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

Steinle‐Neumann, Gerd; Stixrude, Lars; Cohen, R. E.

doi:10.1103/physrevb.60.791

Cited by 370 publications

(375 citation statements)

References 48 publications

Supporting

Mentioning

320

Contrasting

Unclassified

Order By: Relevance

“…We predict the hcp equilibrium volume, bulk modulus, and c=a ratio to be 10:25 A 3 , 293 GPa, and 1.58, respectively. Although little experimental data exist for hcp, our results agree with previous first-principles calculations [20]. Experimental hcp elastic constants are not available.…”

supporting

confidence: 82%

Importance of Shear in the bcc-to-hcp Transformation in Iron

et al. 2004

View full text Add to dashboard Cite

Iron shows a pressure-induced martensitic phase transformation from the ground state ferromagnetic bcc phase to a nonmagnetic hcp phase at 13 GPa. The exact transformation pressure (TP) and pathway are not known. Here we present a multiscale model containing a quantum-mechanics-based multiwell energy function accounting for the bcc and hcp phases of Fe and a construction of kinematically compatible and equilibrated mixed phases. This model suggests that shear stresses have a significant influence on the bcc $ hcp transformation. In particular, the presence of modest shear accounts for the scatter in measured TPs. The formation of mixed phases also provides an explanation for the observed hysteresis in TP. Pressure-driven phase transformations are ubiquitous and important for understanding the mechanical response of materials. In particular, the ground state crystal structure of Fe, ferromagnetic body-centered cubic (bcc), undergoes a pressure-induced martensitic phase transformation to a hexagonally close-packed (hcp) structure at 13 GPa. The measured transformation pressure (TP) varies greatly [1][2][3]. Attempts to simulate this transformation via quantum mechanics [4][5][6][7][8], primarily density functional theory (DFT), have focused on relative phase stability, where the TP is approximated by the Gibbs construction of drawing the line of common tangent between equations of state of the pure bcc and hcp phases. Another DFT model [9] mapped out the energetics of a constrained transformation path between the pure phases, similar to earlier work on Ba [10]. None of these were able to explain the large range of measured TPs. Here, we present a multiscale model containing a first-principles DFT-based multiwell energy function accounting for bcc and hcp Fe and a construction of kinematically compatible and equilibrated mixed phases (laminates) to represent the complicated microstructures often observed in experiments.We confine our attention to transformations occurring at 0 K and therefore the governing principle is energy minimization. In particular, the formation of microstructure is driven purely by energetics. We assume the behavior of the material to be nonlinear elastic with energy density W

show abstract

supporting

confidence: 82%

Importance of Shear in the bcc-to-hcp Transformation in Iron

et al. 2004

View full text Add to dashboard Cite

show abstract

“…(6). An efficient way to do this for the hcp lattice has been proposed by Steinle-Neumann et al 9 . As explained above, bulk and shear moduli are calculated separately.…”

Section: B Elasticity Under Initial Pressurementioning

confidence: 99%

Elastic anisotropy and Poisson's ratio of solid helium under pressure

et al. 2015

View full text Add to dashboard Cite

The elastic moduli, elastic anisotropy coefficients, sound velocities and Poisson's ratio of hcp solid helium have been calculated using density functional theory in generalized gradient approximation (up to 30 TPa), and pair+triple semi-empirical potentials (up to 100 GPa). Zero-point vibrations have been treated in the Debye approximation assuming 4 He isotope (we exclude the quantumcrystal region at very low pressures from consideration). Both methods give a reasonable agreement with the available experimental data. Our calculations predict significant elastic anisotropy of helium (△P ≈ 1.14, △S1 ≈ 1.7, △S2 ≈ 0.93 at low pressures). Under terapascal pressures helium becomes more elastically isotropic. At the metallization point there is a sharp feature in the elastic modulus CS, which is the stiffness with respect to the isochoric change of the c/a ratio. This is connected with the previously obtained sharp minimum of the c/a ratio at the metallization point.Our calculations confirm the previously measured decrease of the Poisson's ratio with increasing pressure. This is not a quantum effect, as the same sign of the pressure effect was obtained when we disregarded zero-point vibrations. At TPa pressures Poisson's ratio reaches the value of 0.31 at the theoretical metallization point (V mol = 0.228 cm 3 /mol, p = 17.48 TPa) and 0.29 at 30 TPa. For p = 0 we predict a Poisson's ratio of 0.38 which is in excellent agreement with the low-p-low-T experimental data.

show abstract

“…[37]. In what follows we will focus on the changes in structural and elastic properties associated with the addition of TM solutes to hcp Re, and the trends which these changes display as a function of bandfilling.…”

Section: A Structural and Elastic Properties Of Pure Rheniummentioning

confidence: 99%

First-principles study of the structural and elastic properties of rhenium-based transition-metal alloys

et al. 2012

View full text Add to dashboard Cite

Structural, energetic and elastic properties of hexagonal-close-packed rhenium-based transitionmetal alloys are computed by density-functional theory. The practical interest in these materials stems from the attractive combination of mechanical properties displayed by rhenium for structural applications requiring the combination of high melting temperature and low-temperature ductility. Single-crystal elastic constants, atomic volumes, axial c/a ratios, and dilute heats of solution for Re-X alloys are computed, considering all possible transition-metal solute species X. Calculated elastic constants are used to compute values of a commonly considered intrinsic-ductility parameter K/G, where K is the bulk modulus and G denotes the Voigt average of the shear modulus, as well as the anisotropies in the Young's modulus and shear modulus. The calculated properties show clear trends as a function of d-band filling, which can be rationalized through tight-binding theory. The results indicate that solutes to the left of rhenium in the periodic table show a tendency to increase the intrinsic ductility parameter, a trend that correlates with an increase of the c/a ratio towards the ideal value associated optimal close packing. The Young's modulus shows a trend towards increasing isotropy with alloying of solutes X to the left of Re, while the shear modulus shows the opposite trend but with an overall weaker dependence on solute additions.

show abstract

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

Cited by 370 publications

References 48 publications

Importance of Shear in the bcc-to-hcp Transformation in Iron

Importance of Shear in the bcc-to-hcp Transformation in Iron

Elastic anisotropy and Poisson's ratio of solid helium under pressure

First-principles study of the structural and elastic properties of rhenium-based transition-metal alloys

Contact Info

Product

Resources

About