Axial crystalline field constant

Size Dependence of Axial Crystalline Field Constant... 

It is known, that axial crystalline field constant D in EPR spectra is proportional to polarization P or for paramagnetic centers without or with inversion center respectively. The coordinate dependence of polarization inside the spherical nanoparticle can be obtained by corresponding Euler-Lagrange equation solution, as it was discussed earlier in the Chap. 3, Sect. 3.2.2.3. The dependence of polarization on r and R can be written as follows [93] ... 

Equation (3.106) allows to calculate /(co) for paramagnetic centers with axial symmetry crystalline field constant D being proportional to P or P. This includes the materials with phase transitions of the first or the second order (see Eq. 3.103) and for any type of nanoparticles size distribution function /(/ ). The EPR spectra for all above cases have been calculated in Ref. [101], All the spectfa have the same characteristic feature at particles size decrease. Namely, it is the broadening of the axial symmetry spectral lines and the increase of intensity of cubic spectral lines. Figure 3.31 illustrates this EPR spectra transformation under the influence of size distribution function parameters Rq,o) and critical radius Rc. 

The polystyrene simulation followed the experiments of Bell and Edie (12) with good agreement. Figure 14.8 shows the simulation results for fiber spinning nylon-6.6 with a draw ratio of 40. The figure demonstrates the wealth of information provided by the model. It shows the velocity, temperature, axial normal stress, and crystallinity fields along the threadline. We see the characteristic exponential-like drop in diameter with locally (radially) constant but accelerating velocity. However, results map out the temperature, stress, and crystallinity fields, which show marked variation radially and axially. 

Microcrystals exhibit properties distinctly different from those of bulk solids. The fractional change in lattice spacing has been found to increase with decreasing particle size in FejOj. Magnetic hyperfine fields in a-FejOj and FejO are lower in the microcrystalline phase compared to those of the bulk crystalline phases. The tetra-gonality (i.e. the departure of the axial ratio from unity) of ferroelectric BaTiOj decreases with decrease in particle size in PZT, the low-frequency dielectric constant decreases and the Curie temperature increases with decreasing particle size. The small particle size in microcrystals cannot apparently sustain low-frequency lattice vibrations. 

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