Why does MnS have the same crystal structure as NaCl?
MnS has the same crystal structure as NaCl, MgO, LiF,… In this structure, the coordination number is 6. So that means that the cation-to-anion ratio is between 0.414 and 0.732. However, the rC/rA-ratio of MnS is 0.364, which means it should have coordination nr 4, why does it have this structure?
1 Answer
I must be honest, when I first learnt of ceramic crystal structures and the estimation of structure using the cation-anion radius ratio, I did not really pay attention to the fact that MnS was listed as having rocksalt structure despite the radius ratio suggesting it should be zinc blende. So good catch and good question, I must say. I do not have a conclusive answer to the question but can take a stab at it.
The first thing I would like to say is that the most common phase is not necessarily the most stable phase. The second is that the cation-anion radius ratio limits are estimated based on pure geometric considerations assuming a hard sphere model, which is not exactly true. The shape of the atomic orbitals and exact distribution of electrons in the lattice is what ultimately determines the structure and its energy. The estimates based on cation-anion radius ratio work as a rule of thumb but may not always be definitive.
As it turns out, MnS has rocksalt as its most common phase but DFT calculations reveal that it is not the most stable phase. The Materials Project database has zinc blende as the most stable polymorph of MnS. The rocksalt phase is the next stable phase with an energy of just 0.06 eV per atom more than the zinc blende structure. One of the reasons rocksalt structure is also relatively stable for MnS is the shape of the d-orbital.
Crystal field theory and the associated splitting diagrams in octahedral and tetrahedral fields suggest that for Mn2+ d-orbitals, with 3 d electrons to be filled, orbital splitting in an octahedral field may result in lower total energy than in a tetrahedral field. This is true particularly in those cases where the spin pairing energy is greater than the energy difference between the split orbitals (high spin case). For most tetrahedral complexes, this is the case. Check ChemWiki: Crystal Field Theory for more details.
So all in all, the actual crystal structure will be a balance between the d-orbital splitting in the cations versus the anion repulsion. For MnS, note that the radius ratio minimum is estimated based on the limit where all the anion hard spheres touch each other. Hence, due to anion repulsion MnS would prefer the tetrahedral coordination zinc blende structure. However, d-orbital splitting in an octahedral field is potentially more favorable to distribute 3 d-electrons. The actual stability order for different structures in such systems is difficult to predict using simple rule of thumb estimations based on the hard sphere model.
This still does not answer why rocksalt phase is the most common one despite zinc blende being more energetically favorable, albeit by a small amount. I couldn't find a reference to a phase diagram for MnS and can only guess that the zinc blende structure for MnS is kinetically hindered and at room temperatures and atmospheric pressures the rock salt phase is easier to form.
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