -phase based on shape anisotropy. As coercivity increases, the larger the aspect ratio of the tods and the smoother thek surface becomes the difference between the saturation polarizations of the two phases also increases. It is thought that Ti increases the coercivity of Alnico because of an increased aspect ratio of the rods and a smoother surface. 

Within the mean-field approximation (MFA), the critical temperature and the saturated polarization are given by the relations ... 

To obtain the dynamic hysteresis loop of a ferroelectric capacitor the polarization is measured versus the applied voltage. Since the hysteresis is neither a linear nor a time invariant property, the hysteresis loop is dependent on the sample history and on the measurement method. To have a standardized and comparable hysteresis loop, certain parameters are commonly fixed. One is the absolute position of the loop on the polarization axis, since the initial (virgin) state of the polarization is unknown in almost all cases, the hysteresis loop is balanced to a reference value. Most commonly the positive and negative saturation polarization are set to... 

From an experimental standpoint, there is a further complication which does not seem to have been discussed within the framework of the M-K theory, namely the observations of the M.I.R. in nonpolar solvents. To take one example, the bell-shaped rate constant vs energy plot shown in Fig. 11 contains points which represent observations of the same e.t. processes in a nonpolar solvent (toluene) as well as a highly polar solvent. Dielectric saturation is usually described as being only of the orientational kind and no suggestion has been made that induction saturation in a nonpolar solvent could also take place. It is then difficult to see, following the M-K model, why a saturable polar solvent and a nonsaturable solvent should lead to similar behaviors with respect to the presence, or the absence, of the M.I.R. 

The hysteresis loop of a single-domain single crystal of BaTiCF is shown in Fig. 2.46(a). The almost vertical portions of the loop are due to the reversal of the spontaneous polarization as reverse 180° domains nucleate and grow. The almost horizontal portions represent saturated states in which the crystal is single domain with a permittivity er of 160 (see Fig. 2.40(d)) measured in the polar direction. The coercive field at room temperature when the loop is developed by a 50Hz supply is 0.1 MVm-1 and the saturation polarization is 0.27 Cm-2. For fields in the approximate range 10 to 100 V mm 1 the hysteresis loop takes the form of a narrow ellipse, a Rayleigh loop, with its major axis parallel to the almost horizontal part of the fully developed loop. 

Generally, isotropic permanent magnets with a remanence ration JJJS > 0.5 are referred as remanence enhanced materials. However, the theoretical limit for the remanence of noninteracting grains depends on the crystal symmetry, the crystallographic orientation of the easy directions, and the volume fraction and the saturation polarization of the phases. The remanence ratio a two-phase nanocomposite magnet is... 

Table 5. Average dipole moments p and saturation polarization values P0 for molecular fragments of unreacted epoxy end groups in networks...

Quenching of the fluorescence of singlet excited electron-acceptor molecules can also be measured in nitrogen-saturated polar solvent by using the Stern-Volmer equation [76] ... 

Using the ion positions for the tetragonal BaTi03 unit cell shown in Fig. 14.16, calculate the electric dipole moment per unit cell and the saturation polarization for BaTi03. Compare your answer with the observed saturation polarization (that is, = 0.26C/m ). Hint Use the Ba ions as a reference. 

Figure 15.13 (a) Crystallographic changes in BaTi03 as a function of temperature. b) Temperature dependence of relative dielectric constant of BaTiO, single crystal, for the c and a axis, (c) Temperature dependence of the saturation polarization for polycrystalline BaTi03. Note similarity between this figure and Fig. 15.4/>. 

Since P, = fx/V, where V is the volume of the unit cell, it follows that the saturation polarization is given by ... 

Cell current vs. applied voltage for 4.5 Ah cells with IS—77% saturation polarized at 22°C [33]. 

Hi is the initial permeability tj is the maximum permeability is the coercive force Jg is the saturation polarization is the hysteresis loss per cycle Tc is the Curie temperature... 

Wac] SEM, coercitive force, saturation polarization 400-600°C, 10 mass% Ni, 0.8 to 1.3 mass% Fe, precipitation kinetics... 

In this section we will briefly discuss some variations of saturation, polarization, or multiphoton spectroscopy that either increase the sensitivity or are adapted to the solution of special spectroscopic problems. They are often based on combinations of several nonlinear techniques. 

Low carbon steels are the most widespread magnetic metallic materials for use in electric motors and inductive components such as transformers, chokes, and a variety of other AC applications which require high magnetic induction at moderate to low losses. This is mainly due to the high intrinsic saturation polarization of the base element Fe, /s = 2.15 T, and to the low cost of mass produced steels. 

Fig. i..3-5 (a) Magnetostriction Xioo and Xm and magneto-crystaUine anisotropy energy K. (b) Electrical resistivity p and saturation polarization Is, as a function of the Si content in Fe—Si alloys... 

Alloys containing 45 to 50 wt% Ni reach maximum saturation polarization of about 1.6 T. Under suitable... 

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