Transition metal incorporation into 1 mackinawite ( tetragonal FeS )

24 Naturally-occurring mackinawite (tetragonal FeS) with incorporated transition metals 25 is an important precursor to the formation of metal sulfides in ore deposits, but experimental 26 results have not been sufficient to establish clear trends in the structure and stability of the 27 transition-metal-enriched mineral. Using density functional theory with dispersion 28 corrections, we report the first systematic examination of the relationship between 29 composition and structure for FeS incorporating bivalent transition metals. Our method was 30 validated by successful calculations of the structures of FeS, FeSe, FeSe1-xSx, Fe1-xMexSe (Me 31 = Co, Ni, Cu), and FeNixTe. Two classes of transition-metal-incorporated FeS structures then 32 were investigated: Fe1-xMexS (metal-substituted FeS) and FeMexS (FeS intercalated by a 33 metal at either a tetrahedral or square-pyramidal interstitial site), where Me = Co, Ni, Cu and 34 x ≤ 0.25. We find that incorporated transition metals can both increase and decrease lattice 35 parameters, depending on the metal and how it is incorporated into the FeS structure. As the 36 mole fraction of substituting metal increases, the FeS unit cell volume decreases for Co, is 37 nearly constant for Ni, but increases for Cu. Metal substitution changes the c lattice 38 parameter, which is sensitive to interactions between the mackinawite sheets, as much as it 39 does the a and b lattice parameters. Upon intercalation, the unit cell volume and c parameter 40 increase but the a and b parameters decrease. Experimental structural data are consistent with 41 our results for metal-substituted FeS. We determined the thermodynamic stability of metal42 incorporated FeS by computing the free energy involved in the metal incorporation reactions 43 as a function of chemical potential of sulfur. The thermodynamic results lead to the general 44 conclusions that metal incorporation into mackinawite most likely occurs via substitution, 45 which may be important to influence phase transformation pathways of mackinawite. 46