Ab initio theoretical study of magnetization and phase stability of the ${(\text{Fe},\text{Co},\text{Ni})}_{23}{\text{B}}_{6}$ and ${(\text{Fe},\text{Co},\text{Ni})}_{23}{\text{Zr}}_{6}$ structures of ${\text{Cr}}_{23}{\text{C}}_{6}$ and ${\text{Mn}}_{23}{\text{Th}}_{6}$ prototypes

Ab initio theoretical study of magnetization and phase stability of the ${(Fe, Co, Ni)}_{23} B_{6}$ and ${(Fe, Co, Ni)}_{23} {Zr}_{6}$ structures of ${Cr}_{23} C_{6}$ and ${Mn}_{23} {Th}_{6}$ prototypes

P. R. Ohodnicki, Jr., N. C. Cates, D. E. Laughlin, M. E. McHenry, and M. Widom

Phys. Rev. B 78, 144414 – Published 14 October 2008

Abstract

We present an ab initio theoretical investigation of the magnetization and phase stability of two different complex cubic structures of prototype ${Cr}_{23} C_{6}$ and ${Mn}_{23} {Th}_{6}$ , with an emphasis on the ${(Fe, Co, Ni)}_{23} B_{6}$ and ${(Fe, Co, Ni)}_{23} {Zr}_{6}$ compositions. These phases have recently been observed as secondary or even primary crystallization products of (Fe,Co,Ni)-Zr-B and related metallic glasses that have been studied for applications as soft magnets with nanocrystalline grain size. We first demonstrate the validity of the theoretical technique employed through a detailed comparison between the predictions of the calculations for the Co-Zr binary system and the experimentally stable phases. We then investigate the magnetization and stability of the binary phases. While the Fe-based binary ${Fe}_{23} {Zr}_{6}$ and ${Fe}_{23} B_{6}$ phases are expected to have the highest magnetization, the Co-based binary ${Co}_{23} {Zr}_{6}$ and ${Co}_{23} B_{6}$ structures are predicted to be the most stable of each prototype. The ${Co}_{23} {Zr}_{6}$ structure is the only binary 23:6 structure predicted to be a stable phase for the ${(Fe, Co, Ni)}_{23} B_{6}$ and ${(Fe, Co, Ni)}_{23} {Zr}_{6}$ systems investigated here. Small additions of Zr atoms to the ${(Fe, Co, Ni)}_{23} B_{6}$ phases tend to substitutionally occupy the $8 c$ Wykoff site and stabilize these structures. In contrast, small additions of B to the ${(Fe, Co, Ni)}_{23} {Zr}_{6}$ phases have a much weaker site preference and tend to destabilize these structures. As a result, ${(Fe, Co, Ni)}_{23} B_{6}$ structures are stabilized in (Fe,Co,Ni)-Zr-B systems relative to the binary ${(Fe, Co, Ni)}_{23} B_{6}$ systems while the ${(Fe, Co, Ni)}_{23} {Zr}_{6}$ phases are not. The results presented in this work are in good qualitative agreement with experimental observations of the compositional modifications tending to promote formation of the 23:6 phases in Fe-Co-Zr-B and related metallic glasses.

Received 20 June 2008

DOI:https://doi.org/10.1103/PhysRevB.78.144414

Authors & Affiliations

P. R. Ohodnicki, Jr.^1,*, N. C. Cates¹, D. E. Laughlin¹, M. E. McHenry¹, and M. Widom²

¹Materials Science and Engineering Department, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
²Physics Department, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

^*Corresponding author; pohodnic@andrew.cmu.edu

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Vol. 78, Iss. 14 — 1 October 2008

