Effect of $R$-site substitution and the pressure on stability of $R$Fe$_{12}$: A first-principles study

TL;DR

This study uses first-principles calculations to analyze how $R$-site substitution and pressure influence the structural stability of $R$Fe$_{12}$ compounds, revealing correlations with atomic radius and potential stabilization strategies.

Contribution

It provides a detailed theoretical analysis of the stability of $R$Fe$_{12}$ compounds with various substitutions and under pressure, offering insights for material design.

Findings

Formation energy correlates with atomic radius of $R$.

Partial Zr substitution stabilizes Nd and Sm-based compounds.

Hydrostatic pressure decreases formation enthalpy up to ~6 GPa.

Abstract

We theoretically study the structural stability of $R$Fe$_{12}$ with the ThMn$_{12}$ structure ($R$: rare-earth elements, La, Pr, Nd, Sm, Gd, Dy, Ho, Er, Tm, Lu, Y, or Sc, or group-IV elements, Zr or Hf) based on density functional theory. The formation energy has a strong correlation with the atomic radius of $R$. The formation energy relative to simple substances decreases as the atomic radius decreases, except for $R=$ Sc and Hf, while that relative to $R_{2}$Fe$_{17}$ and bcc Fe has a minimum for $R=$ Dy. The present results are consistent with recent experimental reports in which the partial substitution of Zr at $R$ sites stabilizes $R$Fe$_{12}$-type compounds with $R=$ Nd or Sm. Our results also suggest that the partial substitution of Y, Dy, Ho, Er, or Tm for Nd or Sm is a possible way to enhance the stability of the ThMn$_{12}$ structure. Under hydrostatic pressure, the formation enthalpy decreases up to $\approx$ 6 GPa and then starts to increase at higher pressures.