Lattice dynamics effects on finite-temperature stability of $R_{1-x}$Fe${}_x$ ($R$ = Y, Ce, Nd, Sm, and Dy) alloys from first principles

Abstract

We report the effects of lattice dynamics on thermodynamic stability of binary $R_{1-x}$Fe${}_x$ $(0<x<1)$ compounds ($R$: rare-earth elements, Y, Ce, Nd, Sm, and Dy) at finite temperature predicted by first-principles calculation based on density functional theory (DFT). We first demonstrate that the thermodynamic stability of $R_{1-x}$Fe${}_x$ $(0<x<1)$ alloys cannot be predicted accurately by the conventional approach, where only the static DFT energy at $T=0$ K is used. This issue can be overcome by considering the entropy contribution, including electronic and vibrational free energies, and we obtained convex hull plots at finite temperatures that successfully explain the thermodynamic stability of various known compounds. Our systematic calculation indicates that vibrational entropy helps stabilize various $R_{1-x}$Fe${}_x$ compounds with increasing temperature. In particular, experimentally reported $R_2$Fe${}_{17}$ compounds are predicted to become thermodynamically stable above $\sim$800 K. We also show that thermodynamic stability is rare-earth dependent and discuss its origin. Besides the experimentally reported structures, the stability of two new monoclinic $R$Fe${}_{12}$ structures found by Ishikawa \textit{et al.} [Phys. Rev. Mater.~\textbf{4}, 104408 (2020)] based on a genetic algorithm are investigated. These monoclinic phases are found to be dynamically stable and have larger magnetization than the ThMn${}_{12}$-type $R$Fe${}_{12}$. Although they are thermodynamically unstable, the formation energies decrease significantly with increasing temperature, indicating the possibility of synthesizing these compounds at high temperatures.

arXiv comment12 pages, 6 figures

References in corpus (10)

• Quantum Theory of Rare-Earth Magnets
• Crystal field splittings in rare earth-based hard magnets: an ab initio approach
• Effect of $R$-site substitution and the pressure on stability of $R$Fe${}_{12}$: A first-principles study
• Materials informatics based on evolutionary algorithms: Application to search for superconducting hydrogen compounds
• (Sm,Zr)Fe${}_{12-x}$M${}_x$ (M=Zr,Ti,Co) for permanent-magnet applications: Ab initio material design integrated with experimental characterization
• Intrinsic magnetic properties of {$R$(Fe${}_{1-x}$Co${}_x$)${}_{11}$Ti$Z$} ($R$ = Y and Ce; $Z$ = H, C, and N)
• First-principles study of intersite magnetic couplings in NdFe${}_{12}$ and NdFe${}_{12}$X (X = B, C, N, O, F)
• Cerium as a possible stabilizer of ThMn${}_{12}$-type iron-based compounds: A first-principles study
• Probability distribution of substituted Titanium in RT12 (R = Nd, Sm, T = Fe, Co) structures
• Monoclinic YFe${}_{12}$ phases predicted from first principles

Cited by in corpus (2)

• Finite temperature effects on the structural stability of Si-doped HfO${}_2$ using first-principles calculations
• First-principles prediction of phase transition of YCo${}_5$ from self-consistent phonon calculations