ε-Fe3N: magnetic structure, magnetization and temperature dependent disorder of nitrogen

Leineweber, Andreas; Jacobs, H.; Hüning, Felix; Lueken, Heiko; Schilder, Helmut; Kockelmann, W.

doi:10.1016/s0925-8388(99)00150-4

Cited by 120 publications

(97 citation statements)

References 28 publications

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“…Firstly, the equilibrium value of r 0 (V ) = arg min r E(V, r) is expanded as Table 3. b Experimental data from [3].…”

Section: Extension To Hexagonal Systemsmentioning

confidence: 99%

“…Equilibrium ratio r = c/a is correctly reproduced by the fitted equations of state. provided [1,3,5]. The complete set of equation of state parameters and fitting errors are given in Table 3 for reference.…”

Section: Fitting the Equation Of Statementioning

confidence: 99%

“…7 and compared with experimental data published in the literature [1,3]. The volumetric thermal expansion coefficient is given by…”

Section: Lattice Parameters and Thermal Expansionmentioning

confidence: 99%

“…Fe 2 N 1 − z has been studied experimentally [2,3,4,5,6] and thermodynamic models accounting for long-range order of the nitrogen atoms were developed and fitted to experimental data [1,7,8]. The ground state stability at 0 K was also investigated from first-principles calculations using density functional theory [9,10].…”

Section: Introductionmentioning

confidence: 99%

“…In the third part of this paper, the predicted lattice parameters and thermal expansion coefficient are given as a function of temperature and compared to experimental data [1,3].…”

Section: Introductionmentioning

confidence: 99%

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Generalization of first-principles thermodynamic model: Application to hexagonal close-packed ε-Fe3N

Bakkedal

Shang

Liu

et al. 2016

Computational Materials Science

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A complete first-principles thermodynamic model was developed and applied to hexagonal close-packed structure ε-Fe 3 N. The electronic structure was calculated using density functional theory and the quasiharmornic phonon approximation to determine macroscopic thermodynamic properties at finite temperatures was generalized in terms of the partition function for any lattice of interest.Specially, thermal expansion of the hexagonal close-packed ε phase with two independent lattice parameters was studied by means of the present model and first-principles phonon calculations. The present predictions of thermal expansion of ε-Fe 3 N are in good agreement with experimental data.

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“…Firstly, the equilibrium value of r 0 (V ) = arg min r E(V, r) is expanded as Table 3. b Experimental data from [3].…”

Section: Extension To Hexagonal Systemsmentioning

confidence: 99%

Section: Fitting the Equation Of Statementioning

confidence: 99%

“…7 and compared with experimental data published in the literature [1,3]. The volumetric thermal expansion coefficient is given by…”

Section: Lattice Parameters and Thermal Expansionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In the third part of this paper, the predicted lattice parameters and thermal expansion coefficient are given as a function of temperature and compared to experimental data [1,3].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Generalization of first-principles thermodynamic model: Application to hexagonal close-packed ε-Fe3N

Bakkedal

Shang

Liu

et al. 2016

Computational Materials Science

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Nitrieren von Eisen mit Ammoniak: Wachstum und Mikrostruktur der Nitride und Porenbildung in ζ-Fe2N

Middendorf¹,

Mader²

2001

Z. anorg. allg. Chem.

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Equations of state of iron nitrides ε‐Fe₃N_x and γ‐Fe₄N_y to 30 GPa and 1200 K and implication for nitrogen in the Earth's core

et al. 2017

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Nitrogen abundance is one of the most uncertain among all elements in the Earth's interior. Recent data indicate an affinity between Fe‐nitrides and Fe‐carbides in the Earth's mantle and inner core. In this work P‐V‐T equations of state of ε‐Fe3N0.8 and ε‐Fe3N1.26 (which is close to Fe7N3) have been determined using a combination of multianvil and synchrotron radiation techniques at pressures up to 30 GPa and temperatures up to 1473 K. A fit of the P‐V‐T data to the Vinet‐Rydberg and Mie‐Grüneisen‐Debye equations of state yields the following thermoelastic parameters for the ε‐Fe3N0.8: V0 = 81.44(2) Å3, KT0 = 157(3) GPa, KT′ = 5.3 (fixed), θ0 = 555 K (fixed), γ0 = 1.83(1), and q = 1.34(18). For ε‐Fe3N1.26 we obtained V0 = 86.18(2) Å3, KT0 = 163(2) GPa, KT′ = 5.3(2), θ0 = 562(90) K, γ0 = 1.85(2), and q = 0.55(24). It is likely that all presumably paramagnetic ε‐Fe3Nx with x = 0.75–1.5 have similar thermoelastic properties with a minor increase of the bulk modulus with increasing N content. The melting temperature of ε‐Fe3Nx increases from approximately 1473 to 1573 K in the pressure range from 5 to 30 GPa. We also determined a preliminary equation of state for γ‐Fe4Ny and calculated y = 0.35(2) from the data at 20–30 GPa. Combining the results with a recent experimental study on the stability of β‐Fe7N3, isostructural with Fe7C3, and a theoretical study of the magnetic transitions in ε‐Fe3Nx, we estimate the density of Fe‐nitrides at the Earth's inner core conditions. Our results indicate that at 5000–6000 K, 2.0–3.2 wt % N can explain the density deficit in Earth's inner core.

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ε-Fe3N: magnetic structure, magnetization and temperature dependent disorder of nitrogen

Cited by 120 publications

References 28 publications

Generalization of first-principles thermodynamic model: Application to hexagonal close-packed ε-Fe3N

Generalization of first-principles thermodynamic model: Application to hexagonal close-packed ε-Fe3N

Nitrieren von Eisen mit Ammoniak: Wachstum und Mikrostruktur der Nitride und Porenbildung in ζ-Fe2N

Equations of state of iron nitrides ε‐Fe₃N_x and γ‐Fe₄N_y to 30 GPa and 1200 K and implication for nitrogen in the Earth's core

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ε-Fe3N: magnetic structure, magnetization and temperature dependent disorder of nitrogen

Cited by 120 publications

References 28 publications

Generalization of first-principles thermodynamic model: Application to hexagonal close-packed ε-Fe3N

Generalization of first-principles thermodynamic model: Application to hexagonal close-packed ε-Fe3N

Nitrieren von Eisen mit Ammoniak: Wachstum und Mikrostruktur der Nitride und Porenbildung in ζ-Fe2N

Equations of state of iron nitrides ε‐Fe3Nx and γ‐Fe4Ny to 30 GPa and 1200 K and implication for nitrogen in the Earth's core

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Product

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Equations of state of iron nitrides ε‐Fe₃N_x and γ‐Fe₄N_y to 30 GPa and 1200 K and implication for nitrogen in the Earth's core