Elastic and magnetic properties of cubic Fe$_{4}$C from first-principles

TL;DR

This study uses first-principles calculations to analyze the stability, elastic, magnetic, and electronic properties of cubic Fe4C, revealing its magnetic ground state and instability due to magnetism, with implications for low carbon steels.

Contribution

It provides a comprehensive first-principles analysis of cubic Fe4C's properties, highlighting its magnetic ground state and dynamic instability related to magnetism.

Findings

c-Fe4C has a ferromagnetic ground state

c-Fe4C is dynamically unstable in magnetic states due to negative shear moduli

c-Fe4C is unlikely to form in low carbon steels at low temperatures

Abstract

First-principles based on density functional theory is used to study the phase stability, elastic, magnetic, and electronic properties of cubic (c)-Fe$_4$C. Our results show that c-Fe$_{4}$C has a ferromagnetic (FM) ground state structure compared with antiferromagnetic (AFM) and nonmagnetic (NM)states. To study the phase stability of c-Fe$_4$C, BCC Fe$_4$C, FCC Fe$_4$C, and BCC Fe$_{16}$C, where C is considered at tetrahedral and octahedral interstitial sites, are also considered. Although, the formation energy of c-Fe$_4$C is smaller than BCC Fe$_4$C, but the shear moduli of c-Fe$_4$C is negative in the FM and AFM states indicating that c-Fe$_4$C is dynamically not stable in the magnetic (FM/AFM) states. However, NM state has positive shear moduli which illustrates that instability in c-Fe$_4$C is due to magnetism and can lead to soft phonon modes. The calculated formation energy also shows that c-Fe$_4$C has higher formation energy compared with the FCC Fe$_4$C indicating no possibility of c-Fe$_4$C in low carbon steels at low temperature. The magnetic moment of Fe in c-Fe$_4$C is also sensitive to lattice deformation. The electronic structure reveals the itinerant nature of electrons responsible for metallic behavior of c-Fe$_4$C.