'Soft' phonon modes, structured diffuse scattering and the crystal chemistry of Fe-bearing sphalerites

Electron diffraction has been used to carefully investigate the reciprocal lattices of a range of iron-bearing sphalerites looking for evidence of Fe clustering and/or Fe/Zn ordering in the form of either additional satellite reflections or a structured diffuse intensity distribution accompanying the strong Bragg reflections of the underlying sphalerite-type average structure. While a highly structured diffuse intensity distribution in the form of transverse polarized {110}* sheets of diffuse intensity has been detected and found to be characteristic of all compositions, it does not appear to arise from Fe clustering and/or Fe/Zn ordering. Rather inherently low frequency, and therefore strongly thermally excited, phonon modes propagating along reciprocal space directions perpendicular to each of the six 〈110〉 real space directions of the average structure are suggested to be responsible for these {110}* sheets of diffuse intensity. Monte Carlo simulation (for a range of Zn-S, Zn-Zn and S-S interaction strengths) and subsequent Fourier transformation is used to confirm the existence of these low-frequency phonon modes of distortion as well as to show that they are an intrinsic, predictable property of the corner-connected tetrahedral structure of sphalerite. The low-frequency phonon modes involve coupled (Zn, Fe) and S motion in one-dimensional strings along 〈110〉 real space directions.