Fe13Ga9 intermetallic in bcc-base Fe–Ga alloy

doi:10.1016/j.intermet.2020.107059

Intermetallics

Volume 131, April 2021, 107059

https://doi.org/10.1016/j.intermet.2020.107059 Get rights and content

Highlights

•
Fe₁₃Ga₉ intermetallic develops in as-cast Fe-38at.%Ga alloy.
•
Crystal structure was refined based on powder X-ray and neutron diffraction data.
•
DFT calculations imply that Fe₁₃Ga₉ is stable at 0 K against other Fe–Ga phases.
•
Crystal structure can be related with crystal structure of bcc matrix.
•
Role of this phase in view of magnetostriction in Galfenols is to be eludicated.

Abstract

Fe−Ga alloys (Galfenols) are of interest due to their pronounced magnetostriction, whereby the mechanistic understanding is limited. By means of powder X-ray and neutron diffraction it is shown that as-cast Fe-38.4 at%Ga alloy consists of Fe₁₃Ga₉ intermetallic with a monoclinic Ni₂In/NiAs-related structure, which coexists with bcc solid solution. By means of electron backscatter diffraction it is shown that the Fe₁₃Ga₉ intermetallic develops with two different but closely related orientation relationships with respect to the matrix, which can be derived by the relation between the atomic structures of Fe₁₃Ga₉ and the matrix. First principles calculations reveal that Fe₁₃Ga₉ should be stable at 0 K and that this phase may also expected to develop in alloys for lower Ga contents and may have to be considered upon interpreting macroscopically observed magnetostriction.

Introduction

Fe−Ga alloys, often referred to as Galfenols, attract considerable interest as rare-earth free magnetostrictive material. The most attractive properties have been reported around 18 at.% and 27 at.% Ga [[1], [2], [3]], whereby, the achievable magnetostrictive constants depend strongly on the heat treatment applied. This suggests a role of changes of the atomic structure and microstructure due to phase transformations in the solid state caused by temperature and composition dependent phase stabilities.

According to current phase diagrams [[4], [5], [6], [7], [8], [9], [10]], Fe−Ga alloys exist in bcc-related (body-centred cubic) crystal structures up to about 50 at.% Ga at elevated temperatures, with composition and thermal history-dependent occurrence of A2 (disordered W type terminal solid solution) and partially ordered B2 (CsCl type) and D0₃ (BiF₃ or binary Heusler type) phases, the latter two being superstructures of A2. At low temperatures formation various non-bcc structures have been reported, with hexagonally close packed (hcp) based D0₁₉ and face centred cubic (fcc) based L1₂ type ordered phases being equilibrium phases occurring around the “Fe₃Ga” composition (25 at.% Ga). Their formation, however, requires some heat-treatment time, see e.g. Ref. [11]. Due to the strong heat-treatment dependence, metastable versions of the phase diagram have been formulated, depicting e.g. only the type of ordering in bcc-type structures [4,9]. An equilibrium phase diagram according to Kubaschewski [7] focusing on the solid phases in an intermediate compositional range is depicted in Fig. 1.

In the course of attempts to better understand the phase transformation behavior upon heat treating bcc-based Fe–Ga alloys by extending the experimental basis to alloys with >30 at.% Ga, initially unaccountable reflections were encountered in powder X-ray diffraction data of as-cast Fe-38.4 at%Ga alloy. In the present work it is shown that these reflections originate from a Fe₁₃Ga₉ intermetallic phase of Ni₁₃Ga₉-type [12] crystal structure. That Fe₁₃Ga₉ phase most likely corresponds to a metastable phase reported previously [4] and which had been suggested (in the passing) to have such a Ni₁₃Ga₉ crystal structure [4]. While the present paper addresses the characteristics of the crystal structure, formation mechanism and thermodynamics of the Fe₁₃Ga₉ phase, the way how formation of this phase affects magnetostricitive behavior has to remain topic of future research.

Section snippets

Experimental

Alloy preparation followed a procedure described in Refs. [13]. The investigated Fe–Ga alloy has a nominal composition of Fe-38at.%Ga and was inductively melted (Indutherm MC-20 V mini furnace) from pure Fe (commercial purity) and pure Ga (99.99%) in a ceramic crucible under protective high-purity argon gas and cast into a copper mould of inner dimension of 4 × 16 × 60 mm³.

