High-pressure and temperature mechanical properties of transition metals: tantalum as prototype.
(a) Isotropic shear modulus, as obtained from first principles calculations via a Voigt average of FP-LMTO single-crystal bcc shear
moduli at zero temperature and as extrapolated from ambient- pressure measurements in the empirical Steinberg-Guinan (SG) strength model.
(b) Ideal shear strength at 45 GPa, as obtained from FP-LMTO total-energy calculations of the deformed ideal bcc lattice along the
observed twinning path. The critical shear stress tau_c separating regions of elastic and plastic deformation is the ideal strength. At
higher pressure, tau_c approximately scales with the calculated shear modulus. (c) The Voigt averaged shear modulus (below the meltline) contains a cold, electron and ion thermal components of the elastic moduli, that were calculated from FP-LMTO methods for the electron thermal, plus
for the ion thermal component a quantum-based, multi-ion potential using either a quasi-harmonic method or a Monte Carlo method to capture full anharmonic effects.
Accurately modeling elastic behavior in metals and alloys is fundamental and crucial to describing their mechanical properties, especially plasticity and strength. For example, knowledge of the single-crystal shear moduli of bcc transition metals (Ta, Mo, V), and their pressure and temperature dependence, help underpin our current efforts to develop predictive multiscale modeling simulations of plastic deformation for these materials. At the same time, useful empirical constitutive models, such as the Steinberg-Guinan (SG) strength model, scale the yield strength of macroscopic polycrystalline materials at high pressure and temperature through the isotropic shear modulus, although the behavior of shear moduli at extreme conditions and across phase boundaries is often not known. We are using first-principles FP-LMTO and EMTO electronic structure calculations together with
GPT and MGPT atomistic simulations to obtain elastic moduli and related quantities, such as the ideal shear strength of the perfect lattice, in d- and f-electron metals and compounds of special interest. The FP-LMTO and EMTO calculations provide zero-temperature and electron- thermal components of high-pressure moduli for known crystal structures, while atomistic models of thermoelasticity have been developed to treat the remaining ion- thermal component. Two separate methods are currently used: one that is within the quasi-harmonic limit and the other that is a Monte Carlo method to fully capture anharmonic effects. We find that the electron thermal component cannot be ignored, even close to melt. To provide experimental validation of our results, we are also working with diamond-anvil-cell experimentalists, who are developing new methods to measure high-pressure elastic moduli. A forefront challenge is to extend both theory and experiment to complex crystal structures and across high-pressure phase boundaries.
In support to the National Ignition Facility (NIF ) for LLNL's Inertial Confinement Fusion (ICF) Program rudimentary strength models (Steinberg-Guinan) are being developed over high pressure and temperature ranges for diamond and BC8 phases of carbon with A. Correa and E. Schwegler (CMMD, PLS) combining plane-wave density functional theory calculations of phonons and elastic moduli with empirical data.
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- A. Landa, P. Söderlind, and L. H. Yang, "Ab initio phase stability at high temperatures and pressures in the V-Cr
system," Phys. Rev. B 82, 020101(R) (2014).
- P. Söderlind, A. Landa, L.H. Yang, and A.M. Teweldeberhan, "First-Principles Phase Stability in the Ti-V Alloy System," J. Alloys and Compnds 581, 856 (2013).
- P. Söderlind, B. Grabowski, L. Yang, A. Landa, T. Björkmann, P. Souvatzis, and O. Eriksson, "High-Temperature Phonon Stabilization of gamma-Uranium from Relativistic First-Principles Theory," Phys. Rev. B
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- A. Landa, P. Soderlind, O. I. Velikokhatnyi, I. I. Naumov, A. V. Ruban, O. E. Peil, and L. Vitos, "Alloying-driven phase stability in group VB transition metals under compression ," Phys. Rev. B 82, 144114 (2010).
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- A. Landa, P. Söderlind, A. V. Ruban, O. E. Peil, and L. Vitos,
"Stability in bcc transition metals: Madelung and band-energy effects due to alloying ," Phys. Rev. Lett. 103, 235501 (2009).
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- A. Landa, J. Klepeis, P. Söderlind, I. Naumov, O. Velikokhatnyi, L. Vitos, and A. Ruban, "Fermi surface nesting and pre-martensitic softening in V and Nb at high pressures ," J. Phys.: Cond. Matter 18, 5079 (2006).
- L. X. Benedict, A. Puzder, A. J. Williamson, J. C. Grossman, G. Galli, J. E. Klepeis, J.-Y. Raty, and O. Pankratov, "Calculation of optical absorption spectra of hydrogenated Si clusters: Bethe-Salpeter equation versus time-dependent local-density approximation ," Phys. Rev. B 68, 085310 (2003).
- N. Franco, J. E. Klepeis, C. Bostedt, T. Van Buuren, C. Heske, O. Pankratov, T. A. Callcott, D. L. Ederer, and L. J. Terminello, "Experimental and theoretical electronic structure determination for PtSi ," Phys. Rev. B 68, 045116 (2003).
- L. X. Benedict, "Screening in the exchange term of the electron-hole interaction of the Bethe-Salpeter equation ," Phys. Rev. B 66, 193105 (2002).
- L. Pizzagalli, G. Galli, J. E. Klepeis, and F. Gygi, "Structure and stability of germanium nanoparticles ," Phys. Rev. B 63, 165324 (2001).
- J. E. Klepeis, O. Beckstein, O. Pankratov, and G. L. W. Hart, "Chemical bonding, elasticity, and valence force field models: A case study for alpha-Pt2Si and PtSi ," Phys. Rev. B 64, 155110 (2001).
- L. X. Benedict and E. L. Shirley, "Ab initio calculation of epsilon2(omega) including the electron-hole interaction: Application to GaN and CaF2 ," Phys. Rev. B 59, 5441 (1999).
Maintained by Randolph Q. Hood