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Figure 1
(Color online) Representations of the ${Mn}_{23} {Th}_{6}$ and ${Cr}_{23} C_{6}$ prototype structures normal to the [100] direction. The interconnected vertex-sharing octahedral networks of Th, large atoms, or C, small atoms, are shown. The remaining atoms are the Mn or Cr intermediate-sized transition-metal atoms. Only atoms in the first layer of the octahedral network are shown for clarity.Reuse & Permissions
Figure 2
(Color online) Structure information and local environments of the various intermediate-sized transition-metal sites for the ${Fe}_{23} B_{6}$ and ${Fe}_{23} {Zr}_{6}$ structures isostructural with the prototype ${Cr}_{23} C_{6}$ and ${Mn}_{23} {Th}_{6}$ structures, respectively. The values were taken from the online alloy database (Ref. 11). In the online version of the manuscript only, the atoms at different special positions are of different colors ( ${Fe}_{23} B_{6}$ structure: $orange = 4 a$ , $blue = 8 c$ , $red = 32 f$ , $green = 48 h$ , and $gray = 24 e$ ; ${Fe}_{23} {Zr}_{6}$ structure: $yellow = 4 b$ , $red = 24 d$ , $peach = 32 f 1$ , $blue = 32 f 2$ , and $green = 24 e$ ). For the ${Fe}_{23} B_{6}$ structure, the B atoms are illustrated as small and gray. For the ${Fe}_{23} {Zr}_{6}$ structure, the Zr atoms are large and green.Reuse & Permissions
Figure 3
(Color online) A comparison between previously measured experimental enthalpies obtained by two different sets of authors using direct reaction calorimetry (DRC) at different temperatures (Ref. 18) and theoretical enthalpies of mixing calculated here for several phases.Reuse & Permissions
Figure 4
(Color online) Enthalpies of mixing for the Co-Zr system with the convex hull illustrated by a solid line. The comments below regarding the color refer only to the online version of the manuscript. $Circles = experimentally$ stable phases from Table , black $symbol = theoretically$ stable, blue $symbol = theoretically$ metastable $(Δ E < 20 meV / atom)$ , and red $symbol = theoretically$ unstable $(Δ E > 20 meV / atom)$ . The circles correspond to phases that are experimentally stable at low temperatures based on experimental phase diagrams (Refs. 15, 16).Reuse & Permissions
Figure 5
(Color online) Theoretical total majority (positive) and minority (negative) spin band independent electron densities of states per f.u. for the (a) ${Fe}_{23} B_{6}$ , (b) ${Co}_{23} B_{6}$ , (c) ${Ni}_{23} B_{6}$ , (d) ${Fe}_{23} {Zr}_{6}$ , (e) ${Co}_{23} {Zr}_{6}$ , and (f) ${Ni}_{23} {Zr}_{6}$ structures. All energies are measured with respect to the Fermi energy $(E_{F})$ . For the ${Fe}_{23} B_{6}$ and ${Fe}_{23} {Zr}_{6}$ structures, the local densities of states (multiplied by a factor of 2 for clarity) for the B and Zr atoms are also illustrated. The arrows indicate approximate energies where the minority band of Zr shows enhancements in amplitude resulting in a net negative moment at each site.Reuse & Permissions
Figure 6
(Color online) [110]-type projection of the $B_{1} {Co}_{23} {Zr}_{6}$ structure predicted to be the least unfavorable way to incorporate one B atom per primitive cell of the ${Co}_{23} {Zr}_{6}$ structure. The B atoms are located at the largest interstitial site in the structure. For clarity, the Co atoms are not shown.Reuse & Permissions

Physical Review B

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Ab initio theoretical study of magnetization and phase stability of the ${(Fe, Co, Ni)}_{23} B_{6}$ and ${(Fe, Co, Ni)}_{23} {Zr}_{6}$ structures of ${Cr}_{23} C_{6}$ and ${Mn}_{23} {Th}_{6}$ prototypes

P. R. Ohodnicki, Jr., N. C. Cates, D. E. Laughlin, M. E. McHenry, and M. Widom

Phys. Rev. B 78, 144414 – Published 14 October 2008

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Physical Review B

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Ab initio theoretical study of magnetization and phase stability of the (Fe,Co,Ni)23B6 and (Fe,Co,Ni)23Zr6 structures of Cr23C6 and Mn23Th6 prototypes

P. R. Ohodnicki, Jr., N. C. Cates, D. E. Laughlin, M. E. McHenry, and M. Widom

Phys. Rev. B 78, 144414 – Published 14 October 2008

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Ab initio theoretical study of magnetization and phase stability of the ${(Fe, Co, Ni)}_{23} B_{6}$ and ${(Fe, Co, Ni)}_{23} {Zr}_{6}$ structures of ${Cr}_{23} C_{6}$ and ${Mn}_{23} {Th}_{6}$ prototypes