The alloy composition was determined on a polished cross section by energy dispersive X-ray spectroscopy as Fe-(38.4 ± 0.1)

DFT calculations

The DFT calculations, basically pertaining to the situation at 0 K, imply that a Ni₁₃Ga₉-type Fe₁₃Ga₉ has ferromagnetic ordering with 2.0–2.3 μ_B for the different Fe sites. The Ga also attain small moments (−0.12 - −0.14 μ_B) due to hybridisation between Fe and Ga and the procedure of local magnetic moment calculation in the VASP code. Fe₁₃Ga₉ phase has a negative energy of formation of E_f = −0.170 meV/atom, which implies its stability with respect to the pure elements of Fe and Ga. The refined

Atomic structure of Fe₁₃Ga₉

The crystal structure of Fe₁₃Ga₉ belongs to the group of Ni₂In/NiAs-based structures (Strukturbericht designations B8₂/B8₁) [23]. In these structures, main group metal B atoms form an hcp like arrangement, which has, for the currently relevant structures, a characteristically small axial ratio c_h/a_h of the order of 1.225; see below, where the index h refers to the hexagonal unit cell pertaining to the hcp structure. In this hcp arrangement, transition metal atoms T(1) usually occupy all

Conclusions

The crystal structure of an intermetallic phase with the formula Fe₁₃Ga₉, earlier proposed in the passing [4], has been determined on the basis of powder X-ray and neutron diffraction data on as-cast Fe-38.4 at.%Ga alloy. The alloy consists of bcc phase likely with A2 type order, from which this phase has developed in agreement with [4,6]. The crystal structure is a Ni₂In/NiAs-based superstructure referred previously to as the Ni₁₃Ga₉ or Pt₄In₃/Pt₁₃In₉ type. The following points can be

Declaration of competing interest

We declare lack of competing interest.

Acknowledgements

ISG, IAB, and AMB are indebted to the Russian Science Foundation for the support (project 19-72-20080). The alloys were produced by A.K. Mohamed, National University of Science and Technology “MISIS”, Russia, who also commented on the manuscript. The authors also thank Dr. T.N. Vershinina for her help with neutron data analysis.

References (43)

Q. Xing et al.
Structural investigations of Fe–Ga alloys: phase relations and magnetostrictive behavior
Acta Mater.
(2008)
O. Ikeda et al.
Phase equilibria and stability of ordered b.c.c. phases in the Fe-rich portion of the Fe–Ga system
J. Alloys Compd.
(2002)
A.K. Mohamed et al.
The Fe–Ga phase diagram: Revisited
J. Alloys Compd.
(2020)
I.S. Golovin et al.
Time-Temperature-Transformation from metastable to equilibrium structure in Fe-Ga
Mater. Lett.
(2020)
M. Ellner et al.
Kristallstruktur von Ni₁₃Ga₉ und zwei Isotypen
J. Less Common Met.
(1969)
I.S. Golovin et al.
Cooling rate as a tool of tailoring structure of Fe-(9–33%)Ga alloys
Intermetallics
(2019)
J. Rodríguez-Carvajal
Recent advances in magnetic structure determination by neutron powder diffraction
Physica B
(1993)
G. Kresse et al.
Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set
Comput. Mater. Sci.
(1996)
D.A. Aksyonov et al.
Understanding migration barriers for monovalent ion insertion in transition metal oxide and phosphate based cathode materials: a DFT study
Comput. Mater. Sci.
(2018)
S. Lidin et al.
A survey of superstructures in intermetallic NiAs-Ni₂In-type phases
J. Solid State Chem.
(1995)

C. Wieser et al.

The monoclinic lattice distortion of η′-Cu₆Sn₅

J. Alloys Compd.

(2019)

A. Leineweber et al.

An orthorhombic D0₂₂-like precursor to Al₈Mo₃ in the Al–Mo–Ti system

J. Alloys Compd.

(2020)

P.K. Panday et al.

Strukturuntersuchungen in einigen mischungen T-B3-B4 (T=Mn,Fe,Co,Ir,Ni,Pd; B3= Al,Ga,Tl; B4=Si,Ge)

J. Less Common Met.

(1969)

M.K. Bhargava et al.

Kristallstruktur von Ni₄GaGe₂

J. Less Common Met.

(1976)

H.W. Mayer et al.

Crystal structure of Pd₁₃Pb₉.r

J. Less Common Met.

(1980)

S. Banerjee et al.

An ordered ω-phase in the rapidly solidified Zr-27 at.%Al alloy

Acta Metall.

(1983)

X. Chen et al.

Determination of the stretch tensor for structural transformations

J. Mech. Phys. Solid.

(2016)

S.K. Sikka et al.

