Magnetism and mechanical stability of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math>-iron

Hsueh, H. C.; Crain, Jason; Guo, Guang‐Yu; Chen, H. Y.; Lee, Chi-Cheng; Chang, Ken-Hao; Shih, Horng-Yuan

doi:10.1103/physrevb.66.052420

Cited by 36 publications

(18 citation statements)

References 19 publications

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“…[4]. The magnetic moment M of bcc Fe at zero pressure is 2.2 µ B (µ B is Bohr magnetic moment) which is accordant with the experimental and other calculated values [15] . is located at 0 eV and indicated by dash dot line, as shown in Fig.…”

Section: Electronic Structuresupporting

confidence: 82%

Properties and electronic structure of iron under pressure up to 30GPa

Yan

2011

J. Shanghai Jiaotong Univ. (Sci.)

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The properties and electronic structure of Fe under pressures of 0-30 GPa have been studied by first principles employing the density functional theory (DFT), the ultra-soft pseudo-potentials (USPP) and the generalized gradient approximation (GGA). The calculating results show that there is a structural transition from magnetic body-centered cubic (bcc) to nonmagnetic hexagonal-close-packed (hcp) structure for Fe around 11 GPa pressure. There is a pseudogap both in the density of states (DOS) for bcc and hcp Fe. The pseudogap of bcc Fe is deeper and wider than that of hcp Fe. The elastic modulus is obtained by Voigt-Reuss-Hill averaging scheme. The results indicate that the elastic properties of bcc Fe enhance with pressure except for elastic stiffness constant C11, shear modulus G and elastic modulus E at the transition pressure, while the elastic properties of hcp Fe increase linearly with pressure. Magnetic bcc Fe is ductile, and hcp Fe becomes ductile from brittle around 25 GPa.Iron is certain one of the most important materials at ambient conditions. The iron phase diagram at high pressure and high temperature is of a considerable interest for modern technology and geophysics. Moreover, iron is thought to be a major component of the Earth's core where it is exposed to high pressure and high temperature.There are some arguments on the structure of Fe under the Earth's core condition. In the pressure range of the Earth's core but at low temperatures, Fe is known to be stable in the hexagonal-close-packed (hcp) structure [1] . While one of the performed studies [2] suggests that the body-centered cubic (bcc) phase is stable at the regarded conditions. The other one [3] suggests instead the stability of the hcp phase, however, free energies of bcc and hcp appear to be very close to each other. Another studies show that metastable double hexagonal-close-packed (dhcp) [4][5] and body-centered tetragonal (bct) [4] phases are found at high pressure.There are researches on the structure of Fe under Earth's core condition, the transformation mechanism of bcc-hcp [6] and the thermodynamics of Fe under Earth's core condition [7] , however, the studies on the properties of Fe at relatively low pressure are rare. In this paper, the authors focus on revealing the properties and electronic structure of Fe under 0-30 GPa. Calculation DetailsAll the calculations are preformed within Cambridge serial total energy package (CASTEP) code based on density functional theory (DFT) [8] . In this code, the Kohn-Sham equations are solved by expanding the wave functions of valence electrons in a basis set of plane waves with kinetic energy smaller than a specified cutoff energy, E cut . Interaction between ion core and valence electrons is represented by non local ultra-soft pseudo-potentials (USPP) of the Vanderbilttype [9] . The state Fe 3d 6 4s 2 is treated as valence electrons. The integration over the Brillouin zone is replaced by discrete summation over special set of k points using Monkhorst-Pack scheme [10] . A plane wave cutoff...

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Section: Electronic Structuresupporting

confidence: 82%

Properties and electronic structure of iron under pressure up to 30GPa

Yan

2011

J. Shanghai Jiaotong Univ. (Sci.)

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“…This approximation has been successfully applied in other DFT studies of paramagnetic systems such as fcc and bcc iron. 24,28,29 In addition, and to get a better understanding of the electronic structure at the surface, we simulated scanning tunneling microscopy (STM) of the surfaces considered in this work. The constant-current mode STM images and line scans for vivianite surfaces with both positive and negative bias voltages were computed.…”

