Zero-field splitting (ZFS) parameters TlInS 2 Fe 3+ a b s t r a c t In this study, using the superposition model (SPM) and crystallographic data, the second-and fourth-rank zero-field splitting (ZFS) parameters (ZFSPs) have been calculated for Fe 3+ ions at two In sites in TlInS 2 single crystal. Since crystallographic data indicate C 1 site symmetry, a full triclinic ZFS Hamiltonian has been employed. Model parameters were adjusted so to obtain best agreement between the SPM calculated ZFSPs and the second-rank ZFSPs measured by electron magnetic resonance (EMR). The effects of site symmetry on the theoretically predicted ZFSPs and interpretation of the available experimental ZFSPs have been considered. The experimental second-rank ZFSPs were obtained using approximated orthorhombic spin Hamiltonian. Hence, to facilitate comparison with the SPM calculated ZFSPs, the ascent in symmetry method has been applied to the crystallographic data to quantify the structural approximation from triclinic to orthorhombic and to tetragonal site symmetry. Our considerations provide additional structural information, especially concerning the low site symmetry aspects, pertinent for Fe 3+ impurity centers in TlInS 2 and related crystals. Our SPM analysis of ZFSPs indicates that satisfactory so tentative agreement can be achieved between the theoretical predictions and the experimentally measured values of the second-rank ZFSPs. The procedure proposed here may serve as a general framework for modelling of ZFSPs for other ion-host systems. More accurate modelling for Fe 3+ ions in TlInS 2 may be carried out when better quality EMR results taking into account the low symmetry effects in EMR spectra and the values of the fourth-rank ZFSPs become available. The results of SPM calculations support earlier suggestions that Fe 3+ ions substitute for In 3+ ions in TlInS 2 .