Omega phase in materials

Prog. Mater. Sci.

(1982)

D. de Fontaine

Mechanical instabilities in the b.c.c. lattice and the beta to omega phase transformation

Acta Metall.

(1970)

J.P. Neumann et al.

Thermodynamics of intermetallic phases with the triple-defect B2 structure

Acta Metall.

(1976)

L.Y. Dubov et al.

Ordering processes in Fe-Ga alloys studied by positron annihilation lifetime spectroscopy

Mater. Lett.

(2016)

Cited by (8)

Comparative study of structures and phase transitions in Fe–(31−35) at% Ga alloys by in situ neutron diffraction
2023, Journal of Alloys and Compounds
The evolution in phase composition of as-cast Fe–(31−35) at% Ga alloys during continuous heating up to 850 °C with subsequent cooling was studied. Based on the results obtained by neutron diffraction, conclusions were drawn about clearly distinguishable stages of phase formation during heating and cooling of metastable high-gallium alloys. Upon heating, the phase composition of studied alloys was found to change in a similar way, namely: BCC + Fe₁₃Ga₉ (absent in Fe–31.1 at% Ga) → BCC+ Fe₁₃Ga₉ + L1₂ → BCC + L1₂ + α-Fe₆Ga₅ → B2 + α-Fe₆Ga₅ → B2. Upon cooling, the following sequence of phase states was realized in Fe–32.9Ga and Fe–34.4 at% Ga alloys: B2 → B2 + α-Fe₆Ga₅ → D0₃ + L1₂ + α-Fe₆Ga₅. Fe–31.1 at% Ga alloy was found to be characterized by the sequence: B2 → B2 + L1₂ → D0₃ + L1₂ + Fe₁₃Ga₉.
Low-temperature metastable-to-equilibrium phase transitions in Fe–Ga alloys
2022, Intermetallics
Citation Excerpt :
L12, Pm3 m (N221), a ≈ 3.72 Å; Fe13Ga9, C2/m (N12), a ≈ 14.22 Å, b ≈ 8.09 Å, c ≈ 8.67 Å, β ≈ 35.4° [15]; α-Fe6Ga5, C2/m (N12), a ≈ 10.06 Å, b ≈ 7.95 Å, c ≈ 7.75 Å, β ≈ 109.3° [15];
Significant differences between the properties of Fe–Ga alloys (Galfenols) in their metastable and equilibrium states, as well as discrepancies between existing Fe–Ga phase diagrams and for the transition rates for the metastable to equilibrium state have been detected and discussed. In view of both the fundamental understanding and the technological importance of these alloys, the exact knowledge of the equilibrium phase diagram, metastable phases, and the transition rates between different phase states towards equilibrium are necessary and require further clarification. We have studied the influence of alloy composition, annealing temperature and annealing time (up to 1800 h) on the metastable-to-equilibrium phase transitions in binary Fe–Ga using a coherent set of complementing methods, including diffraction methods (X-ray and neutron diffraction), scanning electron microscopy, and electron backscatter diffraction. We propose several important changes to the low-temperature part of the binary Fe–Ga diagram close to the Fe-rich corner and a new method based on interdiffusion couples for varying the structure and phase states of Fe–Ga alloys.
Structure evolution of as-cast metastable Fe-38Ga alloy towards equilibrium
2022, Journal of Alloys and Compounds
Citation Excerpt :
Previously, the existence of this phase was only mentioned in Ref. [7] as an M-phase and as Fe13Ga9 at Ref. [8], but information about the atomic structure was not presented. A detailed analysis of neutron and X-ray diffraction patterns and the use of numerical simulation methods allowed the authors of Ref. [5] to establish the cell parameters and the atomic coordinates of the Fe13Ga9 phase. In this paper, the stability of the Fe13Ga9 phase under heating conditions and the features of phase transitions in the nonequilibrium state of the Fe-38.4Ga alloy are studied.
The evolution of the structural phases of the Fe-38.4 at%Ga alloy was studied in neutron diffraction experiments performed with high-intensity continuous scanning in a wide temperature range. The as-cast alloy consists of ~70% Fe₁₃Ga₉ intermetallic and ~30% bcc-based disordered A2 solid solution (or its partially ordered/short-range ordered B2 variant). The research proves that during the first heating of the cast alloy, the Fe₁₃Ga₉ phase is stable up to T ≈ 550 °C, then it transforms into α-Fe₆Ga₅, fcc-based L1₂ and B2 phases. At the same temperature, the disorder-order transition A2 → B2 begins, ending at T ≈ 720 °C. The Fe₁₃Ga₉ phase does not restore during subsequent cooling and next heating and cooling cycles. The structural parameters of the identified phases are refined. The research also shows that the transition temperatures depend on the alloy prehistory.
