The Impact of Vibrational Entropy on the Segregation of Cu to Antiphase Boundaries in Fe₃Al

• Main Authors: Martin Friák, Miroslav Černý, Mojmír Šob
• Format: Article
• Language: English
• Published: MDPI AG 2021-08-01
• Series: Magnetochemistry
• Subjects: Fe3Al; segregation; antiphase boundaries; phonon; entropy; ab initio
• Online Access: https://www.mdpi.com/2312-7481/7/8/108

We performed a quantum mechanical study of segregation of Cu atoms toward antiphase boundaries (APBs) in Fe<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>3</mn></msub></semantics></math></inline-formula>Al. The computed concentration of Cu atoms was 3.125 at %. The APBs have been characterized by a shift of the lattice along the ⟨001⟩ crystallographic direction. The APB energy turns out to be lower for Cu atoms located directly at the APB interfaces and we found that it is equal to 84 mJ/m<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>2</mn></msup></semantics></math></inline-formula>. Both Cu atoms (as point defects) and APBs (as extended defects) have their specific impact on local magnetic moments of Fe atoms (mostly reduction of the magnitude). Their combined impact was found to be not just a simple sum of the effects of each of the defect types. The Cu atoms are predicted to segregate toward the studied APBs, but the related energy gain is very small and amounts to only 4 meV per Cu atom. We have also performed phonon calculations and found all studied states with different atomic configurations mechanically stable without any soft phonon modes. The band gap in phonon frequencies of Fe<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>3</mn></msub></semantics></math></inline-formula>Al is barely affected by Cu substituents but reduced by APBs. The phonon contributions to segregation-related energy changes are significant, ranging from a decrease by 16% at T = 0 K to an increase by 17% at T = 400 K (changes with respect to the segregation-related energy difference between static lattices). Importantly, we have also examined the differences in the phonon entropy and phonon energy induced by the Cu segregation and showed their strongly nonlinear trends.