Tight-binding computations of elastic anisotropy of Fe, Xe, and Si under compression

Cohen, R. E.; Stixrude, Lars; Wasserman, Evgeny

doi:10.1103/physrevb.56.8575

Cited by 105 publications

(120 citation statements)

References 40 publications

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“…These were calculated using VASP by employing a finite displacement approximation [14]. At the equilibrium lattice constant, these calculated single crystal elastic constants are in good agreement with experimental values.…”

Section: Pacs Numbersmentioning

confidence: 75%

Topological Catastrophe and Isostructural Phase Transition in Calcium

2010

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We predict a quantum phase transition in fcc Ca under hydrostatic pressure. Using density functional theory, we find at pressures below 80 kbar, the topology of the electron charge density is characterized by nearest neighbor atoms connected through bifurcated bond paths and deep minima in the octahedral holes. At pressures above 80 kbar, the atoms bond through non-nuclear maxima that form in the octahedral holes. This topological change in the charge density softens the C elastic modulus of fcc Ca, while C44 remains unchanged. We propose an order parameter based on applying Morse theory to the charge density, and we show that near the critical point it follows the expected mean-field scaling law with reduced pressure. PACS numbers:The theory and characterization of solid-solid isostructural phase transitions has been an area of intense experimental and theoretical research since they were described in 1949 [1]. What sets these transitions apart from others is that while crystalline properties change-sometimes discontinuously-crystallographic structure does not, making these transitions purely electronic in nature. Both first order and continuous transitions are known to exist. A well known example of the former is the γ → α transition in fcc Ce [1], while a magneto-volume instability in fcc Fe is an example of the later [2].In the case of Fe, the traditional local order parameter, µ, gave conflicting results computationally, with the transition appearing as first [3] or second [2] order. It was not until the transition was interpreted as a topological change of the elctronic charge density, ρ( r), that the underlying nature of the phase change became apparent [4]. While this approach is promising, no general correlations have been drawn between isostructural phase transitions and ρ( r). We use this approach to predict an isostructural phase transition in calcium under hydrostatic pressure. We then apply Morse theory to the charge density and propose an order parameter for the transition. We show that this order parameter scales in the appropriate way with reduced pressure near the quantum critical point.One of the advantages of casting theories of isostructural phase transition in terms of ρ( r) is that it is a quantum observable. Though ρ( r) is often calculated by way of first principles methods (e.g. density functional theory (DFT)), the total charge density can also be measured via X-ray diffraction techniques, and the spin-polarized charge density can be determined using spin-polarized neutron diffraction. As it is also known that all ground state properties depend on the charge density [5], it seems appropriate to seek relationships between the structure * Electronic address: trjones@mines.edu of ρ( r), changes to that structure, and corresponding changes to properties. We note that previous work has proposed that DFT could be used as a general framework for analyzing quantum phase transitions in electronic systems [6].The electron charge density is a 3 dimensional scalar field. Morse theory tells us the ...

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Section: Pacs Numbersmentioning

confidence: 75%

Topological Catastrophe and Isostructural Phase Transition in Calcium

2010

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“…This failure was a major impetus in the development of the generalized gradient approximation (GGA) [18][19][20] . The equation-of-state of hcp iron under LDA and GGA is well known to high pressures [21][22][23][24] and its elastic constants have been calculated by the full-potential linearized muffin-tin orbital method (FP-LMTO) 24 , and a total energy tight-binding (TB) method 5,25 . For hcp cobalt calculations have been performed with the LMTO method in the atomic sphere approximation for LDA 26 and the linearized combination of atomic orbital method (LCAO) for GGA 27 .…”

Section: Introductionmentioning

confidence: 99%

First-principles elastic constants for the hcp transition metals Fe, Co, and Re at high pressure

1999

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The elastic constant tensors for the hcp phases of three transition metals (Co, Re, and Fe) are computed as functions of pressure using the Linearized Augmented Plane Wave method with both the local density and generalized gradient approximations. Spin-polarized states are found to be stable for Co (ferromagnetic) and Fe (antiferromagnetic at low pressure). The elastic constants of Co and Re are compared to experimental measurements near ambient conditions and excellent agreement is found. Recent measurements of the lattice strain in high pressure experiments when interpreted in terms of elastic constants for Re and Fe are inconsistent with the calculated moduli.

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“…11, [54][55][56][57] We further compared the calculated perturbation energies of moving the wanderer atom in a small 8-atom supercell, and the results for ε-Fe at volume of 60 bohr 3 /atom and c/a ratio of 1.6 are shown in Fig. 1 It is important to perform careful convergence tests of the perturbation energy with respect to the supercell size and the number of k points used in the Brillouin zone integrations.…”

Section: Resultsmentioning

confidence: 99%

Thermal effects on lattice strain inε−Feunder pressure

Sha

Cohen

2006

Phys. Rev. B

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We compute the c/a lattice strain versus temperature for nonmagnetic hcp iron at high pressures using both first-principles linear response quasiharmonic calculations based on the full potential linear-muffin-tin-orbital (LMTO) method and the particle-in-cell (PIC) model for the vibrational partition function using a tight-binding total-energy method. The tight-binding model shows excellent agreement with the all-electron LMTO method. When hcp structure is stable, the calculated geometric mean frequency and Helmholtz free energy of ε-Fe from PIC and linear response lattice dynamics agree very well, as does the axial ratio as a function of temperature and pressure. On-site anharmonicity proves to be small up to the melting temperature, and PIC gives a good estimate of its sign and magnitude. At low pressures, ε-Fe becomes dynamically unstable at large c/a ratios, and the PIC model might fail where the structure approaches lattice instability. The PIC approximation describes well the vibrational behavior away from the instability, and thus is a reasonable approach to compute high temperature properties of materials. Our results show significant differences from earlier PIC studies, which gave much larger axial ratio increases with increasing temperature, or reported large differences between PIC and lattice dynamics results.

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Tight-binding computations of elastic anisotropy of Fe, Xe, and Si under compression

Cited by 105 publications

References 40 publications

Topological Catastrophe and Isostructural Phase Transition in Calcium

Topological Catastrophe and Isostructural Phase Transition in Calcium

First-principles elastic constants for the hcp transition metals Fe, Co, and Re at high pressure

Thermal effects on lattice strain inε−Feunder pressure

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