John Klepeis, Per Söderlind, Daniel Orlikowski, A. Landa and John Moriarty

Methods: FP-LMTO, MGPT and EMTO.

Collaborators: High-Pressure Physics Group (LLNL)

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.

## Collaborations

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.

## Selected Publications

- A. Landa, P. Söderlind, I.I. Naumov, J.E. Klepeis, and L Vitos, "Kohn Anomaly and Phase Stability in Group VB Transition Metals,"
*Computation*, 6(2) (2018) 29. - A. Landa and P. Söderlind, "First-principles phase stability at high temperatures and pressure in Nb90Zr10 alloy,"
*Journal of Alloys and Compounds*, 690 (2017) 647. - 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
**85**, 060301(R) (2012). - 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). - B. Lee, R. E Rudd, and J. E. Klepeis, " Using alloying to promote the subtle rhombohedral phase transition in vanadium ," J. Phys.: Cond. Matter
**22**, 465503 (2010). - 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). - B. Lee, R. E. Rudd, J. E. Klepeis, and R. Becker, "Elastic constants and volume changes associated with two high-pressure rhombohedral phase transformations in vanadium ," Phys. Rev. B
**77**, 134105 (2008). - D. Orlikowski, A. A. Correa, E. Schwegler, and J. E. Klepeis, "A Steinberg-Guinan Model for high-pressure carbon: diamond phase ," Shock Comp. Cond. Matter-2007, eds. M. Elert,
*et al*. American Inst. Phys.: New York (2007) p247. - 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).

Maintained by metals-alloys-web [at] llnl.gov (Lorin X. Benedict)