Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-26T10:21:33.615Z Has data issue: false hasContentIssue false

First Principles Calculations of Defects in Unstable Crystals: Austenitic Iron

Published online by Cambridge University Press:  07 September 2011

G.J. Ackland
Affiliation:
School of Physics, University of Edinburgh, Edinburgh, Scotland EH9 3JZ
T.P.C. Klaver
Affiliation:
School of Physics, University of Edinburgh, Edinburgh, Scotland EH9 3JZ
D.J. Hepburn
Affiliation:
School of Physics, University of Edinburgh, Edinburgh, Scotland EH9 3JZ
Get access

Abstract

First principles calculations have given a new insight into the energies of point defects in many different materials, information which cannot be readily obtained from experiment. Most such calculations are done at zero Kelvin, with the assumption that finite temperature effects on defect energies and barriers are small. In some materials, however, the stable crystal structure of interest is mechanically unstable at 0K. In such cases, alternate approaches are needed. Here we present results of first principles calculations of austenitic iron using the VASP code. We determine an appropriate reference state for collinear magnetism to be the antiferromagnetic (001) double-layer (AFM-d) which is both stable and lower in energy than other possible models for the low temperature limit of paramagnetic fcc iron. Another plausible reference state is the antiferromagnetic (001) single layer (AFM-1). We then consider the energetics of dissolving typical alloying impurities (Ni, Cr) in the materials, and their interaction with point defects typical of the irradiated environment. We show that the calculated defect formation energies have fairly high dependence on the reference state chosen: in some cases this is due to instability of the reference state, a problem which does not seem to apply to AFM-d and AFM-1. Furthermore, there is a correlation between local free volume magnetism and energetics. Despite this, a general picture emerge that point defects in austenitic iron have geometries similar to those in simpler, non-magnetic, thermodynamically stable FCC metals. The defect energies are similar to those in BCC iron. The effect of substitutional Ni and Cr on defect properties is weak, rarely more than tenths of eV, so it is unlikely that small amounts of Ni and Cr will have a significant effect on the radiation damage in austenitic iron at high temperatures.

Type
Research Article
Copyright
Copyright © Materials Research Society 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1] Han, S., Zepeda-Ruiz, L.A.. Ackland, G.J., Car, R. and Srolovitz, D.J. Phys Rev B 66 220101 (2002)Google Scholar
[2] Olsson, P., Abrikosov, I. A., Vitos, L., and Wallenius, J., J. Nucl. Mater. 321, 84 (2003)Google Scholar
[3] Klaver, T. P. C., Drautz, R., and Finnis, M. W., Phys. Rev. B 74, 094435 (2006).Google Scholar
[4] Klaver, T. P. C., Olsson, P., and Finnis, M. W. Phys. Rev. B 76, 214110 (2007)Google Scholar
[5] Ackland, G.J. and Thetford, R., Phil.Mag.A, 56, 15. (1987).Google Scholar
[6] Acet, M., Zahres, H., Wassermann, E.F., and Pepperhoff, W., Phys.Rev. B 49, 6012 (1994)Google Scholar
[7] Jiang, DE and Carter, EA.Phys Rev. B 67, 214103 (2003)Google Scholar
[8] Hasegawa, H. and Pettifor, D.G. Phys.Rev. Letters 50.130 (1983)Google Scholar
[9] Ackland, G.J. Phys.Rev.B 79 094202 (2009)Google Scholar
[10] It is important to be clear precisely what this means. We use the Born-Oppenheimer approximation, that the electronic structure energy is fully minimized. In a magnetic system there are multiple minima, and we are testing the stability of a "nearby" minimum to each possible reference state. The minimum energy with respect to plane wave coefficients is found using the residual minimization method with preconditioning and direct inversion in the iterative subspace. This mathematical algorithm does not correspond to any physical trajectory which the electron could follow (c.f. Time dependent DFT). Consequently "local minimum" means a minimum from which this algorithm cannot escape in this basis set. It does not guarantee that the spin-state will be a local minimum in reality.Google Scholar
[11] In an Ising model, this would correspond to J=0.04eV and a Neel temperature of about 5K.Google Scholar
[12] Karki, BB., Clark, SJ, Warren, MC, Hseuh, HC, Ackland, GJ and Crain, J J.Phys.CM 9 375 (1997)Google Scholar
[13] Zunger, A., Wei, S.-H., Ferreira, L. G., and Bernard, James E. Phys. Rev. Lett. 65, 353 (1990)Google Scholar
[14] Olsson, P, Wallenius, J, Domain, C, Nordlund, K and Malerba, L 2005 Phys. Rev. B 72 214119 Google Scholar
[15] Hepburn, D.J. and Ackland, G.J. 2008 Phys.Rev.B 165115 Google Scholar
[16] Hepburn, D.J., Ackland, G.J. and Olsson, P. Phil.Mag 89 3436 3393 (2009)Google Scholar
[17] Bonny, G, C Pasianot, R and Malerba, L 2009 Modelling Simul. Mater. Sci. Eng. 17 025010 Google Scholar
[18] Ackland, G.J. Phys. Rev. Lett. 97, 015502 (2006)Google Scholar
[19] Castin, N., Bonny, G., Terentiev, D., Lavrentiev, M.Y., and Nguyen-Manh, D. (2010) J. Nuclear Materials in press Google Scholar