Section: ■ Computational Details and Methodsmentioning

confidence: 99%

First-Principles Studies of Paramagnetic Vivianite Fe₃(PO₄)₂·8H₂O Surfaces

2014

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Using density-functional theory, we have computed the structural and electronic properties of paramagnetic vivianite crystal Fe 3 (PO 4 ) 2 ·8H 2 O and its (010)-(1 × 1) and (100)-(1 × 1) surfaces. The properties of bulk vivianite are studied with a set of functionals: HSE06, PBE, AM05, PBEsol, and PBE with on-site Coulomb repulsions corrections (PBE+U). The appropriate U parameter is estimated by considering the HSE06 results, and it is used to study the vivianite surfaces. The computed surface energy predicts the (010) surface to be the most stable. The less stable (100) surface is observed to have important reconstructions with the spontaneous formation of a water molecule at the surface and two hydroxide hydrate anions per unit cell. Using thermodynamical considerations within DFT, we have calculated the phase diagram of the (010) surface in equilibrium with hydrogen gas. The results suggest that under ultralow hydrogen pressure, the (010) surface with two hydrogen vacancies is stable. The electronic structure calculations for the surfaces are complemented with the computed scanning tunneling microscopy (STM) images for constant-current mode. The topology is dominated by the surface Fe-3d states that protrude into the vacuum. ■ INTRODUCTIONThe vivianite Fe 3 (PO 4 ) 2 ·8H 2 O mineral has been experimentally well studied, but there are sparse theoretical models that support those experiments. The surfaces of vivianite have been experimentally less studied, and no reliable atomic-scale model exists for the surface structure and their properties. The reason might be associated with experimental difficulties in preparing clean surfaces free of impurities. Developing and understanding structural models for the surfaces of paramagnetic vivianite Fe 3 (PO 4 ) 2 ·8H 2 O is the aim of this work. The vivianite group of minerals are hydrated iron phosphates having the A 3 2+ (XO 4 ) 2 · 8H 2 O general formula. A 2+ can be any of the following elements: Co, Fe, Mg, Ni, and Zn. The variable X is either As or P. They can be found in coatings of water pipes, soils, morasses, and sediments, which makes them photosensitive. 1,2 Vivianite is a typical member of this mineral group with the Fe 3 (PO 4 ) 2 ·8H 2 O chemical formula. The vivianite crystal structure has a monoclinic lattice with C2/m symmetry and with cell parameters a = 10.021 Å, b = 13.441 Å, c = 4.721 Å, and β = 102.84°. 3 The vivianite crystal is also an antiferromagnet with a Neeĺ temperature T N ∼ 10 K, above this temperature, vivianite has paramagnetic properties. 4 Hydrogen bonding between the H 2 O ligands holds together sheets consisting of linked Fe and PO 4 polyhedra. 5 Vivianite can be oxidized through auto-oxidation or by the air when Fe 2+ is oxidized to Fe 3+ . 1,6 It is typical for anoxic environments and indicative for geochemical conditions where ferric iron oxides usually dissolve. 7 It has great chemical and thermal stability. Vivianite can disintegrate into strongly magnetic magnetite and weakly magnetic hematite upon heating in air. 8−10 Se...

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“…Instead we turn to a combination of molecular dynamics and electronic structure calculations. Souvatzis et al (2008Souvatzis et al ( , 2009) developed the so-called selfconsistent ab initio lattice dynamical (SCAILD) calculations, which is a quantum-mechanical realization of the selfconsistent phonon method (Born, 1951;Hooton, 1958;Koehler, 1968). The self-consistent phonon method was developed to treat strongly anharmonic systems where the harmonic phonon frequencies may even be unstable, such as crystals of noble gases.…”

Section: Self-consistent Phonon Calculationsmentioning

confidence: 99%

“…Ahuja et al (1993) found bcc Ti, Zr, and Hf stabilized at high pressure and T ¼ 0 K; see also Hu, Lu, and Yang (2008), and Hu et al (2010), and references therein. Hsueh et al (2002) noted that the phonon structure in bcc Zr could be stabilized if a magnetic moment was imposed.…”

Section: Scandium Yttrium and Lanthanummentioning

confidence: 99%

Lattice instabilities in metallic elements

et al. 2012

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Most metallic elements have a crystal structure that is either body-centered cubic (bcc), facecentered close packed, or hexagonal close packed. If the bcc lattice is the thermodynamically most stable structure, the close-packed structures usually are dynamically unstable, i.e., have elastic constants violating the Born stability conditions or, more generally, have phonons with imaginary frequencies. Conversely, the bcc lattice tends to be dynamically unstable if the equilibrium structure is close packed. This striking regularity essentially went unnoticed until ab initio total-energy calculations in the 1990s became accurate enough to model dynamical properties of solids in hypothetical lattice structures. After a review of stability criteria, thermodynamic functions in the vicinity of an instability, Bain paths, and how instabilities may arise or disappear when pressure, temperature, and/or chemical composition is varied are discussed. The role of dynamical instabilities in the ideal strength of solids and in metallurgical phase diagrams is then considered, and comments are made on amorphization, melting, and low-dimensional systems. The review concludes with extensive references to theoretical work on the stability properties of metallic elements.

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Magnetism and mechanical stability ofα-iron

Cited by 36 publications

References 19 publications

Properties and electronic structure of iron under pressure up to 30GPa

Properties and electronic structure of iron under pressure up to 30GPa

First-Principles Studies of Paramagnetic Vivianite Fe₃(PO₄)₂·8H₂O Surfaces

Lattice instabilities in metallic elements

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Magnetism and mechanical stability ofα-iron

Cited by 36 publications

References 19 publications

Properties and electronic structure of iron under pressure up to 30GPa

Properties and electronic structure of iron under pressure up to 30GPa

First-Principles Studies of Paramagnetic Vivianite Fe3(PO4)2·8H2O Surfaces

Lattice instabilities in metallic elements

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First-Principles Studies of Paramagnetic Vivianite Fe₃(PO₄)₂·8H₂O Surfaces