Microscopic 57 Fe electric-field-gradient and anisotropic mean-squared-displacement tensors: ferrous chloride tetrahydrate

Abstract

This paper reports the determination of the electric-field-gradient and mean-squared-displacement tensors in 57 Fe symmetry-related sites of1 Laue class in monoclinic FeCl 2 .4H 2 O at room temperature by single-crystal Mössbauer spectroscopy. Contrary to all previous work, the mean-squared-displacement matrix (tensor), <msd>, is not constrained to be isotropic resulting in the determination of physically meaningful estimates of microscopic (local) electric-field gradient (efg) and <msd> tensors. As a consequence of anisotropy in the <msd> tensor the absorber recoilless fractions are also anisotropic. As expected of a low-symmetry site, Laue class1 in this case, no two principal axes of the efg and <msd> tensors are coaxial, within the combined errors in the two. Further, no principal direction of the efg tensor seems related to bond directions in the unit cell. Within error, and in agreement with an earlier study of sodium nitroprusside, it appears that the <msd> tensor principal directions lie close to the crystallographic axes suggesting that they are determined by long wavelength (phonon) vibrations in the crystal rather than by approximate local symmetry about the 57 Fe nucleus. Concurrent with the Mössbauer measurements, we determined as part of a new X-ray structural determination, precise atomic displacement parameters (ADPs) leading to an alternative determination of the <msd> matrix (tensor). The average of the eigenvalues of the Mössbauer-determined <msd> exceeds that of the average of the X-ray-determined eigenvalues by a factor of around 2.2. Assuming isotropic absorber recoilless fractions leads to substantially the same (macroscopic) efg tensor as had been determined in earlier work. Taking 1 3 × the trace of the anisotropic absorber recoilless fractions leads to an isotropic value of 0.304 in good agreement with earlier single crystal studies where isotropy was assumed.

Anisotropic mean-squared-displacement tensor in cubic almandine garnet: a single crystal 57Fe Mössbauer study

“…This calculation is performed by a simple conversion within program MOSREF and the dashed lines are the calculated (fitted) result. As described more fully in Bull et al (2011), the parameter refinement process is iterative. From background-corrected dimensionless areas one first obtains estimates of the efg and msd matrices.…”

“…From background-corrected dimensionless areas one first obtains estimates of the efg and msd matrices. The input data are then corrected for thickness following the theory outlined by Housley et al (1969) based upon that of Bykov and Hein (1963) and detailed in Bull et al (2011) (see ''Appendix'' for details). A couple of iterations of refinement and thickness correction were sufficient to produce convergence.…”

“…That is, the msds for the Möss-bauer case would be a factor of 0:7107 ð Þ 2 = 0:8602 ð Þ 2 ¼ 0:6826 smaller than for the X-ray case. In fact, all measurements to date indicate that the Mössbauer msds are considerably larger, around a factor of two for example, in both sodium nitroprusside (Grant et al 1969) and ferrous chloride tetrahydrate (Bull et al 2011). The Mössbauer experiment differs, of course, in that the lifetime of the excited state must in some way be involved in the scattering process.…”

“…4 and 26, it is possible to refine a matrix of f abs values with the same eigenvectors, and hence principal directions, as the msd h i matrix (further details are given in Bull et al 2011).…”

“…To our knowledge there has been no prior attempted 57 Fe Mössbauer single-crystal study of almandine; hence we undertook the present combined theoretical and experimental single-crystal study. Two recent related studies in monoclinic crystals (Bull et al 2009(Bull et al , 2011 illustrate that anisotropies in both electric-fieldgradient (efg) and mean-squared-displacement (msd) tensors can be obtained readily; however, almandine is more of a challenge. The crystal is cubic which means that observed anisotropies are expected to be small, and the ferrous iron Mössbauer doublet arises, in this case, from six symmetryrelated dodecahedral sites in the unit cell as compared to only two in many monoclinic systems.…”