Weak anisotropy

In contrast, soft magnetic solids and paramagnetic systems with weak anisotropy may be completely polarized by an applied field, that is, the effective field at the Mossbauer nucleus is along the direction of the applied field, whereas the EFG is powder-distributed as in the case of crystallites or molecules. In this case, first-order quadrupole shifts cannot be observed in the magnetic Mossbauer spectra because they are symmetrically smeared out around the unperturbed positions of hyperfine fines, as given by the powder average of EQ mj, d, in (4.51). The result is a symmetric broadening of all hyperfine fines (however, distinct asymmetries arise if the first-order condition is violated). 

The deton vel of RDX and PETN monocrysts, along their different crystallographic axes, was investigated in Ref 43. Data obtd by rotating mirror camera recordings revealed a weak anisotropy of deton vel with ciyst geometry... 

R.J. Leroy, G.C. Corey, J.M. Hutson, Predissociation of weak-anisotropy van der Waals molecules—Theory, approximations, and practical predictions, Faraday Discus. 73 (1982) 339. 

On a phenomenological level the in-plane anisotropy of Hc2 cannot be explained within the (local) GL theory. In principle, non-local extension introduced by Hohenberg and Werthamer (1967) might be helpful to overcome this difficulty. In this approach, which is valid for weak anisotropies, in addition to the second rank mass tensor, a fourth rank tensor is introduced. The non-local effects were predicted to be observable in sufficiently clean materials where the transport... 

One sees that at weak anisotropy the shapes of the respective graphs (a and c, b and d) in both figures nearly coincide. This is explained by the fact that the... 

FIGURE 2. In a heavily Mg-doped sample Glaser and co-workers observed a resonance (gy = 2.080, gi = 2.000) on a band peaked at about 3 eV (as well as on deeper luminescence) [15,16], Kunzer and co-workers looked at a number of p-type samples [22,23]. For their most heavily Mg-doped sample they obtained a resonance (gy = 2.067, gi = 2.022), while for a less highly doped sample, they obtained a somewhat more anisotropic line (g, = 2.084, gi = 1.990). With a Zn-doped layer they obtained a resonance with only very weak anisotropy (gy = 1.997 and gi = 1.992). The Zn acceptor is deeper [24] than the Mg acceptor (-350 meV versus -200 meV) and so can be expected to have a g value more typical of a deep level (i.e. near two and nearly isotropic). Glaser and co-workers have assigned the resonances in the heavily Mg-doped samples to Mg-related acceptors rather than simple on-site Mg acceptors. On the other hand, Kunzer and co-workers have argued that the Mg-related resonance in their more lightly doped film is due to isolated on-site Mg acceptors and that the decreased anisotropy observed in their heavily doped films is due to Mg acceptor pairs. 

Hydrogen is even simpler, but solid hydrogen is very atypical. Because of the large splitting between the rotational states of the free H2 molecule and the weak anisotropy of the H2-H2 interaction potential, the free molecule rotations are nearly unperturbed in the solid. This system has been extensively discussed by van Kranendonk (1983). 

The question of whether this prototype weak-anisotropy system may be accurately described by one of the simple decoupling methods mentioned above is also examined in Table II. The first two approximate methods considered are the space-fixed (SFD) and body-fixed (BFD) versions of the distortion approximation of Levine et al.(40,41) while the third is their "best local" (BL) approximation, according to which the angular functions are optimized at each value of R. it is immediately clear that the space-fixed angular basis functions are the (note, however that... 

Only a few elastic scattering experiments of molecules which contain an alkali atom have been performed. Recently published results on the scattering of alkali dimers on molecules show that the rainbow structure in the differential cross section is only slightly less resolved than the structure for the monomers, thus indicating a weak anisotropy of the long range potential (Hardin and Grice, 1973). For a discussion of total cross section measurements of alkali halides on rare gas atoms with a Boltzmann rotational state distribution and state selected beams see David et al. (1973). 

Small angle neutron scattering measurements of the anisotropy of the main chain conformation of a side-on sidechain LCE under a mechanical stress are described in the isotropic and in the nematic phase [45]. It is found that a weak anisotropy of the main chain conformation exists only in the nematic phase and for sufficiently high values of the elongation. 

Gd has been thoroughly studied because the weak anisotropy (section 3.2) enables practical fields to align the magnetization in any desired direction specified by a,. Since the anisotropy is small, the magnetostriction constants are typically two orders of magnitude smaller than for the other elements we have... 

Figure 2. Effect of piezoelectric anisotropy on the single-crystal orientational behavior. Left inset embodies the polar response of the normalized piezoelectric behavior for different anisotropy factors. Note that the optimal orientation changes as the degree of anisotropy increases. Left inset shows the optimal orientation of each single-crystal, as a function of crystallographic anisotropy. Note that contrary to what it is intuitively expected, in the limit of high anisotropy, A 2/3, the crystallographic orientation at which highest piezoelectric strains will occur will asymptotically align with the direction of the applied field. Furthermore, the optimal orientation for materials with weak anisotropy will asymptotically converge to 0=54.16°.

These normalized electromechanical equations are applicable to any chemistry, and allow you tailor the optimal single-crystal intrinsic response. Furthermore, any improvement on the chemistry of a ferroelectric material will asymptotically converge to an optimal orientation of 54.76° for materials with weak anisotropy, or to zero in the limit of A.. = 2/3. 

Data analysis for Ar-02 and Ar-N2 is currently under way. Comparison of our scattering data with the prediction of previously determined multiproperty PES s shows significant disagreement, indicating a too weak anisotropy and a not sufficiently accurate attractive part of the previous surfaces. 

How such a method survives for realistic, appreciably anisotropic potentials is the focus of this discussion. As a test system, we consider the intermolecular potential between Ar and HF(v=l). This is best described as a strongly hindered internal rotor complex, and on which we have data for the (10 0), (11 0) and (12 0) from the slit jet spectrometer. These three states, respectively, correlate in the limit of weak anisotropy with precisely the three states (the s," and the II and S oriented "p" orbitals) in the above paragraph that sample the full range of angular coordinates. 

PrFc2Ge2 shows a particularly complicated magnetization curve at 4.2 K (see fig. 13). It contains two ranges of a rapid growth. The first one below 1 kOe provides the evidence for a weak anisotropy field, the second one at about 10 kOe is probably connected with a metamagnetic phase transition. The ferromagnetic order is induced by an applied external magnetic field, but even the field of 50 kOe does not produce the saturation. 

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