Paramagnetic Hyperfine Structure and Relaxation Effects in Mössbauer Spectra:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">Fe</mml:mi></mml:mrow><mml:mrow><mml:mn>57</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>in Ferrichrome<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>A</mml:mi></mml:math>

The M\"ossbauer effect of ${\mathrm{Fe}}^{57}$ in the metalloprotein ferrichrome $A$ (FA) has been investigated at temperatures between 0.98 and 300\ifmmode^\circ\else\textdegree\fi{}K; in some cases the absorber was placed in an external field of 18 kOe, oriented perpendicular to the propagation direction. The polycrystalline paramagnetic sample exhibited temperature-, field-, and concentration-dependent magnetic hyperfine structure. At 0.98\ifmmode^\circ\else\textdegree\fi{}K in zero field, a well-resolved six-line spectrum was observed. As the temperature was raised, the pattern coalesced until at 300\ifmmode^\circ\else\textdegree\fi{}K only a single broad non-Lorentzian line was visible. The effect of an applied field was, at all temperatures, to noticeably sharpen the hfs pattern; and at 77\ifmmode^\circ\else\textdegree\fi{}K or below eight lines were easily resolved. Changes of the spectra with temperature and field are attributed to electronic relaxation, and a model is used to calculate relaxation spectra. The model employs the modified Bloch equations as rate equations to describe fluctuations of an effective hyperfine field. The iron-iron separation was increased by dilution of some of the samples in ethyl alcohol. As is well known from ESR work, spin-spin interactions decrease on dilution: a sharpening of the spectrum resulted. The importance of using solutions in studying M\"ossbauer spectra of biologically interesting ${\mathrm{Fe}}^{3+}$ compounds is demonstrated. Some of the consequences of paramagnetic hyperfine interactions for M\"ossbauer spectroscopy are discussed. Differences between the effective hyperfine field and the interaction $A\mathbf{I}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{S}$ are noted, as are certain analogies between M\"ossbauer and optical spectroscopy, under the $A\mathbf{I}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{S}$ interaction. From previous ESR work the electronic spin Hamiltonian for FA was found to be of the form $D[{{S}_{z}}^{2}\ensuremath{-}\frac{1}{3} S(S+1)]+E[{{S}_{x}}^{2}\ensuremath{-}{{S}_{y}}^{2}]$. Rather complex hyperfine spectra are predicted for ${\mathrm{Fe}}^{3+}$ with this spin Hamiltonian, and representative spectra are illustrated. It is shown that these spectra, expected in the absence of spin-spin interaction, would be sufficient to determine the ratio $\frac{E}{D}$ of the spin-Hamiltonian parameters; this illustrates the complementary nature of ESR and M\"ossbauer spectra of the same system.