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Lattice expansion from isotope substitution in the Iron based superconductors

We estimate the changes in lattice parameters due to iron isotope substitution in the iron-based high temperature superconductors using a variational calculation based on the anharmonicity of the Fe-As(Se) bond. For BaFe2As2 and 57Fe to 54$Fe substitution we find a c-axis expansion of 1 10^{-3}Å and in-plane a-axis contraction of 1 10^{-5}Å at 250K in good agreement with experimental values on (Ba,K)Fe2As2 for which a negative isotope exponent α=-\frac{d\ln T_c}{d\ln m}<0 was found [P.M. Shirage et al., Phys. Rev. Lett. 103, 257003 (2009)]. For FeSe in contrast we find an expansion for both a and c lattice parameters. We discuss the relevance of these isotope induced changes of lattice parameters to the isotope effect in light of the well established sensitivity to the Fe-As(Se) coordination.