###### Abstract  
The alloys that crystallize in a tetragonal ThMn\({}_{12}\)-type (space group \(I4/mmm\)) structure and are based on Fe and rare earth elements are believed to have a potential to plug the performance gap between ferrite and Nd-based magnets. Nevertheless, the progress is hindered by their poor structural stability, compared with other phases competing during the synthesis process, e.g., Th\({}_{3}\)Zn\({}_{17}\)-type. In this work, the enthalpies of the formation (and other thermodynamic parameters) of various phases in (Zr, Nd, Ce)-Fe-Si systems were calculated, with paramount focus on the Fe-rich compositions. We compared and discussed the stability range and stabilization routes for amorphous phases, solid solutions, and intermetallics. The beneficial influence of Zr and Si on the crystallization of intermetallic compounds was confirmed, simultaneously being valid for other phases. Among all of the analyzed Fe-rich phases, the lowest values for enthalpy of the formation of the amorphous phase and solid solution were determined for ZrFe\({}_{10}\)Si\({}_{2}\) (\(-17.5\) and \(-18.2\) kJ/mol, respectively). Moreover, substitution by elements with a large atomic radius is indicated as a method for the introduction of topological disorder, giving possibility for the synthesis of metastable phases (even amorphous) and the utilization of more sophisticated synthesis routes in the future.  
ThMn\({}_{12}\)-type phase; permanent magnet; thermodynamic properties; crystalline structure; enthalpy of formation; [PERSON]'s model +
Footnote †: journal: Applied Sciences  
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Footnote 1: email: [EMAIL_ADDRESS]  
Footnote †: journal: Applied Sciences  
as a stabilizer many years ago by [PERSON] [13] and [PERSON] [14], and its role was later confirmed by other authors [15; 16; 17; 18; 19]. The formation of the 1:12-type phase was recently confirmed for the ZrFe\({}_{10}\)Si\({}_{2}\) compound [20] and in some other systems, where Zr was substituted with REE [21]. In this paper, we focus on the formation enthalpy calculations of Fe-Si-based alloys with various substitutions (Zr, Ce, and Nd), with an emphasis put on the Fe-rich compositions.  
The main aim of the paper was to determine the structural stability of various phases in (Ce, Zr, and Nd)-Fe-Si systems. We compared the enthalpy of the formation of hypothetical amorphous phases, solid solutions, and intermetallic compounds of chosen stoichiometry to answer more detailed questions, including the following: (i) Is it possible to synthesize metallic glass (to have an amorphous precursor for further crystallization of 1:12-type phase) with particular compositions and how broad is the glass forming range? (ii) Is it possible to synthesize NdFe\({}_{12}\) or NdFe\({}_{10}\)Si\({}_{2}\) (not synthesized up to date) through the formation of off-stoichiometric alloys (to prepare structurally disordered precursors for further treatment or to restrain the formation of competing 2:17-type phase). To determine the enthalpies of formation, mismatch entropy, and glass forming ability parameter, we utilized a thermodynamic approach based on the semi-empirical [PERSON]'s model [22; 23; 24; 25], which has been proven to be reliable in these types of calculations and matchless when dealing with the use of computing power. It should also be noted here that other thermodynamical models such as the cB\(\Omega\) model [26; 27; 28] have also been applied to magnetic materials [29]. Later, a regular solution model was proposed by [PERSON] and [PERSON] [30]. To take into account the effect of the additive element on the properties of the binary alloy, asymmetric methods have been proposed [31], which in turn, in many cases, generate inaccuracy by the experience-based choice of asymmetric constituents. Therefore, the asymmetric geometric model proposed by [PERSON] et al. [32], independent on the choice of asymmetric element, was successfully implemented before [25; 33; 34; 35] and is utilized in this paper.