Internal friction phenomena in a wide temperature range up to 800°C in long-term annealed Fe-(0−30) at% Ga alloys
2021, Journal of Alloys and Compounds
The internal friction (IF) phenomena were systematically studied in a temperature range from room temperature (RT) to 800 °C for Fe-(0−30) at% Ga alloys annealed at 480 °C for 14 days, which include the magnetic-related high damping plateau (HDP) and the point of ferro-paramagnetic transition (T_c), grain boundary relaxations, Zener relaxations, and the IF peaks associated with phase transitions. It was found that the rapid decay temperature of the HDP decreases with increasing Ga content, which is consistent with the variation of the Curie point (T_c), and the HDP disappears when the Ga content is greater than 18 at%. In the long-term annealed Fe-30at%Ga alloy, a frequency-independent phase transition IF peak was observed and its mechanism was suggested as the phase transition of L1₂→A2/B2. The phase transitions in Fe-(0–30 at%)Ga alloys evaluated by the IF technique are in good agreement with the equilibrium phase diagram. In addition, a new relaxation peak was observed before the displacive phase transitions of L1₂→D0₁₉ and L1₂→A2/B2, and its mechanism could be related to Zener relaxation in the FCC structured L1₂ phase.
Mechanical spectroscopy of phase transitions in Fe–(23–38)Ga-RE alloys
2021, Journal of Alloys and Compounds
Citation Excerpt :
23≤x≤27 D03 homogeneous long-range structure [18,29], 27<x<38 the gradual transition of D03 to B2 order plus Fe13Ga9 (38.4%Ga) ([18, 24, 29] and this paper). Mechanical spectroscopy was used to investigate the phase transition in the second, third, and fourth groups of bulk samples from the above-given classification.
Anelastic effects in Fe-(23–38)Ga binary and ternary alloys doped with rare-earth (RE) elements, RE = Pr, Sm, Tb, Er, and Yb, are studied in a sub-resonance frequency through heating and cooling in the range from 0 to 600 °C. In situ neutron diffraction, vibrating sample magnetometry (VSM), and differential scanning calorimetry (DSC) are used to trace phase transitions during heating and cooling and to interpret anelastic effects due to phase transitions. Besides the thermally activated effects, two transient effects due to the first-order transitions D0₃ → L1₂ and B2/D0₃ → Fe₁₃Ga₉ (later in alloys with Ga content>29 at%) are studied. In most cases, the RE elements decrease the rate of phase transitions. The obtained results demonstrate an excellent correlation between temperature-dependent internal friction, in situ neutron diffraction, and vibrating sample magnetometry tests.
Crystal structure and phase composition evolution during heat treatment of Fe-45Ga alloy
2021, Intermetallics
The atomic structure of the high-temperature β-Fe₆Ga₅ phase, formed in the Fe-45at.%Ga alloy during rapid cooling from the melt, has been refined by X-ray, neutron diffraction techniques, and density functional theory calculations. The regularities of the phase composition evolution of the quenched Fe-45at.%Ga alloy in the process of continuous slow heating and cooling under vacuum conditions have been revealed. It is shown that after the heating-cooling cycle, the structures of the outer layers and the sample volume are completely different.

View all citing articles on Scopus

View full text

Fe13Ga9 intermetallic in bcc-base Fe–Ga alloy

Highlights

Abstract

Introduction

Section snippets

Experimental

DFT calculations

Atomic structure of Fe13Ga9

Conclusions

Declaration of competing interest

Acknowledgements

Acta Mater.

J. Alloys Compd.

J. Alloys Compd.

Mater. Lett.

J. Less Common Met.

Intermetallics

Physica B

Comput. Mater. Sci.

Comput. Mater. Sci.

J. Solid State Chem.

J. Alloys Compd.

J. Alloys Compd.

J. Less Common Met.

J. Less Common Met.

J. Less Common Met.

Acta Metall.

J. Mech. Phys. Solid.

Prog. Mater. Sci.

Acta Metall.

Acta Metall.

Mater. Lett.

Fe₁₃Ga₉ intermetallic in bcc-base Fe–Ga alloy

Atomic structure of Fe₁₃Ga₉