Revision of pyrrhotite structures within a common superspace model

Abstract

The structure of pyrrhotite (Fe(1 - x)S with 0.05 < or = x < or = 0.125) has been reinvestigated in the framework of the superspace formalism. A common model with a centrosymmetric superspace group is proposed for the whole family. The atomic domains in the internal space representing the Fe atoms are parametrized as crenel functions that fulfil the closeness condition. The proposed model explains the x-dependent space groups observed and the basic features of the structures reported up to now. Our model yields for any x value a well defined ordered distribution of Fe vacancies in contrast to some of the structural models proposed in the literature. A new (3 + 1)-dimensional refinement of Fe(0.91)S using the deposited dataset [Yamamoto & Nakazawa (1982). Acta Cryst. A38, 79-86] has been performed as a benchmark of the model. The consistency of the proposed superspace symmetry and its validity for other compositions has been further checked by means of ab initio calculations of both atomic forces and equilibrium atomic positions in non-relaxed and relaxed structures, respectively.

Translation interface modulation in NC-pyrrhotites: Direct imaging by TEM and a model toward understanding partially disordered structural states

“…This model bears resemblance to previously suggested "out-ofstep" and anti-phase defect models (Pierce and Buseck 1974) but is more precise on the actual nature of the involved translation interfaces and flexible enough to explain the variability of NC-pyrrhotite structures and compositions. On the other hand, the superspace approach of Izaola et al (2007) is a single-step occupancy modulation, but in principle fully compatible with our TIM model, which we see as a viable extension toward understanding the real structure of modulated pyrrhotites.…”

“…In general, the uniform sequence out of a set of possible stacking variations is the one with the highest degree of order and corresponding lowest conditional entropy, which can be calculated using the method of Burrows and Sulston (1991). In this context, it can be seen that the superspace approach of Izaola et al (2007) yields in any case the uniform and most ordered sequence for a given N as both the widths and spacings of atomic domains are constant throughout the superspace cell.…”

“…In essence, the superspace model of Izaola et al (2007) produces discretely modulated superstructures by inserting additional F layers into the basic 4C layer sequence, producing either periodic or aperiodic (but uniform) stacking sequences parallel to (001). Because the so-produced double F layers carry an Fe excess, the resulting phases will have higher Fe/S ratios than 4C-pyrrhotite and follow strictly the relation 2x = 1/N c as spacings between double layers are evenly distributed (here 1/N c corresponds to the modulation parameter γ of Izaola et al 2007). A simple model of how more complicated structures can be gradually derived by insertion of extra F layers is shown in Figure 10a.…”

“…Aperiodicity results from the occupation modulation being incommensurately related to the substructure periodicity. Based on this work, Izaola et al (2007) introduced a generalized superspace approach by replacing the continuous occupancy modulation with a steplike function governing discrete site occupancies. By virtue of a "closeness" condition, the model strictly obeys the sequence of ABCD layering as well as the rule that two V layers must not follow consecutively without an interjacent F layer, resulting in the fixed relation 1/N c = 2x between superstructure N c value and composition expressed as x in Fe 1-x S. Depending on the N c value being rational or irrational the model will either produce periodic/commensurate structures, including 4C and integral NC, or yield aperiodic/incommensurate layer sequences, respectively.…”

Sulfidation kinetics of industrial steels in a refinery crude oil at 300 °C: reactivity at the nanometer scale

“…The less irondeficient forms of pyrrhotite have hexagonal and orthorombic (FeS) structures, whereas the more iron-deficient ones possess a monoclinic symmetry (Fe 7 S 8 ). [11] TEM observations TEM observations showed that the pyrrhotite crystals were several hundreds of nanometers large. The comparison between the selected area diffraction (SAD) experimental pattern and the computer generated pattern clearly allows the identification of the pattern of the [001] Fe7S8 zone axis, based on the monoclinic structure.…”