Random strains

Convection of a passive scalar by a quasi-uniform random straining field. Journal of Fluid Mechanics 64, 737-762. 

The ground state behaviour observed for Jahn-Teller impurities in cubic lattices has often been explained a posteriori by fitting experimental data to quantities like the average random strains, the Jahn-Teller energy, E]T, or the % frequency [5]. In particular when EJT/iuov < 1 the observation at low temperatures of a cubic angular pattern is favoured, while if E /Hcoe > 1 a static EPR spectrum is expected [1-3]. 

Let us now say a few words about the separation among three equivalent minima (in the absence of local random strains) which appear once the two contributions (1) and (3) are considered together. Writing [1-3]... 

Frank s research career began at a time when Solid State Physics was a new topic in Physics. He contributed very much to what became an all-embracing topic in both basic physics and in its numerous applications in chemistry as well as physics in areas now frequently described as Condensed Matter . He pointed out how random strains can force a dynamic Jahn-Teller system to reflect distorted static behaviour in certain cases particularly in EPR spectra. This involved considerations of the orbital angular momentum of the magnetic ions present in these systems and he showed how the Ham Effect , as it became known, could explain why the electronic angular momentum could be quenched in many systems. 

Continuing studies have shown that Co decay in MgO can produce Fe+, Fe " ", and Fe " daughter charge states in proportions dependent on the particular sample preparation and the temperature of the Mossbauer measurement [49]. Dilute concentrations of Fe ( 0-03 at. %) in MgO show a small quadrupole splitting at low temperature [50, 51]. This can be interpreted in terms of crystal-field theory assuming the presence of random strains in the crystal although the Fe site symmetry may be perfectly cubic... 

In the previous sections on the Jahn-Teller effect we have been concerned with uniform strains, the same at all lattice sites, at any rate within a domain. Such uniform strains are important below the distortion temperature Tq. Above Tq dynamic random strains are present, varying from site to site, for which the fluctuations slow down as the temperature is reduced. The presence of such effects has been revealed by observation of the EPR spectrum of Gd in substances such as TmV04 and TmAs04 and is described in the review by Mehran and Stevens... 

Typically, broad optical and microwave spectra are observed in low-temperature glasses except those of the Shpol skii type and very little magnetic information can be obtained. This is presumably because there are large contributions to the linewidth arising from the inhomogeneous broadening effects of random strains and sites. 

Fig. 40. Temperatures of the structural (open circles) and antiferromagnetic (solid circles) ordering of Dy Gd, V04 crystals (Bingham et al. 1984b). The solid curves represent the results of calculations of r (p) (1) and Tn(/p) (2, 3) with (1,3) and without (2), taking into account the random strain effects.

Mutation operators use a single parent to produce a child. Lattice mutation applies a stain matrix with zero-mean Gaussian random strains to the lattice vectors soft-mode mutation (which we call softmutation for brevity from now) displaces atoms along the softest mode eigenvectors, or a random linear combination of softest eigenvectors the permutation operator swaps chemical identities of atoms in randomly selected pairs of unlike atoms. 

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