Hyperfine Interactions

, Volume 198, Issue 1–3, pp 273–293 | Cite as

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

  • James N. Bull
  • Christopher M. Fitchett
  • W. Craighead TennantEmail author


This paper reports the determination of the electric-field-gradient and mean-squared-displacement tensors in 57Fe symmetry-related sites of \(\bar {1}\) Laue class in monoclinic FeCl2.4H2O 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 class \(\bar{1}\) 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 57Fe 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 \(\frac{1}{3}\times\) 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.


Mössbauer spectroscopy Single crystals Symmetry-related sites Microscopic and macroscopic efg tensors Atomic displacement parameters Lamb-Mössbauer factors 


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  1. 1.
    Zory, P.: Phys. Rev. 140, A1401 (1965)CrossRefADSGoogle Scholar
  2. 2.
    Zimmermann, R.: Nucl. Instrum. Methods 128, 537 (1975)CrossRefADSGoogle Scholar
  3. 3.
    Gibb, T.C.: Chem. Phys. 7, 449 (1975)CrossRefADSGoogle Scholar
  4. 4.
    Spiering, H., Vogel, H.: Hyperfine Interact. 3, 221 (1977)CrossRefADSGoogle Scholar
  5. 5.
    Grant, R.W., Wiedersich, H., Muir, A.H., Gonser, U., Delgass, W.N.: J. Chem. Phys. 45, 1015 (1966)CrossRefADSGoogle Scholar
  6. 6.
    Ono, K., Shinohara, M., Ito, A., Fujita, T., Ishigaki, A.: J. Appl. Phys. 39, 1126 (1968)CrossRefADSGoogle Scholar
  7. 7.
    Kerler, W., Neuwirth, W.: Z. Phys. 167, 176 (1962)CrossRefADSGoogle Scholar
  8. 8.
    Bull, J.N., Robinson, W.T., Tennant, W.C.: Hyperfine Interact. 194, 347 (2009)CrossRefADSGoogle Scholar
  9. 9.
    Tennant, W.C.: J. Phys., Condens. Matter 4, 6993 (1992)CrossRefADSGoogle Scholar
  10. 10.
    Grant, R.W., Housley, R.M., Gonser, U.: Phys. Rev. 178, 523–530 (1969)CrossRefADSGoogle Scholar
  11. 11.
    Zimmermann, R.: In: Thosar, B.V., Srivastava, J.K., Iyengar, P.K., Bhargava, S.C. (eds.) Advances in Mössbauer Spectroscopy, pp. 273–315. Elsevier, Amsterdam (1983)Google Scholar
  12. 12.
    Penfold, B.R., Grigor, J.A.: Acta Crystallogr. 12, 850 (1959)CrossRefGoogle Scholar
  13. 13.
    Meunier-Piret, P.J., Van Meersche, M.: Acta Crystallogr. B 28, 2329 (1972)CrossRefGoogle Scholar
  14. 14.
    Verbist, J.J., Hamilton, W.C., Koetzle, T.F., Lehmann, M.S.: J. Chem. Phys. 56, 3254 (1972)CrossRefADSGoogle Scholar
  15. 15.
    Bull, J.N., Fitchett, C.M., Maclagan, R.G.A.R., Tennant, W.C.: J. Phys. Chem. Solids 71, 1746 (2010). doi: 10.1016/j.jpcs.2010.09.009 CrossRefADSGoogle Scholar
  16. 16.
    Trueblood, K.N., Bürgi, H.–B., Burzlaff, H., Dunitz, J.D., Gramaccioli, C.M., Schulz, H.H., Shmueli, U., Abrahams, S.C.: Acta Crystallogr. A52, 770 (1996)Google Scholar
  17. 17.
    Johnson, C.K.: A Fortran thermal ellipsoid plot program for crystal structure illustrations. ORNL Report No. 3794. Oak Ridge National Laboratory, Oak Ridge (1965)Google Scholar
  18. 18.
    Golding, R.M., Tennant, W.C.: Quantum mechanics in chemical physics: an exploration. Common Ground Publishing, Melbourne (2008)Google Scholar
  19. 19.
    Tennant, W.C., McGavin, D.G., Patterson, K.H.: New Zealand Institute for Industrial Research, IRL Report No. 8 (1992)Google Scholar
  20. 20.
    Müller, E.W.: Mössbauer spectrum fitting program for universal theories. Institut für anorganische Chemie und analytische Chemie, Johannes Gutenberg Universität, Mainz (1980)Google Scholar
  21. 21.
    Gütlich, P., Link, R., Trautwein, A.: Mössbauer spectroscopy and transition metal chemistry. Springer, Berlin (1978)Google Scholar
  22. 22.
    Housley, R.M., Grant, R.W., Gonser, U.: Phys. Rev. 178, 523 (1969)CrossRefADSGoogle Scholar
  23. 23.
    Bykov, G.A., Hien, P.Z.: Sov. Phys. JETP 16, 646 (1963)ADSGoogle Scholar
  24. 24.
    Wegener, H.H.F., Obenshain, F.E.: Z. Phys. 163, 17 (1961)CrossRefADSGoogle Scholar
  25. 25.
    Weil, J.A., Buch, T., Clapp, J.E.: Adv. Magn. Reson. 6, 183 (1973)Google Scholar
  26. 26.
    Zory, P.: Ph.D. thesis, Department of Physics, Carnegie Institute of Technology (unpublished) (1964)Google Scholar
  27. 27.
    Moré, J.J., Garbow, B.S., Hillstrom, K.E.: User guide for MINPACK Argonne National Laboratory. Argonne, IL, USA (1980)Google Scholar
  28. 28.
    Shapiro, F.L.: Usp. Fiziol. Nauk 72, 684 (1960)Google Scholar
  29. 29.
    Danon, J.: Lectures on the Mössbauer effect, pp. 8–13. Gordon and Breach, Scientific Publishers, Inc., New York (1968)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • James N. Bull
    • 1
  • Christopher M. Fitchett
    • 1
  • W. Craighead Tennant
    • 1
    Email author
  1. 1.Department of ChemistryUniversity of CanterburyChristchurchNew Zealand

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